RISK MANAGEMENT AND ALLOCATION IN DYNAMIC SYSTEMS By EKATERINA VOROTNIKOVA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR O F PHILOSOPHY UNIVERSITY OF FLORIDA 2014
Â© 2014 Ekaterina Vorotnikova
To my dearest mother, Irina, my professors, dedicated nannies for my son, and my future students
4 ACKNOWLEDGMENTS I would like to t hank Dr. VanSickle, chairman of my doctoral committ ee, for the support , wisdom, encouragement , and most importantly, freedom of thought, he has provided me throughout my graduate studies. I would also like to express my appreciation to the other members of my committee Dr. Tatiana Borisova, Dr. James L. Seale , Jr. , and Dr. Andrew S chmitz for their recommendations and constructive criticism during the preparation of this dissertation. I am thankful to Dr. Natalia Peres for conducted experiments at the Gu lf Coast Research and Education Center of University of Florida. Especially, I am grateful to Dr. Denslow , the external member of the doctoral committee, for unique perspectives that transcend conventional use of the risk management models that I initially devised.
5 TABLE OF CONTENTS page ACKNOWLE DGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 THE ECONOMIC FEASIBILITY OF PRECISION MANAGEMENT SYSTEM FOR FUNGICIDE APPLICATION IN FLORIDA STRAWBERRY INDUSTRY ........ 15 Introductory Remarks ................................ ................................ .............................. 15 Background on Strawberry Production ................................ ................................ ... 19 Development of Strawberry Advisory System ................................ ......................... 21 The Difference between SAS and Calendar Based Fungicide Application Methods ................................ ................................ ................................ ........ 24 SAS O peration ................................ ................................ ................................ . 25 Data ................................ ................................ ................................ ........................ 28 Theoretical Model ................................ ................................ ................................ ... 32 Methodology ................................ ................................ ................................ ........... 35 Simulating Key Variables ................................ ................................ ........................ 37 Weather and Weather Intensity Variables ................................ ........................ 37 Applica tion Variable ................................ ................................ .......................... 39 Strawberry Yields and Prices ................................ ................................ ........... 40 State Wide Yields and Prices Based on Historical Average Data .................... 41 Yield Based on Production Experiments ................................ .......................... 43 Yield Based on Production Experiment ................................ ............................ 44 Pr ofit Derivation and Simulation ................................ ................................ .............. 46 Constructing Revenues ................................ ................................ .................... 47 Production Costs ................................ ................................ .............................. 47 Simulation of Net Present Value of Profits ................................ ........................ 49 Results ................................ ................................ ................................ .................... 51 Deterministic Results for Anthracnose Trials ................................ .............. 52 Deterministic Results for Botrytis Trials ................................ ...................... 52 Stochastic Results for Yield ................................ ................................ .............. 53 Res ults and Discussion for Ten Year NPV of Profit ................................ .......... 57 Concluding Remarks ................................ ................................ ............................... 68 3 DEFINED BENEFIT PENSION PLAN RESTRUCTURE: CAN DBS BE VIA BLE AGAIN? ................................ ................................ ................................ ................... 87
6 Introductory Remarks ................................ ................................ .............................. 87 Problem Definition ................................ ................................ ................................ .. 89 Propose d Structure of the Pension Fund ................................ ................................ 92 Data ................................ ................................ ................................ ........................ 94 Descriptive Statistics of Historical Yearly Returns ................................ .................. 95 Simulating Returns ................................ ................................ ................................ . 97 Multivariate Empirical Distribution Methodology ................................ ..................... 97 Model ................................ ................................ ................................ ...................... 99 Results ................................ ................................ ................................ .................. 104 Summary ................................ ................................ ................................ .............. 111 4 EFFECT OF RELATIVE PRICE CHANGES OF TOP PRINCIPAL CROPS ON U.S. FARM LAND ALLOCATION BEFORE AND AFTER 2005 ENERGY POLICY ACT (EPA) ................................ ................................ .............................. 123 Introductory Statement ................................ ................................ .......................... 123 Problem Definition ................................ ................................ ................................ 123 Data ................................ ................................ ................................ ...................... 126 Methodology ................................ ................................ ................................ ......... 127 Results ................................ ................................ ................................ .................. 130 Coefficients ................................ ................................ ................................ ..... 1 31 Elasticities ................................ ................................ ................................ ...... 134 Land e lasticities ................................ ................................ ....................... 134 Own p rice e lasticity ................................ ................................ .................. 135 Cross p rice e lasticities ................................ ................................ ............. 137 Summary ................................ ................................ ................................ .............. 141 5 CONCLUSION ................................ ................................ ................................ ...... 154 APPENDIX A FUNDING RATIO, INFORMATION RATIO, AND SHARPE RATIO ..................... 158 B MULTIVARIATE EMPIRICAL DIST RIBUTION ................................ ..................... 165 LIST OF REFERENCES ................................ ................................ ............................. 172 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 181
7 LIST OF TABLES Table page 2 1 Summary statistics for yield from the Anthracnose field trials ............................. 71 2 2 Summary statistics for yield from the Botrytis field trials ................................ ..... 72 2 3 Anthracnose production trials: t he n u m ber o f d a y s w it h w e a t h e r c on d i t i o ns c ondu c i v e f o r the fruit rot , derived weather variables, and the number of fungicide applications ................................ ................................ ......................... 72 2 4 Botrytis production trials: t he n u m ber o f d a y s w ith w e a th e r c on d i t i o ns c ondu c i v e f o r the fruit rot, derived weather variables, and number of fungicide applications ................................ ................................ ......................... 73 2 5 I ndepende n t v a r i a b l es used i n r e g r e s s i on an a l y s i s f o r s t r a w b e rr y yield ............. 74 2 6 Coefficients from the Anthracnose Regression for the Marketable Weight of Strawberries ................................ ................................ ................................ ....... 75 2 7 The Average Yield Estimates ................................ ................................ ............. 76 2 8 Coefficients from the Botrytis regression f or t h e marketable w e i g ht of strawberries ................................ ................................ ................................ ........ 76 2 9 The Average Yield for Each Treatment ................................ .............................. 76 2 10 Yield Summary Statistics after Monte Carlo Simulation for Anthracnose ........... 77 2 11 Efficient Set Based on Stochastic Dominance with Respect to a Function ......... 77 2 12 Yield Summary Statistics after Monte Carlo Simulation for Botrytis .................... 78 2 13 Efficient Set Based on Stochastic Dominance with Respect to a Function ......... 78 2 14 Profit Summary Statistics after Monte Carlo Simul ation for Anthracnose Case .. 79 3 1 Ten top performing pension funds ................................ ................................ .... 113 3 2 Ten worst performing pension funds ................................ ................................ 113 3 3 Estimated parameters ................................ ................................ ...................... 113 3 4 Summary Statistics for the Distributions Asset Base under Current and Proposed Structures ................................ ................................ ......................... 114 3 5 Summary Statistics for the Value of Contributions and Value of Capital Gains on the Contributions under the Proposed Structure ................................ .......... 114
8 4 1 Coefficien ts of the Rotterdam model, 1960 2004 ................................ ........... 144 4 2 Coefficients of the Rotterdam model, 2005 2013 ................................ ........... 144 4 3 Difference in coefficients before and after 2005 ................................ ............... 145 4 4 Output price and land elasticities of the estimated Rotterdam model, 1960 2004 ................................ ................................ ................................ ................. 145 4 5 Output pric e and land elasticities of the estimated Rotterdam model, 2005 2013 ................................ ................................ ................................ ................. 146 4 6 Difference between output price and land elasticities before and after 2005 EPA policy ................................ ................................ ................................ ........ 146 A 1 Ranking of Funding Ratio, Information Ratio, and Sharpe Ratio for 125 Pension Funds ................................ ................................ ................................ .. 159
9 LIST OF FIGURES Figure page 2 1 Florida strawberry production (millions of lbs), value ($ millions), and acres planted, 1998 2012 ................................ ................................ ............................. 80 2 2 Monthly Strawberry Price Dynamics ................................ ................................ ... 80 2 3 Strawberry Advisory System as Web Based Application ................................ .. 81 2 4 Difference in Calendar and SAS based Application Methods ............................. 82 2 5 Yield PDF in case of Anthracnose Disease for Two Different Cultivars .............. 82 2 6 Yield PDF in Case of Botrytis Disease for Two Different Cultivars ..................... 83 2 7 Profit PDF in case of Anthracnose Disease for Two Different Cultivars ............. 83 2 8 Profit PDF in case of Botrytis disease for two different cultivars ......................... 84 2 9 Stochastic efficiency of NPV of profit function in case of Anthracnose ............... 85 2 10 Stochastic efficiency of NPV of profit function in case of Botrytis ....................... 85 2 11 Added value of SAS based method, Vsas, Anthracnose Case .......................... 85 2 12 Added Value of SAS Based Method for Botry tis Case ................................ ....... 86 2 13 The Difference in Production Processes Resulting in Different Profits ............... 86 3 1 Yearly Return Distribution among 125 Pension Funds, 2001 2009 ................. 116 3 2 Probability density function yearly returns for 125 pension funds in a given year 2001 2009 ................................ ................................ ............................... 116 3 3 Yearly return dynamics average return among 125 funds for each of the eleven years ................................ ................................ ................................ ..... 117 3 4 Decomposition of Trans Cycle Trend and Distribution within Cycle ................. 117 3 5 Historical Linear Trend for the Trans Cycle Dynamics ................................ ..... 118 3 6 Annualized Yearly Returns versus Standard Deviations 2001 2009 ................ 118 3 7 Distribution of Simulated Returns Based on Russell 2000 Index ...................... 119 3 8 Net Present Value of the Asset Bases under the Conventional Pension Plan and th e New Pension Plan Structures ................................ .............................. 119
10 3 9 Net Present Value of the Asset Bases under the Conventional Pension Plan and the New Pension Plan Structures ................................ .............................. 120 4 1 Corn acreage, production quantity, and prices 1980 2013 ............................... 147 4 2 Total acreage in agricultural production and corn acreage ............................... 147 4 3 Crops land shares as percentage of total land in agricultural production 1960 2013 ................................ ................................ ................................ ................. 148 4 4 Corn, wheat, soybean, and cotton production before and after EPA 2005 ....... 149 4 5 Corn plantings expansion after 2005 EPA ................................ ........................ 150 4 6 Soybeans plantings before and after 2005 EPA ................................ ............... 151 4 7 Cotton plantings ................................ ................................ ................................ 152 4 8 Wheat Plantings ................................ ................................ ............................... 153
11 Abstract of Dissertation Presented to the Graduate School of the University o f Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RISK MANAGEMENT AND ALLOCATION IN DYNAMIC SYSTEMS By Ekaterina Vorotnikova August 2014 Chair: John J VanSickle Cochair: Tatiana Borisova Major: F ood and Resource Economics This dissertation includes three essays on risk management and allocation in dynamic systems. I find that dynamic systems need a dynamic response. Economic and statistical models can help with identifying the optimal timing and the optimal amount of inputs. This is true for systems in different industries, for example, fungicide application in strawberry production, funding schedules in the pension funds, and land allocation. In this dissertation, t he first essay evaluates the r isk and profitability of a new expert system, Strawberry Advisory System (SAS). SAS , a temporally variable system of fungicide application , allows for precision application of fungicides to control anthracnose and Botrytis fungi diseases. T he production an d market risks associated with weather and sale price variability is examined using Monte Carlo simulations. Based on stochastic efficiency analysis for risk adjusted profitability criteria, SAS based method is the best for both anthracnose and Botrytis di seases management. Assuming a Florida strawberry farm of 26 acres, the value of SAS is estimated on average to be $1.76 million for anthracnose and $0.89 million for Botrytis, over a ten year horizon of use.
12 Second essay also uses Monte Carlo simulation me thod and NPV framework. However, the methodology is applied to a n evaluation of a novel structure of Defined Benefit (DB) pension plans with contributions tied to the market performance of the fund. The study tests and compares the performances of both pro posed and current based on this comparison the study identifies the marginal value of the new DB structure as compared to the current one. Finally, the optimal discount rate for liabilities projection is derived based on stochastically simulated NPV results for both current and proposed DB structures. mandating specific ratio of ethanol in gasoline. Given that arable land is scarce, there are reasons to believe that following ed at the expense of acreages of other crops.
13 CHAPTER 1 INTRODUCTION Th is work focuses on management of dynamic systems in terms of risk and allocation , specifically systems in which inputs depend on changing exogenous variables affecting the output of the system. Examples of such exogenous variables can be we ather, prices, returns, monetary contributions, or interest rate. The goal of the model is to de termine a n optim al schedule (timing) and/or optimal amount of inputs to manage such dynamic systems . In Agricultural and Resource Economics , fungicide management presents an interesting framework while , in Finance and Economics , management of asset and liabilities of pension fund is an excellent structure for appl ying the risk management method proposed in this work. An a llocation model in a dynamic system is proposed for agricultural land allocation among crops grown in the United States (U.S.) for the years 1960 2013. Specifically, the model handles the effect of relative price changes of the c rops on U.S. farm land allocation among these crops. The allocation model also is equipped to test for structural breaks due to policy changes. The dissertation consists of three chapters. The f irst chapter evaluates farm level risk and profitability of a new web based expert system developed for precision fungicide management for strawberry production in a humid and warm climate. The fungicide management allows for a temporally variable, weather dependent fungicide application to manage anthracnose and Bot rytis fruit rot diseases in strawberry production in the southern United States and specifically Florida. Although the use of the new expert system increases the variability of yield and profit, stochastic efficiency with respect to a function (SERF) ranki ng, applied to the ten year NPV, indicates that the
14 SAS based fungicide application method is preferred for the farmers with various risk aversion levels for both diseases and cultivars . In t he second chapter , I propose a dynamic structure for D efined B ene fit (DB) plans The general idea is that if a fund generates insufficient rate of return in a given year (or period), the contributions should go up, and if the returns are sa tisfactory or outstanding, the contribution can decrease or even be zero. In some ways, this structure is a hybrid between D efined B enefits and D efined C ontribution plans, with an exception that contributions are made flexible wh ile benefits remain predefi ned. In the third chapter , I investigate how the ethanol mandate affects U.S. land allocation among crops grown in the U.S.
15 CHAPTER 2 THE ECONOMIC FEASIBILITY OF PRECISION MANAGEMENT SYSTEM FOR FUNGICIDE APPLICATION IN FLORIDA S TRAWBERRY INDUSTRY Introduct ory Remarks Climate change is amplifying existing challenges in agriculture in many parts of the world (Claessens et al. , 2012). Increased variability in temperatures and moisture can undermine existing disease, pest, and weed m anagement practices in crop production (Lehmann et al. , 2013). Expert systems , involving precision techniques, are , 2009). Precision Agriculture (PA) techniques that rely on expert systems to optimize pr oduction decisions are used as a strategy to help the agricultural sector cope with these challenges. PA is defined as a and informed management to optimize production by accounting for variability and , 2010). The main goal of PA is to facilitate site specific, preventative rather than reactive, cost effective, and environmentally respons ible management prac tices in agricultural systems. Advanced technologies, comprehensive datasets, and improved decision making criteria allow PA and expert systems to increase the efficiency of production input use, which in turn can increase both profitability and the envir onmental sustainability of agricul tural production (Bramley, 2009; Gebbers and Adamchuck, 2010). A key factor affecting PA profitability is the amount and accuracy of information PA technologies can provide to producers about spatially or temporally var iable factors. While the effects of information about spatial factors (e.g., planting patterns, plant diversity, weed pressure, and soil type) have been extensively studied (Brophy and Mundt , 1991; Mundt et al., 19 86 ; Waller et al., 1997; Mitchell et al., 2002; Oliver and
16 Robertson , 2009), the economics of PA technologies a ddressing temporal variability was addressed in only a few studies (e.g., G odwin et al. , 2003 ). Insufficient recognition of temporal variations has been identified as one of the critical issues in PA studies (McBratney et al. , 2005). Risk adjusted profitability of PA systems is found to be the main driver behind the adoption of PA technologies (Batte and Arnholt , 2003), while the difficulties in predicting profitability of PA technologies are elaborated extensivel y in existing studies (Atherton et al. , 1999). Review of published studies shows two critical gaps in PA economic assessment literature. First, while numerous studies explored the economic viability of PA that addresses spatial va riability in production (e.g., soil types, planting patterns, plant diversity, and weed pressure) (Brophy and Mundt, 1991; Godwin et al. , 2003; Mitchell et al., 2002; Mundt et al., 19 8 6 ; Oliver and Robertson, 2009; Waller et al., 1997), temporal variabilit y in production has been examined in on ly a few PA studies (Ellison et al. , 1997 ; Lundy et al., 2014 ). The recognition of temporal variations in production practices has been identified as a critical need for PA development and assessment (McBratney et al. , 2005). The second critical gap in the literature is the lack of studies examining economic viability of PA for small fruit production. The majority of PA studies focuses on field crops such as corn, wheat, soybean, and cotton (Maiorano e t al., 2009; Sell s, 1995; Swinton and Lowenberg DeBoer, 1998), while much less attention is paid to PA technologies for horticultural crops (Bramley, 2009; Griffin and Lowenberg DeBoer, 2005). Even though some studies deal with citrus and grapes (Ellison et al., 1997; Whit ney et al., 1999), no studies were found that examine economic viability of PA for small fruit production, such
17 as berries. In 2011, there were 242,371 hectares under strawberry production around the world, and world strawberry production value in 2011 rea ched its highest level of $4.3 billion. The top countries by value of production in the order of magnitude are: United States, Turkey, Russia, Poland, Germany, and Ukraine (FAOSTAT , 2012). over a quarter of total world production (FAOSTAT , 2012). Given the fierce competition among berry producers, PA technologies that can reduce p roduction costs and increase input use efficiency will create competitive advantage for producer s and help satis fy the growing demand for strawberries. Potential impacts of variable weather and changing climate conditions on international strawberry production have been explored in several studies (Neri et al., 2012; Sun et al., 2012; Palencia et al., 2009). PA tech nologies can also improve env ironmental sustainability of agricultural production. Thus, conducting profitability studies can be timely and urgent and can significantly increase the adoption rate of PAs. To tackle critical gaps in the literature, this pap er evaluates a PA technology that addresses temporal (i.e. weather related) variability in precision management of fungal diseases in strawberry production. Unlike most economic studies that utilize profit maximization or utility maximization models (Griff in and Lowenberg DeBoer, 2005; Lambert and Lowenberg DeBoer, 2000; Thrikawala et al., 1999), we rely on stochastic ranking criteria to evaluate the PA technology. The results of profit maximization or utility maximization studies depend on the assumption a bout the prevailing prices and yields. To improve the economic assessment of alternative production technologies, Just and Pope (2002, 2003) suggested examining the distributions of potential outcomes that
18 would span a range of possible price, yield, and o ther assumptions. In line with this recommendation, some economic feasibility studies captured stochastic distributions of prices and yields ( Asche et al., 2006; Godwin et al., 2003; Richardson, 2000; Richardson et al., 2007 ). Richardson et al. (2000, 200 7 ) used historical data to stochastically simulate the net present value (NPV) of alternative production technologies. In this study, we advance the methodology developed by Richardson et al. (2000, 2007 ) by integrating the historical data with the data fr om field production trials to better capture the impacts of local weather conditions, strawberry varieties, and production technologies on the variability in yields and related variability in sale prices. While utilizing a profit maximization framework, w e use stochastic efficiency with respect to a function (SERF) criterion, which allows us to evaluate the performance of PA strawberry production preferences (Richardson and Outlaw , 2008). This study evaluates the profitability of one PA technology, Strawberry Advisory System (SAS), developed to assist agricultural producers in the southeastern U.S. in managing weather and climate related risks. A review of 210 studies that examined the economic costs and benefits of PA technologies (Griffin and Lowenberg DeBoer , 2005) showed that although 68% of the studies reported positive net benefits associated with precision agriculture technologies, several studies showed net losses. Similarly in another study, research at n ine field sites found PA methods of fertilizer application to be unprofitable for wheat and barley, in some cases profitable for corn, and profitable only for sugarbeets (Swinton and Lowenberg DeBoer , 1998). The profitability of PA depends on the type of t echnology and its costs, farm size, site specifics, and the methods used
19 to evaluate the PA costs and benefits (Batte , 2000 ; Griffin and Lowenberg DeBoer , 2005). This study shows that the new expert system significantly reduces crop losses and fungicide us e, while increasing profit on average by 33% and 50% for more and less resistant cultivars, respectively, in the case of anthracnose and by 26% and 7.65% for more and less resistant cultivars, respectively, in the case of Botrytis. SERF rankings applied to the ten year NPV indicate that SAS based fungicide application is the most preferred. The value of the SAS expert system, identified as the difference between expected NPVs of SAS based and the traditional based fungicide application systems, is estimat ed to be $1.76 million in case of anthracnose and 0.89 million in case of Botrytis, considering a ten year horizon of use on a 26 acre farm. The chapter is arranged as following: the first s ection provides a background on Florida strawberry production . The next looks at Anthracnose and Botrytis fruit rot management and SAS development . T he data from the production experiments used in this study are explained, followed by an economic evaluation of this PA for strawberry production in Florida. Overall, we sho strawberry producers. Specifically, in comparison with the conventional weekly method of fungicide application, this precision disea se management system reduces fungicide applications and costs while e ither leaving strawberry yields unaffected or even are also compared . Background o n Strawberry Production a qu arter of total world production (FAOSTAT , 2012), and Florida is the second largest strawberry producing state in the U.S. after California, consistently producing around
20 15% of the total U.S. annual production for the past ten years ( USDA NASS a , 2013). Str awberry is the most significant berry crop by production value in Florida. During the winter season Florida dominates the national strawberry market. In 2012 Florida strawberry production was 183 million pounds from 8,900 acres planted, which is a decrea s e from its record high of 248 million pounds in 2011. The production value was $200 m illion in 2012, also a decrease from its all time high of $366 Million in 2011 (Figure 2 1). Hillsborough County, west central Florida. The production season starts in November and continues through March of the following year. The heaviest harvesting occurs in the months of February and March, driven by climatic conditions and the dynamics of the strawberry market. P rices for strawberries generally peak in December or January and then experience steady downward pressure until bottoming out i n May or June in response to increasing strawberry supplies from California (Figure 2 2). Fungal diseases su ch as anthracnose (AFR) and Botrytis (BFR) fruit rots are major challenges for strawberry growers (Pavan et al. , 2006 ). Even in carefully managed fields, losses from fruit rot can exceed 50% when conditions favor disease development (Ellis and Grove , 1982; Turechek et al. , 2006). Fungal diseases pose a special challenge for strawberry growers in humid and warm climates conducive for disease development, such as the climate in the southeastern United States. Growers commonly use fungicides to fight the disea ses, applying them on a calendar based, once a week schedule (Mertely and Peres, 2012) . However, there are several issues with this type of application method. First, when/if the conditions are not conducive for disease
21 development, unnecessary fungicide a pplication causes chemical and labor waste, which are neither cost effective nor environmentally optimal. Second, if weather conditions have the potential to deteriorate unexpectedly, the farmer is unable to be proactive (Ellison et al. , 1997). Third, the more farmer applies fungicide, the more resistant the disease can become. Fourth, there are rising public concerns about possible health and environmental effects of fungicide use (Peres et al. , 2010b). In addition, f ungicide costs comprise approximately 7 % of pre harvest variable costs and represent about $690 per acre ( UF IFAS , 2010), and one the significant issues facing the strawberry industry is increasing costs of fungicides (Peres et al. , 2010b). These concerns have increased the interest in PA techn ologies to optimize fungicide management. Production methods that can reduce fungicide rates without negatively affecting strawberry yields and quality can provide significant economi c and environmental benefits to Florida strawberry industry. Development o f Strawberry Advisory System P re harvest disease prevention strategies could have a significant impact on strawberry input use, production costs, and environmental sustainability. T he Strawberry Advisory System (SAS) has been developed to assist producers in the southeastern U.S. to manage weather and climate related risks (Pavan et al . , 2009 ). SAS was launched as a web based tool ( www. AgroClimate.org ) in 2009 by the Southeast Climate Consortium (SECC), Florida C limate Institute, and Florida Cooperative State Extension Service (Pavan et al. , 2011). Given that Florida is the second largest strawberry producing state in the United States (after California), with 1 83 m illion pounds of strawberry harvested in 2012 ( U SDA NASS a , 2013), in 2009, Florida was selected as the first state to launch the SAS web -
22 based expert system (Fig ure 2 3 ). The system can be accessed on line, or strawberry producers can subscribe for location specific SAS issued alerts via text or e mail messages. I n 2012 the web site was accessed 3,099 times by 617 people (interview Natalia Peres, 2013). Based on a 2012 survey of Fl orida strawberry producers, 55 % of respondents (45 growers) were subscribed for text or e mail alerts from SAS. Currently, SA S i s being tested in other strawberry producing U.S. states (Peres, 2012). The main goal s of SAS are to reduce costs and to stem off fruit rot before it has a chance to develop. SAS was developed to optimize the fungicide application timing in Florida str awberry production ( Pavan et al. , 2009). Specifically, SAS uses real time information about air temperature and strawberry leaf wetness duration to tailor fungicide applications to the periods of high risks for anthracnose and Botrytis fruit rot developmen ts. The idea behind SAS is to catch and stem off the disease development in the earliest stages depriving it the opportunity to spread while at the same time minimizing unnecessary use of fungicide without negatively affecting the yield. The benefits of SA S are cost effectiveness in fungicide applications, higher yields due to decrease in disease resistanc e build up, higher profits, reduced health risks and environmental footprint . Modeling risks and economic valuations in agricultural production using met eorological da ta as a source of uncertainty os explored by VanTassell et al. (1990) and Aggarwal (1995). The importance of site specific weather data being used in the simulation design is underpinned by Rivington et al (2005). Possibility of encoding unce rtain events as probabilities using subjective probability is highlighted by Lien et al. (2009). In this study, based on the results of six year field trials we simulate empirical
23 distributions of weather conditions encompassing a full range of possible su btropical weather conditions characteristic to Florida. Based on a simulated set of weather conditions for each production season we estimate and compare two net present values (NPV) of cash flows: one from strawberry production given a traditional (weekly ) fungicide application method and the other given the precision (SAS based) fungicide application method. Multivariate empirical (MVE) probability distributions (Richardson et al. , 2000) and Monte Carlo simulation are used. The marginal value of PA tech nology is determined as the difference between the NPV of cash flows from production under PA fungicide management and that of the traditional method. The analysis is carried out for each disease, anthracnose and Botrytis, and for two different cultivars, more and less resistant ones, separately. There are two main contributions of the modeling approach in this paper. The first is an innovative integration of the weather data points, based on which weather variables and their distributions are obtained. Se cond, these weather variables are cohesively integrated into the simulation of the production process and both revenue and cost structures . Past research shows that accurate information about weather conditions can be used to tailor the fungicide applicati ons to manage the a n t h r a cno s e and Botrytis disease pressure (Wilson et al. , 1990; M ac k en z i e and Peres , 2012 ). Periods with warm and wet weather create favorable conditions for the development and spread of anthracnose and botrytis fruit rots increasing th e risk of harvest losses. In contrast, given cool and dry conditions, the risk of this disease development is relatively minor. Bulger et al. (1987) and Wilson et al. (1990) developed a system that predicts the spread of anthracnose and Botrytis disease o n berries based on the duration of leaf
24 wetness and the average temperature during the wetness period. They found that the most conducive temperature for anthracnose disease development for both immature and mature fruit is between 25 Âº and 30 Âº C, while fo r Botrytis disease development the most conducive temperature is between 15 Âº and 25 Âº C with the absolute optimal temperature being 20 Âº C (Bulger et al. , 1987). Guided by this research, UF scientists conducted strawberry field experiments (Pavan et al ., 2 006, 2011 ; Fraisse et al. , 2006 ; Turecheck et al. , 2006 ; Mertel y et al. , 2010 ) and in 2009 launched the on line Strawberry Advisory System (SAS) (Pavan et al. , 2011). SAS was designed to predict disease conducive conditions by processing leaf wetness durat ion and average temperature during the wetness period, and to issue alerts for fungicide applications when conditions for disease development are favorable (Figure 2 3). A review of 210 studies that examined the economic costs and benefits of PA technologi es (Griffin and Lowenberg DeBoer , 2005) showed that although 68% of the studies reported positive net benefits associated with precision agriculture technologies, several studies showed net losses. In this study, we examine the potential economic benefits provided by SAS for an average Florida strawberry producer. Specifically, we compare the net present value (NPV) from strawberry production for a 10 year planning horizon given a traditional fungicide application method and the precision fungicide applicat ion method that follows SAS recommendations. The analysis is performed for a permutation of two diseases, anthracnose and Botrytis, and two different cultivars, more and less resistant ones, separately. The Difference between SAS and Calendar Based Fungi cide Application Methods The fundamental differences between the two fungicide application methods, Calendar based and SAS based, are demonstrated in Figure 2 4 . The calendar based
25 application method involves routine fungicide application on the same day o f every week during the production season. We define the number of applications for the Calendar based method by (where D index es fungus diseases, D [ AFR : Anthracnose Fruit Rot, BFR : Botrytis Fruit Rot] ). Since the Florida productio n season is on average 15 weeks : = 15 . (Figure 2 4). In contrast, for the SAS based method, the timing of the fungicide application depends on the trigger from SAS. SAS determines the probability of disease development based on the leaf wetness duration (W) and an average temperature during the wetness period (T). If the probability exceeds the thresholds of 15% (for Anthracnose, ) or 50% (for Botrytis, ), then SAS issues a trigger alert for fungicide a pplication respectively for each disease. The total number of applications sums up to The fewer disease conducive days there are throughout the season, the lower is the number of applications under SAS based method. Conversely, the more dis ease conducive days there are, the higher is the number of applications, . In the worst case scenario is equal to . SAS Operation SAS predicts the probability of disease infection based on the relationship between t he wetness duration and temperature during the wet period, originally proposed by W i l son et a l . ( 199 0 ) and B u l g er et a l . ( 198 7 ) for the a nthracnose and Botrytis diseases, respectively . They used a logistic regression model, where the infection level of the disease was accurately described as a function of wetness duration ( W ) and temperature during the wet period ( T ). Equation ( 2 1) describes the relationship,
26 where percentage of infection of ripe fruit and flowers, , is the dependent variables within logistic equation. (2 1) Two factors had to be taken into account in the regression analysis. First, the functional form of the model had to accurately represent the ob served relationship between and T , such that increases to a maximum and then decreases. Second, in the regression model, had to increase with increases in W , but should not exceed 1.0 or fall below 0.0 for any value of W . W i l son et a l . ( 199 0 ) and B u l g er et a l . ( 198 7 ) us e d a l o g i s t i c r e g r es s i on t o m odel t he p r op o r t i on of i m m a t u r e a n d m a t u r e s t r a w b e rr y f r u i t i n f e c t ed by a n t h r a cno s e ( , Equation 2 2) and by Botrytis ( , Equation 2 3 ), respectively, as a f u n c t i on o f temperature, T , and leaf wetness duration, W : (2 2) (2 3) Equations ( 2 2) and ( 2 3) are referred to as the Wilson Madden weather index for each of the diseases respectively. Denoting the left hand side of equations as the disease index, or DI , the proportion of strawberry fruit infected by the fungu s can be specified as: (2 4) where D [1:AFR, 2:BFR] to distinguish between two fungi diseases. The relationships ( 2 2), ( 2 3), and ( 2 4) were used by Mackenzie and Peres (2012) to develop the on line
27 Strawberry Adviso ry System (SAS) that indicates the level of anthracnose and Botrytis disease risks. SAS recommends fungicide application if the disease risk is high (Figure 2 4 ). Specifically, using strawberry production experiments and the knowledge of critical combinati ons of temperature and leaf wetness duration at which the disease pressure becomes critical (Wilson et al. , 1990), Mackenzie and Peres (2012) identified the optimal threshold for an anthracnose disease given Florida growing conditions, which is 15%. Thus, = 0.15 is considered as a threshold to trigger the fungicide application. Thus, when equation ( 2 4) estimates a 15% probability for anthracnose development in and de such as Captan (Captan 80WDG: Mic ro Flo Company LLC, Memphis, TN; Mertely and Peres 2012; Peres , 2010a). Furthermore, when equation ( 2 4) estimates at least a 50% probability of strawberries develop ing the disease ( ide such as Cabrio (Cabrio 20EG: BASF Corporation, Research Triangle Park, NC ; Mertely and Peres 2012; Peres , 2010a). For Botrytis there is only one th reshold ( = 0.50) to trigger a fungicide application. The label restrictions on the maximum rate and frequency of fungicide applications are also accounted for in the SAS recommendations. Specifically, the maximum number of sequential appli cations for Cabrio is limited to two, and the maximum rate of its application is 70 oz (4.375 pounds) per acre per season ( Mertely and Peres, 2012 ). In turn, Captan can only be applied at the rate of one ounce per one gallon of water per 100 square feet of land; and sequential applications should be separated by at least seven days ( Mertely and Peres, 2012 ). To account for these
28 restrictions, producers are asked to enter their past fungicide application practices into SAS, and the system modifies the recomm endation based on the label specifications for each fungicide used by the growers. The potential reduction in fungicide use associated with SAS has been examined by Peres et al. (2010a). However, the study was based on short term production experiments, an d it did not evaluate the economic effects of the SAS based fungicide application method. Meanwhile, the changes in costs and revenues, as well as revenue variability and economic risks, are the key determinants of SAS adoption by producers. In this study, we evaluate the farm level profitability of the SAS based precision fungicide application method as compared with the traditional c alendar based method given the uncertainty and risks in weather conditions, yield, and output prices. The dataset available from extended, six year field production trials allows us to explicitly model strawberry yield as a function of weather, and then relate weather variability to the risks in production and profitability. Data The data are obtained from multiple sources. Fir st, historical data for yearly state average strawberry producer prices and yields were collected from the National Agricultural Statistics Service, NASS, for the years 1984 through 2012. Second, strawberry production budget data was obtained from the work of Smith and Taylor ( 2011 ) and VanSickle et al. (2009).The cost data were itemized and presented as cost per acre. The budget contained price and quantity data for the following inputs: fertilizer, fumigants, fungicides, insecticides, surfactants, labor, contracted services, machinery use, and miscellaneous other materials. Third, data from the six year production experiments
29 were obtained from the University of Florida research farm at the Gulf Coast Research and Education Center in Wimauma, Florida. The field trials were conducted for six consecutive production seasons (November March, 2006 2012). The trials were independently conducted for a permutation of two diseases, anthracnose and Botrytis, and two different cultivars, less and more disease re sistant. For each disease, the trials followed a randomized complete block design with four blocks (four plots), each in a separate plastic mulched, raised bed approximately 300 feet long and 4 feet wide. Each plot was divided into three sections according to the fungicide application method used throughout production season: c alendar based (with weekly fungicide applications), SAS based (with fungicide application follo wing SAS recommendations), and c ontrol (with no fungicide application). Two types of str awberry cultivars were used in the experiments: less disease resistant (Camarosa or Radiance) and more disease resistant (Festival or Treasure). Bare root strawberry transplants were planted into fumigated soil using staggered rows. Berries we r e ha r v es t ed t w i ce a w e e k starting in D ec e m ber and ending in Ma rc h. M a r k e t a b l e f r u it we r e c o un t ed, w e i g hed, and then cumulated for each production season. D i se a sed fr u i t s we r e a l so c oun t ed f o r a n t h r a cnose ( A F R ) and B ot r y ti s ( B F R ) i n c i de n ce s, and also cumulated for each production season . T he nu m ber of b e r ri e s t oss e d f or r e aso n s o t h e r t h an anthracnose and Botrytis diseases (i.e., c u l l) was also recorded and summed up for each season . In summary , since there are f our p l o t s, three fungicide application methods, and six pro duction s e aso n s ( 2 006 07 to 2011 12), there are 72 independent observations for each variable. The variables are m a r k e t a b l e n u m ber of t he be r r i es ( N u m be r ) , m a r k e t ab l e w e i g ht of b e r r i es i n g r a m s ( W e i g h t ) , t h e nu m ber
30 of be r r i es t ossed f or r e a sons other t h a n t he d i s e ase ( C u l l ) , t he nu m ber o f b e r r i es affected by B o tr y t i s ( B o tr y ti a nd a n t h r a cno s e ( A n t h r ac n os e ). The yield summary sta tistics are presented in Tables 2 1 and 2 2 for anthracnose and Botrytis, respectively. During each season, leaf wetness interval ( W ) and the temperature during the wetness period ( T ) were recorded every 15 minutes by sensors placed in the field. Then, the temperature measures were averaged over all temperature readings during the wetness period. These measures were used as independent variables for the Wilson Madden regression ( Equations 2 2 and 2 3 , respectively for each disease). Based on the sensor data, SAS estimated the percentage of infected berries, . For critical infection levels, when , the triggers were issued, and SAS based production plots received fungicide applications. The number of fungicide applications for SAS based, Calendar based, and Control production plots were cumulated over each production season ( Tables 2 3 and 2 4). Definition of Weather Variables Let i index the production seasons, and j be a reverse index for the weeks in the production season, , where is the total number of weeks in season . is also the upper limit on the number o f fungicide applications per season since the maximum rate of fungicide application is once a week. Thus, under the Calendar based system, and the number of fungicide applications for an production season, , is equal to . On the othe r hand, SAS based fungicide application depends on the weather which can influence fungal disease development and, ultimately, yield. Let and define Weather and Weather Intensity variables, respectively . Weather ( ) captures the number of triggers released by SAS in production season i :
31 (2 5) where is the binary variable indicating the SAS trigger was issued on day of the week j . In other words, for each season, we ather variable is the result of a summation of days during which the 15% threshold (for anthracnose) or 50% threshold (for Botrytis) were reached or exceeded. Since weather conditions vary among production seasons, let the variable be such th at , where represent all possible weather conditions during a production season. The earlier the disease occurs in the season, the more severely it may affect the yield (since the early disease incidences increase the probabil ity that the disease will remain on the plant for the rest of the season and infect more newly developing strawberries). To capture this effect, a Weather Intensity measure, , f or the production season is constructed by multiplying the numb er of triggers in the week (i.e., ) by the number of weeks left in the season (i.e., j ), and then summing up all the resulting products across all weeks in the production season (2 6) with where represent all possible states of weather intensity conditions. Lastly, Application variable is quantified by the number of total fungicide applications for the entire season fo r each disease and three application methods, respectively (Tables 2 3 and 2 4). Control group received no applications, thus Application is equal to zero. In anthracnose trials, under the Calendar based application method 10 to 16 applications are adminis tered each production season, averaging around 15. Under the SAS based method 5 to 12 fungicide treatments are applied each season, averaging around 8 applications per season, which is a 56% decrease compared to that of the
32 Calendar based method. In Botryt is trials, under the Calendar based application method 12 to 17 applications are administered each production season averaging around 16. In contrast, under the SAS based method only 3 to 10 fungicide applications are applied averaging around 8 application s per season, which is a 49% decrease compared to the number of applications under the Calendar based method. Manu f a c t u r s p ec i f i c a ti o n s limit the fungicide application rate to once a week. Thus, even if there are several triggers for disease development during a week, only one application is administered. Therefore, for each given season t he n u m ber of a pp li ca t i ons is smaller than the number of days conducive for the disease development . For the anthracnose trials, among all six seasons there were on aver age 15 applications under Calendar based system; and only 9 applications under the SAS based system, which is which is a 44% reduction . For the Botrytis trials, on average there were 16 applications under the c alendar based method, and only 8 for the SAS b ased method, which is 50% reduction in the number of applications. The values of the weather variables based on field trial data are presented in Tables 2 3 and 2 4. These values are used to estimate multivariate empirical (MVE) distributions (Richardson e t al., 2000) for the variables Weather, , Weather Intensity, , and Applications, , spanning a range of possible Florida production conditions, and . All estimations were conducted using SimetarÂ© Add in for MS Excel. Theoretical Model Most often fe asibility analysis for production systems is performed using profit maximization or utility maximization models ( Thrikawala et al. , 1999 ; Lambert and Lowenberg DeBoer , 2000 ; Griffin and Lowenberg DeBoer , 2005 ). However, Just and
33 Pope (2002, 2003) warn that the results of such studies are sensitive to the changes in assumptions made by the researchers and suggest presenting the findings from feasibility studies as a distribution of possible outcomes. In line with this recommendation, some economic feasibilit y studies included the analysis of price and yield variability ( Ramaswami , 1992 ; Coyle , 1999 ; Godwin et al. , 2003 ; Asche et al. , 2006 ; Richardson et al ., 200 4 , 2007); however, none of the studies modeled simultaneously crop yield, price, production cost, a nd profit as functions of weather and weather related disease in the profit maximization framework. For example, Richardson et al. (2000, 200 7 ) simulates yield, crop price, cost variables, and profit variables, but these variables are not weather dependent . Instead, their simulations are based on variation and trend in historical prices and yields. The contribution of this study is that it incorporates weather and disease risk into yield, crop price, fungicide costs, and, finally, profit modeling. The study utilizes Monte Carlo simulations to create a probability density function of profit based on those of yield, cost variables, and crop price , which is correlated with yield to reflect supply/demand relationship . For the general model, let denote fungicide production input, and be the price of fungicide, denote the aggregate quantity of other than fungicide variable inputs, and be the aggregate price of those inputs. Using this notation, is total variable costs (excluding fu ngicide costs), and is total fixed cost. For one production season, profit is revenues less fungicide, variable (ex fungicide), and fixed costs: ( 2 7 ) where represents the price of the crop received by a grower (in th is case, the price of one pound of strawberries in dollars), is acreage planted (in acres), and is
34 production of the crop per acre at the end of the season (pounds per acre). The producer is assumed to be a price taker. Weather conditions (i.e., a c ombination of temperature and leaf wetness) can be denoted by a random weather variable where represents all possible states of weather conditions. Yield is affected by random weather conditions, and fungicide application : . The variabi lity of revenue is a result of yield variability, that depends on the random weather events, and strawberry prices variability, that depends on the market, which in turn is a function of the supply and demand dynamics. Assuming inelastic demand, an increas e in supply depresses prices. To reflect this dependence, the correlation between historical strawberry prices, and historical yields, , is used. The traditional strawberry production practice is to use fungicide on a calendar basis (weekly) to stem off potential disease. For this practice, and for specific realization of the expected profit, , is specified as follows: ( 2 8 ) Alternatively , the producer c an improve his/her knowledge about the random state variable, weather, by seeking additional information from SAS. F or the SAS based production practice, let X denote the set of possible number of fungicide applications, X [0, ] 1 for anthracnose and X [0, ] 2 for Botrytis . SAS predicts the probability of disease development conducive weather, . Given predicted probability, SAS 1 For anthracnose trials the experiments continues fo r an average of 15 weeks, and the maximum fungicide application rate is once a week, the maximum number of fungicide applications is fifteen. 2 For Botrytis trials the experiments continues for an average of 16 weeks, and the maximum fungicide application rate is once a week, the maximum number of fungicide applications is sixteen.
35 also issues a trigger alert for fungicide application, thus, it determines the number of applications X for the entire season. For a 15 week long production season, SAS will result in zero applications if during the season, none of the 15 weeks had days conducive for disease development. The number of applications will be the maximum and equal to the number of applications of the traditional method if the season had days with disease development conducive weather conditions in each week of the season: (2 9 ) Since weather, , and sale price, , vary from season to season, calendar based and SAS based fungicide applications result in a distribution of profits for each application method. By finding the shift in distribution bet ween and , the expected benefits from precision agriculture technology can be identified. Specifically, we define Value of SAS ( ) as the difference between and : (2 10 ) Next s ection defines the specific methodology used in the analysis. Methodology The objective of this research is to value the effect of the new PA technology, i.e., SAS, on the profitability of Florida strawberry production. We accomplish it by comparing the distributions of the 10 year net present values (NPV) given two fungicide application me thods: the traditional weekly (c alendar based) application method and PA application ( SAS based) me thod that is dependent on the information provided by SAS. NPV distributions are generated using Monte Carlo simulations with 10,000 iterations ( Richardson et al., 2007 ) . NPV methodology with Monte Carlo simulations has been
36 previously used in production s tudies (Buccola and McCarl , 1986 ; Thompson and Langworthy , 1989 ; Richardson et al. , 2004, 2007). To determine the added value that the new SAS based application method provides, a difference between NPV of Profits SAS based method and Calendar based method s is found, and also simulated 10,000 using Monte Carlo simulations. The uniqueness of this study is that the NPVs for profit are stochastically forecasted based not only on historical yields and prices, but also coordinated with the results from the six y ears of production experiments where weather is an input variable that introduces disease risk. Using Richardson (2000) methodology we obtain multivariate empirical and multivariate mixed empirical ( MVE and MVM ) distributions for key variables such as Weather, Weather Intensity, and Applications as well as yield and profit functions of each fungicide application method. The difference between NPVs of profits for the two fungicide application models is evaluated for a range of weather conditions typic al to Florida. Thus, the final added value of the new precision technology, is a stochastically modeled distribution that is weather dependent covering a range of weather conditions from most to least conducive to disease development. In this model, a farm is assumed to be 26 acres (an average acreage among Florida strawberry farms ; USDA NASS a , 2013), the prediction horizon is ten years, , as a net cash flow at time n . To obtain fin al NPV of ten year profits, namely, , each is discounted using a Discounted Cash Flow (DCF) method (Damodaran , 1996): (2 11 ) where n = 10 years of future cash flows, and r is the discount rate.
37 Next, Monte Carlo simulations (Neal , 1993 ; Gilks, Richardson and Spiegelhalter , 1996 ) are performed drawing 500 iterations based on the resulted from the e quation 2 11 distribution that consists of data poi nts, using the following steps : (2 12 ) where are generated s amples from the distribution, which is obtained as follows: (2 13 ) where is the probability density function. Simulatin g Key Variables Sections 7 and 8 describe how each input and output in the system is predicted to obtain the profit for every period for the three distinct fungicide application methods. Weather and Weather Intensity Variables The weather, , is represen ted through two variables in the model, Weather and Weather Intensity . The Weather variable is randomly drawn from a normal distribution with mean and variance obtained from the data collected from the field trials (Table s 2 3 and 2 4): (2 14 ) Since there are only six Weather variable observations from the experiment, these data cannot be tested for normality. To understand whether a normal distribution can be used, historical data for temperature and humidity provided by Florida Automated Weather Network (FAWN) system ( http://fawn.ifas.ufl.edu/ ) was tested for normality. The data included 14 production seasons starting in 1998 and continuing to 2013. The
38 hypothesis tha t the weather follows normal distribution could not be rejected at 5% significance level using chi s quare test. The Weather Intensity variable is obtained by using a simple OLS regression with Weather as an independent variable: (2 15 ) where is the error term. Following the methodology of Richardson et al. (2000) we generate stochastic predicted values from the OLS regression (Equation 2 15 ). First, th e deviations from the trend are generated by dividing the error term by the predicted value of Weather Intensity measure as follows: . The deviates are then sorted and arranged from minimum to maximum in a vect or, . Next, a probability is assigned to each of the sorted deviates as having an equal chance of being observed (1/T) in history, where T is the number of historical observations, which are used in the regression. T he distribution of these d probability is represented by . Finally, w e define stochastically predicted Weather Intensity as: (2 16 ) where historical years, and simulated years, is a vector of deviates from trend as a percentage of predicted, and represents distribution of deviates in the vector of sorted deviates , and MVE stands for Multivariate Empirical distribution whose functional form depends on . MVE is a distribution comprised of the deviates from the trend as a percentage of predic ted from the regression of the e quation 2 15 , . Since the regression of
39 e quation 2 15 is dependent on Weather variable, which happens to be Normal distribution, F (.) in this case is also normally distributed. Applicat ion Variable The number of fungicide applications is estimated using simple OLS regression with Weather as an independent variable: (2 17 ) where is the error term. Foll owing the methodology of Richardson et al. (2000) we generate stochastic predicted values from the OLS regression (Equation 2 17 ). The procedures are similar to the ones described when obtaining stochastically predicted Weather Intensity measure. The devia tes from the trend are generated by dividing the error term by the predicted value of Application measure as follows: . The deviates are then sorted and arranged from minimum to maximum in a vector, . Next, a probability is assigned to each of the sorted deviates as having an equal chance of being observed (1/T) in history, where T is the number of historical observations, which assigned probability is represented by . We define stochastically predicted Application as follows: (2 18 ) where historical years, and simulated years, is a sorted vector of deviates from trend as obtained from th e regression (Equation 2 17 ), represents distribution of deviates in the vector of sorted deviates, and MVE stands for Multivariate Empirical distribution whose functional form depends on . MVE is a di stribution comprised of the deviates from the trend as a
40 percentage of predicted from the regression of the e quation 2 17 , . Since the regression in e quation 2 17 is dependent on the Weather variable, which happens to be Strawberry Yields and Prices Predicted yields for ten years are obtained in several steps. First, we project state wide strawberry yield by employing simple OLS trend regression using historical data 1980 2011. This regression is time dependent only and it captures state wide dynamics of yield and state wide level risk. Second, we obtain a regression for yield based on the production experiment data. The goal of this re gression is to capture farm level yield dynamics and farm level risks. Since state level data is a result of significant aggregation, it provides an excellent historical trend. The reason that we use 1980 2011 data for the state wide regression is to refle ct the best fit and correlation between yield and prices. In the meantime production experiment highlights the more specific possibilities of yields. In this regression weather and application related variables are used as independent variables. To incorpo rate state level and farm level yield dynamics and risks into one model, the historical state wide yield for the years 2006 20012 (that matches exactly the years of the experiment) is used as one of the independent variables when obtaining regression est imates based on the production experiment data. This allows us to use the projected state wide yield as one of the variables that determines the final yield in the model. I present the predicted results of the final yield for the ant hracnose disease and Bo trytis disease.
41 State Wide Yields and Prices Based on Historical Average Data To reflect supply demand dynamics, that is if yield increases prices decreases, yield and prices are simulated interdependently. In this section state wide strawberry yield and prices are projected by employing simple OLS trend regression using average historical observations. Historical state wide yields are the dependent variables while the years are the independent variables in this trend regression. The same procedure is perf ormed for the state wide prices. These are deterministic components for the yield, and price, Following the methodology proposed by Richardson et al. (2000) we simulate two jointly distributed variables. More specifically, price and yiel d are related, with low prices generally corresponding to higher yields, and vice versa high prices corresponding to lower yields. The yield, and price, , variables are modeled as elements of 2x1 vector X t : ( 2 19 ) First, the following regression of X t dependent on time is estimated : (2 20 ) where i indexes elements in vector X t , and is the error term. Following the methodology of Richardson et al. (2000) stochastic predicted values are generated from the OLS regression (Equation 2 20 ). The procedures are similar to the ones described when obtaining stochastically predicted Weather Intensity and Application measure. The deviates f rom the trend, are generated by dividing the error term by the predicted value of measure as follows: (2 21 )
42 The intra temporal correlation matrix between yield, and price, is estimated. The intra random variables), and can be presented as follows: (2 22 ) The deviates are then sorted and arranged from minimum to maximum in a vector, . Next, a probability is assigned to each of the sorted deviates as having an equal cha nce of being observed (1/ T ) in history, where T is the number of historical observations (years), which are used in the regression. T he distribution of these . W e defin e stochastically predicted as follows: (2 23 ) where , simulated years, is a sorted vector of deviates from trend as obtained from the regression (Equation 2 20 ), represents distribution of deviates in the vector of sorted deviates, and MVM stands for Multivariate Mixed Empirical distribution whose functional form depends on . MVM is a distribution comprised of the deviates from the trend as a percentage of predicted from the regression of the e quation 2 2 0 , . Since the regression in equation 2 20 is dependent on the Weather variable, which h appens to be from the normal distribution, F is the correlation matrix of price and yield variables. Ten years are predicted, thus the size of the vector is ten, N = 10.
43 Combining Equations 2 1 9 and 2 23 , yield, and price, are obtained: (2 24 ) (2 25 ) where refers to simulated years, and are sorted vector of deviates from trend as obtained from the regression (Equation 2 20 ), and represent distribution of deviates in the and vectors of sorted deviates, respectively, and MVM stands for Multivariate Mixed Empirical distribution. Yield Based on Production Experiments As described in the Data Section, the experiments were conducted for two different fungi disease s, anthracnose and Botrytis, denoted earlier as AFR and BFR, respectively. For each disease, two different cultivars were used in production experiments: a more disease resistant cultivar and a less disease resistant cultivar denoted M and L , respectivel y. In addition, in those trials three different methods of fu ngicide application were used: control, c alendar , and SAS based. Therefore, to , where Cultivar and Method . Thus, the regression expression for the yield in general terms is as follows: 2 26 where Cultivar Method , and is an error term .
44 The descriptive summary of independent variables used in OLS regression to model seasonal strawberry yields is presented in Table 2 5. Yield Based on Production Exp eriment Several functional forms were tested in OLS regre ssion for both anthracnose and B otrytis field trials, and the specifications characterized by the highest adjusted R square d were selected. For both regressions, the yield for the Calendar based app lication method is chosen to be the base case scenario (captured in the intercept of the regression), while the effect s of the SAS based and Control methods are modeled using dummy variables. Based on data collected during the six year experiment, a funct ional form for strawberry yield in anthracnose and Botrytis trials, and were obtained using OLS regression: (2 27 ) (2 28 ) where and are the error terms specific to the m ethod of fungicide application given a more or less resistant cultivar. To be able to have these distinct
45 error terms for each of the Cultivar and Method , White's heteroscedasticity consistent es timator procedure is employed as follows. First, Breusch Pagan test is conducted to check for heteroskedasticity. The procedure tests whether the estimated variance of the residuals from the regression s (Equation s 2 27 and 2 28 ), , is dependent on the values of the independent variables ( Breusch and Pagan , 1979 ) . Specifically, form for the variances of the observations, where explain the difference in the variances. The null hyp othesis is which has parameter restrictions. Auxiliary regression is performed as follows: , and its F statistic . Th us, t he test results in rejection of the null hypothesis of homoskedasticity at significance of 0.05, which indicates presence of heteroskedasticity. Third, to correct for heteroskedasticity, White robust error procedure is used to obtain heteroscedasticit y consistent (HC) estimates and standard errors (White 1980). Specifically, r , have distinct variances , so we obtain by . This provides White's (1980) estimator, also known as HCE (heteroskedasticity consistent estimator): (2 29 ) where are the adjusted estimates , from the original regression of a nthracnose yield (Equation 2 27 ) and from th e original regression of Botrytis yield, and is the matrix of independent variables. The dependent variable Yield is strawberry weight (in pounds/acre). The descriptive summary of independent variables , including , , , , and , and Cultivar, as well as
46 various interactions of these terms is provided in Table s 2 6 and 2 7 . The yield for the c alendar based application method is chosen to be a base case scenario, while the effect of SAS based method and c ontrol are modeled using dummy variables. Th is choice was made because the c alendar based method of fungicide application has persisted historically among the Florida growers; therefore, h istorical s tate average Yield data generall y reflect the practices of the c alendar based fungicide application. In conclusion, based on method of generating stochastic predicted values from the OLS regression (Richardson et al. , 2000), we obtain stochasti cally predicted: (2 30 ) where Cultivar and Method historical years, and simulated years, is a vector of sorted deviates respectively to each met hod given a more or less resistant cultivar for each disease, and is a vector of assigned probabilities to a specific deviate in determined by the OLS regressions in e qu ations 2 27 and 2 28 for the yield o f each disease, given a cultivar respectively. It is important to mention that is unique for each case (2 diseases, 3 methods, 2 cultivars) precisely because in each of those 12 c ases a regression has own specific error term, Profit Derivation and Simulation The following section contains three subsections: construction of revenues, production costs, and simulation of profits. Generally, profi t in a given year n , , is a difference between revenue, , and cost, , during that year: ` (2 31 )
47 Based on this configuration NPV of profits for ten years is found, and then drawing from the distribution simulated using Monte Carlo methodology as described in Methodology. Constructing Revenues Revenue is a product of Yield and Price, so combining Yield Equations 2 27 and 2 2 8 with the p rice e quation 2 24 , the revenue for ea ch method of production is: (2 32 ) w here Cultivar and Method historical years, and simulated years, is a vector of sorted deviations respectively to each method given a more or less resistant cultivar, and is a vector of assigned probabilities to a specific deviate in determ ined by the OLS regressions in E quations 2 27 and 2 28 for the yield of each method given a cultivar respectively. Production Costs As described in the Theoretical Model section, total costs are comprised of variable and fixed costs. For this analysis all costs are measured in dollars per acre ($/acre) for an average farm. Fixed costs is a sum of land rent, machinery fixed cost and overhead. Fixed costs are projected with a 2% inflation rate over the ten year time period, and assumed to be the same for all three production methods. Variable costs are operating costs, harvesting costs, packing and selling costs, and in simple terms they can be expressed as follows:
48 (2 33 ) Operatin g costs include transplants, plastic mulch, scouting, tractor and general farm labor, fumigant, machinery variable costs, transplants, herbicides, insecticide, fertilizer, crop insurance, and interest on operating capital costs per acre. These operating co sts are projected to increase with an inflation rate of 2% and are the same for all three models of fungicide application. Fungicide Costs ($/lb), Harvest Costs ($/lb), and Pack and Sell Costs ($/lb) are based on pr oduction budget developed by UF IFAS (201 0 ), and denoted as FC , HC , and PSC , respectively. Let x denote the quantity of fungicide input, and w be the price of fungicide in $/acre per one application and OC be the fixed portion of the Total Variable Costs for all three production methods. Thus, ex p ected Total Variable costs for control, c alendar, and SAS groups respectively are: (2 34) w here D Cu ltivar , Method and simulated years. Fungicide costs depend on the fungicide application method. Specifically, for control group, fungicide costs are zero. For the Calendar met hod, the number of fungicide applications is equal to the number of weeks in a season (15 on average for anthracnose disease trials and 16 on average for Botrytis disease trials). Finally, for the
49 SAS based method, the number of fungicide applications depe nds on SAS triggered applications. For all three methods, the fungicide cost per season is equal to the product of cost per acre per fungicide application, the number of applications per season, and the number of acres (26 acres, assuming an average Florid a farm). Fungicide price at the year one is $590 per application per acre. It is then projected to increase 2% for every consequent year for 10 years. It is important to note that each Cost function will take functional form from that of Yield and for SAS based Costs the functional form will be a hybrid between the functional form of Yield and Application, however, both of them are normally distributed, thus normality of the cost distribution will also be preserved. Finally, Total Costs for all three metho ds are: (2 3 5 ) and D Cultivar , Method C i s fixed cost that is the same to all methods of production, OC is operating cost that is also the same to all methods, and simulated years. Simulation of Net Present Value of Profits Profit for each year n is expressed as Total Revenue ( Equation 2 32 ) less Total Costs (Equation 2 35 ), therefore:
50 (2 3 6 ) Next, NPV of 10 ye ar profits, , for each method and cultivar are found as described in the Methodology covered in Equation 2 11 : (2 37 ) where D Cultivar , Method , discount rate, r = 4%, and simulated years. Next, based on the Equation 2 1 0 from the Methodology Section, the value of SAS, , SAS based application method and that of Calendar based application method (Equation 2 10 ): (2 38 ) Monte Carlo simulation is performed to obtain a distribution of respective to disease, method, and cultivar for all possible scenarios of weather conditions, , are found based on Methodology developed in previous section (Equation 2 12 ): (2 39 ) To obtain a distribution of the added value of SAS based method, , al so Monte Carlo simulations are performed as described in Methodology (Equation 2 12 ): (2 40 ) Stochastic Efficiency wi th Respect to a Function
51 to a function (SERF) criterion was used to evaluate the NPVs for the two fungicide ty function with absolute risk aversion coefficients of the following form (Richardson and Outlaw, 2008): . In this study, the absolute risk aversion coefficient (ARAC) is , where m signifies the risky alternatives; that is, the method of fungicide application, is the relative risk aversion coefficient with respect to annual profit, , under the method of application, m . SERF calculates the certainty equivalence (CE), that is, the fixed amount of money a producer would accept as an equal exchange for a distribution of potential risky return s. SERF is estimated for various risk aversion levels, using the inverse utility function: (2 40) s risk aversion coefficient, instead it uses a range of ARAC describing a range of coefficients, from risk neutral (ARAC = 0) to extremely risk averse (ARAC = 4) (Anderson and Dillon, 1992) . R esults The results are for the three application methods, SAS b ased, Calendar, and Control, and two diseases, anthracnose and Botrytis, and for the two cultivar s , a more disease resistant and a less disease resistant cultivar . This section contains six subsections that cover deterministic results for each disease and stochastic yield and Monte Carlo simulated NPV of profits and added value of SAS based method results.
52 Deterministic Results for Anthracnose Trials The results of the regression analysis for anthracnose disease are presented in Table 2 7. As defined in t he previous s ection, the intercept contains the effects on the Calendar treatment method. Even though the intercept appears to be negative while Control and SAS based estimates are positive, it does not mean that the Calendar treatment performs worse than the other two since the effect of the interaction variables have to be added in before assessing the final effect. Table 2 7 breaks down the average yield estimates from the results of the above regression from the Table 2 6 according to each method of app lication by configuring dummy variable effect for each estimate in the regression respectively. The errors from this OLS regression were tested for normality using a Chi square test, and the results confirm that at the 5% significance level the hypothesis that the errors are normally distributed cannot be rejected. The results show that c ontrol performs the worst just as expected. For a more resistant cultivar the SAS based application method improves yield over the c alendar based method by 24.5%. For a les s resistant cultivar, the yield of SAS based treatment increased by 30% over that of c alendar. Thus, while the Model application method reduced the number of fungicide applications by 44%, it also resulted in the yield being higher than the yield in c alend ar based applications. Deterministic Results for Botrytis Trials Similarly to previous subs ection, the results of the regression analysis for Botrytis disease are presented in Table 2 8 . The Intercept in this regression did not show significance. Dummy va riable of Cultivar distinguishes its effect on yield within each
53 treatment. To access the full effect of each treatment on yield, the interaction terms have to be accounted. Table 2 9 displays the average yield for each treatment given a more resistant and less resistant cultivars. The results confirm that c ontrol performs the worst just as expected. For a more resistant cultivar the SAS based application method improves yield over the c alendar based method by 9.3%. For a less resistant cultivar, the yield of SAS based treatment i ncreased by 31.8% over that of c alendar. Thus, while the Model application method reduced the number of fungicide applications by 47%, it also resulted in the yield being higher than the yield in c alendar based applications. Stochas tic Results for Yield The results of stochastic simulation for Yield in case of anthracnose and Botrytis disease s, respectively, for a more and a less resistan t cultivars based on Equation s 2 27 and 2 28 are displayed in the form of the probabili ty densi ty funct ions in F igure s 2 5 and 2 6 . It can be seen , that in both diseases, SAS based yield distribution is shifted to the right in comparison wit h the calendar based yield and c ontrol yield, implying that at any given set of weather conditions the SAS bas ed fungicide application method produces the highest yield as co mpared to the calendar application method and c ontrol. Table s 2 10 and 2 12 present summary statistics for the averages of the distributions that confirm visual results of the F igure s 2 5 and 2 6 . The results show that, based on average values, the SAS based application results in higher yields than c alendar based applications. In the case of anthracnose disease, SAS based method reduces the number of fungicide applications by 47% (Table 2 3 ), and it improves yield by 24.5% for a more resistant cultivar and by 22.9%
54 for a less resistant cultivar compared to those of c alendar based applications ( Table 2 10 ). In the case of Botrytis disease field trials, the SAS based system reduces the number of fungicide applications by 49% (Table 2 3 ), and it increases yield by 25.5% for a more resistant cultivar and by 14.5% for a less resistant cul tivar compared to those of the c alendar based method (Table 2 12 ). As expected, c ontrol (with no fungicide applica tion) performs the worst for both diseases and cultivars. Overall, the increase in yields for the SAS based app lication (as compared with the c alendar based application) is substantial for both disease trials and both cultivar types. However, the increase is relatively more significant for the more resistant cultivars (i.e., 24.5% and 25.5% on average for anthracnose and Botrytis field trials, respectively). The strawberry plants for the less resistant cultivars may be more susceptible to fungus development , and the frequent fungicide application procedures required for the c alendar based application may damage the plants to the greater extent, as compared with the more resistant cultivars. However, even for the less resistant cultivar, the yield increase fo r SAS based application was 14.5% and 22.9%, for anthracnose and Botrytis field trials, respectively, which also has application methods, more resistant cultivars outperf orm the less resistant cultivars. Yet the change in fungicide ap plication method from c alendar based to SAS based reduced the average difference in yields between the cultivars. T he results of stochastic simulation for Yield in case of botrytis disease fo r a more and a les s resistant cultivars based on e quation s 2 27 and 2 28 are displayed in the form of the probability density functions in F igure 2 5 . It can be seen that SAS based
55 yield distribution is shifted to th e right in comparison with the calendar based and c ontrol yields, implying that at any given set of weather conditions the SAS based fungicide application method produces the hi ghest yield as compared to the c alendar application method and c ontrol. Table 2 15 presents summary statistics for the averages of the distributions that confirm visual results of the F igure 2 5 . The coefficient of variation of the simulated yield given the c alendar based method is the lowest out of all three (18.83 for a more resistant cultivar and 18.54 for a less resis tant cultivar). In turn, the variance for the SAS based treatment method is higher than that of c alendar (21.45 for a more resistant cultivar and 22.63 for a less resistant cultivar). This shows that the c al endar model runs the least risk out of all three methods; however, its average yield is also lower than that of SAS based. The difference between SAS base Yield and that of c alendar is 7,671 lbs/acre for the more resistant cultivar and 5,587 lbs/acre for the less resistant cultivar. In addition, positive skewness is higher for S AS based Yield (0.39) than for c alendar (0.26). If relation of averag e Yield per coefficient variation implying that risk associated with SAS based model is worth takin g given the increases in yield it provides. Inevitably, the question rises whether a slight risk increase of the SAS based application method is worth taking given that the method provides an increase the yields. Therefore, stochastic dominance analysis is performed. Assuming a negative exponential utility function, methods are ranked by choosing the most efficient set based on stochastic dominance with respect to a function. We find that for more resistant cultivar, SAS based method ranks as most preferabl e given that risk aversion
56 coefficient, RAC, is less than 0.0007, other wise, c alendar based method ranks as first preferable. On the other hand, for less resistant cultivar, SAS based method as first preferable if RAC i s less than 0.0008, otherwise, c alend ar based method is considered most preferable. Table 2 14 reports the results. For convenience, the names of the categories are distinguished by a letter M or L for a more resistant and less resistant cultivars, respectively. Figure 2 6 demonstrates the re sults graphically. Based on Yields (lbs/acre), certainty equivalent (amount of Yield that an individual would view as equally desirable as a risky method) is the highest for SAS based arts trending higher than that of SAS based. For a more resistant cultivar the risk premium starts 6,950 lbs per acre and then drops steadily unt il it becomes equal to that of c alendar based at RAC of 0.0006. As RAC increases from 0.0006, i.e., a fa rmer be comes more risk averse, c alendar method has higher Risk Premium. For Botrytis, SAS based Yield consistently ranks as most preferred for any RAC (Table 2 13) . In conclusion, for farmers with absolute risk aversion coefficient less than 0.0007 and 0.0008 f or more and less resistant cultivars, respectively, SAS based fungicide with higher RAC than 0.0007 and 0.0008 for more and less resi stant cultivars, respectively, c al However, it is more meaningful to look at the similar risk analysis of the ten year NPV
57 of profits because profit results incorporate full production process accounting for both revenues and costs. Results and Discussion for Ten Year NPV of Profit The distribution of NPV of ten year cash flows (CF, referred to also as profits) was generated using Monte Carlo simulation method (see Equation s 2 39 and 2 40 ). These NPV estimates incorporate the d ifference between fungicide application methods in total costs as well as revenues (influenced by yields). As shown in F igure s 2 7 and 2 8 , the Mode l based method outperforms the c alendar based method and certainly the c ontrol method for both more and les s resistant cultivars. Given the savings on the fungicide costs as well as an expected increase in yield (and hence revenues), the graph dem onstrates that the gap between calendar and SAS based application methods has widened compared to the gap that was o bserved in the graphical result of the Yield distributions. This shows that the value that the new fungicide application method provides is increased once costs savings are accounted for. Table 2 15 displays summary statistics of the distributions obta ined by performing Monte Carlo s imulation procedure based on Equation s 2 39 and 2 40 . It can be seen that, for both diseases, the variation coefficient of the c alendar category is indeed the lowest out of the three methods for both cultivars. SAS based metho d has the second lowest variation coefficient, only by one unit more t han that of c alendar expected. The data also shows that the difference between coefficients of vari ation of SAS based and c alendar groups are insignificant even though SAS based method yields higher profits.
58 In the case of anthracnose, the average ten year NPV for a typical farm is $5.9 million for less resistant cultivars and $6.5 million for more res istant cultivars for the SAS based method. For comparison, the average NPV is $3.9 million for less resistant cultivars and $4.8 million for mo re resistant cultivars for the c alendar based method (Table 2 14 ). Even given the worst weather conditions and th e lowest prices that can occur over a ten year planning horizon, the minimum NPV the farmers can expect for the SAS based application is $4.6 million and $4.8 million for less and more resistant cultivars, respectively, compared with $2.7 million and $3.3 million for less and more resistant cu ltivars, respectively, for the c alendar based method (Table 2 14 ). Finally, in the best case scenario, the SAS based application allows receiving the highest NPV values (up to $10 million) that are not achievable wit h other fungicide application methods. In the case of Botrytis, the average ten year NPV for a typical farm is $5.5 million and $6.7 million for less and more resistant cultivars, respectively, for the SAS based method. The average NPV Calendar based met hod is lower at $5.1 million and $5.3 million for less and more resistant cultivars, respectively (Table 2 15 ). Even given the worst weather conditions and the lowest prices that can occur over a ten year planning horizon, the minimum NPV the farmers can expect for the SAS based system is $4.3 million and $5.4 million for less and more resistant cultivars, respectively, compared with the much smaller values of $3.9 million and $4.3 million for less and more resistant cultivars, respectively, for the Cale ndar based system (Table 2 15 ). Finally, in the best case scenario, the SAS based method
59 allows receiving the highest NPV values (up to $8.0 million) that are not achievable with other fungicide application methods. In case of Botrytis, T able 2 15 display s summary statistics of the distributions obta ined by performing Monte Carlo s imulation procedure based on Equation 2 38 . It can be seen that variance coefficient of the Calendar category is indeed the lowest out of the three method for both cultivars. SAS based method has the second lowest variance coefficient, only by 1.74 units higher than that of Calendar based, for both cultivars. difference betw een the coefficients of variation of SAS based and c alendar groups are insignificant even though SAS based method yields higher profits. Interestingly, Calendar has the highest negative skewness. Next, s tochastic dominance analysis is performed. Assuming negative exponential utility function methods are ranked by choosing most efficient set based on stochastic dominance with respect to a ten year NPV Profit function. We find that for both diseases and cultivars SAS based method ranks as most preferred given any risk aversion c oefficient. Figure s 2 9 and 2 10 displays stochastic efficiency with respect to a function (SERF), under negative exponential utility functions. It can be seen that certainty eq uivalent is the highest for SAS based method for both cultivars for any risk av ersion coefficient. Being that the certainty equivalent is the guaranteed amount of money that an individual would take to view as equally desirable as a next alternative, the farmers would view risk adjusted return under SAS based method as the most effic ient. Next, we check ri sk premiums associated with the SAS based method relative to the c alendar one in terms of 10 year NPV of Profits. Risk premium is the minimum
60 amount of money by whic h the expected return given SAS based method mus t exceed the known r eturn on a c alendar based method, in order to induce an individual to operate under a more risky method rather than the traditional one. Thus, in case of anthracnose, the minimum willingness to accept compensation for the risk given zero risk aversion coef ficient starts at $1,641,826 in case of a more resistant cultivar and at $1,639,119 for the less resistant cultivar. As the coefficient increase the risk premium decreases and stabilizes at $1,235,563 and $1,223,226, for more and less resistant cultivar, respectively. In case of Botrytis , the minimum willingness to accept compensation for the risk given zero risk aversion coefficient starts at $1,709,638 in case of the zero absolute risk aversion coefficient (ARAC), and it increase s as risk premium decreas e s and stabilizes at $1,000,000. Finally, the main goal of this paper is to value this new information intensive technology in fungicide application method relative to the presently used traditional fungicide application method. To achieve this goal, we fi nd the added value of the SA S based method compared to the c alendar one by finding the difference between NPVs of the two application methods. Monte Carlo simulation s are performed, drawing 10,000 simulations from the difference of 10 year profits between the two models. For anthracnose, t he result presented in Figure 2 11 shows that the simulated difference in NPV is positive, ranging from just over $642,954 to $3,278,434 with an average around $1,654,552. This result confirms that the Model based applica tion meth od outperforms the traditional c alendar based application method for any given
61 weather condition. In addition, since the NPV of the difference is always positive it means that the reward of higher yields is well worth a slightly increased yield ri sk. Based on the distribution of as obtained by the Equation 2 38 and displayed in Figure 2 11 , that for risk averse farmers, SAS based metho d will perform better than the c alendar one without taking on additional risk as compared to Calendar even though farmers would be getting a higher profit. Figure 2 12 displays an example of the difference in production processes resulting in different profits between two methods of fungicide application during one randomly chosen year. In case of Botrytis, t he added value of the SAS based method, , compared to the Calendar one is presented in F igure 2 13 shows that the simulated difference in NPV is positive, ranging from $1,054,128 to $2,481,899 with an average around $1,713,998. This result confirms that the Model based application meth od outperforms the traditional Calendar based application method for any given weather condition even on a risk adjusted return basis. In addition, since the NPV of the difference is always positive it means that the reward of higher yields is well worth a slightly increased yield risk. In conclusion, for farmers of absolute risk aversion coefficient for both more and less resistant cultivars, respectively, SAS ranked as first preferable. Next is the risk analy sis of the ten year NPV of profits because profit results incorporate full production process accounting for both revenues and costs.
62 Discussion Warm and wet weather conditions are especially conducive for fungi disease development. Current climate cha nge patterns can severely increase the disease profits. Traditional fungicide management methods used extensively in the past may prove to be insufficient remedies in the future in the face of increased variability of weather conditions Expert systems equipped with real time sensors can be a valuable alternative in fungicide management and potentially decrease environmental footprint in agriculture of specialty crops. While severa l published studies focus on fungi management in agricultural production, very few examine the economics of alternative fungi management strategies. For example, Maiorano et al. (2009) qualitatively evaluates a fungi contamination in corn production, and E llison et al . (1997) model Botrytis contamination in grapes; however, these studies focus on the prediction of the disease development, and not on the effect on farm level profitability. In our study, we perform a whole farm profitability simulation, and w e also do it for a permutation of both anthracnose and Botrytis diseases and more and less resistant cultivars. We find that the new expert system SAS considerably improves the fungicide decision making process in strawberry production. SAS leads to signi ficant reductions in the average number of fungicide applications, and the reduction is especially significant for Botrytis control (likely due to the higher critical value of used in SAS to generate triggers and recommend fungicide spraying). Furtherm ore, SAS based fungicide management leads to a significant increase in marketable
63 yields. Specifically, u nder the SAS based fungicide application method, o n average, yields increase by 24.5% and 22.9% (for more resistant and less resistant cultivars, respe ctively) in the case of anthracnose management, and by 25.5% and 14.5% (for more and less resistant cultivars, respectively) in the case of Botrytis management, compared to those under the Calendar based method. The increase in yields for the SAS based a pplication can be linked to the reduction in plant damage associated with the spraying procedure. In addition, frequent spraying used on Calendar based applications may also result in carrying the fungus from one plant to the next, increasing the likelihoo d of spreading the disease. Fungicide application can also suppress the development of pests beneficial for strawberry production, and contribute to fungicide resistance build up. When stochastic prices and costs are considered in the NPV analysis, the di fference in the performance of the two fungicide application methods is even higher. The simulated NPV of profits under the SAS based method are on average higher than those of Calendar based method by 33% and 50% (for more and less resistant cultivars, re spectively) for anthracnose trials and 26% and 8% (for more and less resistant cultivars, respectively) for Botrytis trials. Lowenberg DeBoer (1999) finds that, for site s pecific nutrient management, the precision farming technology has risk reducing ben efits, but does not increase net returns. However, we find that, for fungicide management, SAS expert system increases the variability of yield and profits, which can be perceived as risk increasing. However, stochastic efficiency with respect to a functio n indicates that despite increased risk, significant growth in net returns makes the use of SAS the
64 most preferred fungal fruit rot management strategy for producers with a variety of risk preference levels. SAS can result in a significant increase in prof its given both less or more disease resistant cultivars, anthracnose and Botrytis management, and a variety of seasonal weather and market conditions. may differ from those of Lowenberg DeBoer (1999) for nutrient management because there is a fundamental difference between the processes of disease and nutrient management . Expert systems for fungicide application in disease management are especially va luable because disease has a contingent nature. When it comes to disease management, the time of the treatment is extremely important since the pathogens develop and spread exponentially fast into the healthy crops. Without timely fungicide treatment in the early stages of the diseas e contamination, even one day of disease growth can severely harm large numbers of a crop. The uniqueness of SAS is that it targets a fungicide application exactly on the day with the disease conducive conditions. In turn, the timing in fertilizer manageme nt is also important, but fertilizer deficiency in one part of the field does not spread to other parts of the field. Thus, the marginal effect of a timely fungicide application in disease management could be much larger th a n that of a timely and site spec ific fertilizer application . s in disease management vital. A farmer using less disease resistant cultivars can have two alternative fruit rot management strategies: (a) use the more cost ef ficient, SAS based fungicide application method and/or (b) switch to more disease resistant cultivars. Given the data from the field trials, this study shows that these two strategies lead to the similar
65 outcomes. Specifically, Calendar based management wi th more disease resistant cultivars results in similar distributions of the estimated NPV, compared to the SAS based management of less disease resistant cultivars (for both fruit rot diseases analyzed). This result is important for both producers and the policy makers funding research related to the alternative fungicide management strategies. It shows that precision agriculture strategies may be at least as cost effective as the development of new, more disease resistant crop varieties. Overall, this stu dy contributes to the literature by investigating the farm level impact of the expert system on disease management and profitability in a small fruit production operation, specifically a strawberry farm. Most previous studies of expert systems focus on lar ger operations for cereals like corn (Maiorano et al., 2009), wheat, soybeans (Sells, 1995); field crops like cott on (Barham et al., 2011) and sugarcane (Bramley, 2009); horticultural crops like citrus (Whitney et al., 1999) and grapes (Ellison et al., 199 7); livestock and cattle operations (Villalba et al., 2006); and integrated crop livestock operations (Nyang lin et al., 1995 ). Given that world strawberry production has been increasing, worth about $4.3 billion in value in 2013, the development and adopti on of expert systems for small fruit production operations can benefit millions of farmers worldwide. This study is also one of the few that focus on the expert systems that optimize agricultural practices over time, as opposed to spatial precision. Impro ving the temporal precision is usually more difficult, since it requires constant monitoring of the production conditions over time. A primary advantage of the expert system examined in this study is its simplicity combined with the accuracy. In contrast t o
66 other expert systems, it requires a relatively low number of input variables (only wetness periods and temperature during the wetness) to implement. Since SAS is fully automated and relies on data from meteorological stations (assuming the necessary wetn ess sensors are installed), farmers do not need to gather additional information to use SAS, which does not require an initial investment in equipment or machinery on behalf of farmers. The ease of use and the lack of economic barriers for adoption make SA S a practical and economical tool for farmer use, and increase the likelihood of SAS adoption. To our knowledge this is the first comprehensive economic feasibility analysis that combines historical and field trial data in stochastic simulation of weather, yield, and sales price to analyze a pre harvest expert system. Existing studies (Nyangito et al., 1996) perform whole farm economic feasibility analyses of precision agriculture and expert systems using stochastic dominance ranking criterion, and we contr ibute to that literature by extending the risk analysis to SERF. We find SERF to be a valuable risk analysis tool because it incorporates a utility function and a range of decision maker risk preferences whereas stochastic dominance criterion does not. Th is study proposes an approach to joint modeling of production risks (captured in yield variability) and market risks (reflected in price variability). By combining site specific data from field experiments with the statewide data, we explicitly account for the effect of weather variability on both production levels and sales prices. Other studies (Asche et al. , 2006; Godwin et al., 2003) also conduct profitability studies, but they do not include weather variables in their analyses. Given the increasing int erest in understanding weather variability and climate change
67 impacts on agriculture, this study offers an approach to explicitly model these impacts on both the production and markets. One of the limitations of the present study is that we do not account for the difference in pathologies and development of the two diseases. New strawberry plants are usually infected with AFR in nurseries ( Mertely and Peres, 2012 ). The farmers may not know whether the plants are infected by the disease until anthracnose les ions appear on the green berries. Usually, if the plants are infected in the nursery, then all plants have the disease, and the entire crop of strawberries can suffer. Given that the strawberry plants were inoculated with the disease in the production expe riments examined in this study, our results represent the value of SAS in conditions similar to anthracnose inoculation of plants in the nursery. We can hypothesize that if anthracnose inoculum is not present in the field, the SAS based fungicide applicati on system will still result in sufficient benefits to the producers, given that it reduces fungicide application frequency, and hence, costs and the plant damage during the application procedure. However, choosing trusted nurseries can be as important for anthracnose control, as proper fungicide management on the fields. In contrast, for Botrytis, the proper fungicide management should be the priority. Botrytis inoculum is usually present in the field, where it is spread by water and touch (by machinery or humans). Because the results of the production experiments examined in this study closely resemble the typical risk conditions that producers face, in the future, it would be important to model the value of SAS for the joint control of both fruit rot disea ses, while accounting for the likelihood of the presence of each disease in the field.
68 Conclu ding Remarks Precision techniques allow agriculture to cope with the challenges of satisfying increasing consumer demand for food and energy while at the same time improving environmental sustainability of food production, managing input costs, and improving the quality of work environment (Gebbers and Adamchuck , 2010). The o b j e c ti v e of t h i s s t udy w as t o exa m i ne t he e cono m i c b e ne f i t s a s so c i a t ed wi t h p r e c i s i on f un g i c i de app l i c a t i on method f or F l o r i da s t r a w b e rr y p r o du c ti o n . G i v en SAS, t he w e at h er a nd d i s e ase f o r e ca s t s y s t em de v e l oped by t he U n i v e r s it y of F l o r i da r e s ea r ch e r s ( Pavan et al., 2011) , s t r a w b e rr y g r o w e r s c an p o t e n t i a l l y: 1) r edu c e f u n g i c i d e ap p l i c a ti o n r a t es d u r i ng cool and d r y cond i t i ons wi t ho u t a f f ec t i n g y i e l ds, t h u s r e du c i ng p r odu c t i on c o s t s 2) ap p l y f un g i c i de a t t he p r e c i s e ti m e of h i g h d i s e ase p r e ssu r e du r i ng w a r m and w et w ea t h e r , t h e r e f o r e, de c r e a s i ng anthracnose d i sea s e de v e l o p m ent a n d sp r ead, a nd i nc r ea s i ng t he y i e l ds a nd p r o f i t s; 3) reduce fungicide resistance build up, which helps to control the disease in the long run. The d a t a f r om six y ear s t r a w b e rr y p r od u c t i on e xp e r i m en t s w e r e e xa m i ned u s i ng r e g r es s i on an a l y s i s t ech n i q u es. S tr a w b e r r y ha rv es t s g i v en t he t r ad i ti o nal ( ca l e nd a r b ased) a n d t h e p re c i s i on (SAS m ode l base d ) f u n g i c i d e t r e a t m ent w e r e co m pa r e d w i t h t h e c o n tr o l g r oup w i t h n o f un g i c i de ap p l i ca t i o n s. Monte Carlo simulations were used for the analysis for the NPV ten year profit for each fungicide appl ication method forecasted for a 26 acre Florida Strawberry farm and a 4% discount rate. P r odu c t i on d a t a sho w ed t h a t f or t he six production seas o ns ( 2006 07, 2007 08, 2 0 08 09, 2009 10, 2010 11, 2011 12 ) , for anthracnose SAS b a sed tr e a t m ent r eq u ir e d on a v e ra g e 44% l e ss f un g i c i de a pp li ca t i ons as c o m p a r ed wi t h t h e C a l e nd a r ba s ed tr e a t m ent while increasing the yield by 26%. Forecasted and simulated results confirmed the
69 preliminary results by demonstrating that indeed a probability density function of SAS based yield was outperforming that of Calendar based application method at any given weather condition. Most importantly, the distribution of the NPV of 10 year Profits have proven that on risk adjusted basis SAS based method outperforms that of Calendar. For An thracnose we conclude that there is 82% probability that by employing SAS based method, the farmers will produce more yield with risk equivalent to the old Calendar based method. In case of Botrytis the probability goes up to 100%. Therefore, a precision d isease management system while reducing fungicide use and costs, either leaves yields unchanged or actually increases the yields compared to the current conventional Calendar application method, thus the precision disease management system can increase pro fits for the grower without exposing him to significant additional risk. O v e r a ll , t he p r e c i s i on disease management s y s t e m i s a v iab l e f un g i c i de application s y s t em t h a t adds significant economic value to the Florida strawberry producer. At a representative 26 acre strawberry farm during ten year period, SAS based method added value on average of $1.65 Million in case of anthracnose and $1.74 Million in case of Botrytis by re d ucing f un g i c i de use and c o s t s while i n c r ea s ing t he y i e l d s and thus profits. This study examines the profitability of site specific PA expert systems to optimize agricultural input use over time. Specifically, we comprehensively evaluate the risk and profitability of SAS, which improves temporal precision of fungicide application in st rawberry production based on weather information. We show that SAS based application is more profitable than the traditional method for all possible weather conditions, market price scenarios, and risk aversion levels for producers.
70 Assuming a 10.5 hectare strawberry farm with a time horizon of ten years, the average value of SAS would range from $1.21 million to $1.70 million. This value is linked to increased cost effectiveness in fungicide applications, improved yields, and increased profits, compared to the traditional Calendar based application method. The PA disease management system increases profits while compensating the farmer for the additional risk associated with higher yield and profit variability. The main goal of Precision Agriculture (PA) e xpert systems is to facilitate site specific, preventive, rather than reactive, cost efficient, and environmentally responsible management practices in agriculture. Profitability studies for PA technology that assess the financial impacts of new technologi es at farm level can reveal the economic advantages of and barriers to PA adoption, and they can significantly increase PA adoption rates. O v e r a ll , SAS fungi management i s a v iab l e and practical decision support system for f un g i c i de application t h a t can i ncrease profit, and potentially reduce the environmental footprint from strawberry production. It can add significant economic value to the strawberry producer in the United States and in other countries. Furthermore, similar systems can be adopted for pro duction of other high value crops like grapes, blueberries, and blackberries. In the past decade, changing dynamics of weather patterns have affected global agricultural production. Climate change causes increased fluctuations in weather patterns, creati ng a variety of negative effects on agricultural operations. Some of the effects can be mitigated by the use of technology and expert systems similar to the system examined in this study.
71 Table 2 1. Summary statistics for yield from the Anthracnose field trials Control Calendar based SAS based Season Mean (lbs/acre) Standard Deviation Mean (lbs/acre) Standard Deviation Mean (lbs/acre) Standard Deviation More Disease Resistant Cultivar 2006 2007 n=4 27893.77 4005.86 29174.20 167 2.00 31774.31 993.92 2007 2008 n=4 8342.41 1161.66 13472.47 2283.44 13234.42 2540.62 2008 2009 n=4 33049.72 2777.29 34067.88 2053.24 38131.32 5212.98 2009 2010 n=4 37058.05 6517.04 40762.35 10543.82 46669.19 6128.74 2010 2011 n=4 11147.99 1912.5 4 17393.10 2492.42 16755.81 3578.73 2011 2012 n=4 30580.74 8360.63 34127.19 4209.18 36878.48 2115.40 Less Disease Resistant Cultivar 2006 2007 n=4 19623.19 1395.07 24369.88 363.49 27191.33 2529.9 0 2007 2008 n=4 3599.06 1458.36 9162.61 14 85.42 11239.03 1329.71 2008 2009 n=4 25563.44 1488.26 30721.90 3583.50 30021.13 3631.47 2009 2010 n=4 15959.82 3303.83 28901.07 1917.18 38477.13 1834.35 2010 2011 n=4 18274.28 823.96 17192.64 2346.55 17755.59 1707.12 2011 2012 n=4 7269.12 2753.0 5 15265.73 1479.40 24050.82 2060.33
72 Table 2 2 . Summary statistics for yield from the Botrytis field trials Control Calendar based SAS based Season Mean (lbs/acre) Standard Deviation Mean (lbs/acre) Standard Deviation Mean (lbs/acre) Standard Deviation More Disease Resistant Cultivar 2006 2007 n=4 30501.61 2172.42 35126.55 2105.57 36540.46 993.92 2007 2008 n=4 9593.77 1161.66 14127.46 934.34 16435.62 2320.71 2008 2009 n=4 36662.44 1941.02 40522.8 1157.78 43851.04 52 12.98 2009 2010 n=4 21945.45 1396.09 30108.73 842.92 33647.28 3961.53 2010 2011 n=4 18932.99 2099.15 21777.11 804.00 22981.62 1403.27 2011 2012 n=4 19268.83 3740.80 24277.65 1117.92 25237.9 1002.06 Less Disease Resistant Cultivar 2006 20 07 n=4 22566.67 1395.07 28025.36 363.49 31067.35 2830.12 2007 2008 n=4 4138.919 1458.36 11842.37 584.63 14529.93 1124.77 2008 2009 n=4 29397.96 1488.26 32877.96 3336.06 36976.54 2599.84 2009 2010 n=4 30209.6 0 837.48 33113.28 2187.02 35953.57 152 1.39 2010 2011 n=4 18091.57 996.19 20896.32 785.69 22096.97 581.51 2011 2012 n=4 18727.44 1363.48 20145.18 683.07 20836.76 835.39 T a b l e 2 3 . Anthracnose production trials: t he n u m ber o f d a y s w it h w e a t h e r c on d i t i o ns c ondu c i v e f o r the fruit rot , de rived weather variables, and the number of fungicide applications Season Number of Days Critical for Anthracnose Development ( 0.15 ) Number of Fungicide Applications Percentage Change in Applications between SAS based and Calendar Weather Variables Control Calendar SAS based Weather ( ) Weather Intensity ( ) 2006 2007 33 0 16 10 33 344 2007 2008 34 0 16 12 34 289 2008 2009 13 0 17 5 13 173 2009 2010 36 0 14 6 36 653 2010 2011 14 0 10 6 14 46 2011 2012 32 0 15 8 32 649 Mean 27.00 0 14.7 7.8 47% 27 359 St. Deviation 5.27 0 1.3 1.4 5.3 124.1
73 Table 2 4. Botrytis production trials: t h e n u m ber o f d a y s w ith w e a th e r c on d i t i o ns c ondu c i v e f o r the fruit rot, derived weather variables, and number of fungicide applications Season Number of Days Critical for Botrytis Development ( Number of Fungicide Applications Percentage Change in Applications between SAS based and Calendar Weather Variables Control Calendar SAS based Weather ( ) Weather Intensity ( ) 2006 2007 13 0 17 8 13 53 2007 2008 1 7 0 16 8 17 72 2008 2009 4 0 17 3 4 16 2009 2010 6 0 18 8 6 37 2010 2011 13 0 12 8 13 26 2011 2012 14 0 14 10 14 55 Mean 11.17 0 15.67 8 49% 11.17 43.17 St. Deviation 5.04 0 2.25 2.35 5.04 20.68
74 T a b l e 2 5 . I ndepende n t v a r i a b l es used i n r e g r e s s i on an a l y s i s f o r s t r a w b e rr y yield Variable (notation) Description Disease Expected Effect on Yield Mean Standard Deviation State Yield (S) State Yield during the production seasons from 2006 to 2012 as obtained from NASS, in pounds per acre. AFR BFR P ositive 26,333 26,333 3,124.08 3,225.77 Cumulated number of days conducive for the development of the decease according to SAS for the entire season. AFR Negative 26.5 5.54 Weather Intensity Metric that measures how early in the season each SAS trigger occurs. The measure is cumulated for all triggers for the entire production season. AFR BFR Negative 332.64 141.66 219.24 93.75 Applications (N) Cumulated number of fungicide applications for one production season. AFR Positive 6.34 7.48 Control (m) Dummy variable, indicating the experimental plots that did not receive any treatment. AFR BFR Negative 0.33 0.33 0.47 0.47 SAS based (m) Dummy variable, indicating the experimental plots treated with the SAS based method (i.e., precisi on disease management). AFR BFR Positive 0.33 0.33 0.47 0.47 Cultivar (U) Dummy Variable, indicating less disease resistant cultivar AFR Negative 0.36 0.48 Cultivar*Control An interaction of Cultivar and Control group, indicating less disease resis tant cultivar's effect within Control group AFR Negative 0.12 0.33 Weather*Control An interaction of Weather variable and Control group, indicating Weather's effect on Control group. AFR Na 9.82 15.52 Weather*SAS based An interaction of Weather varia ble and SAS based group. Weather's effect on SAS based group. AFR BFR Negative 9.82 3.66 15.52 5.83 Weather*Cultivar An interaction of Weather and Cultivar variables. Weather effect on less disease resistant cultivar. AFR BFR Negative 11 5.5 15.91 6.39 W eather Intensity*Control An interaction of Weather Intensity variable and Control group. The effect of Weather Intensity in the Control group. AFR Negative 110.88 201.98 Weather Intensity*Cultivar An interaction of Weather Intensity variable and Cultiva r group. The effect of Weather Intensity in the less disease resistant cultivar. AFR Negative 132.63 206.32 Weather * Applications An interaction of Weather and Applications variables. Weather effect given number of Applications. AFR Positive 226.67 22 3.46 SAS based*Application An interaction of SAS based group and Applications variables. Applications' effect in the SAS based group. AFR BFR Positive Positive 2.61 2.5 3.99 3.76
75 Table 2 5 Continued Variable (notation) Description Disease Expected Ef fect on Yield Mean Standard Deviation Weather Intensity*SAS based An interaction of Weather Intensity and SAS based group. The effect of Weather Intensity in the SAS based group. BFR Negative 47/22 86.14 Notes: * AFR indicates yield model estimated fro m anthracnose fruit rot field trials, and BFR indicates yield model estimated from botrytis fruit rot field trials Table 2 6 . Coefficients f rom the Anthracnose Regression for the Marketable Weight of S trawberries Anthracnose Robust Variable Es timates Standard Error Intercept 56916.78*** 10249.89 State Yield 1.48*** 0.10 Weather 2119.72*** 29.93 Weather Intensity 86.23*** 1.79 Applications 3280.93*** 46.80 Control 51617.73*** 667.48 SAS based 23017.80*** 662.45 Weather*Control 3771.54* ** 25.60 Weather*SAS based 1636.35*** 18.19 Weather*Cultivar 191.64** 16.13 Weather*Applications 215.19*** 1.51 Weather Intensity*Control 30.56*** 2.17 Weather Intensity*Cultivar 31.31*** 1.31 Application*SAS based 1189.27* 62.89 Cultivar*Control 5108.55*** 655.32 R 2 0.904 0.893 Notes: *** signifies 0.01 significance level ; ** 0.05 significance level ; * 0.10 significance level .
76 Table 2 7 . T he Average Y ield E stimates Anthracnose Average Yield Resistance of Variety (lbs/acre) Mo re Less Control 23910.756 14031.130 Calendar 27355.692 22584.616 SAS based 34054.395 29283.319 R2 0.904 RBar2 0.893 T a b l e 2 8 . Coefficients from the Botrytis regression f or t h e marketable w e i g ht of strawberries Variable Estimate White Robust S tandard Errors State Yield 1.26*** 0.13 Weather Intensity 81.96*** 3.93 SAS based 8612.15*** 864.26 Control 3767.96*** 806.77 Weather*SAS based 2868.93*** 66.01 Weather*Cultivar 203.94*** Weather Intensity *SAS 117.52 *** 51.55 SAS*Applications 1111.41*** 1052.50 R 2 0.986 0.985 Notes: *** signifies 0.01 significance level ; ** 0.05 significance level ; * 0.10 significance level . Table 2 9. T he Average Yield for Each T reatment Botrytis Average Yield (lbs/acre) Resistance of Variety More Less Control 23942.38 18029.14 Calendar 26185.28 20272.04 Model 28627.50 26718.26 R2 0.97 RBar2 0.968
77 Table 2 10 . Yield Summary Statistics after Monte Carlo Simulation for Anthracnose Name Mean (lbs/acre) Std Dev Coef Var Skewness Minimum More Resistant Cultivar 1 Control 19,017.61 8,588.02 45.16 0.34 4,269.45 2 Calendar 24,018.12 8,211.71 34.19 0.62 8,255.80 3 SAS based 30,968.59 11,310.99 36.52 0.50 8,091.55 % Change from Calendar to SAS based 24.5% Less Resistant Cultivar 1 Control 11,586.97 6,379.48 55.06 0.48 603.08 2 Calendar 19,566.59 5,946.78 30.39 0.36 7,869.88 3 SAS based 27,981.94 8,685.44 31.04 0.09 6,753.95 % Change from Calendar to SAS based 22.9% Table 2 11 . Efficient Set Based on Stochastic Domin ance with Respect to a Function Risk Aversion Coefficient More Resistant Cultivar Less Resistant Cultivar (RAC) RAC>0.0006 RAC>0.0008 Ranking Level of Preference Level of Preference 1 Most Preferred SASbasedM CalendarM SASbasedL CalendarL 2 2nd Most Preferred CalendarM SASbasedM CalendarL SASbasedL 3 3rd Most Preferred ControlM ControlM Co ntrolL ControlL
78 Table 2 12 . Yield Summary Statistics after Monte Carlo Simulation for Botrytis Name Mean (lbs/acre) Std Dev Coef Var Skewness Minimum More Resistant Cultivar 1 Control 22 , 462 . 28 4 , 437 . 46 19 . 75 0. 27 13 , 054 . 26 2 Calendar 24, 357 . 75 3 , 481 . 39 14 . 2 9 0. 03 15 , 703 . 21 3 SAS based 30, 559 .5 0 4 , 609 . 44 15 . 08 0.32 18 , 510 .5 4 % Change from Calendar to SAS based 25.5% Less Resistant Cultivar 1 Control 20 , 306 . 48 3,457.70 17.02 0 . 11 9,985 . 53 2 Calendar 22 , 021 . 44 2 , 777 .8 5 12.61 0. 03 14 , 131 . 10 3 SAS based 25 , 113 . 97 3 , 439 .4 2 13.70 0.04 15 , 345 . 54 % Change from Calendar to SAS based 14.5% Table 2 13 . Efficient Set Based on Stochastic Dominance with Respect to a Function Risk Aversion Coefficient More Resistant Cultivar Le ss Resistant Cultivar (RAC) For any RAC For any RAC Ranking 1 Most Preferred SASbasedM SASbasedL 2 2nd Most Preferred CalendarM CalendarL 3 3rd Most Preferred ControlM ControlL
79 Table 2 14 . Profit Summary Statistics after Monte Carlo Simulati on for Anthracnose Case Name Mean ($) Std Dev Coef Var Minimum Maximum More Resistant Cultivar Control $ 3,758,899 711,562 18.9 $1,869,660 $6,035,017 Calendar $ 4,896,177 633,781 12.9 $3,332,686 $6,729,006 SAS based $ 6,523,064 949,346 14.6 $4,662 ,344 $9,885,858 Percentage Change in Yield between Calendar and SAS Based 33.2% Less Resistant Cultivar Control $ 1,850,662 559,788 30.3 $457,944 $3,655,138 Calendar $ 3,964,865 466,045 11.8 $2,768,000 $5,171,689 SAS based $ 5,949,079 830,250 14.0 $4,662,344 $8,918,693 Percentage Change in Yield between Calendar and SAS Based 50.1% Table 2 15 . Profit Summary Statistics after Monte Carlo Simulation for Botrytis Name Mean ($) Std Dev Coef Var Minimum Maximum More Resistant Cult ivar Control $4,591,732 530,249 11.6 $3,497,532 $5,912,307 Calendar $5,332,367 398,267 7.5 $4,281,188 $6,223,888 SAS based $6,720,443 588,654 8.8 $5,456,623 $8,056,733 Percentage Change in Yield between Calendar and SAS Based 26% Less Resis tant Cultivar Control $3,868,077 507,211 13.1 $2,653,374 $5,080,511 Calendar $5,141,301 426,876 8.3 $3,866,429 $6,081,026 SAS based $5,534,806 516,011 9.3 $4,372,764 $6,724,873 Percentage Change in Yield between Calendar and SAS Based 7.65%
80 Figure 2 1. Florida s trawberry p roduction ( m illions of lbs), v alue ($ m illions), and a cres p lanted, 1998 2012 Source: Based on data obtained from the National Agricultural Statistical Services ( USDA NASS a ), 2013 Figure 2 2. Monthly Strawberry P rice D ynamics Source: Based on data from the USDA NASS a , 2013 . 201 183 0 2,000 4,000 6,000 8,000 10,000 12,000 0 50 100 150 200 250 300 350 400 Acres Planted Production Value in $ Millions and Production in Millions of lbs Production Value in $ Millions Production in Million Pounds Acres Planted (Secondary Axis)
81 Figure 2 3. Strawberry Advisory System as Web Based Application Source: the system can be accessed at http://agroclimate.org/tools/strawbe rry/
82 Figure 2 4 . D iffer ence in Calendar and SAS based Application M ethods Figure 2 5 . Yield PDF in c ase of Anthracnose D isease for T wo D ifferent C ultivars 0.00 10000.00 20000.00 30000.00 40000.00 50000.00 60000.00 Yield (lbs/acre) Control (More Resistant Cultivar) Calendar (More Resistant Cultivar) SAS Based (More Resistant Cultivar) Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SASbased (Less Resistant Cultivar) Decision About Fungicide Application Calendar based SAS based SAS 1 1 0 Apply Weekly Apply Don t Apply Nsas 15 NC=15 Cumulative Number of Applications (N) per Season per Acre Method Of Application Application Trigger Application Temperature During Wetness Leaf Wetness Duration T W From production experiments: 5 Nsas 12 0.15 True F alse 0.50
83 Figure 2 6 . Yield PDF in Case of Botrytis D isease for Two Different C ultivars Figure 2 7 . Profit PDF in case of A nthracnose Disease for Two Different C ultivars 2,000 12,000 22,000 32,000 42,000 52,000 62,000 Control (More Resistant Cultivar) Calendar (More Resistant Cultivar) SAS Based (More Resistant Cultivar) Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SASbased (Less Resistant Cultivar) $0.0 $1.0 $2.0 $3.0 $4.0 $5.0 $6.0 $7.0 $8.0 $9.0 $10.0 Millions Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SASbased (Less Resistant Cultivar) Control (More Resistant Culivar) Calendar (More Resistant Cultivar SASbased (More Resistant Cultivar)
84 Figure 2 8 . Profit PDF in case of Botrytis disease for two different cultivars 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 Millions Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SAS Based (Less Resistant Cultivar) Control (More Resistant Cultivar) Calendar (More Resistant Cultivar) SAS Based (More Resistant Cultivar) $0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 0 1 2 3 4 Certainty Equivalence Millions Absolute Risk Aversion Coefficient (ARAC) Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SASbased (Less Resistant Cultivar) Control (More Resistant Culivar) Calendar (More Resistant Cultivar SASbased (More Resistant Cultivar) Risk Neutral Normally Risk Averse Moderately Risk Averse Extremely Risk Averse
85 Figure 2 9 . Stochastic e fficiency of NPV of p rofit f unction in case of Anthracnose Figure 2 10 . Stochastic e fficiency of NPV of p rofit f unction in case of Botrytis Figure 2 1 1 . Added v alue of SAS based m ethod, Vsas , Anthracnose Case 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0 1 2 3 4 Certainty Equivalent Millions ARAC Control (More Resistant Cultivar) Calendar (More Resistant Cultivar) SAS Based (More Resistant Cultivar) Control (Less Resistant Cultivar) Calendar (Less Resistant Cultivar) SAS Based (Less Resistant Cultivar) $1.92 Million $1.59 Million $0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00 Millions Less Resistant Cultivar More Resistant Cultivar
86 Figure 2 1 2 . Added Value of SAS Based Method for Botrytis C ase Figure 2 13 . T he Difference in Production Pr ocesses Resulting in Different P rofits $0.40 Million $1.37 Million -$0.50 $0.00 $0.50 $1.00 $1.50 $2.00 $2.50 Millions Less Resistant Cultivar More Resistant Cultivar
87 CHAPTER 3 DEFINED BENEFIT PENSION PLAN RESTRUCTURE: CAN DBS BE VIABLE AGAIN? Introductory Remarks Given the difficult investment environment in the past several years, historically low interest rates, and recent mark et crash, Defined Benefit (DB) plans have faced difficulties meeting their investment goals to fund their projected long term liabilities. As a result more and more state and local governments are considering moving to Defined Contribution (DC) plans. The main difference between the two retirement plans is that a DB plan provides a pre specified monthly benefit to the employees upon reaching the retirement age whereas a DC plan predefines contributions to the plan throughout the working years of the employe e, but the annual benefits during retirement are not known in advance ( U.S. Department of Labor ). In 2010, funding ratios (ratios of assets to projected li abilities) of approximately 36% (45 out of 126) of large public DB pension funds around the country fell below 70%. The Illinois SERS pension fund had the lowest funding ratio at 37.4%. Funding ratios of 23% (29 out of 126) of pension funds were between 70 % and 80% (Public Plans Database, 2001 2009). There are several reasons behind these low funding ratios, which include failures to meet required contributions, high projected rates of return, generous benefits, and the market crash. For most state and loc al governments the problem is not immediate insolvency but the difficulty of the long run recovery and restoration of funding ratios . Improved asset allocation such as investing more in stocks and alternative assets may provide some boost in returns, but h igh rates of returns in stocks may be unrealistic in the
88 environment of low bond yields. In addition, the potential risk of higher yielding assets may not be appropriate for the current structure of pension plans. Moving from DB to DC may prove to be a poo r decision because it would increase the near term underfunding since it would likely apply to new hires, who would have to b ear more than their share of funding for DB plans. There is a chance that a well designed DB plan would prove to be more valuable t han a DC one for the taxpayer in the risk return trade off. The idea of the proposed structure for DB plans in this paper is to allow a higher expected return portfolio in that trade off. We propose a dynamic structure for DBs, in which contributions are market performance of the pension fund. The general idea is that if a fund generates an insufficient rate of return in a given year (or period), the contributions should go up, and if the returns are satisfactory or outstanding, the contribu tion can decrease or even be zero. In some ways, this structure is a hybrid between DB and DC plans, with the exception that contributions are made flexible while benefits remain predefined. Given this structure, it is important to discuss what portion of risk should be born by the taxpayers. There are two reasons why the risk should not be born entirely by the taxpayer: (1) quadratic deadweight loss fro m taxes, and (2) taxpayers can not offset all risks with their own portfolios. In the current pension sy stem structure the risk sharing between the taxpayers and employees is asymmetric. For example, employees get higher benefits (politically) when the market soars, and the taxpayers are the ones negatively affected by the declining market. More importantly, the benefit increases obtained in the rising market are not scaled back when the market declines. Thus, the optimal split in risk sharing should depend on parameters such as wealth of taxpayers
89 s. By design, the taxpayers and the employees should share the market risk proportionally to their wealth and income, respectively to each. The taxpayer can bear a larger proportion of the tly larger than that of an individual employee and contributions to the fund represent only a small portion of Using a stochastic simulation and Net Present Value (NPV) framework the study tests and compares the performances of bot h proposed and current structures of DB by comparison the study identifies the marginal value of the new DB structure as compared to the current one. Finally, the optimal disc ount rate for liabilities projection is derived based on stochastically simulated NPV results for both structures. Problem Definition DB plans have two major issues, which are interdependent: significant underfunding and ineffective design whose attr ibutes often run counter to the economic realities of state and the local government s . Several factors cause the underfunding of retirement plans: insufficient contributions, asymmetry in asset liability risks, poor overall risk management, and asymmetric structure in benefit increase provisions. Deficiency in contributions is in some part caused by shrinking tax revenues, inability to raise taxes, and an increased demand for states services. In most part underfunding is caused by the overstated measuremen t of the funding ratio (Brown, Clark and Rauh , First, the numerator (that reports the
90 values over a specific number of years. Second, the denominator (the present value of the an unrealistically high rate. Specif allow using past market values adjusted for investment returns that are smoothed over a number of past years. The smoothing period can be chosen arbitrarily between three and seven year s with a usual choice of five (Gokhale , 2012). The problem is that in a declining market, smoothing biases the measure of asset values upward. them at inappropriately hig h rates, which is a consequence of accounting guidelines for public pensions. Specifically, Government Accounting Standard Board (GASB) allows Marx and Rauh, 2010). This incentivizes management to prefer higher yielding asset classes. However, some such assets may have riskier profiles, yet their returns are not risk adjusted when used for liability discounting. Such asymmetry of asset liability risks contradicts the valua tion principle, namely, that the underlying quantity of risk should determine the disco unt rate (Lucas and Zeldes, 2009 ). For example, t he unexpected post 2007 implosion of asset values an d dismal investment returns sharply cut funding ratios in som e case s by 20% (Gokhale, 2012). Compounding the problem is the masking of risks due to the smoothing of asset values over time technique that further reduces the incentive to reduce investm ent risk (Lucas and Zeldes, 2009 ). Naturally, this leads to understatemen t of risks to the taxpayer, and gives a false sense of financial strength (Biggs, 2010). In summary, the
91 accounting rules combined with the pressure of rising fund ing costs cause managers to tend to overexpose plans to risky investment classes while the pl designed to withstand such risks. In addition, while these high discount rates lower the projections of liabilities, they contribution deficiencies pe rsist even more. Many economists advocate a risk adjusted discount rate procedure (Biggs, 2010). Some suggest that liabilities should be discounted at lower risk profile rate s , such as municipal or U.S. Treasury yield curves (Gokhale, 2012 ; Lucas and Zelde s, 2009; Novy Marx and Rauh, 2010). Admittedly, historically low Treasury yields, which are a consequence of the unique environment Given these complications, finding the right risk adjusting procedure for the discount rate is a challenging task, so instead this paper approaches the problem from a structural rather than a procedural point of view. Making contributions depend on the return in the market internalizes the risk, which helps to account for risk in the overall risk management. One of the contributions of the modeling in this paper is that the newly proposed structure shows that the optimal discount rate is endogenous to the e xpected market rate of return. Las tly, the asymmetry in asset liabilities risks overtly induces the asymmetry in benefit increase provisions, namely, excessive benefit increases during times of reported overfunding (Brown, Clark and Rauh, 2011). Specifically, in booming economic times when plans may be temporarily overfunded due to high asset values, a permanent increase in benefits sometimes is negotiated, but by the nature of the claim,
92 it cannot be scaled back when market corrections diminish asset values, causing the plan to go back qui ckly to the underfunded status. Furthermore, there are also cases when the asset returns are over their projected level, and the excess of that gain goes to benefit increases even in the face of deficient contributions. Biggs (2010) argues that in these ca ses the excess returns (surplus) should be used for improving pension plan funding and not the benefits, then the risk bearing tax payer benefits from the risks taken in the equity markets (Pennacchi and Rastad, 2011). Our study identifies best structure b ased on the parameters used. Proposed Structure of the Pension Fund In search of a more viable structure for the DB plans, this paper proposes to restructure Defined Benefit plans in the following way: member and taxpayer contributions are to vary annually the portfolio underperforms, and the funding ratio falls below a specified threshold, the member and the taxpayer contributions increase. If the portfolio performs above a threshold that is implicit ly dependent on the funding ratio, then contributions fall. In the case of strong market conditions, no contributions are needed. On the other hand, in the case of extremely poor market conditions, it is unrealistic and politically costly to sharply increa se employee contributions. To avoid such a possibility, a five year exponential smoothing technique could be used that introduces a continuous lag in the relationship between the funding ratio and member contribution level changes. In this paper, we will a ttempt to devise an optimal stochastic funding path with unconstrained annual adjustments, and then compare it to a path with politically constrained annual adjustments. The difference in the NPVs of the two can be considered as a cos t of political constra ints.
93 In this study, we gene rate simulations for the next 35 years (2015 2050) using a Monte Carlo methodology and an NPV framework. The member composition of the plan is projected and the same projections are used for both structures to keep the analysis comparable. Thirty five year performances of these plans are then compared to see how much value the new structure adds. The model also makes it possible to identify the optimal discount rate that should be used in actuaria l projections of liabilities. The goal of this study is to test the new flexible DB structure, in which employee contributions are portfolio (and market) performance dependent. In a fully optimal model, the portfolio allocation would be endogenous. We consider two cases: (a) all stocks, a nd (b) the current model entailing a 70/30 split between stocks and bonds. To accomplish this task a stochastic model of performance is created based on the following components: an asset and liability base of a representative pension plan and a distributi on of possible returns dependent on money manager skill and overall market performance. Based on these parameters the Net Present Value of performance of two structures is tested: a current structure, where contributions are fixed; and a proposed one, whe re contributions fluctuate depending on the funding ratio that is influenced by the returns of the pension fund. Specifically, the study simulates the performance of the plans under a wide range of market conditions using a Monte Carlo simulation framework , and then compares the performance of both structures based on the Net Present Values of the two structures. The next expected gain from the new structure is a fifty year NPV of the total assets difference between current and proposed structures.
94 Some mo deling has already been done, like market values of taxpayer guarantees by using an Options Pricing model (Biggs, 2010), optimal allocation (Lucas and Zeldes, 2009) and analysis of revenue demands (Novy Marx and Rauh , 2011). However, in the previous litera ture, valuation of only one or several aspects of the plan of an entirely new pension plan structure, one with optimal annual adjustment of taxpayer and employee contribu tions. Data The data for this research were obtained from the Public Plans Database (PPD) provided by the Center for Retirement Research at Boston College (Public Plans Database, 2001 20 09 ). T he data spans nine years, 2001 20 09 , reported at the end of the calendar year as of September 30th. The panel data contains 126 state and local pension plans from the fifty different U.S. states. Due to some missing values for one of the plans, this stud y concentrates on 125 pension plans. There are six different types of plans: Teachers, School Employees, State Employees, Municipal, Police Officer, and Fire Fighters, while in some states Police and Fire Fighters are combined in one plan. Washington is t he only state with six different plans. There are seventy four cities and thirteen counties. The total number of observations is 1302. Out of 90 variables available at PPD, the following key variables are chosen for this study: plan membership and composi tion (indicating how many members actively withdraw from the plan and how many contribute); actuarial liabilities, unfunded actuarial accrued liability, and projected actuarial liabilities; tax base (indicating the number of people paying taxes and tax lev els); market assets; yearly returns on assets;
95 allocation within portfolios by asset class; funding ratio, assumed inflation, and actual inflation. In addition, the data on the returns for a 10 year US Treasury bond, used in the model as the risk free rate , are obtained from the U.S. Federal Reserve for the years 2001 2009 . Portfolio return is one of the key variables which directly influences the long term asset base. The next section looks at the historical dynamics of this variable. Descriptive Statistic s of Historical Yearly Returns The following series of graphs display some of the descriptive statistics of the returns data. Figure 3 1 displays the distribution of returns among 125 pension plans in each year to form a ten year trend. In Figure 3 1 each vertical blue column represents 125 different returns and it appears one dimensional; however, each one has its own two dimensional distribution. Figure 3 2 displays the distribution as a probability density function (PDF) of the 125 returns in a given fis cal year obtained from each plan for the ten year period. The distributional shape in each year is surprisingly consistently normal if a few outliers are excluded. Figure 3 3 displays the average return for each year obtained by averaging returns of 125 pe nsion plans for each year. The vertical lines represent the mean. Now define one cycle as 1 year time horizon. Since there are 10 years of data, there are 10 cycles, which forms a trans cycle trend. Since there are 125 different plans, there is a distribut ion of possible returns for each 1 year cycle. Figure 3 4 decomposes the returns distribution within a 1 year cycle and the cycle itself. It also displays the trans cycle trend. A consistency in distribution among within cycle returns is observable. The do tted blue line at the end predicts the return distribution within the next (predicted) cycle. Figure 3 5 plots data and extrapolates a linear fit trend for the trans cycle
96 dynamics given 126 different possible returns in each given year. This linear trend is slightly upward sloping. For each plan define the for a given year n , where n N years, and N = 10. The annualized return, , is: (3 1) Th e t en year standard deviation of plan is . Figure 3 6 plots versus to display the relationship between the ten year annual return of each pension plan to its standard d eviation for the years 2001 2009 . Next, we compare funds on a risk adjusted performance basis. For this purpose, the Information Ratio ( ) is calculated by finding the excess return, for plan , which is a difference between the risk free rate, . For the risk free rate we use the annualized return of t e n year 2009: (3 2) Then, the Information Ratio is the ratio of the to the standard deviation of the . (3 3) Based on the risk adjusted annualized returns relative to a ten year Treasury for the years 2001 2009 , Texas Municipal is the top performing pension plan providing excess return of 0.052% and standard deviation of 6.46%. Specifically, the plan yielded annually 7.60% with a relatively small standard deviation of only 5.77% (Figure 3 6, Table 3 1). On the other hand, Arizona Public Safety Personnel is the worst performing pension plan that provided a negative excess return of 0.02% and a relatively high
97 standard deviat ion of 13.71%. The annualized yield for the plan is a quite low 0.33%, and the standard deviation is one of the highest , 13.99% (Figure 3 6, Table 3 2). As a consequence of these returns, the Funding Ratio of Texas Municipa l in 2010 was 83 % while Funding Ratio of Arizona Public Safety was significantly lower, only 63 % . Simulating Returns Define as a predicted return at year t , where is a subset of all possible returns that can occur in the market. Since the main agenda in this paper is to compare the performance of the two funding structures for the pension fund industry, in order to then forecast the asset base, the Russell 2000 index is chosen to model the returns. The index is a broad market index which yi elds results that are independent of the quality of the money manager in any particular pension fund. Thus, the results based on the Russell 2000 index indicate solely the relative performances of the structures and not the management. Based on the h istori cal data for the Russell 2000 indexes for the years 1988 to 2012, mixed harmonic regression is fitted to forecast the rate of return, : (3 4) where is a rate of return for the portfolio at time t , Trend is defined as , and is the error term. Asset Allocation is designed to the preferences of the board of the constituency given investment talent, statutory obligations, and actuarial planning. Multivariate Empirical Distribution Methodology This section describes the process used to generate a distribution of a stochastic variable, , using values estimated from the OLS mixed harmonic r egression (Equation 3 3) and the distribu tion of the error term. Consider an OLS regression of a stochastic variable X . To generate a distribution of the stochastic variable, from the OLS
98 r egression we obtain the deviation from the trend expressed as a percent of the predicted values, . In other words, the deviations are estimated as the ratios of the residual e t to the predicted values . The residual from equation ( 3 3 ) is: (3 5) for each year t . The deviation are expressed as the following : (3 6 ) for each of the t years and for each random variable, The deviation are sorted from minimum to maximum: (3 7) for all years t and each random variable with clearly defined . Each of the deviates has an equal chance of being observed, thus a probability, P* , of 1/ T , where T is the total number of historical observations, is assigned to each sorted deviate, : P* = 1/ T . The procedure allows the simulation process to preserve this assum ption. Next, if the same deviation occurs several times in the sequence, the final probability, for that deviate gets accumulated to reflect its higher probability of occurrence. (3 8 ) To summarize, the following parameters for the multivariate empirical (MVE) distribution should be defined: (3 9 ) where historical years, and simulated years.
99 Next, for each , a vector of independent Standard Normal Deviates, , is generated (R ichardson et al., 2000, 2007). Fifty years are predicted, thus the size of the vector is ten: (3 10 ) Next, Uniform Deviates ( ) are obtained: (3 11 ) Finally, predicted values with the stochastically adjusted component are: (3 12 ) For convenience, stochastically predicted value can be represented using Mul tivariate empirical (MVE) distribution notation: (3 13 ) where historical years, and simulated years, and F (.) is a functional form of the distribution . Model Two structures, Current and Proposed , are modeled for a given plan. Each structure has and bases at time t . Each year t withdrawals, occur in order to cover member benefits. The liability base and withdrawals ar e the same for both structures for the purposes of this model in order to make the most relative comparison of the outcomes between the two structures. Adopt the following notation then the as set base at time t is . At the end of the year t investable asset base,
100 , by the expec ted withdrawals at the year t 1 that are projected to cover member benefits at year t . The withdrawal happens at the end of year t 1, such that . Since usually the amount of the contributions to the pension plans depend on the payroll, define payroll dependent contributions to the plan as . The contributions occur every year regardless of the return of the mar ket. In case of the structure, there are two portions of the contributions : the first portion is tied to the payroll similarly to that of the structure, , but the second portion is triggered by the drop in the funding ratio, which intrinsically depends on the market return, . Thus, we further refer to the first portion of the contr ibution as payroll dependent and to the second as market dependent. The fundamental difference then between the amounts and timing of the contributions between these two pension plan structures is the following: in the current structure payroll dependent contributions occur every year irrespective of the market returns, but in case of the proposed structure, both portions, payroll and market dependent, of the contributions are triggered only if the Funding Ratio ( FR ) falls below a predetermined threshold. All contributions are added at the end of year t 1, and since the Funding Ratio ( FR ) is calculated as of the end of the year prior to t 1 year, we define it as . Therefore, the following equations express investable assets at year t for each s tructure: (3 14 )
101 (3 15 ) Next, the funding ratio ( ) that determines the level of contributions a t the end of year t is: (3 16 ) where is projected liability discounted to time t based on the composition of t he pension plan and defined benefits discounted to present value. The same liabilities project ions are used in modeling in both the Proposed and Current structures of the plan to be able to perform accurate relative valuation consistently. In the next sect ion the methodolog ies for Net Present Value and Monte Carlo simulations are described. The section describes methodologies on the Net Present Value (NPV) and Monte Carlo stochastic framework in the context of the model described in the previous section. A ccording to the literature on NPV methods (Damodaran , Net Cash Flow at time t , is discounted as follows: (3 17 ) where t T years of future cash flow s, and is the discount rate. Thus, net present value of the asset for each structure is: (3 18 ) where t T years of future cash flows, is the asset discount rate, and is the rate of return during year t . For our study T = 35 .
102 Using Richardson et al. (2000) methodology we obtain distributions for all p ossible asset values under each structure given all possible returns, generated by Equation 3 12 and presented in Figure 3 7: (3 19 ) where represents values of the asset base under each structure and represents the probability density function associated with these values. Now, the variable of interest for the study is the increase in the asset base of the proposed structure as compared to the current one . This calculation is valuable because it expresses the difference between plans with most relevance between the two structures . More speci fically, since is expected to be higher than , the overall increase in the asset base should be higher for the Proposed plan than that of the Current one, especially compounded over years. Therefore, the NPV of the increase in the asset base is the difference between the net present value of the asset base of the proposed and current structures, which we define as the total added value of the Proposed structure over Current structure, : (3 20 ) The distribution for all possible values of given all possible returns, , is: (3 21 ) where represents all possible values of and represents the probability density function a ssociated with these values. To obtain the probability distribution function the asset bases under Current and Proposed, and added value of the proposed structure,
103 , w e sampled 500 random draws using Monte Carl o simulations, which represent the value of the proposed structure given all possible market conditions which were based on the randomly sampled variable, , which in turn was modeled using Russell 2000 inde x returns. The distribution is estimated separately for each of the structures and then the added value of the proposed structure given . All estimations are conducted using Simetar Â© Add in for MS Excel. The liability base , need ed for the Funding Ratio ( F R ) calculation , is modeled the same for both structures. At each time t , future liabilities are projected and the present value of those projections is found, , as follows: (3 22 ) where t T years of future cash flows, and is the liability discount rate . For the purposes of this model, the liability is modeled as a function of payroll. Since each pension plan, state, and constituency are different, these variables have to be configured for each particular plan. Since in the pro posed structure, if the Funding Ratio of the proposed structure, , which intrinsically depends upon the market return, falls below a predetermined funding ratio threshold, an amount of both payroll and market return dependent c ontribution s is required to be deposited at the end of that year. It is important to consider the unfortunate case of extremely poor market returns in a given year, can decrease significantly, which would then trigger a large sum of contribution required. However, it is not realistic that the state and employees can co me up with an unreasonably large amount to compensate for such a decrease in the asset base due to the market loses in one year. T hus , we install a rule that an amount of contribution
104 should not exceed an equivalency of more than a certain percentage (for example, 2%) of decline in the funding ratio in one particular year as compared to the previous year. The rule should serve as a smoothing technique for the amount of contribution required in each given year. Since each particular plan has its own specifi cs such as initial asset base, tax base, number of employees, payroll, health of the state budget, and urgency to improve the proposed structure and payroll under the cu rrent structure can vary based on these fundamentals of the plan. Results Since pension plans across United States range from well to poorly managed, each pension plan has to be considered individually. A model should be devised according to specification s feasible for that particular plan and economic fundamentals of the state. In this section we present the result of one such pension fund. For example, consider a pension plan with a starting asset base of $9,739,331 and liabilities value of $14,284,119, which is equivalent of 0.68% funding ratio as of 2013. Liabilities are modeled as a function of payroll, and payroll is assumed to grow at the rate of domestic economic growth (2%) plus the inflation rate (2%), which totals to 4%. Next, yearly payroll dep endent contributions on the historical basis are approximately 11% of the yearly payroll, which is a sum of 5% employee and 6% 0.90, which means that if the funding r atio goes above 0.90, no contribution would be required, conversely, if the funding ratio falls below 0.90 at the end of a particular year, both payroll and market dependent contributions are required to be made at the
105 beginning of the next year. To ensu re that an unreasonably large amount due to potentially low market returns is not mandated in one given year, we smooth the contribution portion that depends on market return over time using the following rule: the amount of contribution in each given year cannot exceed that of an amount associated with a 2% improvement in the funding ratio as compared to the previous year. The simulations run for the next 35 years from 2015 to 2050. The distribution of the predicted returns based on the Russell 2000 index returns is shown in the Figure 3 7. The distribution runs from the left, where the worst market conditions with the lowest market returns are, to the best market conditions, represented by highest returns, on the right. Based on these returns we obtain the distributions of the asset values for the current and proposed pension fund structures, respectively, and they are presented in Figure 3 8. relative to that of the current one, which indicates that the proposed structure outperforms that of the current one in any given set of market conditions (i.e. from extremely low to high market returns). It can be noticed that the bandwidth (width of the distribution) of the proposed st indicates that the distribution of the asset values of the proposed structure is less volatile (or less risky) than that of the current one. To understand risk reward dynamics of these distribution s in detail, we explore the summary statistics associated with these two distributions, which are listed in Table 3 4. The table contains the mean, standard deviation, minimum, maximum, and coefficient of variance measures. The graphical results observed i n Figure 3 8 are
106 confirmed by the numerical results presented in Table 3 4. For example, the mean of the asset value distribution under the proposed structure is approximately $ 4 .4 billion, higher by 39% than that of the current one, which is valued at app roximately $3.2 billion. The next measure worthy of mention is the minimum, which is associated with the performance of the fund if the most unfavorable market conditions, i.e. a set of the lowest returns, dominate the 35 year period. The minimum for the a sset base under the current structure is $ 375 , 314 ,002, and that under the proposed structure is $ 1 , 498 , 374 , 949 , which is 299% higher than that under the current structure. This result is important because it demonstrates that the asset base under the prop osed structure significantly shifts the lower bound of the distribution to the right, outcomes of the low asset base in case of persistently adverse market conditions. This suggests that the proposed structure demonstrates higher margin of safety than the current structure, and margin of safety implies the outcome in the worst case scenario. The maximum measure captures the best outcome, which is associated with the event of most favorable market conditions (i.e. a set of high returns) happening in the 35 year simulated period. The maximum for the current structure is around 10.0 billion, whereas the maximum for the proposed structure is approximately 11.7 billion, which is a n increase of 17%. This suggests that proposed structure offers a higher upside in the event of the favorable returns occurring in most of the years during the period of interest. The mean, minimum, and maximum measures confirm a significant shift of the d istribution to higher asset values.
107 Next, the standard deviation of the possible outcomes of the assets under the current structure is $ 1 , 592 , 656 ,071 while that of the proposed structure is $1,511,314,805, which is lower by approximately 5%. Thus, the dis tribution of the asset values under the proposed structure demonstrates several advantages in comparison with that of the current structure: increased margin of safety, increased upside, and lower standard deviation. These measures are then reflected in a lower Coefficient of Variance (CV) measure calculated based on the distribution under the proposed structure as compared to that of the current distribution. Specifically, the CV of the current structure is 50, while that of the proposed structure is 34, w hich is a decrease of 32% (Table 3 4). This improvement in the CV measure is a confirmation of the graphical results displayed in the Figure 3 8, where the distribution of the proposed structure has a lower bandwidth and significantly shifts to the right r elative to the current one. The added value of the proposed structure, obtained by the difference between the asset bases under the proposed and current structures and simulated using the Monte Carlo method, is displayed in Figure 3 9. It can be seen that the value is always positive, ranging from $312 million (in case of the lowest rates of return during the most of the years in the 35 year period) to $3.0 billion (in case of the favorable returns occurring most of years during the period of interest). Thi s indicates that indeed the proposed structure outperforms the current one given any set of returns, from adverse to favorable market conditions. Now, added value distribution is comprised of two distributions: 1) that of cash contributions made by pension fund management in the course of 35 years that are triggered by fallen below the threshold funding ratio and 2) capital gains on those
108 additional cash contributions. The capital gains on the principal are not a part of this distribution because the return s on the principle are the same for the proposed and current structures. Thus, when we subtract one from the other we separate capital gains on the principal from the capital gains on contributions due to the schedule of the proposed structure. Since the sequence of returns for the 35 year period is different every time due to random sampling from the simulated Russell 2000 return distribution (which change the funding ratio that then triggers contributions to be made), the total amounts within the 35 year period of contributions vary. Figure 3 10 displays the distribution of all possible sums of all contribution amounts simulated for each of the 35 years and discounted to present time. Figure 3 11 shows the distribution of capital gains generated from the additional contributions. This value is too discounted to the present time. Table 3 4 displays the summary statistics for this distribution. It is interesting to notice that the CV measure for the contributions (58) is larger than that of the capital gain s on the contributions (37) by 36%. This means that capital gains on the additional contributions stabilize the performance of the fund while market dependent contributions although highly variable provide the capital pool to realize these capital gains. I t is important to note that the total value of contributions that would be required under the proposed structure ranges from $414,022 to $8.8 million under different scenarios of the funding ratios runs depending on the market returns, but the capital gain s on those contributions actually range from $232 million to $2.2 billion, which is a significant return over these 35 years. This demonstrates why the proposed structure makes the pension fund more sustainable in the long run.
109 In addition, the proposed st ructure seems to provide an investment timing advantage. Since market returns tend to mean revert, after a year (or several years) of adverse market conditions, the market rebounds, which makes the contributions triggered by the funding ratio very well tim ed for investment. Specifically, when market is strong yielding high returns, the funding ratio tends to stay above predetermined threshold. However, when the returns are negative, the funding ratio drops and triggers additional contributions, which get re invested the next year. This allows to buy securities at depressed valuations, which provides the margin of safety and increased probability of robust capital gains. This indeed explains the shift in the distributions of the proposed in Figure 3 8. To d emonstrate how the proposed structure performs relative to the current structure for a given pension plan, a run of an exemplary scenario of a 35 year simulation is performed and presented in Table 3 6. It shows a run of returns, asset values, contribution s, and funding ratios for both proposed and current structures. The graphical description of the funding ratios as well as timing and the amount of the contributions are presented in Figure 3 12. The return and performance of the asset values for each stru cture are presented in Figure 3 13. The figures demonstrate how for the proposed structure funding ratio goes down to 0.62 in 2016 then slowly recovers back to over 0.90 by 2026, gets even over 1 in 2032, then after a series of negative returns drops down below the threshold to 0.76 in 2045, but surely enough it recovers to over 0.90 and finally goes to over 1 by 2048. What we observe is that though in several business cycles the funding ratio of the proposed plan falls, italways recovers, demonstrating res ilience and sustainability over
110 the long term. However, this is not the case for the funding ratio of the current structure. Under the same set of market conditions as the proposed structure, the funding ratio of the current structure rises over the thresh old of 0.90 only once during the entire period, specifically in 2024. It then fluctuates, but never rises over 0.90 (Table 3 6, Figure 3 12). As a result of market dependent contributions and flexible schedule, the asset value for the current structure in 2050 is approximately $58 billion while that of the proposed is $92 billion, which is 59% increase. In addition, it can be seen from the Table 3 6, that the total amount of the market dependent contributions triggered by the funding ratio under this scenar io is $10.7 million, while the total capital gain on those contributions is $24 million. This is equivalent to total return of 218% over 35 years or 3.3% annual return. Two important notes follow from this result. First, the long term viability of the pro posed structure is very much attributed to these accumulated capital gains on the market dependent contributions triggered by the funding ratio. Second, this annual rate should be used as a discount rate for the liabilities because it can be seen that it i s endogenous in this model. Thus, one of the most important contributions of this study and niche of the model is that once the simulations are run for a given plan with its particular attributes and guidelines, the discount rate for the liabilities can be determined above, the discount rate, , should be used to discount liabilities when valuing the fund. One of the caveats is that as a plan progress from o ne year to the next the discount rate can be adjusted on a yearly basis, if need be.
111 Summary Based on the simulated returns using historical data of Russell 2000 index, the results indicate that the proposed structure significantly outperforms the cur rent one for the next thirty five years. When we extend the number of years to 50, 75, and 100, the same outcome is observed the proposed structure outperforms under any market uch as 0.95 or 0.85, the proposed structure also outperformed the current one. Note that the threshold of the funding ratio and other parameters such as limitations on the amount of required market dependent contributions per each given year can be adjuste d to fit local economic realities and desires and/or guidelines of the board members of the pension fund. There are several contributions of this study. First, the model is equipped to value the performance of the two structures, current and proposed, rela tive to each other under a range of market conditions. Second, the model also quantifies the added value of the proposed structure. Third, the model demonstrate that the optimal rate is endogenous to the expected market rate of return and the dynamics of t he funding ratio, and it can calculate exactly the optimal discount rate used to value liabilities. The proposed structure demonstrates several advantages over the current o ne. antage of the favorable market opportunities, keeping the plan running sustainably in the long run. Second, the structure intrinsically helps with the timing of investment because it deploys capital during the adverse market conditions allowing the plan to capitalize during the
112 term performance against risks that sometimes cannot be predicted or anticipated. The model can b e adopted for any distribution other than the Russell 2000 index when simulating a scenario. It can also be extended to include a portfolio of different investment classes with returns. Each pension fund has to be considered individually in order to build liability bases, and local economic conditions.
113 Table 3 1. Ten top performing pension funds Annualized Yearly Return Standard Deviation Total Return Funding Ratio, 2010 Excess Return St. Dev. Of Excess Return IR Texas Municipal 7.60% 5.77% 108.03% 82.9 5 . 2% 6.46% 0. 81 Nevada Police & Firefighter 6.72% 7.17% 91.62% 67.8 4 . 3% 7.46% 0. 58 Denver Schools 8.25% 10.72% 120.93% 88.9 5 . 8% 11.25% 0. 52 Illinois Munici pal 7.73% 11.78% 110.47% 83.3 5 . 3% 12.44% 0. 43 Colorado State 7.45% 11.97% 105.13% 62.8 5 . 0% 12.44% 0. 41 Vermont State Employees 6.16% 11.29% 81.87% 81.2 3 . 9% 10.68% 0. 36 Missouri State Employees 6.18% 11.25% 82.20% 80.4 3 . 9% 10.71% 0. 36 Houston Firefighters 6.62% 12.60% 89.87% 93.4 4 . 3% 12.03% 0. 36 Vermont Teachers 6.19% 11.75% 82.32% 66.5 3 . 9% 11.13% 0. 35 Contra Costa County 7.17% 13.15% 99.83% 80.28 4 . 8% 13.59% 0. 35 Table 3 2. Ten worst performing pension funds Annualized Yearly Return St. Dev Total Return Funding Ratio, 2010 Excess Return St. Dev. Of Excess Return IR Maryland PERS 2.11% 12.79% 23.16% 62.8 0 . 2% 12.31% 0. 02 Maryland Teachers 2.11% 12.79% 23.16% 65.41 0 . 2% 12.31% 0. 02 Duluth Teacher s 1.93% 14.83% 21.03% 81.66 0. 4% 14.32% 0. 03 North Dakota PERS 1.89% 13.44% 20.56% 73.4 0. 4% 12.52% 0. 03 Illinois SERS 1.81% 12.17% 19.67% 37.4 0. 5% 11.49% 0. 04 Idaho PERS 1.24% 15.15% 13.14% 78.9 1. 1% 14.62% 0. 07 Delaware State Employees 0.89% 14.41% 9.24% 96 1 . 4% 13.93% 0. 10 Chicago Teachers 0.73% 15.31% 7.50% 66.9 1 . 6% 14.71% 0. 11 Connecticut Teachers 0.48% 14.73% 4.88% 61.4 1 . 8% 14.19% 0. 13 Arizona Public Safety Personnel 0.33% 13.99% 3.31% 67.7 2.0 % 13.71% 0. 15 Table 3 3 . Est imate d parame t ers Estimate S tandard E rror 0.14 00* 0.071 0.00 4 0.005 0.05 0.048 0.128 *** 0.049 Notes: * signifies 0.10 significance level; ** 0.05 significance level; *** 0 .01 significance level.
114 Table 3 4. Summary Statistics for the Distributions Asset Base under Current and Proposed Structures Asset Base Mean Standard Deviation Coefficient of Variance Minimum Maximum Current Structure $3,162,313,004 $1,592,656,071 50 $37 5,314,003 $10,023,615,094 Proposed Structure $4,397,321,777 $1,511,314,805 34 $1,498,374,949 $11,691,764,180 Percentage of Difference 39% 5% 32% 299% 17% Table 3 5. Summary Statistics for the Value of Contributions and Value of Capital Gains on the C ontributions under the Proposed Structure Mean Standard Deviation Coefficient of Variance Minimum Maximum Discounted Present Value of all Contributions $4,447,050 $2,561,802 58 $414,023 $8,812,254 Value due to the Market Return on Contributions $1,000,9 66,165 $374,224,277 37 $232,615,740 $2,234,905,932
115 Table 3 6 . Simulated Run for One Scenario Current Structure Model Structure Year Liabilit ies Predicted Returns Asset Base Funding Ratio Contributions Asset Base Funding Ratio 2014 $14,284,119 5.26% $9,739,331 0.68 $9,739,331 0.68 2015 $14,998,325 4.40% $9,158,504 0.61 $214,262 $9,359,987 0.62 2016 $15,748,241 5.99% $11,773,330 0.75 $224,975 $12,321,546 0.78 2017 $16,535,653 25.48% $13,953,958 0.84 $236,224 $14,883,690 0.90 2018 $17,362,436 5.61% $13,698,492 0.79 $0 $14,611,202 0.84 2019 $18,230,558 4.60% $12,025,733 0.66 $260,437 $13,055,623 0.72 2020 $19,142,086 2.60% $11,575,039 0.60 $273,458 $12,829,542 0.67 2021 $20,099,190 29.00% $14,347,039 0.71 $287 ,131 $16,257,865 0.81 2022 $21,104,149 17.40% $12,126,632 0.57 $301,488 $13,996,560 0.66 2023 $22,159,357 2.58% $13,099,860 0.59 $316,562 $15,461,827 0.70 2024 $23,267,325 5.69% $12,672,468 0.54 $332,390 $15,278,920 0.66 2025 $24,430,691 6.71% $12,893,217 0.53 $349,010 $15,900,162 0.65 2026 $25,652,225 11.97% $20,271,000 0.79 $366,460 $25,574,742 1.00 2027 $26,934,837 15.64% $24,612,222 0.91 $0 $31,051,810 1.15 2028 $28,281,579 1.79% $22,951,726 0.81 $0 $28,956,859 1.02 2029 $29,695,658 2.01% $25,202,552 0.85 $0 $31,796,595 1.07 2030 $31,180,440 7.31% $23,486,460 0.75 $0 $29,631,500 0.95 2031 $32,739,462 5.48% $24,470,845 0.75 $0 $30,873,443 0.94 2032 $34,376,436 13.17% $28,045,587 0.82 $0 $35,383,48 6 1.03 2033 $36,095,257 2.14% $24,932,501 0.69 $0 $31,455,887 0.87 2034 $37,900,020 6.88% $27,735,041 0.73 $541,429 $35,593,977 0.94 2035 $39,795,021 1.54% $27,030,420 0.68 $0 $34,689,696 0.87 2036 $41,784,772 35.21% $27,486,116 0.66 $ 596,925 $35,881,506 0.86 2037 $43,874,011 34.51% $30,369,045 0.69 $626,772 $40,337,511 0.92 2038 $46,067,711 6.61% $29,101,941 0.63 $0 $38,654,488 0.84 2039 $48,371,097 6.33% $29,555,469 0.61 $691,016 $39,958,668 0.83 2040 $50,789,652 6 .01% $28,622,680 0.56 $725,566 $39,400,215 0.78 2041 $53,329,134 28.80% $33,221,388 0.62 $761,845 $46,614,761 0.87 2042 $55,995,591 30.92% $37,649,798 0.67 $799,937 $53,735,074 0.96 2043 $58,795,371 6.57% $33,530,021 0.57 $0 $47,855,189 0.81 2044 $61,735,139 12.97% $35,715,984 0.58 $881,931 $51,914,497 0.84 2045 $64,821,896 3.70% $33,681,803 0.52 $926,027 $49,831,026 0.77 2046 $68,062,991 16.70% $43,787,593 0.64 $972,328 $66,046,244 0.97 2047 $71,466,141 19.69% $56,848,2 08 0.80 $0 $85,745,993 1.20 2048 $75,039,448 4.58% $52,971,546 0.71 $0 $79,898,699 1.06 2049 $78,791,420 11.78% $60,867,798 0.77 $0 $91,808,872 1.17 2050 $82,730,991 0.21% $57,823,011 0.70 $0 $87,216,320 1.05
116 Figure 3 1. Y early Retu rn Distribution among 125 Pension F unds , 2001 20 09 Figure 3 2. Probability density function yearly returns for 125 pension funds in a given year 2001 20 09 -40 -30 -20 -10 0 10 20 30 40 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 2001 2002 2003 2004 2005 2006 2007 2008 2009
117 Figure 3 3. Yearly return dynamics average return among 125 funds for each of the eleven y ears Figure 3 4. Decomposition of Trans Cycle Trend and Distribution within Cycle -15 -10 -5 0 5 10 15 20 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Returns (%) -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 63 263 463 663 863 1063 1263 1463 Return Distribution for Each Year Yearly Average Return Trend Yearly Average Returns Distribution of Returns among Plans
118 Figure 3 5. Historical Linear Trend for the Trans Cycle Dynamics Figure 3 6. Annualized Yearly Returns v ersus Standard Deviations 2001 20 09 -40 -30 -20 -10 0 10 20 30 40 63 263 463 663 863 1063 1263 1463 ret_1yr Average Yearly Return Trend Arizona Public Safety Personnel NY State & Local ERS Texas Municipal 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00% Annulized Returns Risk (Standard Deviation)
119 Figure 3 7. Distribut ion of Simulated Returns Based on Russell 2000 Index Figure 3 8 . Net Present Value of the Asset Bases under the Conventional Pension Plan and the New Pension Plan Structures -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 Predicted Return based on Russell 2000 Index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Billions NPV of Asset Base under the Conventional Pension Plan Structure NPV of the Asset Base under the New Pension Plan Structure
120 Figure 3 9 . Net Present Value of the Asset Bases under the Conventional P ension Plan and the New Pension Plan Structures Figure 3 10 . The Distribution of the Net Present Value of All the Possible Amounts Required as Determined by the Proposed Structure 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Billions Added Value of the New Structure 0.00 2.00 4.00 6.00 8.00 10.00 Millions Discounted Present Value of all Contributions
121 Figure 3 11 . The Distribution of the Net Present Value of the Capi tal Gains Earned on the Amounts of Contribution Required under the Proposed Structure Figure 3 12 . Funding Ratios of the Current and Proposed Structures and Market Contributions under Proposed Structure Schedule 0.00 0.50 1.00 1.50 2.00 2.50 Billions Value due to the Market Return on Contributions 0 0.2 0.4 0.6 0.8 1 1.2 1.4 $$200,000.00 $400,000.00 $600,000.00 $800,000.00 $1,000,000.00 $1,200,000.00 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050 Years Funding Ratio (FR) Contributions Market Depedent Contribution (Primary Axis) Funding Ratio under the Current Structure (Secondary Axis) Funding Ratio under Proposed Structure (Secondary Axis)
122 Figure 3 13 . Asset Bases under the Current and Proposed Structures -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% $$10 $20 $30 $40 $50 $60 $70 $80 $90 $100 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050 Millions Asset Base under the Current Structure (Primary Axis) Asset Base under the Proposed Structure (Primary Axis) Predicted Return (Secondary Axis)
123 CHAPTER 4 EFFECT OF RELATIV E PRICE CHANGES OF TOP PRINCIPAL CROPS ON U.S. FARM LAND ALLOCATION BEFORE AND AFTER 2005 ENERGY POLICY ACT (EPA) Introductory Statement The Energy Policy Act of 2005 (EPA , 2005) mandates mix i ng ethanol with gasoline sold in the United States (U.S.), which increases the demand for corn an d, as a consequence, corn price rise s (Carter et al., 2012) . In response to high prices farmers allocate more land to growing corn ( USDA NASSb , 2011 ). However, since arable land is fairly fixed (Hertel , 2011), there are reasons to believe that the expansion of corn production take s away land from other staple crops. For instance, in the New York points out that Kansas, traditionally known as the Wheat State, to the surprise of all produced 23% more corn than wheat. This study tests if EPA 2005 introduces statistically significant structural changes to the U.S. farm land allocation dynamics. Speci fically, it provides the effect of the relative price changes on acreage in crop specific pairs before and after the introduction of EPA 2005 policies. Problem Definition The official rationale for the Energy Policy Act (EPA), passed by the U.S. Congress i n 2005, is to combat a growing problem of uncertainty in energy supplies as well as environmental issues (Farrell et al. , 2006). It introduces a mandated blend of gasoline and ethanol with the end goal of retail gasoline having at least 10% of ethanol. The Act mandates 7.5 billion U.S. gallons of corn based ethanol to be mixed with the gasoline sold by 2012. This policy has initiated the Renewal Fuel Standards (RFS) program, and two years later the Energy Independence and Security Act of 2007 (EISA ,
124 2007) t hat extends the previous corn based ethanol target to 15 billion U.S. gallons by 2022 ( US EPA , 201 3; De Gord er and Just , 2009). Detailed description and timeline of other intricacies of biofuel related policies and mechanisms are reported by Carter et al. (2012). Ethanol content in gasoline due to EPA 2005 and EISA 2007 has expanded from 2.9 percent in 2005 to 9.8 percent in 2011 ( US EIA , 2013). As a result, corn prices have risen sharply (Roberts and Schlenker , 2010 ; Hausman et al. , 2012), and, in respons e to the high prices, plantings of corn have increased (USDA NASSb , 2011) as can be seen in Figure 4 1. By 2006, the U. S. surpassed Brazil as the largest ethanol producer in the world ( US EIA , 2013), producing 116 million barrels comprising 45% of world e thanol production that year. Since 2006, U.S. production of ethanol has steadily increased. Diversion of corn stocks into ethanol production has increased significantly , accounting for 2 0% of the corn crop in 2006 to a n average of 40% in the last three yea rs (USDA ERS, 2013). The transformation of onward has had a significant effect on the U.S. corn market. Corn acreage has expanded significantly after 2005 while the overall land in agricultural pr oduction remains relatively flat (Figure 4 2 ). In fact, total acreage in production trends downwards ever so slightly after 2005 as demonstrated in Figure 4 2. As overall total acreage among the crops remains relatively flat, the expansion of corn acreage is at the expense
125 Figure 4 3 demonstrates the land shares of the five top c rops produced in the U.S.: corn; cotton; hay; soybeans; and wheat. Of the total agricultural land in production corn, cotton, hay, soybeans, and wheat are the top five crops grown in the U.S. , and they constitute 95% of U.S. crops. Land share s of these crops relative to total U.S agricultural land, 1960 2013, are plotted in Figure 4 2 . The land share of corn has increased after 20 05 significantly while the s oybean land share gyrates around relatively the same level. The land share of w heat, hay , and the category other crops have downward. The motivation for the study co mes from the fact that RFS policies initiated by the EPA 2005 may be affecting not just biofuel crops like corn, but they may be indirectly affecting acreages of other crops. Figures 4 3 and 4 4 suggest that acreages of other principal crops in the U.S may be reduc ed by these policies. Analysis of the state production data confirms these dynamics (Figure 4 4). Using a differential framework this study analyzes whether there is a statistically significant structural change in la nd allocation dynamics among f ive principal crops produced in the U.S. after EPA 2005. The study identifies crops and the intensity with which they compete for land with each other before and after the enactment of EPA 2005. The model then allows test ing whether the changes in the land competition dynamics in each crop specific pair are significant. The model in this study provides crop pair specific dynami cs of competition for land, that is and after the ethano l mandate of 2005. The study tests the overall hypothesis whether
126 EPA 2005 introduces a statistically significant structural change in U.S. land allocation dynamics by testing for statistical significance of the changes in acreage response to prices in the crop specific pairs. Based on 1960 2013 price and production data for crops such as corn, cotton, hay, soybeans, wheat, the analysis shows that the structural changes due to EPA 2005 are statistically significant. The study identifies specific crops whose acreages respond statistically different to its own and other crops price changes before and after 2005. The effect of prices on acreages is expressed as an elasticity measure. The magnitude of changes between two periods is also calculated. The results in this study are valuable, especially in lieu of the recent findings of Carter et al . (2012) who estimates that corn prices are about 30 percent higher, on average, between 2006 and 2010 than they would have been if ethanol production had remained at 2005 levels (Carter et al ., 2012). Coupling the estimated effect of the EPA 2005 on corn prices estimated by Carter et al . (2012) and the effect of corn price changes onto acreages of other crops estimated in this study, we are able to link ethanol policy to c hanges in the acreages of other crops and finally interpret the indirect effect of the ethanol mandate on the acreages of specific crops. Data The data span years 1960 to 2013 and are collected from National Agricultural Statistical Service ( NASS , 2014 ). T he data includes the annual quantity of produced crops, prices, and acreages for the following crops: corn, cotton, hay, wheat, and soy contains: 1) rice; 2) potatoes; 3 ) beans; 4) peas; 5) rye; 6) oats; 7) barley; 8) tobacco; 9) flaxseed; 10) peanuts; 11) sweet potatoes; and 12) sorghum wheat. In the U.S. the
127 the top five crops sin ce they comprise only 5% of agricultural output. This allows the aggregation of quantity, weighted prices and acreage for this category. Thus, in our model, for the years from 1960 to 2013 , the American agricultural sector is described by the prices of six outputs, principal crops such as wheat; corn; cotton; soybeans; hay; crop is quantified as a share of the acreage used in the production of that crop to the total farm land. Methodology (4 1)
128 To estimate the parameters for two periods, 1960 2004 and 2005 2013, we implement a dummy variable, ( =1,2) , into the model to distinguish the years 1960 2004 ( for which =0) from the years 2005 2013 ( for which =1 ). This methodology is chosen because the number of observations after 2005 is only 8, and running a model just for eight years would be impossible because there would not be enough degrees of freedom. Thus, we use a dummy variable to distinguish between t he two periods. This yields : (4 2 ) where , and .
129 significance of the coefficient changes that occurs after the year 2005. , , and the difference s for price elascticities, , as well as their significance level
130 Results Next, we test whether there is statistical evidence that EPA 200 5 introduces structural changes in U.S. l and allocation. We conduct a log l ikelihood test between a model without the dummy variable s (Equation 4 1) and a model with the dummy variable (Equation 4 2) The test statistics are higher than the critical values for unrestricted, homogeneity imposed, and homogeneity and symmetr y imposed cases. This indicates tha t there is structural change after 2005 . Next, the specific changes among crops are indicated by the parameter on the interactive terms of the dummy variable times the exogenous variables. If the parameter of the interact ion of the coefficient and the dummy variable is signif icant, it indicates that
131 the change occurs due to EPA 2005 . A positive sign of the dummy coefficient means that the coefficient is higher in magnitude after 2005, implying that it has increased signifi cantly after 2005. On the other hand, negative dummy coefficient means that it is lower by magnitude after 2005 , and thus, the coefficient has decreased after 2005. Coefficients for both 1960 2004 and 2005 2012 periods Table s 4 1 and 4 2, respectively. i , To check whether the difference between the two period land coefficients is statistically significant, we look at the dummy coefficients , , listed in Table 4 3. If the difference is significant by different from zero the structural change is identified and
132 attributed to the effect of EPA 2005. Out of all land dummy coefficients only that of c otton is significant at 0.01 level, an d it happens to be negative. Indeed the coefficient in the later period is larger in absolute terms than the corresponding one in the earlier period such reversed , turning from positive before 2005 to negative after 2005. The model indicates that this change is due to the effect of the EPA 2005 policy. The own price coefficients for both 1960 2004 ( for i=j) and 2005 2012 ( for i= j) periods are all positive as production theory suggests (Table s 4 1 and 4 2 , respectively ). For the 1960 2004 period own price coefficients for four crops corn , cotton, soybeans , and wheat are positive , as production theory requires, and statisticall y significant at 0.01 level for the exception of corn , which is significant at 0.10 level (Table 4 1) . For the 2005 2013 period own price coefficients are significant for five crops: co rn, cotton, soybeans, and wheat at the 1% level and that for hay is s ignificant at the 5% level. Assessing point estimates of the own price coefficients, it is noticed that the coefficient magnitudes for all four crops increase in the later period , while the coefficient of hay becomes statistically significant after 2005. T o check whether the difference (or the increase) between the two period own price coefficients , for i=j, is statistically significant, we look at the own price dummy coefficient s listed in Table 4 3. If the difference is significant, it means that the structural change due to EPA 2005 policy has affected significantly that crop structure . The positive and significant own price d ummy coefficients for corn, soybeans , and hay ( 0.11, 0.07, and 0.03 , respectively) indicates that the own pr ice coefficients for these crops have indeed increased due to the effect of EPA 2005 . This implies that after the
133 year 2005, the own price coefficients for corn and soybeans have increased 5.4 and 2.6 times, respectively, compared to those of the 1960 2004 period , and the own price coefficient of hay becomes statistically significant whereas it was not significant before 2005. Cross price c oefficient indicate s the relationship between the changes in the quantity demanded of land for one crop to the change of . If a cross price coefficient is positive, the crops behave as compliments, and if the cross price coefficient is negative, the crops behave as substitutes. Thus, before 2005 cross price coefficients ( ) of the following crops (in the order of magnitude) were significant and negative: corn soybeans; corn wheat; wheat hay; and cotton soybeans. The same is true in reverse combination since symmetry is imposed for coefficients. These crops behave as substitutes (c ompetitors) when it comes to land allocation . After 2005, the cross price coefficients ( ) , in the order of magnitude , significant and negative for the combination corn soybeans, corn wheat, wheat hay , hay cotton, and cotton other cr ops . This means they behave as competitors relative to each other. Comparing these results with those before 2005, it can be noticed that the competition between corn soybeans , corn wheat, and wheat hay have intensified, and hay cotton as well as cotton ot her crops combinations became statistically significant. T o understand whether the change is significant on a crop case and thus attributed to EPA 2005 policy, the cross price dummy coefficients are explored in Table 4 3. The significant ones indicate c hange due to EPA 2005 policy. The cross price dummy coefficients of t he following pairwise crops are significant and negative:
134 soybeans corn, hay cotton , and wheat hay which means that the intensification of their competition maybe attributed to the effe ct of EPA 2005 policy . Elasticities An e lasticity measure is important because it presents the information about the competition or complementary behavior as percentage of price of one crop to L and , own and cross price elasticities for both periods, 1960 2004 ( and ) and 2005 2012 ( and ) , are discussed and presented in Tables 4 4 and 4 5 , respectively. We then test whether the difference between the two periods o utput price land elasticities are statistically significant f or each pair of crops (Table 4 6 ). Land Elastici ties corn, cotton, wheat, and soybeans corn, cotton, wheat, and soybeans 1.99%, 1.68%, 1. 52%, and 0.54%,
135 Own p rice e lasticity
136 To understand which crops price elasticities a re affected by the EPA 2005 policy , we calculate the significance of the differences in own price ela sticities between the two periods (Equation 4 8), which are list ed on the diagonal of the Table 4 6. Own price elastic ities differences are significant f or corn and soybeans at the 1% significance level and for hay at the 10% significance level. This means that the own price
137 elasticities of corn, hay, soybeans have increased statistically significantly as a result of the EPA policy effect . The increase in own price elasticity point estimates for wheat and cotton are not statistically significant. Cross p ric e e lasticities
138 The results for the 2005 2013 period are listed in Table 4 5. Judging by point estimates and comparing them with the results for the 1960 2004 period, i t can be observed that t he dynamics of competition for land change . Specifically, there are only four statistically significant elasticities for the 1960 2004 period, but for 2005 2013 period, there are now seven statistically signif i c an t elasticities . T hr ee of which are for the same combinations of crops as the before 2005 period ( i.e. corn soybeans, corn wheat , and wheat hay) , but four other elasticities have become statistically significant in the after 2005 period ( i.e. hay cotton, hay wheat, wheat cott on, other crops cotton, and corn other) . Point estimates suggest that t he competition for land between corn and soybeans as well as corn and wheat intensifies.
139 The cross price elasticity of corn and other crops is significant at t he 10% level and is positive suggesting that these crops behave as compliments when it comes to acreage. It is important to understand whether the changes in the competition dynamics for these crops are due to EPA 2005. Table 4 6 shows the significance of the calculated differences in cross price elasticities between the two periods. T he significance of the difference identifies which elasticities have been changed due to the policy. The c orn soybeans cross price elasticity difference is significant at the 1% significance level . Corn wheat, and corn other crops cross price elasticity differences are not statistically significant. Thus, the competition for land between corn and soybeans has intensified by 4.2 times due to EPA 2005, where as post 2005 the corn wheat combination a nd corn and other crops behave as compliments. For the 1960 2004 period,
141 Summary Assessing point estimates in the results for 1960 2004 and 2005 2013 periods, it can be seen that a number of changes occur for land . T he mod el developed in this study is equipped to determine whether there has been a structural change due to EPA 2005 policy and to identify the crops that have experienced a statistically significant change due to this policy . For example, even though the compe tition for newly available land has changed for corn, cotton, soybeans, wheat, and other crops, only change s in land elasticities are statistically associated with the effect of EPA 2005 policy . Specif ically, the following changes a re a result of the policy. Before 2005 land expands when newly available arable land is added to cultivation, but after 2005 2005, arable land i s added to cultivation, but after 2005, when additional land becom es available. Changes in the are associated with the EPA 2005 policy. Own price elasticity poin t estimates suggest that even thoug h acreage responsiveness to own price changes have increased in magnitude for corn, cotton, hay, soybeans, and wheat, only those of corn and soybean are statistically significant and thus associate d with the EPA 2005 poli cy. Own price elasticities have increased 4.7
142 and 2 times for these two crops, respectively. price elas t i ci ty becomes significant after 2005 whereas it was not significant prior to 2005, this change is associated with EPA 2005 policy. The rest of changes in acreage responsiveness to own price changes for other crops are not statistically different and therefore can not be attributed to the EPA 2005 policy . The results of the cross price elasticities suggest that before 2005 corn competes for land with soybeans and wheat, while soybeans compete with cotton, and wheat competition intensifies by 4.2 and 3.29 times , respectively , with soybeans and wheat land . Corn also st art competing for land with other crops after 2005. However, only corn soybeans competition intensification is actually due to EPA 2005 policy. Before with wheat, and it also starts competing with cotton. Both changes are associated with the effect of the EPA 2005 policy. After 2005 soybeans no longer compete for cotton land , but this change can not be associated with the policy. After 2005 other crops begin competing f or land with cotton is not statistically attributed to EPA 2005 policy. Wheat and cotton start behaving as compliments when it comes to land allocation after 2005, which is determined to be a result of the effect of EPA 2005 policy. T he evidence suggest t hat the structural change in land allocation among these crops occurred after 2005. The following changes that are statistically attributed to EPA 2005 policy : c hanges in the way acreages of corn and cotton respond to the changes in newly available quantit y of land, changes in the effect of the acreage responsiveness of corn and soybeans to their own prices, the way soybean acreage respond to the
143 changes in prices of corn, and lastly wheat and cotton behave as compliments when it comes to land being allocat ed among them . In conclusion, it is interesting to notice that even though EPA 2005 policy was designed towards crops like corn and soybeans, it affected the production and land allocation of other crops such as cotton, hay, wheat, and other crops as well . This is the case because arable land is not limitless and often times land allocation decisions cannot be made in favor of one crop without negatively affecting another. The expansion of acreage of one crop may mean a contraction of acreage for another, and the model developed in this study identifies the crops that experience a change and the magnitudes of changes. It is important to understand the dynamics of completion for land because land allocation decisions will affect how much of and what kind of crop is planted, and this will then affect the total supply of a particular crop.
144 Table 4 1 . Coefficients of the Rotterdam m odel, 1960 20 04 Crops Crop Prices Land Corn Cotton Hay Soybeans Wheat Other Crops Corn 0.024 * 0.004 0.009 0.018** 0.014* 0 .003 0.458*** (0.013) (0.005) (0.006) (0.008) (0.008) (0.009) (0.039) Cotton 0.020 *** 0.002 0.009** 0.006 0.003 0.067*** (0.004) (0.003) (0.004) (0.004) (0.005) (0.018) Hay 0.002 0.000 0.011** 0.002 0.024 (0.006) (0.005) (0.005) (0.006) (0.023) Soybeans 0.045 *** 0.010 0.006 0.094** (0.009) (0.007) (0.008) (0.037) Wheat 0.047 *** 0.007 0.312*** (0.010) (0.007) (0.043) Other Crops 0.015 0.312*** 0.024 * 0.004 0.009 0.018** 0.014* 0.003 (0.043) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant at 1% level. Table 4 2. Coefficients of the Rotterdam m odel, 2005 2013 Crops Crop Prices Land i ) Corn Cotton Hay Soybeans Wheat Ot her Crops Corn 0.130 *** 0.011 0.001 0.100*** 0.043** 0.022* 0.182 (0.023) (0.009) (0.012) (0.018) (0.020) (0.013) (0.180) Cotton 0.029 *** 0.016** 0.012 0.023** 0.013* 0.278*** (0.008) (0.007) (0.011) (0.012) (0.007) (0.083) Hay 0.029 ** 0 .016 0.043*** 0.013 0.106 (0.013) (0.013) (0.016) (0.009) (0.107) Soybeans 0.117 *** 0.008 0.012 0.316* (0.026) (0.022) (0.014) (0.179) Wheat 0.089 *** 0.018 0.378* (0.033) (0.015) (0.216) Other Crops 0.008 0.297* (0.014) (0.168) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.
145 Table 4 3 . Difference in c oefficients before and after 2005 Crops Crop Prices Land Corn Cotton Hay Soybeans Wheat Other Crops Corn 0.106 *** 0.006 0.008 0.082*** 0.029 0.019 0.276 (0.026) (0.010) (0.014) (0.020) (0.022) (0.016) (0.184) Cotton 0.009 0.018** 0.003 0.029** 0.010 0.346*** (0.008) (0.008) (0.012) (0.012) (0.0 09) (0.084) Hay 0.027 * 0.016 0.032* 0.015 0.082 (0.014) (0.014) (0.017) (0.011) (0.109) Soybeans 0.073 *** 0.002 0.006 0.222 (0.027) (0.023) (0.016) (0.183) Wheat 0.041 0.011 0.066 (0.034) (0.017) (0.220) Other Crops 0.0 08 0.253 (0.018) (0.172) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant at 1% level. Table 4 4 . Output price and land elasticities of the estimated R otterda m model, 1960 20 04 Crops Crop Prices Land Corn Cotton Hay Soybeans Wheat Other Crops Corn 0.10* 0.02 0.04 0.08 ** 0.06 * 0.01 1.99 *** (0.06) (0.02) (0.03) (0.04) (0.04) (0.04) (0.17) Cotton 0.11 0.50*** 0.05 0.23 ** 0.14 0.08 1.68 *** (0.12) (0.09) (0.08) (0.10) (0.09) (0.12) (0.45) Hay 0.05 0.01 0.01 0.00 0.06 ** 0.01 0.13 (0.03) (0.02) (0.03) (0.03) (0.02) (0.03) (0.12) Soybeans 0.10 ** 0.05 ** 0.00 0.25*** 0.06 0.04 0.54 ** (0.05) (0.02) (0.03) (0.05) (0.04) (0.04) (0.21) Wheat 0 .07 * 0.03 0.05 ** 0.05 0.23*** 0.03 1.52 *** (0.04) (0.02) (0.02) (0.03) (0.05) (0.04) (0.21) Other Crops 0.02 0.02 0.01 0.04 0.04 0.10 0.28 (0.06) (0.03) (0.04) (0.05) (0.05) (0.08) (0.23) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.
146 Table 4 5 . Output price and land elasticities of the estimated Rotterdam model, 2005 20 13 Crops Crop Prices Land Corn Cotton Hay Soybeans Wheat Other Crops C orn 0.47*** 0.04 0.00 0.36 *** 0.15 ** 0.08 * 0.65 (0.08) (0.03) (0.04) (0.06) (0.07) (0.05) (0.65) Cotton 0.27 0.74*** 0.42 ** 0.32 0.60 ** 0.33 ** 7.24 *** (0.22) (0.20) (0.18) (0.29) (0.30) (0.19) (2.15) Hay 0.01 0.08 ** 0.15** 0.08 0.23 *** 0.07 0.56 (0.06) (0.04) (0.07) (0.07) (0.08) (0.05) (0.57) Soybeans 0.42 *** 0.05 0.07 0.50*** 0.04 0.05 1.34 * (0.07) (0.05) (0.05) (0.11) (0.09) (0.06) (0.76) Wheat 0.23 ** 0.13 ** 0.24 *** 0.05 0.48*** 0.10 2.07 * (0.11) (0.06) (0.09) (0.12) (0.18 ) (0.08) (1.18) Other Crops 0.29 * 0.17 * 0.17 0.16 0.23 0.10 3.94 * (0.17) (0.10) (0.12) (0.18) (0.20) (0.19) (2.23) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant a t 1% level. Table 4 6 . Difference between output price and land elasticities before and after 2005 EPA policy Crops Crop Prices Land Corn Cotton Hay Soybeans Wheat Other Crops Corn 0.36 *** 0.02 0.0 4 0.28 *** 0. 0 9 0.07 1.33** (0.09) (0.04) (0. 05) (0.07) (0.08) (0.06) (0.67 ) Cotton 0.17 0.2 5 0.47 ** 0.0 9 0.74 ** 0.25 8.9 1 *** (0.25 ) (0.22) (0.20) (0.30 ) (0.31 ) (0.23) (2.20) Hay 0.04 0.10 ** 0.14* * 0.09 0.17 * 0.08 0.43 (0.07) (0.04) (0.07) (0.07) (0.09) (0.06) (0.58) Soybeans 0.3 2 *** 0.01 0.07 0.24** 0.01 0.02 0. 80 (0.0 9 ) (0.05) (0.06) (0.12) (0.10) (0.07) (0.79 ) Wheat 0.16 0.15 ** 0.18 * * 0.01 0.2 5 0.06 0.55 (0.12) (0.07) (0.09) (0.13) (0.19) (0.09) (1.20 ) Other Crops 0.2 7 0.1 5 0. 19 0. 12 0.19 0. 0 0 3 . 66 (0.18 ) (0.1 0 ) ( 0. 12 ) (0.19 ) (0.22) (0.2 0 ) ( 2.24 ) Note: figures in parenthesis are standard deviations. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.
147 Figure 4 1. Corn acreage, production quantity, and prices 1980 201 3 Source : USDA NASS b, 2014 . Figure 4 2. Total acreage in agricultural production and corn acreage Source: USDA NASS b, 201 4 .
148 Figure 4 3. Crops land shares as percentage of total land in agricultural production 1960 2013 Source: USDA NASS b, 2014 .
149 Figure 4 4. Corn, wheat, soybean, and cotton production before and after EPA 2005
150 Figure 4 5. Corn plantings expansion after 2005 EPA
151 Figure 4 6. Soybeans plantings before and after 2005 EPA
152 Figure 4 7. Cotton plantings
153 Figure 4 8. Wheat P lantings
154 CHAPT ER 5 CONCLUSION The dissertation looks into risk management as well as allocation in the dynamic systems. Since the information age we live in offers readily available information with relative ease, it can be used for managing the dynamic systems. I look in practical ways to use data to manage effectively otherwise risky or perhaps unstable systems. In the past decade, changing dynamics of weather patterns have affected global agricultural production. Climate change causes increased fluctuations in weathe r patterns, creating a variety of negative effects on agricultural operations. Some of the effects can be mitigated by the use of technology and expert systems similar to the system examined in this study. The main goal of Precision Agriculture (PA) exper t systems is to facilitate site specific, preventive, rather than reactive, cost efficient, and environmentally responsible management practices in agriculture. Profitability studies for PA technology that assess the financial impacts of new technologies a t farm level can reveal the economic advantages of and barriers to PA adoption, and they can significantly increase PA adoption rates. The first chapter examines the profitability of site specific PA expert systems to optimize agricultural input use over time. Specifically, we comprehensively evaluate the risk and profitability of SAS, which improves temporal precision of fungicide application in strawberry production based on weather information. We show that SAS based application is more profitable than the traditional method for all possible weather conditions, market price scenarios, and risk aversion levels for producers. This value is linked to increased cost effectiveness in fungicide
155 applications, improved yields, and increased profits, compared to the traditional Calendar based application method. The PA disease management system increases profits while compensating the farmer for the additional risk associated with higher yield and profit variability. O v e r a ll , SAS fungi management i s a v iab l e and practical decision support system for f un g i c i de application t h a t can increase profit, and potentially reduce the environmental footprint from strawberry production. It can add significant economic value to the strawberry producer in the United States and i n other countries. Furthermore, similar systems can be adopted for production of other high value crops like grapes, blueberries, and blackberries. The second chapter indicates that the proposed structure significantly outperforms the current one for the next fifty years. The modeling is pension category specific because there are pension funds funding ratios range from severe underfunded to well funded statuses. Each tier of pension funds had to be handled separately, which makes it difficult to generali ze on the optimal discount rate at this time. However, from the preliminary results it can be seen that the optimal rate is endogenous to the expected market rate of return. Five year smoothing technique is utilized to lag the increases or decreases in the contribution levels to prevent any dramatic changes in keep the plan running sustainably in the long run. Such is the objective of the newly proposed structure term performance against risks that sometimes cannot be predicted or expected. The results suggest that such goal can be obtained by making ch anges at the structural level.
156 fter the year 2005, own output price land elasticities for corn and soybeans have gone up by 37 8 and 268 percent, respectively, compared to those of 1960 2004 period. No statistically significant difference in own price elasticities for crops like cotton, hay, wheat are detected. rop pairs such as corn soybeans, hay cotton, wheat cotton, cor n other crops, and hay other crops have experienced a statistically significant structural change due to EPA 2005. Specifically, assessing land allocation dynamics in terms of point estimates before and after 2005, it can be seen that before 2005 corn pric e changes negatively affects cotton, soybeans, and wheat acreages whereas after 2005 only soybeans land s oybeans completion for
157 .40 percent. Wheat cotton, corn other crops, and hay other crops display statistically significant complimentary behavior in respect to acreage after 2005 whereas their relationships are not significant before 2005.
158 APPENDIX A FUNDING RATIO, INFORMAT ION RATIO, AND SHARPE RATIO
159 Table A 1 . Ranking of Funding Ratio, Information Ratio, and Sharpe Ratio for 125 Pension Funds Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010
160 Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010 35 Illinois Universities 2.53% 13.14% 28.34% 0. 2% 0. 02 12.64% 0. 02 46.37 36 Indiana PERF 3.34% 12.22% 38.89% 1 . 1% 0. 09 11.62% 0. 09 85.2 37 Indiana Teachers 4.52% 10.98% 55.60% 2 . 2% 0. 20 10.32% 0. 22 44.3 38 Iowa PERS 3.60% 10.99% 42.45% 1 . 3% 0. 12 10.46% 0. 12 81.37 39 Kansas PERS 3.37% 12.52% 39.34% 1 . 1% 0. 09 11.97% 0. 09 62 40 Kentucky County 3.24% 10.93% 37.60% 0. 9% 0. 09 10.50% 0. 09 65.5 41 Kentucky ERS 3.08% 11.06% 35.46% 0. 8% 0. 07 10.63% 0. 07 40.3 42 Kentucky Teachers 3.17% 8.87% 36.69% 0. 9% 0. 10 8.40 % 0. 10 61 43 LA County ERS 3.57% 12.04% 41.95% 1 . 3% 0. 11 11.37% 0. 11 83.3 44 Louisiana SERS 3.65% 12.82% 43.10% 1 . 3% 0. 11 12.32% 0. 11 57.7 45 Louisiana Teachers 3.63% 13.97% 42.79% 1 . 4% 0. 10 12.54% 0. 11 54.4 47 Maine State and Teacher 2.49% 11.86% 27.8 4% 0. 2% 0. 01 11.42% 0. 02 66.03 48 Maryland PERS 2.11% 12.79% 23.16% 0. 2% 0. 02 12.31% 0. 02 62.8 49 Maryland Teachers 2.11% 12.79% 23.16% 0. 2% 0. 02 12.31% 0. 02 65.41 50 Massachusetts SERS 3.69% 14.23% 43.70% 1 . 4% 0. 10 13.54% 0. 10 81
161 Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010 51 Massachusett s Teachers 3.69% 14.23% 43.73% 1 . 4% 0. 10 13.54% 0. 10 66.3 52 Michigan Municipal 5.11% 14.66% 64.59% 2 . 7% 0. 18 15.05% 0. 18 74.5 53 Michigan Public Schools 3.18% 12.30% 36.80% 0. 8% 0. 07 11.98% 0. 07 71.1 54 Michigan SERS 3.10% 12.28% 35.77% 0. 8% 0. 06 11.95 % 0. 06 72.6 55 Minneapolis ERF 2.90% 12.06% 33.04% 0. 6% 0. 05 11.58% 0. 05 65.62 56 Minnesota PERF 2.91% 12.78% 33.25% 0. 6% 0. 05 12.24% 0. 05 76.4 57 Minnesota State Employees 2.89% 12.80% 32.96% 0. 6% 0. 05 12.26% 0. 05 87.3 58 Minnesota Teachers 2.89% 12.8 0% 32.96% 0. 6% 0. 05 12.26% 0. 05 78.45 59 Mississippi PERS 2.30% 12.64% 25.57% 0. 0% 0. 00 12.08% 0. 00 64.2 60 Missouri DOT and Highway Patrol 3.11% 13.31% 35.79% 0. 8% 0. 06 12.55% 0. 07 42.22 61 Missouri Local 3.68% 11.82% 43.50% 1 . 4% 0. 12 11.30% 0. 12 81 6 2 Missouri PEERS 3.19% 10.74% 36.83% 0. 9% 0. 08 10.10% 0. 09 79.1 63 Missouri State Employees 6.18% 11.25% 82.20% 3 . 9% 0. 35 10.71% 0. 36 80.4 64 Missouri Teachers 3.17% 10.89% 36.58% 0. 9% 0. 08 10.26% 0. 09 77.7 65 Montana PERS 2.36% 12.01% 26.22% 0. 1% 0. 00 11.45% 0. 01 74.2 66 Montana Teachers 2.35% 12.01% 26.14% 0. 1% 0. 00 11.45% 0. 00 65.44 67 Nebraska Schools 4.80% 15.66% 59.80% 2 . 4% 0. 15 16.04% 0. 15 82.4 68 Nevada Police Officer and Firefighter 6.72% 7.17% 91.62% 4 . 3% 0. 61 7.46% 0. 58 67.8 69 Nevada Regu lar Employees 3.41% 9.42% 39.90% 1 . 1% 0. 12 8.82% 0. 13 71.2 70 New Hampshire Retirement System 2.46% 11.52% 27.46% 0. 2% 0. 01 11.00% 0. 01 58.5
162 Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010 71 New Jersey PERS 2.42% 11.36% 27.06% 0. 1% 0. 01 10.97% 0. 01 69.49479 72 New Jersey Police & Fire 2.42% 11.36% 2 7.06% 0. 1% 0. 01 10.97% 0. 01 77.06 73 New Jersey Teachers 2.42% 11.36% 27.06% 0. 1% 0. 01 10.97% 0. 01 67.14 74 New Mexico PERF 3.04% 13.07% 34.94% 0. 8% 0. 06 12.42% 0. 06 78.5 75 New Mexico Teachers 4.43% 12.42% 54.25% 2 . 1% 0. 17 12.11% 0. 17 65.7 76 New York City ERS 2.47% 12.46% 27.60% 0. 2% 0. 01 11.99% 0. 01 100 77 New York City Teachers 2.47% 12.43% 27.59% 0. 2% 0. 01 11.97% 0. 01 100 78 New York State Teachers 2.70% 12.77% 30.58% 0. 4% 0. 03 12.11% 0. 03 100 79 North Carolina Local Government 3.73% 9.27% 44.19 % 1 . 4% 0. 15 8.82% 0. 16 99.6 80 North Carolina Teachers and State Employees 3.73% 9.27% 44.19% 1 . 4% 0. 15 8.82% 0. 16 95.4 81 North Dakota PERS 1.89% 13.44% 20.56% 0. 4% 0. 03 12.52% 0. 03 73.4 82 North Dakota Teachers 2.11% 15.63% 23.22% 0. 2% 0. 01 14.94 % 0. 01 69.85 83 NY State & Local ERS 3.75% 16.93% 44.48% 1 . 4% 0. 08 16.70% 0. 09 100 84 NY State & Local Police & Fire 3.75% 16.93% 44.48% 1 . 4% 0. 08 16.70% 0. 09 100 85 Ohio PERS 5.48% 16.26% 70.48% 3 . 1% 0. 19 15.79% 0. 19 76.10 86 Ohio Police & Fire 5.59% 16.20% 72.22% 3 . 2% 0. 20 16.52% 0. 19 69.4 87 Ohio School Employees 2.38% 13.30% 26.48% 0. 1% 0. 01 12.62% 0. 01 72.6 88 Ohio Teachers 3.42% 13.58% 39.94% 1 . 1% 0. 08 12.83% 0. 09 59.1 89 Oklahoma PERS 3.26% 10.72% 37.86% 0. 9% 0. 09 10.32% 0. 09 66
163 Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010 90 Oklahoma Teachers 4.51% 12.16% 55.46% 2 . 2% 0. 18 11.78% 0. 19 47.9 91 Oregon PERS 3.47% 14.08% 40.65% 1 . 2% 0. 08 13.54% 0. 09 86.9 92 Pennsylvania School Employees 3.53% 15.31% 41.43% 1 . 3% 0. 08 14.61% 0. 09 75.1 93 Pennsylvania State ERS 4.79% 16.50% 59.63% 2 . 4% 0. 15 16.48% 0. 15 75.2 94 Phoenix ERS 2.92% 13.28% 33.29% 0. 6% 0. 05 10.39% 0. 06 69.3 95 Rhode Island ERS 4.66% 12.99% 57.64% 2 . 4% 0. 18 11.20% 0. 21 48.4 96 Rhode Island Municipal 4.66% 12.99% 57.64% 2 . 4% 0. 18 11.20% 0. 21 73.6 97 San Diego County 3.61% 14.00% 42.59% 1 . 3% 0. 09 13.46% 0. 10 84.34 98 San Francisco City & County 2.83% 13.38% 32.13% 0. 5% 0. 04 12.77% 0. 04 91.08 99 South Carolina Police 3.88% 9.68% 46.35% 1 . 6% 0. 16 9.17% 0. 17 74.5 100 South Carolina RS 4.02% 9.73% 48.35% 1 . 7% 0. 18 9.23% 0. 19 65.5 101 South Dakota PERS 5.30% 13.36% 67.59% 3 . 0% 0. 23 12.80% 0. 23 96.3 102 St. Louis School Employees 5.81% 14.27% 75.91% 3 . 4% 0. 24 14.69% 0. 23 88.6 103 St. Paul Teachers 4.08% 12.66% 49.24% 1 . 8% 0. 14 11.96% 0. 15 68.05 104 Texas County & District 6.66% 14 .94% 90.59% 4 . 2% 0. 28 15.36% 0. 28 89.4 105 Texas ERS 3.42% 8.94% 39.94% 1 . 1% 0. 12 8.56% 0. 13 85.4 106 Texas LECOS 3.42% 8.94% 39.94% 1 . 1% 0. 12 8.56% 0. 13 86.3 107 Texas Municipal 7.60% 5.77% 108.03% 5 . 2% 0. 90 6.46% 0. 81 82.9 108 Texas Teachers 3.06% 12 .57% 35.24% 0. 8% 0. 06 12.05% 0. 06 82.9 109 TN Political Subdivisions 3.06% 8.66% 35.18% 0. 7% 0. 09 7.71% 0. 10
164 Annualized Return St. Dev . Total Return Excess Return Sharpe Ratio St. Dev. of Excess Return IR (%) Funding Ratio, 2010 110 TN State and Teachers 3.06% 8.66% 35.18% 0. 7% 0. 09 7.71% 0. 10 111 University of California 2.29% 12.12% 25.42% 0. 0% 0. 00 11.60% 0. 00 86.7 112 Utah Noncontributory 5.30% 13.94% 67.53% 2 . 9% 0. 21 14.30% 0. 20 82.2 113 Vermont State Employees 6.16% 11.29% 81.87% 3 . 9% 0. 34 10.68% 0. 36 81.2 114 Vermont Teachers 6.19% 11.75% 82.32% 3 . 9% 0.3 3 11.13% 0. 35 66.5 115 Virginia Retirement System 3.07% 13.58% 35.32% 0. 8% 0. 06 12.97% 0. 06 72.4 116 Washington LEOFF Plan 1 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 127 117 Washington LEOFF Plan 2 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 100 118 Washington PERS 1 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 74 119 Washington PERS 2/3 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 100 120 Washington School Employees Plan 2/3 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 100 121 Washington Teachers Plan 1 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 85 122 Washington T eachers Plan 2/3 3.95% 13.85% 47.30% 1 . 7% 0. 12 13.08% 0. 13 100 123 West Virginia PERS 4.35% 11.48% 53.12% 2 . 0% 0. 18 10.44% 0. 20 74.6 124 West Virginia Teachers 4.04% 11.63% 48.55% 1 . 7% 0. 15 10.55% 0. 16 46.5 125 Wisconsin Retirement System 3.70% 11.87% 4 3.87% 1 . 4% 0. 12 11.29% 0. 12 99.8 126 Wyoming Public Employees 4.24% 15.95% 51.49% 1 . 8% 0. 11 16.37% 0. 11 84.6
165 APPENDIX B MULTIVARIATE EMPIRICAL DISTRIBUTION This section of the Appendix describes the process used to generate a distribution of a stochast ic variable, X, using values estimated from the OLS Regression, and the distribution of the error term from the same OLS regression. Consider an OLS regression of a stochastic variable X: (B 1) ( B 2) To generate a distribution of the stochastic variable, from the OLS regression we obtain the deviates from the trend expressed as a percent of the predicted values, . In other words, the deviates are e stimated as the ratios of the residual e t to the predicted values . The residual from equation (1) is: ( B 3) for each year t . The deviates are expressed as the following: ( B 4) for each of the t years and for each random variable, The deviates are sorted from minimum to maximum: (B 5) for all years t and each random variables with clearly defined . Each of the deviates has an equal chance of being observed, thus a probability, P* , of 1/ T , where T is the total number of historical observations, is assigned to each sorted deviate, : P* = 1/ T . The procedure allows the si mulation process to preserve this assumption. Next, if the same deviate occurs several times in the sequence, the final
166 probability, for that deviate gets accumulated to reflect the higher probability of occurrence. (B 6) To summarize, the following parameters for the multivariate empirical (MVE) distribution should be defined: (B 7) where historical years, and simulated years. Next, for each , a vector of independent Standard Normal Deviates, , is generated (Richardson et al 2000 , 2007). Ten years are predicted, thus the size of the vector is ten: (B 8) Next, Uniform Deviates ( ) are obtained: (B 9) Finally, predicted v alues with stochastically adjusted component are: (B 10) For convenience, stochastically predicted value can be represented using Multivariate empirical (UVE) distribution notation: (B 11) where historical years, and simulated years, and F (.) is a functional form of the distribution.
167 Multivariat e Mixed Empirical Distribution This section describes the process of simulatin g the distributions of stochastically predicted values of two jointly distributed variables. Define , where i = t = 1, 2, (B 12) (B 13) To add stochastic component, from the same OLS regression we obtain the deviates from the trend, which are a percent of the predicted values, estimated as the ratios of the errors to the predicted val ues of yield. The residual from the yield and price equations are respectively: ( B 14) for each year t . The deviates are expressed as the following: ( B 15) for each of t years and for each random variable, The deviates are sorted from minimum to maximum: (B 16) for all years t and each random variables with clearly defined . Each of the deviates has an equal chance of the being observed in history, thus a probability, P* , of 1/ T , where T is the total number of historical observations, is assigned to each sorted deviate, : P* = 1/ T . The procedure all ows the simulation process to preserve this assumption. Next, if the same deviate
168 occurs several times in the sequence, the final probability, for that deviate gets accumulated to reflect the higher probability of occurrence. (B 17) Now we find intra temporal correlation matrix between unsorted random components between and . The correlation matrix of 2x2 size is as fo llows: (B 18) Since correlation of the variable to itself is unity, then Next, square root of is taken: . Thus, the following parameters for the multivariate mixed empirical (MVM) distribution should be assessed: (B 19) w here is a vector of sorted deviates from minimum to maximum, and variables, and historical years, and is a vector of assigned probabilities to a specific deviate in vector, and simulated years. Next, for each , a vector of independent Standard Normal Deviates, , is generated (Richardson et al ., 2000, 2007) of size N : (B 20) Correlated Standard Normal Deviates ( ) are obtained, there is one for each predicted year, n : (B 21) Next, Correlated Uniform Deviates ( ) are obtained:
169 (B 22) Finally, predicted values are: (B 23) Furthermore, for convenience, stochastically predicted values in Equations B 23 and B 24 can be represented using multivariate mixed empirical (MVM) distribution notation: (B 24) where historical years, and simulated years, and F (.) is a functional form of the distribution. Test for Normality of Weather Variable Observations Each Weather data point is a summation of days, during whic h 15% threshold was reached, for each production season there are six observations in total since there are six production seasons. The 15% variable since 15% threshold is more sensitive and indicative of the we ather conditions conducive for the disease development. Normal distribution is chosen to represent this variable after the analysis of the historical data obtained from Florida Automated Weather Network (FAWN) system ( http://fawn.ifas.ufl.edu/ ). Specifically, FAWN data contains 15 minute interval data on Temperature and Relative Humidity (RH) for the period from 1998 to 2013 yielding total of 14 production seasons. RH data is translated into Wetness Duration as foll ows. If RH>0.90 for a 15 minute interval, then the interval (1993). They found that disease incidence was correlated highly with this humidity level along with another variable, temperature between 15Â°C and 25Â°C (Wilcox and Seem ,
170 Duration and the average temperature during the wetness period is found. These two variables are then put through Wilson Madden weather model, and the number of triggers is found and summed up for each season obtaining the Weather data point for each season, yielding in total 14 retrospective observations. Hypothesis that these observations follow normal distribution is then tested by Chi square test. The hypothesis cannot be rejected at 5% significance level. Thus, the distribution for the simulated weather variable is chosen as normal while the mean and variance are calculated from the quantified Weather variable data from the six year field trials. Weather Intensity measures how early in the season and how intensive, i.e. close to each other, the triggers occur. This intensity measure may affect the overall d the earlier disease occurs in the season, the more significant the impact on the following yield might be. The measure is quantified by the following logic: for each trigger issued by the SAS system, we count the number of weeks left in the season respec tive to that trigger, so the number of weeks left in the season at the time of the trigger is recorded at every occurrence and then cumulated in the Weather Intensity measure for the entire season. These data points are then used to forecast Weather Inten sity as a variable. OLS regression is used to model the relationship between Weather Intensity as the independent and Weather as dependent variable. Thus, Weather Intensity is a function OLS regression deviates are calculated by dividing the error term by predicted values of Weather
171 Intensity and then randomly fitting them around the projected values, creating a distribution. Furthermore, it is important to test the distribution of the re siduals from the Yield regression where Weather is used as an independent variable. Normality of the error terms is necessary to validate the choice of normal distribution for the Yield. The errors from this OLS Yield regression are tested for normality by conducting Chi square test with null hypothesis that the errors are normally distributed. The results of the test show that at 5% significance level the test fails to reject the null hypothesis .
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181 BIOGRAPHICAL SKETCH Ekater ina Vorotnikova received both PhD in Resource and Applied Economics and a degree of M aster of S cience in Finance, Hough Program, at Warrington College of Business at Univers ity of Florida in 2014 . Ekaterina holds a b Computer Engineering (2004) an economics, production economics, welfare economics and externalities, international trade, applied econometrics, commodity markets, precision a griculture, expert systems in production. Her past research focused on land allocation amongst staple crops using the differential framework in the U.S., China, Russia, and Ukraine, valuing new expert system technology in production using stochastic NPV ap proach, and developing methodology for valuing and pricing positive externalities. Her interests also include asset management, international finance, equity markets (IPO of food and agricultural firms space). She has developed a structural change to the D efined Benefits pension fund contribution system, which make the funds more viable. Ekaterina serves as a President of Graduate Student Organization (GSO), and she also serves as a member on the Research Committee at the Food and Resource Economics departm ent and is affiliated with International Agricultural Trade and Policy Center. In addition, she serves on the Pension Review Committee to the Board of the City of Gainesville Pension Fund since 2012.