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PAGE 1 1 ASSESSING THE RATIONALITY OF FARMLAND PRICE MOVEMENTS By CODY POWELL DAHL 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 201 1 PAGE 2 2 2011 Cody Powell Dahl PAGE 3 3 To Ellie, Mom and Dad PAGE 4 4 ACKNOWLEDGMENTS I thank God, my wife and my parents I also thank Michael Gunderson, Cha rles Moss, James Seale, Chunrung Ai, Timothy Taylor, Gary Fai rchild, Mathew Salois, and Kenneth Erickson I could not have completed this work without your help and support. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABST RACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 Overview ................................ ................................ ................................ ................. 13 Motivation ................................ ................................ ................................ ............... 14 Problem Statement ................................ ................................ ................................ 17 Objectives ................................ ................................ ................................ ............... 18 2 LITERATURE REVIEW ................................ ................................ .......................... 19 Efficient Market Hypothesis ................................ ................................ .................... 19 Portfolio Analysis ................................ ................................ ................................ .... 22 Capital Asset Pricing Model ................................ ................................ .............. 22 Arbitrage Pricing Theory ................................ ................................ ................... 27 The Present Value Model of Farmland ................................ ................................ ... 31 Supply and Demand Price Determination ................................ ......................... 32 Theoretical Models ................................ ................................ ........................... 33 3 THEORY AND EMPIRICS ................................ ................................ ...................... 39 Theoretical Framework ................................ ................................ ........................... 39 Modeling the Return to Farmland in Agricultural Production ............................ 40 Mode ling the Rate of Return on Farmland in Agricultural Production ............... 42 Modeling the Change in Farmland Price ................................ .......................... 44 Defending the Endogen ous Rate of Return ................................ ...................... 45 Econometric Procedure ................................ ................................ .......................... 49 4 DATA AND RESULTS ................................ ................................ ............................ 51 Data ................................ ................................ ................................ ........................ 51 Research Findings ................................ ................................ ................................ .. 54 ITGMM Estimates ................................ ................................ ............................. 55 IT3SLS Esti mates ................................ ................................ ............................. 58 PAGE 6 6 FIML Estimates ................................ ................................ ................................ 58 Results from Hypotheses Tests ................................ ................................ ........ 59 Anal ysis of Residuals ................................ ................................ .............................. 61 Graphical Analysis of Residual ................................ ................................ ......... 62 Regression Analysis of the ITGMM Residuals ................................ ................. 64 Regression Analysis of the IT3SLS Residuals ................................ ................. 66 Regression Analysis of the FIML Residuals ................................ ..................... 66 Capitalization Value and the Rate of Return ................................ ........................... 68 Analysis of Fundamental ................................ ................................ ......................... 69 The Rate of Interest and the Price of Food ................................ ....................... 70 Agricultural Imports and Exports ................................ ................................ ...... 72 Summary ................................ ................................ ................................ ................ 73 5 DISCUSSION AND CONCLUS ION ................................ ................................ ...... 107 Implications of Empirical Results ................................ ................................ .......... 107 The Residual Return and the Rental Price of Illinois Farmland ............................. 110 Summary of Results ................................ ................................ .............................. 113 Suggestions for Future Research ................................ ................................ ......... 114 A Parting Note ................................ ................................ ................................ ...... 114 APPENDIX A THE SCHMITZ MODEL ................................ ................................ ........................ 116 B RECURSIVE SYSTEM ESTIMATION ................................ ................................ .. 119 C THE FAMA MODEL ................................ ................................ .............................. 126 D THE MARKET MODEL ................................ ................................ ......................... 128 E ECONOMETRIC PROCEDURE ................................ ................................ ........... 131 LIST OF REFERENCES ................................ ................................ ............................. 135 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 145 PAGE 7 7 LIST OF TABLES Table page 4 1 Para meter estimates ................................ ................................ .......................... 74 4 2 Wald test results ................................ ................................ ................................ 75 4 3 Results from the regression of on ................................ ........................... 76 4 4 Results from the regression of on ................................ ........................... 76 4 5 Results from the regression of on ................................ ......................... 76 4 6 Results from the regression of on ................................ ............................ 77 4 7 Results from the regression of on ................................ ............................ 78 4 8 Results from the regression of on ................................ ........................... 79 4 9 Order of magnitude for the FIML, ITGMM, and IT3SLS estimators .................... 80 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Rates of return on farmland and government securities ................................ ..... 38 4 1 The times they are a changing, especially in 1972 ................................ ............. 81 4 2 Return series and the data gathering process over time ................................ .... 81 4 3 TGMM: actual and estimated return to Illinois farmland ................................ ..... 82 4 4 ITGMM: actual and estimated rate of return on Illinois farmland ........................ 82 4 5 GMM: actual and estimated change in the price of Illinois farmland ................... 83 4 6 ITGMM: actual and estimated Illinois farmland price ................................ .......... 83 4 7 IT3SLS: actual and estimated return to Illinois farmland ................................ .... 84 4 8 IT3SLS: actual and estimated rate of return on Illinois farmland ........................ 84 4 9 IT3SLS: actual and estimated change in the price of Illinois farmland ................ 85 4 10 IT3SLS: actual and estimated Illinois farmland price ................................ .......... 85 4 11 FIML: actual and estimated return to Illinois farmland ................................ ........ 86 4 12 FIML: actual and estimated rate of return on Illinois farmland ............................ 86 4 13 FIML: actual and estimated change in the price of Illinois farmland ................... 87 4 14 FIML: actual and estimated real Illinois farmland price ................................ ....... 87 4 15 ITGMM residual lag plot: return equation ................................ ........................... 88 4 16 I TGMM residual lag plot: rate of return equation ................................ ................ 88 4 17 ITGMM residual lag plot: farmland price change equation ................................ 89 4 18 IT3SLS residua l lag plot: return equation ................................ ........................... 89 4 19 IT3SLS residual lag plot: rate of return equation ................................ ................ 90 4 20 IT3SLS residual lag plot: farmland price change equation ................................ 90 4 21 FIML residual lag plot: return equation ................................ ............................... 91 4 22 FIML residual lag plot: rate of return equation ................................ .................... 91 PAGE 9 9 4 23 FIML residual lag plot: farmland price change equation ................................ ..... 92 4 24 ITGMM time series residual plot: return equation ................................ ............... 9 3 4 25 ITGMM time series residual plot: rate of return equation ................................ .... 93 4 26 ITGMM residuals: farmland price change equation ................................ ........... 93 4 27 IT3SLS time series residual plot: return equation ................................ ............... 94 4 28 IT3SLS time series residual plot: rate of return equation ................................ .... 94 4 29 IT3SLS time series residual plot: farmland price change equation ..................... 94 4 30 FIML time series residual plot: return equation ................................ ................... 95 4 31 FIML time series residual plot: rate of return equation ................................ ....... 95 4 32 FIML time series residual plot: farmland price change equation ......................... 95 4 33 ITGMM: Estimated yield and capital growth, and the rate of return .................... 96 4 34 IT3SLS: Estimated yield and capital growth, and the rate of return .................... 96 4 35 FIML: Estimated yield and capital growth, and the rate of return ........................ 97 4 36 ITGMM: estimated capital appreciation and rate of return expectations ............. 97 4 37 ITGMM: estimates of the rate of return interval and capitalization value ............ 98 4 38 IT3SLS: estimated capital appreciation and rate of return expectat ions ............. 98 4 39 IT3SLS: estimates of the rate of return interval and capitalization value ............ 99 4 40 FIML: estimated capital appreciation an d rate of return expectations ................. 99 4 41 FIML: estimates of the rate of return interval and capitalization value .............. 100 4 42 Residual return s to Illinois farmland less the cash rental price ......................... 100 4 43 Annual average ................................ ................................ ............................ 101 4 44 Annual when the rate increases from one year to the next ........................... 101 4 45 Relationship between and ................................ ................................ ....... 102 4 46 First difference of changes in and the consumer price index ........................ 102 4 47 Standard score of and ................................ ................................ ....... 103 PAGE 10 10 4 48 Annual and annual average ................................ ................................ ..... 103 4 49 Real and average real Illinois farmland price per acre ................................ ...... 104 4 50 Standard score of and ................................ ................................ ......... 104 4 51 and ................................ ................................ ............................ 105 4 52 and ................................ ................................ ................................ 105 4 53 Standard score of and ................................ ................................ ...... 106 5 1 Nominal Illinois farmland and rental prices and residual returns ....................... 115 PAGE 11 11 LIST OF ABBREVIATION S APT Arb itrage pricing theory model BGLM Breusch Godfrey Lagrange multiplier CAPM Capital asset pricing model EMH Efficient market hypothesis ERS Economic Research Service FIML Full information maximum likelihood IT3SLS Iterated three stage least squares ITGMM Ite rated generalized method of moments LB Ljung Box MVP Mean variance efficient portfolio model OLS Ordinary least squares PPI Producer price index TSP Time Series Processor USDA United States Department of Agriculture PAGE 12 12 Abstract of Dissertation Presented to t he Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ASSESSING THE RATIONALITY OF FARMLAND PRICE MOVEMENTS By Cody Powell Dahl December 2011 Chair: Michael Gun derson Major: Food and Resource Economics The majority of research on farmland valuation focuses on market efficiency. Despite opposing views and contrasting results, one consensus emanates from the research: the price of farmland p eriodically departs from the value of farmland in agricultural production. The problem is agricultural economists still do not understand what causes the departure. This research identifies two new variables that help explain what people expect to earn fr om using farmland in agricultural production. The research also develops a new way to estimate the price of land. The new method enables researchers to determine if expected agricultural returns determine the price of farmland. The results show peop le ap propriately capitalize expected returns in to farmland price L arg e changes in the price of food and the T bill rate, and changes in agricultural exports and imports precede changes in the price of farmland. The new empirical findings suggest market funda mentals cause changes in the price of farmland. PAGE 13 13 CHAPTER 1 INTRODUCTION Overview In 1899 Andrew Sloan Draper then University of Illinois president said "The His words have withst oo d the test of time In 2010, Illinois farm land sold for an average of $4,650 an acre During the same year the national value of farmland exceed ed $ 1.78 trillion, which makes up about 85% of the assets on the US farm balance sheet. While the price to purchase an acre of farmland in Illinois ave rage d $4,650, the price to re nt an acre average d only $169. Agricultural producers endure chronic li quidity problems because of the relativ ely low current return on assets and experience periodic solvency issues due to large changes in the price of farmlan d. Because these changes often constitute the bulk of returns in agriculture production, financers require producers to pledge farmland as collateral for loans. Considering the relatively low current return s on assets and the prevalence of farmland on th e US farm balance sheet the use of farmland as collateral hampers the debt servicing capability and credit worthiness of the agricultural sector and leaves producers and financiers susceptible to downward swings in farm income and farmland prices (Barry et al. 2000). For example, m ore than 200,000 producers went bankrupt in the 1980s (Briggeman et al. 2009). Given the substantial price swings throughout the recent half century t he rise in farmland price relative to the rental price during the past deca de raise s questions about the current farm economy. Did the returns people expect to earn from farmland in PAGE 14 14 agricultural production cause the prevailing farmland prices? More important, can these expected returns sustain the current wealth position of the farm economy? Motivation On October 18, 2010, Chairperson of the Federal Deposit Insurance Corporation Sheila Bair said, are subject to change. A sharp decline in farmland prices similar to the early 1980s could have a expanding literature on farmland valuation would rouse similar apprehe nsion. Research establishes the price of farmland depends on agricultural returns in the long run ( Tegene and Kuchler 1990 a 1993 a ). Turbulent short run periods exist in which the price seems to move independently of the returns (Schmitz 1995). When spec ulators enter a market, asset prices may no longer depend on fundamentals. Consequently, farmland valuation research attributes unexplainable price movements to speculative behavior. Some research purports short run rational bubbles disrupt equilibrium p rices ( Roche and Mc Q uinn 2001; Gabriel and Turvey 2010 ). Other research alleges fading investor sentiment takes the price of farmland hostage ( Falk 1992, 1997; Falk and Lee 1998). Whatever the case, current methods cannot distingu ish a fad from a bubble (Clark et al. 1993). Moreover, transaction costs may constrain the rational flow of capital and people may rationally discount returns at d ifferent rates depending on the state of the economy. Time varying discount rates and high transaction costs, simi lar to fads and bubbles, appear to drive a wedge between the price of farmland and the value of farmland in agricultural production. If no wedge exists, then people valuate farmland PAGE 15 15 using market fundamentals and price of farmland will reflect th e intrinsi c value of farmland. The relevance and outcome of agricultural policy depend s on whether farmland price s reflect intrinsic value. By suggesting speculation creates land price boom bust cycles that harm farm operations researchers imply the competitivenes s of the land market fails to allocate resources efficiently. In such instances, the usual argument for government interventio n stipulates the need for agricu ltural policymakers to weigh the benefits of increasing the cost of transacting in the farmland m arket against the cost of reducing the liquidity of an already illiquid asset Alternatively, i f agricultural returns determine the price of farmland, but high transaction costs prevent the exchange of capital, the usual argument for government interventi o n stipulates the need for agricultural policy makers to create in itiatives that reduce the cost of trans acting in the farmland market. Both arguments for government intervention must assume policy makers have the capacity and information to create better outcomes than the market. This assumption further relies on the assumption that policy makers can measure the intrinsic value of farmland better than the people in the farmland market can. Again, the relevance and outcome of agricultural policy depend s on whether farmland price s reflect intrinsic value. Whether farmland price reflects intrinsic value depends on whether people generate fundamentally sound earnings expectations and use these expectations to determine price. Unfortunately, a consensus amon g researchers on the cause of the price increases in the 1970s and decreases in the 1980s does no t exist (Lavin and Zorn 2001). Researchers began questioning valuation methods, and particularly the present PAGE 16 16 value model, after the methods failed to explain the price of farmland during the turbulent 1970s and 1980s. Despite recent performance Goodwin et al. ( 2003 ) argue the present value model remains the standard in farmland valuation research According to present value theory, the price of an asset equal s the present value of the returns people expect from the asset. The present value of the current return to farmland also determines th e rental price of farmland, because people who own and rent farmland base the rental price on the expected residual retu rn to farmland. Almost all applications of the present value model spanning the turbulent 1970s and 1980 s reject the hypothesis that the price of farmland reflects the intrinsic value of farmland ( Falk 1991; and Clark et al. 1993). Researchers often use s uch findings to suggest the competitiveness of the farmland market fails to allocate resources efficien tly. Do these rejections mean the market for farmland is inefficient? Perhaps the rejection s indicate model failure and not market failure. Ironically an accurate assessment of the efficiency of the market depends on the efficiency of the model. A review of the literature reveals a pervasive theme: almost all studies rejecting market efficiency estimate expected returns using historical returns. Do th ese studies reject market efficiency or the ability of historical returns to predict expected returns? Fama (1990) argues historical returns generate noisy forecasts of expected returns, and Gutierrez et al. (2007) find structural breaks in the farm econo my during the 1970s and 1980s. At the onset of a structural change in the economy, the accompanying new information may alter the business environment in such a way that people begin relying on signals from the factors causing structural change rather tha n relying on previous PAGE 17 17 price and return information. Essentially, in a rapidly changing environment, previous farmland prices and returns may not contain sufficient information about expected prices and returns. Previous research that uses historical retur ns to generate expected returns may falsely conclude that the price of farmland deviates from its intrinsic value. Such conclusions misinform policy makers. Farmland valuation research can benefit from a better understanding of how people generate expect ations of returns. Problem Statement Almost all farmland valuation research focuses on efficiency tests. Researchers use models to test for bubbles and fads, to establish Granger causality, to examine the time series properties of data, and if necessary, to discover the best way to mathematically portray how people discount and form expected returns. Despite opposing views and contrasting results, a consensus emanates from the research ; the price of farmland periodically abandons the value of farmland in agricultural production. The problem is agricultural economists and land market participants still do not understand the cause of the departure. Farmland valuation research will benefit from a better understanding of how people generate expectations. Add itionally, the research will benefit from a better understanding of how people capitalize expected returns into the price of farmland. Theoretically, price reflects the capitalized value of expected returns. Modeling farmland price changes as a function of expected returns and the capitalized value of expected returns will enable researchers to determine if the price of farmland changes according to changes in expected returns. PAGE 18 18 Objectives The objectives of this study are three fold: Identify what informat ion helps people form an expectation of the residual return to farmland ; Formulate a model to d etermine whether the expectation of the return to farmland justifies the price of farmland ; and Estimate the system of equations, report the findings, and develo p policy implications. I expect p eople to form an expectation of the return to farmland in agriculture production, and capitalize the return into the price of farmland. Schmitz (1995) models changes in the price of farmland as a function of the expectatio n of the return to farmland in agriculture production and the capital value of the return to farmland in agriculture production. If speculative forces influence the farmland market, farmland price will move independently of the capitalization value of agr icultural returns. If return expectations determine the price of farmland, return expectations should justify the capitalization value, and hence, the price of farmland. PAGE 19 1 9 CHAPTER 2 LITERATURE REVIEW Asset valuation research in agriculture fits broadly into two categories. In the first category, portfolio analysis, systematic risk expo sure determines the price of an asset. In the second category, present value analysis, wealth generating potential determines the price of an asset. This literature review outlines the two categories and presents an overview of major research findings pe rtaining to agricultural land valuation Portfolio and present value theory develop models of market equilibrium. The models describe how people formulate prices and test whether they do so efficiently. The literature review, therefore, begins with an o verview of the efficient market hypothesis (EMH). Efficient Market Hypothesis In a seminal paper on market efficiency, Fama ( 1970) develops the theory of efficient markets and derives three testable hypotheses. First, the weak form test of market efficien cy tests whether past returns can predict future returns. Second, the semi strong form test of market efficiency tests whether the price of an investment appropriately responds to a public announcement. Third, the strong form test of market efficiency te sts the whether people can profit from private information. A growing body of evidence in the finance (Campbell and Shiller 1988a, 1988b; French and Roll 1986; Roll 1984; Rozeff 1984) and the accounting ( Penman 1983; and Oh and Penman 1989a, 1989b) literat ure compels Fama (1991) to clarify, among other things, the weak form test of market efficiency. The original weak form test of market efficiency sought to lay waste to the notion of profiting from simple technical analysis. The original intention of the weak form efficiency hypothesis was to test whether people could predict returns using past returns. PAGE 20 20 Fama (2000) and others ( e.g. Chen 1991) argue the predictive content in returns track asset prices equilibrating with asset profitability. For example, F ama (1988) reports for a three to five year horizon, predictable variation explains 25% of the return variance of large firm portfolios and 45% of the return variance of small firm portfolios. Fama and French (1989) find systematic patterns in investment returns and suggest the predictable part of returns results from rational people using market fundamentals to price assets. Fama refers to the phenomena as the mean reversion in profitability. In agriculture, mean reversion in profitability suggests if f armland price s rise relative to farmland return, people move investment capital out of agricultural and into another more profitable investment. The outflow of capital causes the price of farmland to revert downward to reflect the intrinsic value of farm land in agriculture production. Conversely, if farmland price falls relative to the residual return, then investment capital flows into agriculture from less profitable sectors. People seeking profits bid for farmland and cause the price to revert upward to reflect the intrinsic value of farmland in agriculture production. Mean reversion across different sectors of the economy complicates efficiency analysis. For example, suppose today, the price of farmland reflects the fundamental value of farmland. T onight, a structural change occurs in another sector. Tomorrow, because the relative profitability in another sector changes, the price of farmland no longer reflects its fundamental value even if nothing in the agriculture sector changes. The heterogenei ty of farmland prevents its exchange using standardized transactions. Since stocks trade in standardized equity markets, the accuracy and frequency of stock price and earnings information exceeds the accuracy and frequency PAGE 21 21 of farmland price and earnings i nformation. For example, the current study uses annual survey data collected by the United States Department of Agriculture (USDA). The USDA averages the survey data and reports state level statistics. Stock markets however, record real time exchange pr ices and companies must report quarterly financial statements. Using the availability of information as a gauge, asset pricing search and information costs appear higher in the farmland market than in the stock market. Even so, farmland valuation research finds evidence of mean reversion. For example, Burt (1986) detects mean reversion in profitability: The regression disturbance obeys a first order moving average process which is interpreted as follows: when land price is surprisingly large (large residu al) this year, it will adjust downward next year, and vice versa. The residuals in adjacent years are thus inversely correlated (correlation coefficient equal to 0 .5), but uncorrelated, or at least nearly so, when the distance in time is more than one ye ar. This behavior in the disturbance term might be interpreted as a tendency for the market to recognize its The h igh transaction cost s the high concentration of pricing information sourc es, the low frequency of public pricing information release, and the high likelihood of changes in the public pricing information lowers the dependability of the information and raises the cost of arbitrage. The high arbitrage costs create problems for as set pricing models. Fama (1997) also lists two inherent problems with asset pricing models. First, no model can provide a complete description of reality. In this sense the specification of returns in a model may suit one investment but not another. Sec ond, even a supposedly true representative model of an asset, over any sample period, produces systematic deviations from the predictions of the model and sample specific patterns in average returns arise by chance. If an event sample tilts toward sample specific PAGE 22 22 patterns in average returns, a spurious anomaly may arise even with risk adjustment using the true asset pricing model. Portfolio Analysis The origins of asset pricing theory data back to what Fama (2004) refers to as the mean variance efficient p ortfolio model (MVP) by Markowitz (1952, 1959). According to the MVP, a wealth maximizing, risk averse person generates an expectation of the mean and variance of investments, and the correlation of returns among investments. The person uses the expectat ion to derive the optimal portfolio of investments. A person maximizes the yield on a portfolio of risky investments subject to an acceptable risk (or minimizes the variance of the portfolio subject to an acceptable yield) to maximize utility. The MVP sh ows how the risk preferences of people determine the optimal combination of investments, and how the optimal combinations link together to create a frontier of efficient portfolios. People create an optimal portfolio by selecting investment combinations a long their upper left most indifference curve. The MVP was perhaps the first model to advocate portfolio diversification as a means of reducing risk. T he MVP was the first model to convey mathematically the notion that people should value assets according to both the expected return of the asset and the co variation of its returns among other assets. Capital A sset P ricing M odel Building on the MVP model of Markowitz (1952, 1959) Sharpe (1964), Lintner (1965), and Mossin (1966) independently develop the ca pital asset pricing model (CAPM). Sharpe (1964) perceives of the market as a system of investments. Accordingly, Sharpe divides investment risk into a systematic and an unsystematic part. The systematic part of investment risk is about how the returns o f an investment PAGE 23 23 correlate with the returns of the market. The unsystematic part of investment risk concerns the particular risk specific to an investment. Since people can eliminate particular risk through diversification, they will only pay for systemat ic risk. With two more assumptions, the CAPM shows that the rates of return on individual investments adjust to reflect the systematic risk that each asset contributes to the market portfolio. First, the CAPM assumes people freely borrow or lend capital a t a expectations about the joint distribution of investment returns. To use the CAPM, assume rational risk averse people do not incur taxes, transaction costs, or other ma rket frictions. Assume also the complete divisibility of investments, so people freely adjust their portfolios to maximize expected utility. Additionally assume people assess investments when formulating expectations of the rat e of return on each investment, People then determine the variance of each investment, and the covariance between investments and the market portfolio, Let represent the percentage of investment in a portfolio of investments, where for each investment, and: ( 2 1 ) The CAPM formulates the rate of return people expect from holding a risky investment as linear func tion of the rate of return on a risk free investment, the multiple of a term measuring the risk aversion of a person, ,and, the covariance between the rate of return on inves tment and the rate of return on the market portfolio: PAGE 24 24 ( 2 2 ) Since people only expect compensation for the systematic risk, the variance of the market portfolio, equals the systematic risk of each investment in the market: or, ( 2 3 ) Using the result from the above equation, the equation for the expected return to o n a risky investment can also represent the rate of return people expect from holding the market portfolio : ( 2 4 ) Solving Equation ( 2 4 ) for the relative risk aversion coefficient, and substituting into Equation ( 2 2 ) shows independence between the rate of return expectation and the preferences of peopl e: ( 2 5 ) To obtain the common representation of the CAPM, let : ( 2 6 ) where or Beta, mea sures the co variation between asset and the market portfolio relative to the variation of the market portfolio. A rearrangement of Equation ( 2 6 ) PAGE 25 25 shows how the systematic risk exposure of an asset determines the premium people require in excess of the rate of return on a risk free investment: ( 2 7 ) In an interview, Sharpe explains the significance Beta in his own words: Why should anyone expect to earn more by investing in one security as opposed to an other? You need to be compensated for doing badly when times are bad. The security that is going to do badly just when you need money when times are bad is a security you have to hate, and there had better be some redeeming virtue or else who will hold i t? That redeeming virtue has to be that in normal times you expect to do better. The key insight of the Capital Asset Pricing Model is that higher expected returns go with the greater risk of doing badly in bad times. Beta is a measure of that. Securit ies or asset classes with high betas tend to do worse in bad times than those with low betas (Burton 1998). Jensen (1968) develops the time series counterpart of Equation ( 2 7 ) : ( 2 8 ) The second term, captures the rate of return on an investment in excess of the risk free rate. The intercept term or Alpha captures the premium or discount attributable to idiosyncratic risk. Alpha should not significantly differ from zero i n an efficient market. Barry (1980) uses the CAPM to determine whether people require a premium for investing in farmland. He examines the US farmland market and ten production regions from 1950 to 1970 using an index of investments to approximate the mar ket rate of return. The results show agricultural assets exhibit little systematic risk and the estimates of the rate of return on agricultural assets exceed nonagricultural assets with the same systematic risk. Specifically, the Betas for the US and the ten regions range from 0.10 to 0.29 and do not differ statistically from zero. The rate of return on PAGE 26 26 agricultural investments should therefore equal the risk free rate of return. In the US and in eight out of ten production regions however, the risks p articular to agricultural assets earn a premium. The Alphas range from 3.91 to 7.62 and differ statistically from zero. In his comments on the article by Barry (1980), Carter (1981) cites Roll (1977), arguing the assumptions of risk aversion, borrowing an d lending of capital at a risk free rate, and agreement on the distribution of returns hardly resembles the actual farmland comprised of bonds, stocks, and farmland and it is unsuitable to investigate them with is simply a reflection of the 18% weight (Barry) gave farmland in his index of wealth (the independent variable behavior, the market index he constructed should not contain a significant amount of Carter (1981) re gresses farmland returns on stock returns. Using stock returns to approximate the market portfolio, the application of the CAPM by Carter generates a statistically insignificant Beta estimate of estate returns a add to the diversification of the stock portfolio, and hence its inclusion in a nonfarm following paragraph: This comment is concerned with the use of the CAPM for the purpose of valuing farm real estate and it points out that farm real estate adds nothing PAGE 27 27 in the way of diversification to a standard market portfolio because farm real estate is virtual ly a risk less asset. The response by Carter (1981) illustrates two important points. First, many people thought the price of farmland was appropriate in 1981 (Melichar 1978, 1981). Second, farmland price correlates little with stock returns. Carter (19 81) also reveals another difficult point : researchers must arbitrarily choose the composition of an index to approximate the unobservable market portfolio. Almost all applications of the CAPM to farmland ( for instance Barry 1980; Bjornson 1992a; and Arthu r et al. 1988) undervalue high Beta investments and overvalue low Beta investments. The same anomaly regularly occurs in empirical applications of the CAPM in the finance literature ( for instance, Black, Jensen, and Scholes 1972 ; and Fama and MacBeth 1973 ; and Fama 2004). Arbitrage P ricing T heory however, led to the creation of the arbitrage pricing theory model (APT) by Ross (1976). Ross (1976) recognizes the i nherent difficulty of constructing an all encompassing index of the market portfolio and instead assumes investments correlate with market factors. Therefore, the exposure of an investment to a factor constitutes risk, and the risk dictates the price of t he investment. In an interview with Jonathon Burton ( 1998 ), Dr. William Sharpe describes a subtle difference between the CAPM and the APT: The APT assumes that relatively few factors generate correlation, and says the expected return on a security or an a sset class ought to be a function of its exposure to those relatively few factors. That's perfectly consistent with the Capital Asset Pricing Model. But the APT stops there and says the expected return you get for exposure to factor three could be anythi ng. The CAPM says no if factor three does badly in bad times, the expected return PAGE 28 28 for exposure to that factor ought to be high. If that factor is a random event that doesn't correlate with whether or not times are bad, then the expected return should be zero (Burton 1998 ). Confirming the results by Barry (1980), early applications of the APT to agricultural assets find farmland investments do not contribute systematic risk to the approximate market portfolio proxy. For example, the four factor APT by Art hur et al. (1988) fails to price farmland returns accurately Specifically, farmland was one of three investments, out of nineteen, to exhibit no significant reaction to all four of the factors. Arthur et al. (1988) conclude farmland returns generate a s tatistically insignificant risk premium of 0.06% in excess of the rate of return on the approximate risk free investment. Arthur et al. (1988) also use the CAPM to check the robustness of the APT results with earlier CAPM results. Countering the results by Barry (1980), the Alpha estimates from the CAPM do not differ statistically from zero. Irwin et al. (1988) extend the sample Barry (1980) uses by six years to include the period immediately following World War II (1946 1950) and a portion of the period when 1984). Additionally, Irwin et al. (1988) broaden the approximate market portfolio by adding an uncertain inflation factor. Using the same sample period as Berry (1980), 1950 to 1970, the two factor APT by Irwin et al. (1988) reduces Beta from 0.19 to 0.15. No statistically significant difference exists between the Beta estimates by Berry (1980) and the estimates by Irwin et al. (1988). The addition of the unanticipated inflation factor however, increases the Alph a estimate from 4.78 to 7.80. A statistically significant difference exists between the two Alpha estimates. Using the sample 1947 to 1987 and the unanticipated inflation factor, the Alpha estimate becomes statistically insignificant and drops to 4.40. Beta PAGE 29 29 remains insignificant at 0.25. The reaction coefficient for unanticipated inflation however, becomes statistically significant at 0.86. Irwin et al. (1988) conclude: (a) returns to farm real estate have not been relatively low during the 1947 84 pe riod; (b) farm real estate returns contribute little systematic risk to a well diversified portfolio, and farm real estate returns are not strongly related to the performance of the market portfolio; and (c) returns have been systematically related to unce rtain inflation. Assuming rates of return to all farm capital approximate rates of return to farm real estate, the owners of farm capital, in aggregate, have similarly not experienced relatively low risk adjusted return. These returns have responded to i nflation but have had little response to the performance of the US economy. his own business, and the rates of return to the owner of Illinois farmland using a six fact or implicit A P provides a hedge against unexpected inflation. The researchers however, find returns to farm assets negatively correlate with changes in expected inflation. The estimate average, than investments in APT comparable risk non agricu to 1986. During the same period, the Alpha estimate for returns to farm operators indicates farm assets earn significantly lower returns, on average, than investments in comparable non agricultural assets. The explicit APT model by Bjornson and Innes (1992b) also find farmland investments earn significantly higher returns, on average, than investments in APT comparable risk non agricultural assets (except for Illinois farmland during the period 1963 1982). Further, Bjornson and I nnes (1992b) find farmland exhibits no systematic risk. PAGE 30 30 The research by Barry (1980), Carter (1981), Irwin et al. (1988), Arthur et al. (1988), and Bjornson and Innes (1992a, 1992b) suggests the portfolios researchers use to approximate the actual market p ortfolio fail to explain farmland returns: farmland contains no systematic risk. The research also finds farmland accrues a higher risk adjusted return than non agricultural assets with (approximately) comparable risks, while total agricultural assets acc rue a lower risk adjusted return. Until Bjornson (1994), the analysis of agricultural assets in an efficient portfolio context relies on unconditional asset pricing models. Unconditional asset pricing models hold constant the risk premium on investments a nd the rate of return people require on investments. Ghysels (1998) cautions improper specification of a conditional asset pricing model potentially generates larger pricing errors than unconditional asset pricing models Nevertheless, Bjornson (1994) de monstrates how conditioning the risk premium and return expectations on changes in the economy better predicts expected returns than unconditional models. While Hanson and Myers (1995) reject the CAPM with time varying risk premium, Bjornson (1995) uses t he APT with time varying expected returns and finds farmland returns correspond to the business cycle and changing market risk premiums. Before the CAPM revolution Modigliani and Miller (1963) caution against using government bonds to approximate the mark et discount capital: a common approach in empirical work has been simply to ignore the problem (that the cost of capital is not a directly observable magnitude) and to use without comment or explicit justification some standard index of current, nominal yi elds on high grade corporate bonds (or even government bonds) as a m easure of the cost of capital. the use of such measures is still unknown, though even a cursory survey of the (micro theory of capital) suggests many ground s for apprehension on this score. PAGE 31 31 Dr. Steven Landsburg reminds everyone of how the Treasury defaulted on a bill he bought, bill #GS7 2 179 46 6606 occurrences is not known. This particular investor went on to write a textbook in price proves government bonds contain risks. Researchers never observe the true risk of investing in US securities. The risk likely varies over time, but more important, how could a risk free rate exist when there is no such thing as a free lunch? The Present Value Model of Farmland Portfolio analysis maintains that the exposure of an asset to systematic risk determines the price of the asset in an efficient market. Present value analysis posits that the wealth generating potential of an asset determines price. The fundamental present value equation expresses price, as a function of the expected returns, and a constant discount factor, that converts the future values into present values: ( 2 9 ) Pederson (1982) suggests capitalization models depend critically on variable selection and the level of analysis. Two methodologies dominate the application of the present value model to farml and price analysis. The first strand, the atheoretic method, looks at the time series properties of data and uses vector auto regression to test for co integration and Granger causality. Sims (1980) advocates the atheoretic method to circumvent identific ation problems arising from misspecification and improper selection of variables. The second strand, the theoretical method, uses theory to model the PAGE 32 32 relationship between the price of farmland and the independent variables. Th is section continues with an overview of historical farmland price models and of the theoretic and atheoretic methodologies that derive from the present value model. Supply and D emand P rice D etermination Almost all of the valuation research before the 1970s treats farmland as a varia ble factor of production. The simultaneous equation framework performs well. For example, Tweeten and Martin (1966) develop a five equation model of the U.S. Cochrane (1966) conclude the expectation of rising income from technological advances and commodity price supports determine the price. Pope et al. (1979) report how Reynolds and Ti mmons (1969) find that farm enlargement, conservation payments, expected capital gains, predicted voluntary transfe rs of farmland, government land diversion payments, and the rate of return on common stock explain movements in the price of farmland. The re lationship between the price of farmland and the return to farmland changes in the 1960s. Pope et al. (1979) update these data and re estimate the three structural models. Results using the original model specifications with new data generate coefficient s with different signs and sizes. The models fit the sample data well, but Pope et al. (1979) find the single equation model by Klinefelter (1973) generates the best out of sample predictions Pope et al. (1979) suggest the structural models fail to iden tify the farmland supply schedule. Results from later studies substantiate the findings by Pope et al. (1979) and treat farmland as an economic rent. Using a ten year sample, Chavas and Shumway (1982) purportedly explain 99% of the variation in land PAGE 33 33 pric e. Burt (1986) argues a classic supply function for farmland does not exist. Phipps (1984) too finds that shifts in supply of farmland likely have no effect on the price of farmland. Phipps (1984) also notes that the USDA uses acreage statistics from th e five year agriculture census to impute acreage statistics in years when no agriculture census occurs. The linear imputations will further reduce variation in the supply schedule. The study by Pope et al. (1979) purges aggregate farmland valuation resear ch of the simultaneous equation framework. Nearly all studies proceeding Phipps (1984) treat farmland as an economic rent, fix the supply of farmland, and model price as a function of demand characteristics (Shi et al. 1997). Theoretical M odels The presen t value model remains the standard in farmland valuation research (Goodwin et al. 2003). According to present value theory, the price of an asset equals the present value of the returns people expect from the asset. The largest drawback of the present va lue model pertains to the measurement of the unobservable expectations. Theory expects profit to motivate people to look for information relevant to the future value of an asset. People actively looking for profit opportunities indirectly engage in the d iscovery of price. The present value of the returns to farmland determines the rental price of farmland since people who own and rent farmland base the rental price on the residual return to farmland. A wave of present value modeling begins to investigate why the price of land rose relative to returns in the late 1970s. Shalit and Schmitz (1982) find agricultural income, capital gains, debt carrying capacity of farmland, and credit access determine the price of farmland. Chavas and Shumway (1982) found r ising commodity prices and technological progress mainly drive farmland prices. Alston (1986) found real growth in PAGE 34 34 net rental income, likely driven by foreign demand and not domestic demand or technology, accounts for the increase in farmland prices from 1963 to 1982. Alston also found that inflation had no significant effect on farmland price. Melichar (1984) attributes changes in the value of farmland to changes in income from the rental price of farmland. Burt (1986) determines the rents account for 13% of the annual change in primarily determine the price of farmland. C ontrary to findi ngs by Melichar (1979), market participants do not capitalize a steady upward growth in rents into the price of farmland. Additionally, Burt (1986) finds no long term relationship between interest rates and farmland prices. According to Just and Miranowsk i (1993), an adequate model of farmland price must reflect that holding farmland facilitates holding debt and inflation reduces debt. The researchers suggest farmland prices serve as a hedge against inflation since inflation erodes personal savings. Just and Miranowski (1993) concur with Feldstein (1980) that inflation causes changes in land price and offsets the opportunity cost of other capital investments. The researchers also offer that people in the market for land may suffer from money illusion. Sc hmitz (1995) finds that the long run price of farmland depends on market fundamentals, but the present value model fails to account for short run deviations. He writes that in the 1970s people mistook a temporary rise in the price of farmland for an incre ase in real wealth. The linkage connecting land price and return between 1910 and 1950 broke in the 1960s and 1970s when the price of land rose relative to the PAGE 35 35 return to land (Shalit and Schmitz 1982). But according to Schmitz, financers in the 1970s and early 1980s continued accepting farmland as collateral and people continued using the collateral value of land to b uy more land or pay off short term debt. Ricardian rent, not return, sustained the high price of land (Schmitz et al. 2002). Schmitz et al (2002) suggest greater credit availability, government transfers, and a temporary increase in commodity prices sparked a boom cycle. The performance of the present value model wanes after the 1980s farm crisis. Phipps (1984) however, tests for Granger causality and concludes farm based returns Granger cause farmland price and farmland prices do not Granger cause farm based returns. Using the framework that Sims (1980) proposes for identification purposes, Featherstone and Baker (1987) use an unrestricte d VAR to model farmland price, returns, and an interest rate. Featherstone and Baker (1987) find that returns and earlier asset prices Granger cause asset price, and interest rates Granger cause returns, thus indirectly affect asset prices. Returns did n ot Granger cause interest rates, asset prices, or past returns. Featherstone and Baker (1987) also find that asset values overreact to shocks in the real price, real return, and real interest rate. The authors attribute rising farmland prices in the 1970 s to a propensity for the land market to bubble, as Diba and Grossman (1988) suggest. Falk (1991) uses the methodology that Campbell and Shiller (1987) use to test fi nds the land price and return statistics change as a difference stationary process, and the rational forecast of the present value of future changes in rents Granger causes PAGE 36 36 rents. Falk however, rejects the cross equation restrictions of the present value model. Most important, Falk finds statistically and economically significant predictable excess returns in the Iowa farmland market for the period 1921 to 1968. The results as a whole strongly reject the EMH under the assumptions of a constant discount rate and first difference stationary rent and price statistics. Falk (1992) again follows Campbell and Shiller (1988a) by modeling returns and price in a logarithm dividend ratio framework. He reaches the same conclusion (Falk 1991). Falk (1992) uses the annual rate of return on one month U.S. Treasury bills to underlying his methodology: assume the rate of return on a government security equals the efficient market discount rate. Figure 2 1 contains a graph of the annual rate on a three month t bill, the annual rate on the ten year constant maturity g overnment bond, and the annual rate on Illinois farmland, where The rate of return equates the expectation of cash flow with the price of land in Equation ( 2 9 ) From the graph, the rate on government securities appears to correlate negatively with From the onset, Falk mistakenly injects market inef ficiency into the analysis by requiring to equal the rate of return on a government bond. Effectively, Falk (1991, 1992) shows the farmland discount rate varies over time and farmland discount rate does not equal the rate on a g overnment security. The recent research by Falk and Lee (1998) abandons the present value model and uses a general three variable VAR representation of the price, the rent, and the PAGE 37 37 discount rate. Similar to Featherstone and Baker (1987), and Hansen and My ers (1995), Falk and Lee (1998) use the six month commercial paper rate to measure the nominal interest rate and the rate on a comparable asset rate. Similar to the present value models, using interest rates in an unrestricted VAR requires the asset retur n rate to equal the interest rate. Portfolio theory and present value theory suggest the rate of return on farmland capital does not correspond to the rate of return on tradable financial securities. The farmland pricing literature has yet found conclusiv e evidence against the efficient market hypothesis, exclusive of transaction costs, time varying risk premiums, and inappropriate discount rates. PAGE 38 38 Figure 2 1. Rates of return on farmland and government securities 20% 0% 20% 40% Actual Rate of Return Annual, 10 Year Treasury Rate Annual, 3 Month T Bill Rate PAGE 39 39 CHAPTER 3 THEORY AND EMPIRICS This research acknowledges transaction costs prevent arbitrage between the farm economy an d the non farm economy. The acknowledgement implies the existence of two discount rates: one for the farm economy and another for the nonfarm economy. The rate of return people expect to earn from farmland in agricultural production determines the discou nt rate in the farm economy This research constructs a simultaneous equation system to estimate the residual return, the discount rate for the farm economy, and the change in farmland price. Theoretical Framework The simultaneous equation system consists of the following three theoretical equations : ( 3 1 ) ( 3 2 ) ( 3 3 ) Farmland constitutes a fixed factor of production because its quantity cannot change in the short run Fixed factors accrue a residual return, or t he return that remains after paying for the use of variable factors of production The cash rental price of an acre of farmland represents the average amount of money a renter of land will pay an owner of land for the right to claim the residual return that accrues to farmland in agricultural production. The dependent variable in Equation ( 3 1 ) represent s PAGE 40 40 the residual return people expect to earn from an acre of farmland in agricultural production, conditional on the information set The dependent variable in Equation ( 3 2 ) represents the rate of return people expect to earn from farmland in agricultural production conditional on the information set The rate of return comprises of a rate of return from rent and of a rate of return from changes in the value of farmland capital Lastly, denotes the price of farm land an d denotes the change in the price of farmland. The model in Equation ( 3 3 ) is a variant of the model by Schmitz (199 5 ) in Appendix A The dependent variable in Equation ( 3 3 ) represents the change in farmland price that people expect conditional on the info rmation set If the return people expect to earn from an acre of farmland determines the price of land, then causes changes in The coefficients in Equation ( 3 3 ) equal when the return people expect from an acre of farmland determines the price of land. Farmland has an inelastic supply schedule Theref ore, u nlike traditional models where rational expectations equilibrate supply with demand the demand for farmland determines the price of farmland because. The following sections describe each equation in more detail. Appendix B describes the identifica tion scheme for the recursive system of equations. Modeling the R eturn to F armland in A gricultural P roduction Following the market model by Fama (1976) in Appendix C assume events in discrete intervals of time. Let represent th e current period and let represent the PAGE 41 41 period before In people formulate an expectation of future random variables using the information set The information set contains all information in including but can contain speculative information or unnecessary information that would not lead to t he rational pricing of an asset. Fama (1976) describes as : contains what people know in about the evolution of the state of the world through time, including current and past values of variables and the relationship between variables. Assume people acquire at the end of At the end of people use t o f orm an expectation of This research expects people use three variables in to form : the return the ratio of agricultural exports to imports and the change in aggregate food price minus the real three month treasury bill rate The dependent variable in Equation ( 3 1 ) depicts an unobservable expectation of An estimable econometric representation of Equation ( 3 1 ) requires an observable regressand. This research assumes deviates from by the random error and estimates the following empirical counterpart of Equation ( 3 1 ) : ( 3 4 ) If the error term in Equation ( 3 4 ) consists of white noise and : ( 3 5 ) the n the fitted values from Equation ( 3 4 ) represent the rational forecast of : ( 3 6 ) PAGE 42 42 I nformation in suggests lacks information o r people fail to appropriately use the information in Whatever the circumstance, does not represent the rational expectation of if d oes not consist of white noise. Modeling the R ate of Return on Farmlan d in A gricultural P roduction Recall people form at the end of People use to determine the price of farmland in The d etermination of marks the start of period So p eople observe at the start of Similar to the model of market equilibrium by Fama (2002) in Appendix D this research uses the growth of returns (dividends) to approximate the growth of farmland capital (stock ) This research however, uses an estimate of to simultaneously estimate the capital growth in and the return yield in This research expects people use the expectations of return growth and return yield and earlier realizations of return growth and yield, : to form where equals: for ( 3 7 ) The dependent variable in Equation ( 3 2 ) represents an unobservable expectation of An estimable econometric representation of Equation ( 3 2 ) requires an observable regressand. This research assumes deviates from by the random error and estimate s the following empirical counterpart of Equation ( 3 2 ) : PAGE 43 43 ( 3 8 ) For the regressand in Equation ( 3 8 ) to rep resent the rational expectation of the return to farmland, the model must account for idiosyncratic risk so that A ccording to Fama ( 197 6 ), the mode l must only generate positive estimates (see The Complete Market Model section): ( 3 9 ) and the residuals must comprise of white noise and ( 3 10 ) Finally, stationarity between and implies the necessary condition in Equation ( 3 2 ) (although Fama (2002) argues that his estimators continue to produce estimates of the average stock return even with reasonable forms of non stationarity). If no premium exists and the conditions in Equations ( 3 9 ) and ( 3 10 ) hold, the estimate from Equation ( 3 8 ) represents the rational prediction of where equals: ( 3 11 ) Conditioning on the growth rate of the return yield of and on the lag values of forces the opportunity cost of capital in farmland to equal the rate of return people expect to earn from farmland in agricultural production. PAGE 44 44 Modeling the C hange in F armland P rice The dependen t variable in Equation ( 3 3 ) represents an unobservable expectation of An estimable econometric representation requires an observ able regressand. This research assumes deviates from by the random error and estimates the following empirical counterpart of Equation ( 3 3 ) : ( 3 12 ) The first term on the right hand side of Equation ( 3 12 ) represent s the present value of The coeff icient on the term should equal negative one The second term on the right is more difficult to interpret Let equal : ( 3 13 ) Recall, the opportunity cost of capital strictly measures the rate of return people expect to earn from farmland in ag ricultural production. Moreover, i n this research i s exogenous. Define If the growth rate of returns equals the growth rate of capital. When represents the value of that people capitalize into : ( 3 14 ) PAGE 45 45 When then is not the sole determinate of and represents the capital val ue of the return people expect to earn from farmland not in agricultural production Alternatively if people formulate an expectation of the return to farmland using non fundamental information, then could also represent an irration al capital value w hen When people do not appropriately capitalize into When agricultural return s determine the pric e of farmland and Assuming the residuals comprise of white noise and ( 3 15 ) then the fitted values from Equatio n ( 3 12 ) represent the rational forecast of where equals: ( 3 16 ) Defending the E ndogenous R ate of R eturn From to farmland generates a rate of return from capital growth and a rate of return from the cur rent return Farmland g enerates rate of return, equal to: ( 3 17 ) PAGE 46 46 G ordon and Shapiro (1956) define The researchers recognize equates the expectation of returns with the current price of the asset: ( 3 18 ) The discount rate uired captures the notion of an opportunity cost of investing capital in one investmen t and not in another investment with the same systematic risk exposure or revenue earning potential. Researchers commonly use an exogenous rate of return to approximate the opportunity cost of holding capital in farmland ( Moss et al. 1989; Falk 1992; Jus t and Miranowski 1993; Schmitz 1995; Falk and Lee 1998). Moss et al. (1989) mention since occurs at the end of also occurs at the end of So peop le estimate and to determine Fama and French (1988) also recognize the expectation of the rate of return corresponds roughly to the discount rate that relates a current stoc k price to the expectation of future dividends According to the logic by Fama and French (1988) and Moss et al. (1989), i f people do not observe at the start of Equation ( 3 17 ) becomes: ( 3 19 ) and Equation ( 3 18 ) becomes : PAGE 47 47 ( 3 20 ) Th is logic fundamentally changes the present value model of farmland since the price becomes a function of two endogenous variables. In reality, researchers only observe the outcome variable Almost all researchers use an exogenous discount rate to circumvent the problem of having to estimate two endogenous variables. Therefore, almost all tests of market efficiency depe nd on people to assess the joint probability density function of all asset prices. The assessment generates the exogenous market rate of return that equilibrates the entire economy. The exogenou s rate acts as an economy wide opportunity cost of capital. Such market efficiency tests in present value analysis essentially determine whether a statistically discernible difference exits between the that equates the expectation of returns wit h the price of an asset (or what Gordon and Shapiro (1956) To test the efficient market hypothesis using the present value model, res earchers use the rate of return on a government bond (Falk 1992) or the commer cial paper rate (Falk and Lee 1998; Tegene and Kuchler 1991 b ) to proxy the nominal interest rate, or the market rate of return. Such a proxy explicitly makes the rate of return on the government bond or commercial paper the opportunity cost of capital. I f the f ederal a higher rate of return on government bonds, PAGE 48 48 then from Equation ( 3 19 ) rational people must expect the pr esent value of agricultural returns to change and must adjust the price of farmland accordingly For example, let symbolize the rate of return on some government bond. Using to proxy implies: ( 3 21 ) The exogenous rise of in raises and and must adjust to ensure equilibrates with According to the present value model and the efficient market hypotheses, must equal A static analysis using Equation ( 3 19 ) suggests one of the following scenarios must immediately occur to ensure equilibrates with a fter a one time exogenous increase : 1) increases and stays the same 2) increases and stay s the same. 3) decreases and increases enough to compensate for both the exogenous increase and the dec rease in 4) decreases and increases enough to compensate for both the exogenous increase in and the decrease in 5) and both increase. In scenarios 1) through 5), moves in lock step with The dependence of on changes, h owever, in scenarios 1) through 4). Specifically, in scenarios 2) and 4), decreases relative to A graph of scenarios 1) and 3) could exhibit the PAGE 49 49 start of a price bubble. Alternatively, under scenari os 1) and 3), increases relative to An opportunity to arbitrage would exist in scenarios 1) and 3) (given the difficulty of short selling farmland, scenarios 2) and 4) would not offer an opportunity t o arbitrage). Only in scenario 5) does the relationship between and not change, initially. If remains constant after the exogenous increase, however, and must continue growing to equilibrate with in scenario 5). In all five scenario s using the present value relationship in Equation ( 3 18 ) the exogenous increase in changes the relative relationship between and Constraining to equal injects friction into the relationship between and Specifying as a function of enable s people to consid er changes in when setting Usually, when researchers find a rbitrage opportunities, noisy residuals, or other prospects for people to profit they reject the efficient market hypothesis. When researcher they could just as likely conclude that does not accurately represent in an efficient market. Econometric Procedure This research us es iterated generalized method of moments (ITGMM) to estimate the parameters of the system of Equations ( 3 1 ) ( 3 2 ) and ( 3 3 ) After iteration, the resulting parameter estimates update the variance until the errors change less than a prespecified convergence criterion. Hansen (1982) develops generalized method of PAGE 50 50 moments (GMM) to estimate a model of consumption without invoking distributional assumptions about asset returns. GMM offers a way to estimate a system of equations in which the moment conditions exceed the unknown parameters in the system. ITGMM is robust to heteroskedastic of unknown form and does not require information about the distribution of the errors. The generality and the ability to handle hete roskedasticity make GMM applicable to financial models (Ferson and Foerster 1994). Appendix D contains the derivation of the GMM estimator. This resea rch also uses an iterated three stage le ast squares (IT3SLS) estimator and a full information maximum lik elihood (FIML) estimator to check the robustness of the estimates against other system estimators. IT3SLS assumes the data are distributed identically and independently, but no specific assumption of distribution for the errors is required. IT3SLS accoun ts for endogeneity in the dependent variable and cross equation correlation among the random errors. FIML does not require the specification of instrumental variables and will generate efficient estimates assuming the errors have a multivariate normal dis tribution. The efficiency of FIML, however is not known when the errors are not multivariate normal. The ITGMM and IT3SLS estimators generate consistent parameter estimates regardless of whether the empirical model represents the true model. The FIML es timator only generates consistent parameter estimates if the empirical model equals the true model. Unlike the ITGMM, the FIML and IT3SLS estimators spread specification error from one equation to other equations in the system. Additionally, ITGMM become s more efficient than IT3SLS in the presence of heteroskedasticity. PAGE 51 51 CHAPTER 4 DATA AND RESULTS Data T he vector from Equation ( E 4 ) in Appendix E contains fourteen instruments including a constant : Specifically, contains the returns for the return yield in for and the square of the return yield in Moreover contains the rate of return from Equation ( 3 7 ) in the square value the rate of return from Equation ( 3 17 ) in and the ratio of agricultural exports to agricultural imports, in for Economic Research Service of the USDA maintains statistics on Agricultural imports and Exports ( ERS ). Lastly, contains three variables to capture the state of the gene ral economy in contains a one period lag of the annual ten year average price to earnings ratio and the dividend yield f rom the Stand index Dr. Robert Shiller ( Shiller ) co mputes and Additionally, contains Moody's seasoned AAA corporate bond yield from the Federal Reserve Bank of St. Louis, The system of equations e stimates the return, rate of return and change i n farm land price from 1959 to 2008. The lag value of in Equation ( 3 2 ) requires o bservation of and fro m 1956 to 2008 The data requirements create a problem because the cash ren tal rates prior to 1967 represent the price to rent whole farms and PAGE 52 52 not just farmland. To incorporate the period prior to the farmland price rise in the 1970s and fall in the 1980s, this re search appends residual return statistics from 1956 to 197 1 onto cash rental statistics from 197 2 to 2008. The appendage requires justification. Recall, unobservable expec tations of the residual return to farmland theoretically determine the price of farmland. The cash rental price of farmland represents an observable secondary market counterpart to the unobservable residual returns. The price to rent farmland and the res idual return to farmland should theoretically cointegrate in a rationally functioning market. The appendage between 1971 and1972 was chosen because from 1970 to 1973, the rental price of farmland closely resemble s the residual return to Illinois farmland. The Russian grain purchase in 1973 an d other significant events marked the beginning of the farm economy boom and brought altered the relationship between the cash rents and residual return s Figure 4 1 contains th e standard scores for a host of USDA farm income statistics from 1959 to 2008 and d epicts the marked change that the Illinois farm economy underwent during the 1970s. Cash renal prices exceed the residual return statistics from 1976 to 1984. This contrad icts economic theory because a person who rents farmland expects compensation for the risks associated with production lanations of the occurrence. Researcher often prefer to use the cash rental price because, u nlike the residual return series that depends on multiple data imputations the cash rent series comes directly from a survey. While the cash rent price series d oes not require the multiple imputations a break in the survey method exist s. In 1994 the June Agriculture Survey PAGE 53 53 began collecting the cash rent data. In 1994 the original cash rent price estimate was $107.3, while the June Survey estimate was $100. Figure 4 2 plots the official USDA cash rent data. The d ot ted line beginning in 1994 shows how the cash rent seri es would appear if the USDA used $107.30 in 1994, rather than $100. Schnitkey (2010) also mentions the l ow rent al price in 1985 may not be entirely attributable to a reduction in the cash rent price The University of Illinois at Urbana Champaign maintains the informative online farm decision outreach center, farmdoc .com An article by Schnitkey (2010) prov ides an appendix of the cash rental price s for Illinois farmland from 1976 to 2008, and a graph of cash rental price s from 1970 to 2008. T he series of returns to farmland consists of the residual return to farmland before 1972 and the cash rental price of farmland from 1972 onward The residual return to farmland statistics originate from farm income statistics from the Economic Research Service ( ERS ) To calculate the residual returns to farmland, subtract non factor payments, excluding operator dwelling s and factor payments to non operators, excluding operator dwellings from gross receipts of farms. Then add net returns to non operators, including landlord capital consumption and interest expenses, excluding operator dwellings. Finally, t his research ex pects that in the aggregate, people form an expectation of the residual return to farmland, at using the change in the aggregate price of food the real 3 month T bill agricultural imports a nd exports PAGE 54 54 This research employs to approximate the aggregate price of agricultural outputs and to ap proximate the aggregate cost of agricultural inputs. The difference between and approximates an aggregate price cost margin for agriculture production. When changes in increase faster than changes in the potential for profit rises. If that potential has value, people who own farmland should capitalize the value into the price of land. T he ratio of t o approximates the purchasing power of the US dollar relative to foreign currency The Bureau of Labor Statistics maintains data on the price of food for all urban consumers (CPI). The rate of change in the food price index provides a measure of the aggregate change in food price. The producer price index (PPI) originates from the Economic Research Service and the National Agricultural Statistical Service and converts all nominal statistics in levels (not rates) into real statistics. Research Findings In an efficient market, p resent value theory suggests the returns people expect from an asset determine its price. In an inefficient market, speculators and people with irrational expectations dri ve a wedge between the price of an asset and the pres ent value of expected returns. This research tests the hypothesis that the expected return determines the discount rate, and together the rate and return determine price To test the hypothesis, this re search estimates an empirical model, tests the parameters estimates, and inspects the residuals The research also uses statistical facts to substantiate the empirical results. PAGE 55 55 The findings focus on estimates from the iterated generalized method of moment s (ITGMM) estimator; however, the findings discuss d ifferences among the ITGMM, iterated three stage le ast squares (IT3SLS) estimator and the full information maximum likelihood (FIML) estimators. The results are robust to each estimator S ome estimates differ from their theoretical counterparts, but estimates from the three methods are statistically indiscernible ITGMM E stimates Table 4 1 contains p arameter estimates heteroskedasticity robust standard errors, robu st t statistics, and p values from the ITGMM system estimator The intercept in Equation ( 3 4 ) has a statistically significant e ff ect on G iven no other information, people expect an acre from farmland in agricultural production Since constitutes only part of the rate of return, does not have the same meaning as and from Equation s ( 3 8 ) and ( 3 12 ) Market efficiency does not hinge on the significance of The statistical significance of implies peop le use 80% of to form : if then people expect to increase above T he statistical significance of indicates people expect to increase $5.98 when the ratio of agricultural exports to imports rises a percent age point from to The statistical s ignificance of suggests people expect to increase when the price of food rises a percent age point relative to the T bill or the T bill falls a percent age point relative to the price of food at PAGE 56 56 The intercept from Equation ( 3 8 ) in Table 4 1 is not statistically di fferent from zero Counter to the findings by Barry (1980) and Irwin et al. (1988) this research suggests people do not value risk s specific to Illinois farmland The coefficient estimate meet s the market model condition in Equation ( D 5 ) from Appendix D which suggests expected return growth closely approximates capital growth The results in Table 4 1 show s past return growth and yield rates, and differ statistically from zero The coefficient estimates and i ndicate people use 17% and 19% of and to form : if then people expect to increase 0.36 % above The intercept in Equation ( 3 4 ) also does not differ statistically from zero but and each have a statistically significant impact on Figure 4 3 plots the ITGMM estimates of the annual real return an acre against the actual return from 1959 to 2008. Actual r eturns exceed ed expectations from 1976 to 1978 and from 1980 to 1986. Recall however, the price to rent farmland approximates the residual return people expect from farmland in agricultural production. Figure 4 42 shows the actual price to rent farmland exceeded the actual residual return from 1976 to 1978 and 1980 to 1984. From the perspective of people who own farmland, their return exceeded expectations From the perspective of people who paid to rent farmland, the price they paid to rent farmland rental price exceeded expected return. The people who paid to rent farmland expected short term lose s or expected higher return s than the model predicts throughout the period PAGE 57 57 Figure 4 4 contains a plot of the actual and estimated rate of return from 1959 to 2008 and Figure 4 5 plots the actual and estimated change in farmland price The actual rate of return and actual change in land price exceed the expected rate of return and expected change in land price in 1976 to 1978, 1980, 1981, and 198 4 The expected rate of return and land price change do not systemically deviate from the actual values. Figure 4 6 contains a graph of the estimated and standalone farmland price Recall the regressand in Equation ( 3 12 ) is the change in farmland price in year Adding the fitted value to generates The stand alone price results from adding to for For example, t he stand alone farmland price estimate in 1959 equals plus In 1960, equals plus A fter 1959, the d epend only on previous estimates of The stand alone price estimate provides a visual of how well the model forecasts the price The ITGMM estimator fails to account for just under $1,000 of the farmland price increase in the 1970s. In 1977, Illinois farmland increases $1,119 an acre. The ITGMM estimator generates an estimate of $149 an acre. The standalone price underestimates the actual price in the 1970s because of the $970 error in 1977. This section provides an interpretation of the coefficient estimates and a description of the figures containing graphs of the estimates. The following two sections review only differences betwe en IT3SLS and ITGMM coefficients, and the FIML and ITGMM coefficients. Recall estimates from the three estimators are not statistically discernible. PAGE 58 58 IT3SLS E stimates Table 4 1 contains p arameter estimates and robust s ta ndard errors from the IT3SLS system estimator A noticeable difference exists between the ITGMM estimates and the IT3SLS estimates of The ITGMM estimator generates and estimate of and the IT3SLS e stimator generates and estimate of Considering two standard deviations of each estimator however t he IT3SLS and ITGMM estimates are statistically indiscernible. The IT3SLS parameter estimates have the same statistical signif icance as the ITGMM estimates. Figure 4 7 plots the actual and estimated IT3SLS return s to Illinois farmland Figure 4 8 plots the actual and estimated IT3SLS rate of return on Illinois farmland Figure 4 9 plots the actual and estimated IT3SLS change in the price of Illinois farmland Figure 4 10 plots the actual and estimated IT3SLS Illinois farmla nd price FIML E stimates The parameter estimates from the FIML estimator, the standard errors, the t statistics, and the correspo nding p values appear in Table 4 1 The FIML estimates do not differ statistically from the ITGMM and IT3SLS estimates. T he coefficient for the ratio of agricultural exports to agricultural imports however does not statistically differ from zero. The coeffi cient for the lag value of also does not statistically differ from zero. Figure 4 11 plots the actual and estimated FIML return to Illinois farmland Figure 4 1 2 plots the ac tual and estimated FIML rate of return on Illinois farmland Figure 4 1 3 plots the actual and estimated FIML change in the price of Illinois farmland. Figure 4 1 4 plots the a ctual and estimated FIML real Illinois farmland price PAGE 59 59 Results from H ypotheses T ests Recall an objective of this research is to determine that expected returns can justify the price of farmland. I test w hether the expected return justifies the price of fa rmland using the null hypotheses and In words, I test the null change in proportion to the capitalization value of the return people expect from farmland in any use Failure to reject the null hypothesis means I fail to reject that expected agricultural returns justify the price of farmland. In an efficient farmland market, expected agricultural returns cause the pr ice of farmland. Portfolio theory suggests people only value systematic risk in an efficient market. I test w hether people value the idiosyncratic risks specific to Illinois farmland using the null hypothesis and The market model suggests the growth rate of capital should equal the growth rate of returns if returns determine the price of farmland. I test w hether growth in expected returns equals growth in capital using the null hypothesis Table 4 2 contains the Wald test statistics from the ITGMM estimates Using the results, I fail to reject the hypothesis with 95% confidence. In testing the efficient market hypothesis, I fail to reject that people do not value the idiosyncratic risks specific to Illinois farmland. Additionally, I fail to reject the hypothesis with 95% confidence and I reject the hypothesis with 95% co nfidence. Recall, p resent value theory and market efficiency requires Rejecting the hypothesis however provides negligible evidence against market PAGE 60 60 efficiency considering And I fail to reject the joint hypotheses and with 95% confidence. Further, using the Wald statistics from the IT3SLS and FIML estimates in Table 4 2 I fail to reject the hypot hes e s and Taken together, the evidence is consistent with the efficient market hypothesis. For an informal (and statistically inaccurate, but nonetheless informativ e) explanation of the test rejection suppose in p eople expect the returns in to rise a percentage point. The ITGMM estimator suggests the capitalization value of expected r eturns increases between 1.0028% and 1.0516 % for a percentage p oint increase in expected return. More important, the absolute value of the confidence interval for the expected return coefficient contains the confidence interval for the capitalization value of the expected retur n, A rejection of the hypothesis suggests is statistically different from one, but the rejection is not economically significant. Lastly, the results from the Wald tests in Table 4 2 I reject the hypothesis with 95% confidence. Using the Wald statistics from the IT3SLS estimat or in Table 4 2 I fail to reject the hypothesis with 95% confi dence and I fail to reject the hypothesis with 95% confidence. Moreover, I fail to reject the hypothesis and The J statistic for the test of over identifying restrictions e quals 30.41, and with thirty one degrees of freedom, the critical chi square value equals 44.98. I cannot reject PAGE 61 61 the null hypothesis that the instruments are valid (p value: 0.496). The final value of the ITGMM criterion function from Equation ( E 12 ) in Appendix E equals 0.608. The parame ter estimates are robust to three kinds of system estimator s The consistency adds credibility to the model specification With a probability of 0.05, a statistically discernable difference exists between and one. No discernable difference exists however, between and one. With a probability of 0.10, a statistically discernable difference also exists between and negative one, but no difference exists between and negative one. The rejections are statistical sig nificance, but not economically significant given the size of the discrepancy The coefficient estimates are consistent with the efficient market hypothesis. Figure 4 3 3 Figure 4 3 4 and Figure 4 3 5 plot ITGMM, IT3SLS, and FIML estimates of the return yield and return growth from Equation ( B 20 ) in Appendix B against the actual rate of return. The size of the estimates follows some semblance of an order: Moreover, the size of the parameter estimates exhibit the same order. For exampl e, the absolute value of the IT3SLS or FIML coefficients exceeds the ITGMM coefficients. Table 4 9 displays a ranking of the coefficients from largest (1st) to smallest (3rd). Analysis of Residuals This research calculates the residu als by subtracting the fitted values from the observed values Since three equations comprise the system, each estimator generates three sets of residuals. Let and d enote the residuals PAGE 62 62 from Equation ( 3 4 ) Equation ( 3 8 ) and Equation ( 3 12 ) respectfully. Additionally, let denote the residuals of Equation f rom the ITGMM estimato r, and let indicate residuals from the IT3SLS estimator, and let stand for the residuals from the FIML estimator. This section starts with an analysis residual plots and concludes with a regression analysis of the residuals. Graphical A nalysis of R esidual A residual lag plot graphs the residual against the prior residual Residual l ag plots offer an initial indication of the ra ndomness of the data. Figure 4 1 5 Figure 4 1 8 and Figure 4 21 contain the residual lag plots of on from the ITGMM, IT 3SLS, and FIML estimators The residuals from the three estimators contain four large deviations in the second quadrant, and a single large deviation in the first and fourth quadrant. The random pattern suggests no s ystematic or complex dependence exists between and A residual time plot provides an initial indication of the de pendency of the error on time. Figure 4 2 4 Figure 4 2 7 and Figure 4 30 contain plots of the error from the ITGMM, IT3SLS and FIML estimato rs, respectively, against time. The errors from Equatio n ( 3 8 ) appear to contain heteroskedasticity. For example, Figure 4 2 4 shows the values of from 1959 to 1979 are relatively larger than the values of from 1980 to 2008. Figure 4 1 6 Figure 4 1 9 and Figure 4 2 2 contain residual lag plots of on from the ITGMM, IT 3SLS, and FIML estimators Additionally, Figure 4 2 5 Figure 4 2 8 PAGE 63 63 and Figure 4 31 plot against time. The figures containing the residual lag and time plots of show no sign of first order au tocorrelation or heteroskedasticity. Figure 4 1 7 Figure 4 20 and Figure 4 2 3 contain the ITGMM, IT3SLS, and FIML lag plots o f on The lag plots of from all three estimators appear random. The third and fourth quadrants contain a single large deviation, and the first quadrant contains two large deviations. T he large deviations in the first quadrant of Figure 4 1 7 Figure 4 20 and Figure 4 2 3 correspond to the errors at point (1976, 1977), and (1977, 1978). The culprit error transpires in 1977 when the price of farmland in Illinois increased $1,119 an acre The ITGMM estimator generates a value of $970 for while the IT3SLS and FIML estimators generate values of $8 93 and $978 The second largest deviation occurs in 1985 when the price of farmland in Illinois decreased $849 The ITGMM, IT3SLS and FIML estimators generate a value of $661, $630, and $697, respectively, for The time plots of from the ITGMM, IT3SLS, and FIML estimators in Figure 4 26, Figure 4 29, and Figure 4 32 also appear random. The results from the residual lag plots suggest returns are heteroskedastic H eteroskedastic robust standard errors will maintain the validity of the statistical inference. Appending residual returns onto the rental price could cause the heteroskedasticity. The heteroskedasticity could also result from using the PPI, or from improvements in the data gathering p rocess. Green also notes heteroskedasticity can result from data aggregation. Lastly, the plots show the system of equations fail s to account for the $1,119 price increase in 1977 and the $849 decrease in 1985 PAGE 64 64 Regression A nalysis of the ITGMM R esiduals The final tes ting stage requires regression analysis to learn whether people properly use information and whether the system of equations accurately forecast the price of Illinois farmland The estimation of a system of three equations by three system es timators generates nine sets of residuals. The analysis requires an ordinary least squares (OLS) regression of the residual on the one period lag residual and an OLS regression of residual on the formation set A regression of on will detect problems with the expectation model If contains information about people do not appropriately use the information in does not contain enough information or the model is misspecified. A regression of the residuals on the set of instruments will dete rmine whether people properly use information. If helps predict people made systematic errors in formulating expectations of the dependent variables, does not contain the ap propriate set of instruments, specification er ror exists in the model, or the data contain errors. Table 4 6 Table 4 3 contains the parameter estimates and robust standard errors from an ordinary least squares (OLS) regression of on the constant and the previous residual Similarly, Table 4 7 contain s the parameter estimates and robust standard errors from a n OLS regressions o f on the constant and the prior residual Lastly, Table 4 8 contain s the parameter estimates and robust standard errors from a n OLS regression o f on a constant and the prior PAGE 65 65 residual Using the results, for every equation I fail t o reject the hypothesis that a statistically discernable differ ence exists between the lag residual coefficient and zero. Using the results from an F test, with 95% confidence, I fail to reject the hypothesis of zero intercept and slope coefficient for three equations. The previous residual does not appear to contai n information about the future residual. The Time Series Processor (TSP) software has an OLS program that performs a myriad of auxiliary tests. The auxiliary tests of and generate results similar to the OLS residual regressions I fail to reject a null hypothesis of no first order autocorrelation using the h, h tests with 95% confidence. Additionally, with 95% confidence, I fail to re ject a hypothesis of no autocorrelation in the first five lags using the Breusch Godfrey Lagrange multiplier (BGLM) test Lastly, with 95% confidence, I fail to reject the hypothesis of no autocorrelation in the first five lags in the three equations usin g a Ljung Box (LB) test. Table 4 3 contains parameter estimates and robust standard errors from the OLS regression of on the constant and Similarly, Table 4 4 and Table 4 5 contain the results from the regressions and on Table 4 6 Because none of the coeffi cients differ statistically from zero, I fail to reject the hypothesis that people made appropriate use of the information in From t he BGLM test results, I fail to reject a hypothesis of no autocorrelation in the first five lag s in the regression of of Using the BGLM tests however, I reject a hypothesis of no first order autocorrelation in with 9 5% confidence, a nd reject no second order autocorre lation in with 95 % confidence. Countering the BGLM results I fail to PAGE 66 66 reject a hypothesis of no first order autocorrelation in and using a DW te st and fail to reject a hypothesis of no autocorrelation in lags one to five using an LB test Lastly, using an F test with any conventional level of confidence, I fail to reject a hypothesis that the slopes of the parameters equal zero Regression A nalys is of the IT3SLS R esiduals Table 4 3 contains the results from an ordinary least squares (OLS) regression of on a constant and Similarly, Table 4 4 and Table 4 5 contain results from the regression of the residuals from Equation ( 3 2 ) and Equation ( 3 3 ) on lagged residuals and a constant T he IT3SLS results are identical to the ITGMM results. Addition ally, the statistical significance of the parameters in Table 4 6 Table 4 7 and Table 4 8 and the auxiliary test results are identical to the results for the ITGMM regressions of the residuals on Regression A nalysis of the FIML R esiduals The results from of the regressions of the FIML residuals, and on lag residuals and on however, do differ from the results of the ITGMM and IT3SLS residual reg ression. With 95% confidence, in the regression of on I fail to reject an F test that of the joint hypothesis that a constant and a coefficient of equal zero. The results o f the hypothesis using the BGLM, DW, and LB tests are identical to the results from the ITGMM and IT3SLS lag residuals regressions. Table 4 6 Table 4 7 and Table 4 8 contain the parameter estimates from the regression of and on the instrument set From the results in PAGE 67 67 Table 4 6 with 90% confidence, I fail to r eject the hypothesis that the coefficient for contains no information about The regression results of the FIML estimator in Table 4 6 suggest people do not formulate rational retu rn expectations. Specifically, people could profit from the observation that a percent age point increase in agricultural exports relative to agricultural imports should increase the expectation of returns $35.78 dollars an acre Figure 4 50 depicts the relationship between and during the sample 1959 to 2008. The statistical significance of could result from people shift ing the importance of and when generating expectations of returns. For example, suppose depends on and and depends on During the 1970s and 1980s correlate s more with than with Starting in 1987, seems to correlate more with than with Since does not contain by specification, the influence of on does not offset the influence of on Unl ike the ITGMM and IT3SLS estimators, using the results from the BGLM tests with 95% confidence, I fail to reject the hypothesis of no autocorrelation in the first five lags of the regression of on With 90% confidence using the BGLM test, I fail to reject the hypothesis of no first order autocorrelation in the regression of on To counter the BGLM evidence, using the results from DW tests with 95% confidence, I fail to reject the hypothesis of no first order auto correlation in the regression of on Further, using the results from the LB te st with 95% PAGE 68 68 confidence, I fail to reject the hypothesis of no auto correlation in the first five lags in the regression of on Lastly, the results of all three regressions cannot reject an F test with a null hypothesis that the slopes of the parameters equal zero. Capitalization Value and the Rate of Return If people who own farmland expect the residual returns to grow, the rental price (or potential rental price) of farmland will increase. People who own farmland essentially bid the expectation of higher residual returns into the price of farmland. The change in price attributable to the higher residual return expectations represents the capitalization value of returns. Equation ( B 23 ) in Appendix B formulates estimates of the capitalization value Recall from Equation ( 3 19 ) return yield and capital growth comprise This study uses expected yield and expected return growth, and past realizations of yield and return growth, to estimate If people rationally value using then from Equation ( 3 11 ) represe nts the rate of return rational people expect from farmland in agricultural production. Equation ( B 23 ) in Appendix B formulates an estimate of the capitaliza tion value The z score provides a means of converting the and estimates into a standard scale for the purpose of comparing the expectation of the rate of return on farmland in agricultural production and the expectation of the capitalization value. Figure 4 3 6 Figure 4 3 8 and Figure 4 40 depict the standar d score estimates of and from the FIML, IT3SLS, and ITGMM from 1959 to 2008. The red dot lines indicate periods when farmland capital appreciates more rapidly than the one period PAGE 69 69 rate of return. The r ed dot lines show the capitalization value estimates of all three estimators exceeds the rate of return estimates from 1976 to 1980, and 1997 to 2008 The ITGMM and IT3SLS estimators estimate a capitalization value in excess of the rate of return estimate for the period 1995 to 2008, and an estimate of the capitalization value from the FIML estimator exceeds the rate of return estimate in 1983. The standard score has a standard deviation of one. The upper and lower interval limits in Figure 4 3 7 Figure 4 3 9 and Figure 4 4 1 encompass two standard deviations above and below the rate of return estimate of from Equation (3 17). The ITGMM and FIML estimato rs generate estimate s of the capitalization value exceed ing the rate of return in terval from 1977 to 1979. O nly in 1979 did the IT3SLS estimate exceed the rate of return interval. The ITGMM and FIML estimates fall below the interval in 1962, and the FIML estimate exceeds the interval in 2005. On average the rate of return estimates of the three estimators justifies changes in th e value of farmland capital throughout 64% of the sample period T he capitalization value exceeds the upper r ate of return confidence interval throughout only 5% of the sample. Analysis of Fundamental To substantiate the coefficient estimates, this section examines the behavior of statistics that comprise the independent variables in Equation ( 3 1 ) This section also examines the relationship between the residual return to farmland and the cash rental price of farmland, and examines how the two statistics evolve with the price of farmland. PAGE 70 70 The R ate of I nterest and the Price of F ood Figure 4 43 shows averages 5.5% from 1959 to 2008. The highest value of occurs in 1981 at 14 %, while the lowest value occurs in 2008 at 1.4%. increases five consecutive periods from 1977 to 1981. Aside from 1962 to 1966, does not increase more than two consecutive years. rose 2.4% from 2.8% in 1962 to 4.9% in 1966. In contrast, rose 8.4% from 5.6% in 1977 to 14% in 1981. Should people have expected such stark increases in the cost of de b t from 1977 to 1981? Were they irrational for not foreseeing such increases? Figure 4 44 plots only value s of that increase from one year to the next from 1934 to 2010. The increases from 1977 to 1981 were unprecedented and likely surpr ised people, unless people knew inflation would continue to rise and knew how the Federal Reserve would respond. averages 4% from 1959 to 2008. Figure 4 4 5 shows the largest value of occurs in 1973 at 14.5%. Figure 4 46 shows the first difference of and the first difference of general price inflation as measured by the CPI. The bundle of goods comprising also comprises a portion of the CPI. Figure 4 46 shows that the goods comprising rise and fall faster than the rest of the basket of non food goods th at comprise the CPI. Figure 4 4 5 suggests the r elationship between and underwent seven distinct changes from 1959 to 2008. First, from 1959 to 1972, averages 2.4% annually. Second, from 1973 to 1975, averages 12.4% annually. Third, averages 7.9% from 1976 to 1981. Fourth, drops to 2.9% from 1983 to 1986. PAGE 71 71 Figure 4 47 shows closely follows from 1959 to 1986. Fifth, increases slightly to 5% from 1987 to 1990. Sixth, remains relatively stable at 2.5% from 1991 to 2006. The seventh and most recently distinct period corresponds to the uptick in the price of farmland when averages 4.7% during 2007 and 2008. During this period, nearly doubles its average from the previous sixteen years. An in depth analysis of Figure 4 48 and Figure 4 49 bring to bear the complex relationship b etween and Figure 4 48 plots from 1959 to 2008 and the average excess of for the period The seven drop l ines in Figure 4 48 trace to a datum marker and the corresponding year when the price of farmland rose more than 9%. exceeds zero in each year directly proceeding or preceding the seven y ears except 1998 and exceeds zero throughout only 38% of the sample period. Figure 4 49 plots the real price of Illinois farmland from 1912 to 2010 and contains the same drop lines corresp onding to periods when the price of farmland rose more than 9%. Figure 4 49 exhibits three periods after 1959 during which prolonged increases in occur. First, rose 44% from 1961 to 1969. Second, rose 94% from 1973 to 1978. Third, rose 38% from 2001 to 2008. The three prolonged price increases comprise 40% of the sample period. Figure 4 48 shows exceeds zero throughout 38% of the sample. Figure 4 49 shows prolonged increases in the price of farmland constitutes 40% of the sample period. Taken toge ther, Figure 4 48 and Figure 4 49 show 73% of the years when exceeds zero occur during the prolonged land price increases and 95% of the years PAGE 72 72 when exceeds zero occur during the years directly preceding and during the prolonged land price increases. If mimics the price of agricultural outputs and mimics the price of agr icultural inputs, then after each of the three post 1950s booms, the input cost output price squeeze favors the pocketbook of farmers. Graphically, a nalysis of the price of food and the cost of debt suggests people logically bid the favorable conditions o f the farm economy, and the corresponding expected returns, into the price of farmland. Agricultural I mports and E xports This research does not attempt to validate a particular macroeconomic theory or analyze the effectiveness of a particular policy outcom e. Instead, this research takes the data as given and expects the ratio or the ratio of exports to imports to influence the returns that people expect to earn from farmland in agricultural production. Figure 4 51 plots and During the 1970s, rose faster than and surge d to very high levels. After a brief decline in the mid 1980s, rose slightly during the early 1990s. During the late 1990s and early 2000s, agricultural imports rose relative to ex ports and fell to a level not seen since the 1960s. In 2007 and 2008, rose faster than and jumped sharply higher. Figure 4 51 shows agricultural imports steadily advance from 1959 to 2010. Exports, however, rose sharply in the 1970s, maintained a general level through the early 1980s, fell somewhat in the mid 1980s, and then began a steadier climb that cont inues into the present day. PAGE 73 73 Figure 4 52 plots the correspondence between and In 1973, among other events, a crop failure in the Soviet Union and a continual we akening of the U.S. dollar lead agricultural exports to increase by 52% in real terms. Exports rose again by 27% in 1974. Farmland prices began the ascent after the large increases in Negligible movement in occurs from 1978 to 1980, but land prices drop as fall s in 1981. rose slightly in 1984, but relatively less than so that falls. The growth rate of roughly coincides with the growth rate of from 198 6 to 200 6. In 2007 and 2008, rose 12% and 25%, while rose only 3% and 1%, respectfully To eliminate scale effects, Figure 4 53 plots the s tandard score s of and The high values of that occur during the 1970s and early 19 80s appear to coincide with high values of T he rise of relative to in recent years shows a less pronounced correspondence between and in recent years. Summary The coefficient estimates offer strong evidence for and slight evidence against the joint hypothesis of market efficiency and correct model specification. T he coefficient estimates largely conform to economic theory The analysis of the residuals suggests people appropriat ely use market fundamentals to form return expectations and rationally bid these expectations into the price of farmland. PAGE 74 74 Table 4 1 Parameter estimates Parameter ITGMM A IT3SLS B FIML C 37.02 ** 51.11 ** 20.00 ** (5.33) (16.49) (7.64) 0.80 ** 0.72 ** 0.89 ** (0.03) (0.09) (0.04) 5.98 ** 13.88 ** 3.96 (1.90) (5.94) (2.83) 242.37 ** 308.88 ** 150.08 ** (38.18) (115.98) (52.06) 0.00 0.00 0.00 (0.01) (0.02) (0.03) 0.94 ** 0.85 ** 1.30 ** (0.14) (0.28) (0.37) 0.17 ** 0.18 0.09 (0.03) (0.09) (0.06) 0.19 ** 0.34 ** 0.09 (0.03) (0.11) (0.05) 8.11 23.33 51.99 (8.87) (46.86) (40.34) 0.99 ** 1.21 ** 1.37 ** (0.05) (0.26) (0.22) 1.027 ** 1.06 ** 1.05 ** (0.01) (0.05) (0.06) A Iterate d generalized method of moments B Itera ted three stage least squares C Full information maximum likelihood Note: Standard errors are with in parenthesis below the respective coefficients. ** denotes statistical significance at 5% level denotes statistical significance at 10% level PAGE 75 75 Table 4 2. Wald test results Parameter ITGMM A IT3SLS B FIML C 0.002 0.004 0.004 (0.0 09) (0.024) (0.027) 0.056 0.147 0.295 (0.135) (0.276) (0.372) 8.107 23.330 51.984 (8.873) (46.865) (40.345) 0.008 0.209 0.366 (0.048) (0.259) (0.219) 0.027 ** 0.061 0.048 (0.013) (0.052) (0.059) 0.036 0.148 0.036 (0.049) (0. 261) (0.049) 8.071 23.182 8.071 (8.824) (46.606) (8.824) A Iterated generalized method of moments. B Iterated three stage least squares. C Full information maximum likelihood. Note: Standard errors are within parenthesis below the respective coefficients. ** denotes statistical significance at 5% level denotes statistical significance at 10% level. PAGE 76 76 Table 4 3 Results from the r egression of on Parameter ITGMM A IT3SLS B FIML C 2.137 0.945 1.481 (2.704) (2.609) (2.679) 0.195 0.137 0.266 (0.186) (0.134) (0.194) A Iterated generalized method of moments. B Iterated t hree stage least squares. C Full information maximum likelihood. Note: Standard errors are within parenthesis below the respective coefficients. Table 4 4 Results from the r egression of on Param eter ITGMM A IT3SLS B FIML C 0.001 0.003 0.003 (0.010) (0.011) (0.011) 0.112 0.008 0.008 (0.145) (0.146) (0.146) A Iterated generalized method of moments. B Iterated three stage least squares C Full information maximum likelihood. Note: Standard errors are within parenthesis below the respective coefficients. Table 4 5 Results from the r egression of on Parameter ITGMM A IT3SLS B FIML C 1.140 8.654 8.447 (31.025) (31.779) (32.151) 0.068 0.047 0.178 (0.116) (0.146) (0.146) A Iterated generalized method of moments. B Iterated three stage least squares. C Full inform ation maximum likelihood. Note: Standard errors are within parenthesis below the respective coefficients. PAGE 77 77 Table 4 6 Results from the r egression of on Parameter ITGMM IT3SLS FIML 17.561 31.68 0.51 (80.817) (86.20 ) (74.11 ) 1,177.66 1002.54 1420.58 (2,683.67) (2,862.21) (2,471.51) 200.09 137.33 287.15 (888.4 3 ) (912.89 ) (868.28 ) 7,791.90 6983.17 8913.79 (16,650.20) (18,028.80) (14,892.50) 350.92 350.93 350. 90 (245.6 8 ) (247.29) (250.69) 28.34 16.5 3 0.2 3 (22.11) (23.81 ) (2.59 ) 7.60 10.48 0.0 3 (18.2 4 ) (19.24) (2.73 ) 0.35 0.41 138.93 (2.4 7 ) (2.42) (585.42) 0.2 1 0.3 4 35.78 (2. 60 ) (2.54 ) (20.4 9) 99.93 71.8 2 3.60 (560.44) (550.2 7 ) (17.32) 0.31 0.36 0.2 5 (1. 30 ) (1.31 ) (1.29 ) 31.19 32.52 29.33 (57. 90 ) (59.80) (56.87) 140.05 150.029 126.21 (1,381.550) (1,396.560) (1,374.51) 217.38 138.692 326.55 (381.925) (407.978) (350.92 ) Note: is a constant. is the current yie ld at for and are the rates of return at from Equation ( 3 7 ) and Equation ( 3 17 ) respectfully. is agricultural exports divided by imports at for and are the S&P dividend yield and ten year average price to earnings ratio. is Moody's seasoned AAA corporate bond yield at Note: Standard errors are within parenthesis below the respective coefficients. ** denotes statistical significance at 5% level and denotes statistical significance at 10% level PAGE 78 78 Table 4 7 Results from the r egression o f on Parameter ITGMM IT3SLS FIML 0.259 0.246 0.300 (0.292) (0.324) (0.274) 3.22 3. 264 3.614 (7.306) (8.315) (6.852) 0.45 0.338 0.500 (2.376) (2.744) (2.177) 16.78 13.561 19.898 (38.8 63) (45.706) (35.693) 0.38 0.382 0.398 (0.928) (1.174) (0.773) 0.02 0.040 0.000 (0.062) (0.070) (0.010) 0.11 0.114 0.000 (0.073) (0.082) (0.010) 0.00 0.003 0.128 (0.011) (0.012) (2.067) 0.00 0.003 0.048 (0.011) (0.012) (0.059) 0.09 0.442 0.101 (2.228) (2.555) (0.069) 0.00 0.003 0.002 (0.007) (0.007) (0.006) 0.16 0.181 0.164 (0.268) (0.285) (0.258) 1.27 0.594 1.726 (5.811) (6.223) (5.615) 1.67 1.215 2.038 (1.589) (1.703) (1.542) Note: is a constant. is the current yield at for and are the rates of return at from Equation ( 3 7 ) and Equation ( 3 17 ) respectfully. is agricultural exports divided by imports at for and are the S&P dividend yield and ten year average price to earnings ratio. is Moody's seasoned AAA corporate bond yield at Note: Standard errors are within parenthesis below the respective coefficients. ** denotes statistical significance at 5% level and denotes statistical significance at 10% level PAGE 79 79 Table 4 8 Results from the r egression of on Parameter ITGMM IT3SLS FIML 71 6.48 655.17 765.83 (920.55) (1,031.38) (864.65 ) 4,347.45 3 626.55 5,514.83 (22,641.60) (25,282.10) (21,636.20) 1,429.49 2,579.50 548.71 (7,558.64 ) (8,735.60 ) (6,892.76) 2 2,338.60 14 025.20 27 962.30 (118,770.00 ) (137,025.00 ) (111,174.00 ) 301.83 347.572 350.99 (2,424.37 ) (2,892.02) (2,179.70) 7.55 116.3 8 3.33 (30.20 ) (208.01 ) (29.00 ) 7.12 320.5 9 3.28 (30.72 ) (244.67 ) (29.52 ) 995.71 11.09 302.33 (6,410.61) (33.02 ) (6,124.87) 30.79 10.67 68.03 (188.06 ) (33.53 ) (178.75 ) 322.91 1 850.68 311.07 (223.2 2 ) (7,062.45) (211.6 1 ) 7.21 7.56 7.59 (21.18 ) (22.06 ) (20.5 9 ) 515.32 569.79 532.7 5 (808.51 ) (833.5 6 ) (791.50 ) 2,621.64 1,064.24 4,088.65 (18,640.90) (19,463.30) (18,108.90) 5,900. 35 4 638.14 6 ,602.14 (5,135.58) (5,314.01) (5,075.96) Note: is a constant. is the current yield at for and are the rate s of return at from Equation ( 3 7 ) and Equation ( 3 17 ) respectfully is agricultur al exports divided by imports at for a nd are the S&P dividend yield and ten year average price to earnings ratio. is Moody's seasoned AAA corporate bond yield at Note: Standard errors are within parenthesis belo w the respective coefficients. ** denotes statistical significance at 5% level and denotes statistical significance at 10% level PAGE 80 80 Table 4 9 Order of magnitude for the FIML, ITGMM, and IT3SLS estimators Parameter FIML A ITGMM B IT3SLS C 3 rd 2nd 1 st 1 st 2nd 3 rd 3rd 2nd 1 st 3rd 2nd 1 st 2nd 3rd 1 st 1st 2nd 3 rd 3rd 2nd 1 st 3rd 2nd 1 st 1st 3rd 2 nd 1st 3rd 2 nd 2nd 3rd 1 st A Iterated generalized method of moments. B Iterated three stage least squares. C Fu ll information maximum likelihood. PAGE 81 81 Figure 4 1. The times they are a changing, especially in 1972 Figure 4 2 Return series and the data gathering process over time Nominal Direct Government Payments Per Acre Nominal Illinois Cash Receipts Per Acre Nominal Illinois Value of Ag Production Nominal Illinois Residual Returns Nominal Illinois Cash Rents Nominal Illinois Land Price $0 $40 $80 $120 $160 Nominal return series Discontinuity in the DGP PAGE 82 82 Figure 4 3 ITGMM: actual and estimated return to Illinois farmland Figure 4 4 ITGMM: actual and estimated rate of return on Illinois farmland $100 $150 $200 $250 $300 Real Return Estimated Return 45% 30% 15% 0% 15% 30% 45% Real Rate of Return Estimated Rate of Return PAGE 83 83 Figure 4 5 ITGMM: actual and estimated change in the price of Illinois farmland Figure 4 6 ITGMM: actual and estimated Illinois farmland price $1,400 $700 $0 $700 $1,400 Real Change in Land Price Estimated Change in Land Price $1,500 $2,500 $3,500 $4,500 $5,500 Real Land Price Estimated Land Price Estimated Stand alone Land Price PAGE 84 84 Figure 4 7 IT3SLS: actual and e stimated return to Illinois farmland Figure 4 8 IT3SLS: actual and estimated rate of return on Illinois farmland $100 $150 $200 $250 $300 Real Return Estimated Return 45% 30% 15% 0% 15% 30% 45% Real Rate of Return Estimated Rate of Return PAGE 85 85 Figure 4 9 IT3SLS: actual and estimated change in the price of Illinois farmland Figure 4 10 IT3SLS: actual and estimated Illinoi s farmland price $1,400 $700 $0 $700 $1,400 Real Change in Land Price Estimated Change in Land Price $1,500 $2,500 $3,500 $4,500 $5,500 Real Land Price Estimated Land Price Estimated Stand alone Land Price PAGE 86 86 Figure 4 11 FIML: actual and estimated return to Illinois farmland Figure 4 1 2 FIML: actual and estimated rate of return on Illinois farmland $100 $150 $200 $250 $300 Real Return Estimated Return 45% 30% 15% 0% 15% 30% 45% Real Rate of Return Estimated Rate of Return PAGE 87 87 Figure 4 1 3 FIML: actual and estimated change in the price of Illinois farmland Figure 4 1 4 FIML: actual and estimated real Illinois farmland price $1,400 $700 $0 $700 $1,400 Real Change in Land Price Estimated Change in Land Price $1,500 $2,500 $3,500 $4,500 $5,500 Real Land Price Estimated Land Price Estimated Stand alone Land Price PAGE 88 88 Figure 4 1 5 ITGMM residual lag plot: return equation Figure 4 1 6 ITGMM residual lag plot: rate of return equation $80 $40 $0 $40 $80 $100 $50 $0 $50 $100 40% 20% 0% 20% 40% 50% 25% 0% 25% 50% PAGE 89 89 Figure 4 1 7 ITGMM residual lag plot: farmland price change equation Figure 4 1 8 IT3SLS residual lag plot: return equation $1,000 $500 $0 $500 $1,000 $1,250 $625 $0 $625 $1,250 $80 $40 $0 $40 $80 $100 $50 $0 $50 $100 PAGE 90 90 Figure 4 1 9 IT3SLS residual lag plot: rate of return equation Figure 4 20 IT3SLS residual lag plot: farmland price change equation 40% 20% 0% 20% 40% 50% 25% 0% 25% 50% $1,000 $500 $0 $500 $1,000 $1,250 $625 $0 $625 $1,250 PAGE 91 91 Figure 4 21 FIML residual lag plot: return e quation Figure 4 2 2 FIML residual lag plot: rate of return equation $80 $40 $0 $40 $80 $100 $50 $0 $50 $100 40% 20% 0% 20% 40% 50% 25% 0% 25% 50% PAGE 92 92 Figure 4 2 3 FIML residual lag plot: farmland price change equation $1,000 $500 $0 $500 $1,000 $1,250 $625 $0 $625 $1,250 PAGE 93 93 Figure 4 2 4 ITGMM time series residual plot : return equation Figure 4 2 5 ITGMM time series residual p lot : rate of return equation Figure 4 2 6 ITGMM residuals: farmland price change equation $100 $50 $0 $50 $100 50% 25% 0% 25% 50% $1,200 $600 $0 $600 $1,200 PAGE 94 94 Figure 4 2 7 IT3SLS time series residual plot : return equation Figure 4 2 8 IT3SLS time series residual plot : rate of return equation Figure 4 2 9 IT3 SLS time series residual plot : farmland price change equation $100 $50 $0 $50 $100 50% 25% 0% 25% 50% $1,200 $600 $0 $600 $1,200 PAGE 95 95 Figure 4 30 FIML time series residual plot : return equation Figure 4 31 FIML time series residual plot : rate of return equation Figure 4 3 2 FIML time series residual plot : farmland price change equation $100 $50 $0 $50 $100 50% 25% 0% 25% 50% $1,200 $600 $0 $600 $1,200 PAGE 96 96 Figure 4 3 3 ITGMM: Estimated yield and capital growth, and the rate of return Figure 4 3 4 IT3SLS: Estimated yield and capital growth, and the rate of return 45% 30% 15% 0% 15% 30% 45% Actual Rate of Return Estimated Yield plus Estimated Growth Rate of Capital 45% 30% 15% 0% 15% 30% 45% Actual Rate of Return Estimated Yield plus Estimated Growth Rate of Capital PAGE 97 97 Figure 4 3 5 FIML: Estimated yield and capital growth, and the r ate of return Figure 4 3 6 ITGMM: estimated capital appreciation and rate of return expectations 45% 30% 15% 0% 15% 30% 45% Actual Rate of Return Estimated Yield plus Estimated Growth Rate of Capital 3 2 1 0 1 2 3 Standard Score Estimated Capitalization Value Estimated Rate of Return PAGE 98 98 Figure 4 3 7 ITGMM: estimates of the rate of return interval and capitalization value Figure 4 3 8 IT3SLS: estimated capital appreciation and rate o f return expectations 3 2 1 0 1 2 3 4 Standard Score Upper Interval Limit Estimated Capitalization Value Lower Interval Limit 3 2 1 0 1 2 3 Standard Score Estimated Capitalization Value Estimated Rate of Return PAGE 99 99 Figure 4 3 9 IT3SLS: estimates of the rate of return interval and capitalization value Figure 4 40 FIML: estimated capital appreciation and rate of return expectations 3 2 1 0 1 2 3 4 Standard Score Upper Interval Limit Estimated Capitalization Value Lower Interval Limit 3 2 1 0 1 2 3 Standard Score Estimated Capitalization Value Estimated Rate of Return PAGE 100 100 Figure 4 4 1 FIML: estimates of the rate of return inte rval and capitalization value Figure 4 42. Residual returns to Illinois farmland less the cash rental price 3 2 1 0 1 2 3 4 Standard Score Upper Interval Limit Estimated Capitalization Value Lower Interval Limit $130 $65 $0 $65 $130 Average Excess an acre Residual returns in excess of nominal cash rents Average Excess = $8.26 PAGE 101 101 Figure 4 43 Annual average Figure 4 44 Annual when the rate increases from one ye ar to the next 0% 3% 6% 9% 12% 15% Annual Average 3 month T bill Rate 0% 4% 8% 12% 16% PAGE 102 102 Figure 4 4 5 Relationship between and Figure 4 46 First difference of changes in and the consumer price index 3% 0% 3% 6% 9% 12% 15% Annual Average Change in Food Price Annual Average 3 month T bill Rate 9% 6% 3% 0% 3% 6% 9% First Difference of the Change in the Personal Consumer Price Index First Difference of the Change in the Price of Food PAGE 103 103 Figure 4 47 Standard score of and Figure 4 48 Annual and annual average 4 3 2 1 0 1 2 3 4 Standard Score Change in the Price of Food less the Real 3 month Tbill at t 1 Change in Real Illinois Farmland Price 1966 1974 1976 1977 1998 2005 2006 9% 6% 3% 0% 3% 6% 9% Average Excess = 1.1% Annual Food Price Change in Excess of the 3 month T bill PAGE 104 104 Figure 4 49 Real and average real Illinois farmland price per acre Figure 4 50. Standard score of and 1966 1974 1976 1977 1998 2005 $0 $1,000 $2,000 $3,000 $4,000 $5,000 Average Real Illinois Land Price Real Illinois Land Price 4 3 2 1 0 1 2 3 4 Stamdard Score Change in the Price of Food less the Real 3 month Tbill at t 1 Real Illinois Farmland Price PAGE 105 105 Figure 4 51. and Figure 4 52 and 0.00 0.50 1.00 1.50 2.00 $0 $50 $100 Ratio Billions of Dollars Real Agricultural Exports Real Agricultural Imports Ratio of Exports to Imports 0.20 0.20 0.60 1.00 1.40 1.80 $1,000 $500 $0 $500 $1,000 $1,500 Ratio Dollars per acre Change in Real Illinois Farmland Price Ratio of Exports to Imports in Year t 1 PAGE 106 106 Figure 4 53 Standard score of and 2 1 0 1 2 3 Standard Score Ratio of Agricultural Exports to Imports at time t 1 Real Illinois Farmland Price PAGE 107 107 CHAPTER 5 DISCUSSION AND CONCLUSION This research examines whether the return people expect to earn from farmland in agricultural production justifies the price of farmland. In general, the empirical results ind icate that people appropriately price farmland, or that people use market fundamentals to determine farmland prices consistent with economic theory More specifically, I fail to reject the efficient market hypothesis that people rationally for m expectatio ns of the return to farmland, and based on these expectations appropriately bid on farmland. Implications of E mpirical R esults From a research perspective, the results of the empirical model oppugn the validity of conventional present value model s of farml and price The empirical results offer three significant insights into the lackluster performance of the present value model in previous farmland valuation research. First, the rate of return on government securities or other liquid financial instruments often do not reflect the true opportunity cost of farmland capital. Conventionally, models based on present value theory in the farmland valuation literature use the rate on these securities to discount agricultural returns. By construction, these models force the opportunity cost of having capital in these securities to equal the opportunity cost of having capital in farmland. The cost of transacting in the farmland market, however, significantly exceeds the cost of transacting in a standardized market for tradable securities, and substantial technological advances must occur before the flow of farmland equity remotely resembles the flow of equity in the financial sector. Figure 2 1 depicts the actual rate of PAGE 108 108 retu rn on government securities and on Illinois farmland. Any analysis of the farmland market that constrains the two rates to equal each other likely imposes an outcome of irrationa lit y from the onset. Second, an assessment of the rationality of the farmla nd market should not entirely depend on the discount rate of the non farm economy. As suming transaction costs impede capital from flowing in and out of the farm economy, the discount rate of the farm and non farm sectors m ight not equilibrate in the short run even in a rationally functioning farmland market. The empirical results find that the return people expect to earn from farmland in agricultural production determines the price of farmland, which contradicts previous research that found predictable e xcess returns. To avoid using an exogenously determined discount rate, the current research constructs a system of equations that determines the discount rate of farmland endogenously Third, previous returns to farmland reflect expected returns to farm land in so much as the previous state of the farm economy reflects the future state of the farm economy. Again, the empirical results of this research found that the return people expect to earn from farmland in agricultural production determines the pric e of farmland, which contradicts research that found predictable excess returns This research however, forecasts returns to farmland using the previous return to farmland in conjunction with the change in the price of food less the 3 month T bill and th e ratio of agricultural exports to imports. Chapter 2 presents studies that use a vector auto regression framework to describe the evolution of agricultural returns. The logic of this framework follows from the identification argument set forth by Sims ( 1980). The current research argues in the rapidly changing farm economy of the 1970s and 1980s, previous returns PAGE 109 109 to farmland did not contain sufficient information about expected returns. Additionally, a The r esidual return and the rental price of actual farmland returns failed to meet expected farmland returns. Researchers must therefore evaluate the benefit of using mathema tical arguments to identify the long run evolution of agricultural returns against the benefit of using theoretical arguments to identify and structure short run phenomena. The current research leaves the evaluation for future research. The efficient mark et results also have two implications for investors. First, the results provide evidence against the existence of profitable short term trading strategies, which implies fads in investor sentiment and rational bubbles do not exist because market fundament als rationally explain the price of farmland. Second, the results discredit the use of optimal timing strategies as a means of determining when to enter or exit investments in farmland because the price of farmland at any point in time should reflect the intrinsic value of farmland. From a policy perspective, the empirical results have three important implications. First, the results imply that new agricultural policy initiatives cannot allocate resources more efficiently than the uncoordinated efforts of people in the market for farmland (the current study, however, does not attempt to assess efficiency that can result from the removal of current agricultural policy). Second, the results suggest that to enhance the effectiveness of agricultural policy ob jectives without want of efficiency, new farmland policy initiatives should focus on manipulating the factors that form the basis of the expectations of people in the market for farmland. Third, the present research also PAGE 110 110 suggests agricultural policy simul taneously affects the expectation of return to farmland and the rate at which people discount the return expectation. Therefore, people will capitalize into the price of land any policy incentives that attempt to increase current returns in agriculture. T he R esidual Return and the Rental Price of Illinois Farmland To complement the empirical results, this section presents an analysis of some variables that in theory influence the expectations of people in the farm sector. The analysis provides further sup port of the efficient market hypothesis and leads to a radically powerful but simple finding about the farm economy in Illinois from 1976 to 1984 ; either actual farmland returns failed to meet expected farmland returns, significant errors exist in the data spanning the period, or some combination of failed exp ectations and data errors exist The residual return accrues to the fixed factor of production. As a fixed factor, farmland earns a residual return. Farmland however, has no use for money. People w ho own farmland own the right to claim the residual return and own the right to rent the property. They farm their farmland if they expect to earn a residual return in excess of the going rental price. A person who pays to rent farmland (renter) buys the right t o claim the residual return. R enter s rent farmland if they expect the residual return to equal or exceed the re t al price. Figure 4 42 depicts the nominal residual return in excess of the nominal rental price from 1972 to 20 08. The average excess during the period was $8.26 an acre. The excess represents the premium a renter accrues for production risk. Apart from 1979, the rental price exceeds the residual return from 1976 to 1984. The excess return in 1979 was only $6.8 8, or $1.37 less than the average excess. PAGE 111 111 How could the average rental price surpass the average residual return for nine consecutive years? This research presents t wo plausible explanations. The first explanation follows from a logical progression of ev ents. People form an expectation of return and pay an appropriate rental price for farmland at the beginning of the year. At the end of the year, however, the residual return does not meet the expectation. The second explanation puts forth the possibili ty that the cash rent and residual return details these three explanations. A simple argument forms the foundation for the first explanation. If people who pa id to ren t farmland fail ed to anticipate rising input costs, then the cost of input s could outpace the price of outputs over the course of a year For the cash rental price to track farmland price, but exceed the residual return to farmland in eight out of nine y ears, people who rented and owned farmland must have failed to anticipate the rising cost of debt and other inputs. Figure 5 1 shows the nominal average price and average rental price of Illinois farmland rose conti nually from 1972 to 1981, while the nominal residual return trended downward from 1974 to 1981. Thus, the price and cash rental price of farmland and the residual return to farmland behave consistently with the explanation that the residual return never m et the expectations of people in the market for farmland. The rental price in excess of the residual return offers simple but powerful evidence against fads in investor sentiment and rational bubbles. Bubbles and fads arise when people continually disrega rd market fundamentals and form price expectations using speculative information. A person wishing to rent farmland, PAGE 112 112 however, does not benefit from a higher rental price of farmland, which prevents a bubble or fad from arising in the farmland rental marke t. The spread between the rental price of farmland and the residual return to farmland from 1973 to 1984 adds credibility to the argument that the actual res idual return did not live up to the expected residual return Illinois agriculture underwent a tra nsformation in 1973. The immediate dispersion following 1973 in the normalized agricultural statistics in Figure 4 1 suggests the transformation was radical. Perhaps after 1973, farmland owners began capitalizing di stant return expectations into the price of farmland. The second explanation results from farmland price statistics. In Despite the progress made, important issues in f actology remain in an unsatisfactory state. USDA still has far to go in describing in detail how its published data are constructed. For intelligent use of these data in econometric work, the details are crucial. For example, Hauver and Ball (1991) desc ribe and present data for a new total factor productivity index. They made great strides in meaningful aggregation, but are still stuck with real estate data before 1970 that are based in part on farm sales, as discussed earlier. And the reader still get s no clue how these underlying data were constructed. Econometric land mines remain in place. The USDA has made substantial changes to their statistics long after the original release. For example, in August of 1977 the USDA revises the estimates of farm income in 1974, 1975, and 1976. In billions of dollars, the estimate of farm income in 1974, 1975 and 1976 went from $26.5, $25.6, and $22.8 down to $21.6, $24.3, and $20.0 respectively ( AgOutlook ). People willingly paid a rent in excess of the residu al return in eight out of nine years following 1974. The expectations of renters align with the expectations of people transacting in the farmland market. The land mine argument put forth by Gardner, PAGE 113 113 however, potentially nullifies statistical inference d rawn from samples encompassing the period. Summary of Results The empirical results show people appropriately capitalize the expected returns to farmland. The value of farmland that results from the capitalization value of the expected agricultural return s does not significantly differ from the price of farmland. Analysis of the residuals from the system of equations favors the joint hypothesis of market efficiency and correct model specification. Further analysis of the USDA residual retur n and cash re nt statistics show the rental price exceeds the residual returns for nearly nine consecutive years. The second longest period when the rental price exceed ed the residual return last ed three years. Since a bubble in the farmland rental market can not exist people who paid the higher rent expected farmland to earn a higher residual return. The argument is consistent with the efficient market hypothesis: expected returns determine the price of farmland. But the rent and residual return statistics could con tain large measurement errors during the 1970s and 1980s. Such an explanation cannot rule out the possibility that the farmland price statistics also contain large measurement errors. Lastly, large changes in the price of food, the T bill rate, and chang es in the values of agricultural exports and imports precede large changes in the price of farmland throughout the sample. Given the empirical results, the congruenc e between the capitalized value and the ra te of return and the e vidence of people paying a rental price above the residual return for nine years the earnings expectations of people went unmet I conclude, market fundamentals cause changes in the price of Illinois farmland. PAGE 114 114 Suggestions for Future Research Contrasting the results of this resear ch with previous work suggests the opportunity cost of capital in farmland can rationally deviate from conventional measurements of the discount rate (e.g. T bills, commercial paper rates, and other portfolio constructs) for temporary periods The exact c ause of the deviations remains unclear. Future research should incorporate the endogenous discount rate into transaction costs models or models with time varying risk premiums to establish better the determinants of the deviations. A Parting Note In the i ntroduction of Anatomy of an American Agricultural Credit Crisis (Peoples et al. 1992), Dr. Emanuel Melichar wrote: In 1955, when I was a student and still knew everything, I wrote the are near the expected peak of the farm real estate cycle and future prospects of a level o f income to support land prices at this peak are not five years later, I was pointing out that real income from farmland had risen at an ave rage annual rate of at least 4% during the intervening period! I also then reported at the Agricultural Outlook Conference in 1980 that, based on asset pricing theory, the price of farmland in 1980 implied expectations of continued earnings growth at abou t the same rate. Calculations using the five year forecasts of farm commodity prices published at that time in Business Week and Farm Journal would easily result in such earnings growth to 1985. Farmland was appropriately priced in the light of such fore casts. I had also just published, in the American Journal of Agricultural Economics, a table showing that, if expectations of annual growth in real earnings of farmland were to fall from 4% to 0% (flat earnings), farmland prices would theoretically fall by 52%. This soon became reality, and farmers and lenders who had make the most enlightened calculations and forecasts went bankrupt. Under similar circumstances, it has to happen again. Anything else would be irrational! In hindsight in the booming Illi nois farm economy of the 1970s and 2000s, betting against rising farmland prices was, perhaps, pure speculation. PAGE 115 115 Figure 5 1 N ominal Illinois farmland and rental price s and residual returns $10 $60 $110 $160 $210 $260 $0 $1,000 $2,000 $3,000 $4,000 $5,000 Return per acre Price per acre Nominal Illinois Farmland Price Nominal Cash Rental Rate of Illinois Farmland Nominal Residual Return to Illinois Farmland PAGE 116 116 APPENDIX A THE SCHMITZ MODEL The price of an asset equals the present value of all return expectations: ( A 1 ) where equals the price of the asset in represents the return in symbolizes the expectation operator, and denotes the information set in In the return expectation in becomes In the denominator, equals the rate of discount rate (or the interest rate representing the opportunity cost of capital) in and the multiplication operator indicates the product of the sequence of from period through period The lower bound of the summation operator indicates that t he sequence of the expectation of returns begins in To derive the Schmitz (1995) model, subtract from in Equation ( A 1 ) : ( A 2 ) where symbolizes the change in the price of an asset from period to period Focusing on the right hand side of Equation ( A 2 ) multiply and divide the first term in brackets by : ( A 3 ) PAGE 117 117 Since remains constant, place inside the summation operator. The lower bound of the multiplication operator in the denominator of Equation ( A 3 ) changes from to by placing inside the summation operator: ( A 4 ) The first term in Equation ( A 4 ) expands to: ( A 5 ) Extra cting the return expectation in that people formulate in from the second term in brackets on the right hand side of Equation ( A 5 ) changes the lower bound of the summation operator from to and leaves: ( A 6 ) Substitute the right hand sides of Equation ( A 5 ) and Equation ( A 6 ) into Equation ( A 4 ) to obtain: ( A 7 ) Focusing on the second term in brackets in Equation ( A 7 ) bring outside of summation operator so that the lower bound of the multiplication operator changes from to : ( A 8 ) PAGE 118 118 From Equation ( A 1 ) the summation operator in the second term of Equation ( A 8 ) equals the price of the asset in : ( A 9 ) Substitute Equation ( A 9 ) into Equation ( A 8 ) and combine the last two terms of Equation ( A 8 ) into a single summation operator to yield: ( A 10 ) Let represent the change in the expectation returns from period to period or the term in the summ ation operator in Equation ( A 10 ) : ( A 11 ) to obtain the same model Schmitz (1995) estimates: ( A 12 ) The analog to the first difference formulation in Equation ( 3 3 ) in levels equals: ( A 13 ) PAGE 119 119 APPENDIX B RECURSIVE SYSTEM EST IMATION The in estimable system consists of Equations ( 3 1 ) ( 3 2 ) and ( 3 3 ) reproduced here : ( B 1 ) ( B 2 ) ( B 3 ) To ease the notational burden, substitute Equation ( B 1 ) into Equation ( B 2 ) and combine similar terms: ( B 4 ) and substitute Equation ( B 1 ) and Equation ( B 2 ) into Equation ( B 3 ) : ( B 5 ) Next, define the first term in brackets on the right hand side of Equation ( B 4 ) as: ( B 6 ) PAGE 120 120 and substitute Equation ( B 6 ) into Equation ( B 4 ) to obtain: ( B 7 ) Finally, define the first term in brackets on the right hand side of Equation ( B 5 ) as: ( B 8 ) and define the second term in brackets on the right hand side of Equation ( B 5 ) as: ( B 9 ) and substitute Equation ( B 8 ) and Equation ( B 9 ) into Equation ( B 5 ) to obtain: ( B 10 ) After condensing the notation, Equations ( B 1 ) ( B 2 ) and ( B 3 ) become, respectively ( B 11 ) ( B 12 ) ( B 13 ) Present value theory suggests the price of an asset equals the present value of the returns people expect from the asset. Consequently, the current value of expected returns determines price. The economic literature assumes an exogenous phenomenon sets the discount rate. Thus, the economic literature specifies that an exogenous interest rate determine s the price of an asset. PAGE 121 121 This research acknowledg es the conditions, under which an exogenous phenomenon sets the proper rate of discount, do not hold in the market for farmland. Therefore, this research deviates from the economic literature by model ing the price of farmland as a function of expect ation of the return to farmland and the expectation of the rate of return to farmland. Hence, this research implies the expectation of the return to farmland determines the expectation of the rate of return to farmland, and both the return expectation and the e xpectation of the rate of return determine the price of farmland. Consequently, the system of Equations ( B 11 ) ( B 12 ) and ( B 13 ) make up a pseudo recursive system. The system solves recursively in the sense that exo genous factors and predetermined variables identify the endogenous variable in Equation ( B 11 ) In Equation ( B 12 ) and other predetermined variables identify and determine Lastly, in Equation ( B 13 ) and identify and determine In this research, exogenous and predetermined vari ables determine Equation ( B 11 ) Equation ( B 11 ) determines Equation ( B 12 ) and Equations ( B 11 ) and ( B 12 ) determine Equation ( B 13 ) Unlike in a typical recursive system, howe ver, the dependent variable in lower equations do not enter upper equations as a distinct endogenous variable, and In Equation ( B 11 ) represents a predetermined variable and the exogenous variables include the constant and the random error term The predetermined variables and exogenous variables determine and identify In PAGE 122 122 Equation ( B 12 ) and represent the predetermined variables and the exogenous variables include the constant and the random error term Again the predetermined variables and exogenous variables determine and identify which in turn are used to calculate Finally, in Equation ( B 13 ) and represent the predetermined variables and the exogenous variables include the constant and the error term Once again the predetermined variables and exogenous variables determine and identify which in turn are used to calculate In theory predetermined and exogenous variables determine and identify all dependent and endogenous variables Setting the system of Equations ( 3 4 ) ( 3 8 ) and ( 3 12 ) into operation illustrates the identification scheme. By assumption, for all the white noise random error terms satisfy the conditions: ( B 14 ) Thus, taking the expectation on both sides of the system of Equations ( 3 4 ) ( 3 8 ) and ( 3 12 ) generates: ( B 15 ) ( B 16 ) ( B 17 ) PAGE 123 123 To verify the identification o f the variable predictions, substitute Equation ( B 15 ) into Equation ( B 16 ) to obtain: ( B 18 ) Next, substitute Equation ( B 15 ) and Equation ( B 16 ) into Equation ( B 17 ) to obtain: ( B 19 ) Equations ( B 15 ) ( B 16 ) and ( B 17 ) contain only exogenous and predetermined variables. To condense the notation, define the term in brackets on the right hand side of Equation ( B 16 ) as: ( B 20 ) and substitute Equation ( B 20 ) into Equation ( B 16 ) to obtain: ( B 21 ) Define the first term in brackets on the right hand side of Equation ( B 17 ) as: ( B 22 ) and define the second term in brackets on the right hand side of Equation ( B 17 ) as: PAGE 124 124 ( B 23 ) and substitute Equation ( B 22 ) and Equation ( B 23 ) into Equation ( B 17 ) to obtain: ( B 24 ) In the fitted form the system of Equations ( B 11 ) ( B 12 ) and ( B 13 ) yields: ( B 25 ) ( B 26 ) ( B 27 ) To understand better the mathematics of Equat ion ( 3 3 ) drop the expectation of farmland price, and set : ( B 28 ) and rearrange Equation ( B 28 ) to yi eld: ( B 29 ) If the equality in Equation ( B 29 ) holds, and change at the same rate. Since cannot change, the capitalization value, the first ter m in brackets on the right hand side of Equation ( B 29 ) must fully account for changes on the left hand side of Equation ( B 29 ) People should capitalize part of the return they expect from PAGE 125 125 farmland into the price of farmland. If changes according to the current value of the return exp ectation, then people capitalize: ( B 30 ) PAGE 126 126 APPENDIX C THE FAMA MODEL Fama (2002) uses the concept underlining the Gordon (1962) dividend growth model to estimate the long term unconditional expectat ion of the return on stocks. Fama (2002) notes a stationary dividend price ratio, implies the compound rate of dividend growth approaches the compound rate of capital gain yield: ( C 1 ) Therefore, Fama approximates capital growth, using only market fundamentals, by estimating dividend growth. T o obtain the long term unconditional expectation of stock growth, Fama adds the long run average dividend yield to the estimate of the real dividend growth from the following model: ( C 2 ) where is the real return on the S&P portfolio for period and and denote the nominal S&P dividends and earnings in Fama (2002) cites Campbell and Shiller (1989) in noting that varies through time because of varying expectations o f conditional point in time stock return and dividend growth. Stationary stock and dividend growth, however, implies a stationary Fama (2002) adds the long term average dividend yield, PAGE 127 127 to the estima te from Equation ( C 2 ) to approximate the unconditional rate of return on stocks : ( C 3 ) The implication of the stationarity of extends to this research. The stationarity o f implies the growth of approaches the growth of : ( C 4 ) Further, if determines then: ( C 5 ) PAGE 128 128 APPENDIX D THE MARKET MODEL To descri be the market model and farmland price determination, this research uses the formal discussion of an efficient capital market by Fama (1976). This research tries to determine whether the expectation of the return to farmland determines the price of farmla nd. Therefore, the market model and price formulation process differs from the outline by Fama (1976). Assume all events transpire at discrete points in time. At people access the information set whe n formulating expectations of future random variables. The information set contains the information available at which is relevant for determining the price of an asset at is a subset of At most, contains but can contain less information. Fama (1976) describes the contents of Further, contains what people know in about the processes describing the evolution of the state of the world through time, including current and past values of variables and the relationship between variables. Define as the price of asset in where and equals assets in the ec onomy. A rational assessment of the information set in equals The assessment of the joint probability density function of all asset prices in made by people in equals The joint pro bability density functions in imply marginal density functions in for the price PAGE 129 129 of asset Specifically, implies and implies The mean of equals the expectation Following Fama (1976), market efficiency implies people make use of all relevant information when determ ining the price of assets. If people make use of all relevant information, then: ( D 1 ) Market efficiency implies: ( D 2 ) According to Fam a (1976), Equation ( D 1 ) implies Equation ( D 2 ) The two eq uations together imply people have access to all relevant information when determining the price of assets, and people use the information correctly. The first model of market equilibrium that Fama (1976) proposes simply states that in the market sets the price so that the expectation of the return to asset from time to is positive: ( D 3 ) This research creates a slight variation of the market model by Fama (1976). In this study, people set the price of farmland at a level that capitalizes and ensures always remains positive. At the end of period people form an expectation of the retu rn to farmland, The determination of the price of farmland, marks the beginning of PAGE 130 130 period Unlike the market model by Fama (1976), people know and determine using and People set to ensure meets the following condition: ( D 4 ) Equation ( D 4 ) implies: ( D 5 ) If Equation ( D 4 ) holds, Equation ( D 5 ) holds with equality. Rational people with perfect foresight set to ensure Equation ( D 5 ) holds with equality. Realistically, risk and transaction costs prevent the equality, but the market model in equation ( D 4 ) implies the price of farmland changes when people change PAGE 131 13 1 APPENDIX E E CONOMETRIC PROCEDURE Following the notation from Hayashi (2000) the system of Equations ( 3 1 ) ( 3 2 ) and ( 3 3 ) consists of linear equations. Equation ( 3 1 ) contains parameters, Equation ( 3 2 ) contains parameters, and Equation ( 3 3 ) contains parameters. The system contains parameters. Each equation in the system shares the same instruments for moments. Thus, the system contains over identifying restrictions. Let represent the vector of regressors of dimension where ( E 1 ) and let represent a conformable vector of coefficients, where : ( E 2 ) Lastly, let symbolize the unobservable error term for equation The system of Equations ( 3 1 ) ( 3 2 ) and ( 3 3 ) in Matrix notation equals: for ( E 3 ) PAGE 132 132 Let represent the vector of instruments common to the linear equations, where equals: ( E 4 ) The determination of the variables in occurs be fore Thus, the variables in satisfy the following orthogonality conditions: for ( E 5 ) The orthogonality or moment conditions equals instruments times the equat ions. Let contain each unique and non constant element in and In accordance with Assumption 4.2 in Hayashi (2000), assume is jointly stationary and ergodic to ensure: ( E 6 ) Let represent a vector containing the orthogonality conditions: ( E 7 ) or in compact notation, The moments represent the difference between the return or price, and the prediction of the price or return : ( E 8 ) The information in reduces the difference between the prediction and the actualization. To satisfy the rank condition for identification, by assumption, the block PAGE 133 133 diagonal matrix and the sub matrices of in Equation ( E 9 ) must have full rank, : ( E 9 ) The jointly stationary and ergodic assumption about that ensures the condition in Equation ( E 6 ) implies has finite second moments and follows a martingale difference sequence. Thus the sample moments converges in distribution to: ( E 10 ) where The sample analog to Equation ( E 9 ) equals: ( E 11 ) Since the instruments over identify the moments, which prevents the inversion of Instead, a positive definite and symmetric weighting matrix minimizes the quadratic crite rion function: ( E 12 ) Thus, the multiple equation GMM estimator solv es: ( E 13 ) PAGE 134 134 The estimator in Equation ( E 13 ) produces a consistent, but generally inefficient estimator. Hansen (1982) shows how to obtain the parameter vector with the smallest asymptotic variance: simply set the weighting mat rix equal to the inverse of the asymptotic covariance matrix (the covariance of the moment conditions): The weight Since, the efficient GMM estimator sets and solves: ( E 14 ) To check the robustness of the results to different system estimators, I also estimate the equation system using iterated three stage least squares and full information maximum likelihood. 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Martin, 1966, A Methodology for Predicting U.S. Farm Real Estate Price Variation, Journal of Farm Economics 48, 378 393. Vantreese, Valerie L. Jerry R. Skees, and Michael R. Reed, 1986, Using Capitalization Theory to Model Farmland Prices, North Central Journal of Agricultural Economics 8, 135 142. Veeman, M. M., X. Y. Dong, and T. S. Veeman, 1993, Price Behavior of Canadian Farmland, Canadian Journal of Agricultural Economics 41, 197 208. PAGE 144 144 Weersink, Alfons, Steve Clark, Calum G. Turvey, and Rakhal Sarker, 1999, The Effect of Agricultural Poly on Farmland Values, Land Economics 75, 425 439. PAGE 145 145 BIOGRAPHICAL SKETCH Cody Dahl was born in Urbana, I llinois in 1981. After graduat ing from Black Hawk community college with Cody went on to receive his degree in a gribusiness, f arm and f inancial m anagement from th e University of Illinois, ate in food and resource economics from the University of Florida. 