DEPARMNI4T OV EcOOAICS & SOC-OLO! COLORP.,Uo STATE Ijj!RIy ro1aT COLLINS, OOk ECONOMIC RESEARCH IN THE USE AND DEVELOPMENT OF RANGE RESOURCES
ADJUSTMENTS IN THE RANGE LIVESTOCK INDUSTRY
Report No. 3
Committee on the Economics of Range Use and Development of
Western Agricultural Economics Research Council 1961
ECONOMIC RESEARCH IN THE USE AND DEVELOPMENT
OF RANGE RESOURCES
Report No. 3
Adjustments in the Range Livestock Industry
Committee on Economics of Range Use and Development of the
Western Agricultural Economics Research Council Ft. Collins, Colorado, August 11 and 12, 1961,
The Committee on Economics of Range Use and Development of the
Western Agricultural Economics Research Couincil has met annually over the last several years to consider problems and new areas of research in Western range use and improvement. This is the second numbered report and the fourth report of the series.
The Committee's first report, released in 1957, was entitled "Economic Research in the the Use and Development of Range Resources--A Methodological Anthology." The report was unnumbered.
The second report released in 1959 was entitled "Economic Research in the Use and Development of Range Resources--Economics of Range and Multiple Use." This report was identified as Report No. 2.
In January of 1961 the Range Committee met jointly with the Committee on the Economics of Water Resources Development of the Western Agricultural Economics Research Council. The theme of this conference was "Methodology for Measuring Change in Value of Products from Altered Management of Multiple Use Watershed Lands." The proceedings of this joint meeting was published as Report No. 9 of the Water Committee.
The report herein includes the papers and discussions presented at the Range Comte' annual meeting in Fort Collins, Colorado, on August 11 and 12, 1961. This report focuses attention on the current adjustment problems of the range industry and individual ranch firms.
The program title was selected by the Range Committee at its business meeting in Tucson, Arizona. At that time three research proposals were submitted to the Committee. It was pointed out that two
of the proposals had been subjects discussed by speakers at previous meetings. The third proposal had not. Therefore, the committee decided to make this third proposal the subject for discussion at the meeting represented by this report.
The program subcommittee was primarily responsible for designing
the program and selection of speakers. Each member of the Range Committee made constructive suggestions. The program subcommittee was J; R. Gray, chairman, Calvin C. Boykin, Perry F. Philipp, D. F. Jones, and C. 0. McCorkle, Jr. The report was processed under the direction of N. Keith Roberts at Utah State University.
The attendance of committee members and guest speakers at these and previous meetings of the Committee was made possible by a generous grant from the Farm Foundation. Reproduction costs associated with this report were paid from funds contributed by the Agricultural Experiment Stations of the twelve western states and the ERS-USDA.
James R. Grey, 1961 Chairman
Committee on Economics of Range
Use and Development
N. K. Roberts, Editor,
Report No. 3
ECONOMICS & SOCIOLOGY
COLORADO STATE UNIVERSITY
FORT COLLINS, COLORADO
TABLE OF CONTENTS
PART I TECHNIQUES OF RESEARCH IN INDUSTRY WIDE ADJUSTMENT PROBLEMS
Experimental Design and Accumulation Problems
Wilbur R. Maki 1
Discussion- D. D. Caton. 23
Analysis Techniques in Industry-Wide Adjustments
Don Bostwick .. 35
Discussion William G. Brown 57
PART II IMPACT OF ADJUSTMENTS AT THE FIRM LEVEL
Decision Theory and Range Livestock Operations
R. J. McConnen 61
Discussion- N. K. Roberts .. 91
Adoption of Range Improvement Practices
Ronald D. Krenz ..... 97
Discussion Harry G. Sitler .. .... 115
PART III MARKET AND POLICY EFFECTS ON RANCH ADJUSTMENTS
Market Effects on Ranch Adjustments
R. E. Seltzer . ... 117
Discussion- D. F. Jones .... .. ... 135
The National Land Reserve Adjustments in the
Range Livestock Industry
Harold R. Hockmuth ...... 137
Roster of Attendance at the 1961 Meeting of the Range
Committee, Fort Collins, Colorado,
August ll-12, 1961 ......... 151
EXPERIMENTAL DESIGN AND ACCUMULATION PROBLEMS By Wilbur R. Makil'
The operation of the cattle cycle illustrates an accumulative economic process of broad national scope but yet of wide local diversity in its impact on resource use. The 17 western states, for example, account for 60 percent of the beef cows on hand at the low point of the cattle cycle. During the upturn of the cycle, however, these states account for 70 percent of the net change in beef cow numbers in the United States, while during the downswing of the cycle the decline in beef cow numbers in these states is over 90 percent of the net decline for the nation as a whole.
Much of the variability in the western cattle industry occurs on the marginal range land. Moreover, the accumulation of cattle numbers and the corresponding increase in stocking rates on range land actually may induce drought conditions, thus sharply reducing the ability of these lands to handle the existing cattle numbers. Because of this and related phenomena the question might be asked: How can the man-land relation in the West sustain the long-run ecological balance of plant and animal life in the range areas? In response to this question, I would like to focus our discussion on the nature of the cattle cycle and its relation to the development of appropriate research procedures for dealing with range management problems. Finally, I would like to direct our attention to the role of experimental research in improving decision making processes in the livestock industries and particularly in the cattle industry of the West.
Associate Professor, Department of Economics and Sociology, Iowa State University, Ames, Iowa.
Experimental Approaches in Economic Research
At the outset we can observe a remarkable lack of experimental research on industry adjustment problems. Except for the interdisciplinary studies in plant and animal nutrition' and the controlled experiments in retail merchandising, I empirical work in agricultural economics is almost wholly dependent on the use of cross-sectional survey and time-series data. Nevertheless, the "systematic study of human relations by making observations under conditions of control" is recognized by one eminent sociologist as an important way to appraise, by scientific methods of research, the effectivbness of specific means to achieve certain ends and to isolate causeand-effect relationships in the complicated area of human relations.4Analyses of industry-wide adjustment problems that involve observations of economic phenomena under conditions of control (obtained by selecting two groups of like elements subject to different treatment) would appear' also, to be potentially important contributions to achieving desired patterns and rates of change in our economic structures.
Before we attempt to examine the possible uses of experimental design in dealing with accumulation problems, the case for a modified stimulusresponse causality will be reviewed. In this context, a recursive model of the beef economy is presented as a system of causal relations. The
William G. Brown, Suggested methods of the analysis of experimental data relating to production functions, Proceedings, Western Farm Economics Association, Twenty-third Annual Meeting, August 23-26, 1960, pp. 356-372.
Murray A. MacGregor, Uniformity trial experiments in marketing
research, Methods in Research, Paper Number 6, Department of Agricultural Economics, Cornell University, September, 1958.
4/ F. Stuart Chapin, Experimental Designs in Sociological Research, Harper and Brothers, New York, 1955, p. 29.
findings based on the aggregative analysis are presented as a series of hypotheses to serve as a guide for more rigorous examination and analysis. Finally, alternative experimental approaches are examined as part of research strategy in data construction and utilization.
Control of a Multivariable System
Changes in the number of beef cows on hand, January 1, together with changes in the number of steers on hand, account for subsequent variations in commercial cattle slaughter and market prices. An increase in feeder calf prices, which follows closely an increase in slaughter, steer prices, encourages inventory accumulations of steers by the beginning of the following year and of cows, heifers and calves 2 years later. The increase in calves is associated with an increase in heifers a year later, while the increase in heifers is associated with an increase in beef cows during the same period. Using the least squared method, a direct. association can be estimated between changes in feeder calf prices in a given year and changes in beef cownumbers and an indirect association can be estimated through changes in heifer and calf numbers; the estimated values of the entire set of inventory, slaughter and price relationships are summarized in tables I and 2. To lay the groundwork for further discussion of research strategy, the interacting components of the beef economy are examined in detail.
Beef cattle inventories
Xn the statistical model of the beef economy (based on time series
data for the United States), the number of a specified class of cattle and calves on farms and ranches, January 1, is related to (1) the number of other specified cattle on farms a year earlier, (2) the number of cows
Table 1, Estimated change in total number of selected classes of cattle on hand, January 1, associated with
a 1-unit change in specified explanatory variables, United States, 1949-1958.
Cattle on hand, January 1 Feeder calf price
Heifer and Constant
Beef cattle Beef calves, Beef heifers, Beef cows, Lagged Lagged cow, FIS term R
inventory lagged 1 year lagged 1 year lagged 1 year 1 year 2*years 3
H21t-l H22t-1 H23t-1 P2t-1 P2t-2 C2jt-1 1
Calves, H21t 0.664' 95.356 -10.8 0.964
21 (0.049) (32.611)
Heifers,H22t 0.232 53.531' 780.2 0.892
Cows AH2t 1.823"-/ -0.319 2,902.0 0.841
Steers, H24t 0.403 76.118 4.6 0.909
SSignificantly different from zero at the 0.05 probability level
Significantly different from zero at the 0.01 probability level
a/ First difference of yearly values (e.g.,aH22t-1 H22t-1 H22t-2)
Table 2. Estimated change in total slaughter of selected classes of cattle associated with a 1-unit
change in specified explanatory variable, United States, 1949-1958
Cattle on hand, January 1
Slaughter Beef Dairy Cow Constant 2
equation cows cows Steers slaughter Time term R
2 t 1
23t H13t H2ht 23t t 1
Heifers, C22t -0.742 428.3" 1,377.2 0.974
Cows, C23t -1.369 0.656" 5,383.6 0.970
Steers, 2t -0.832 0.986 330.1 0.908
Steers, C2t (0.294) (0.217)
Bulls, C25t 0.056 63.3 0.875
Cattle, 2t-3.631 1.642 8,414.3 0.926
Calves, C1t -1.952' 1.026 -13,103.3 0.884
Significantly different from zero at the 0.05 probability level Significantly different from zero at the 0.01 probability level.
and heifers slaughtered under federal inspection during the preceding year, and (3) the average Kansas City feeder calf' price during the last 2 years. (The standard error of' each regression coefficient in table 1 is shown directly below the regression coefficient.) If' ideal data were available,
year-to-year change in the number of' beef' cows onf'arms, January 1, would be represented by an accounting identity; namely, year-to-year change in beef heifers, lagged 1 year, and total disappearance (i.e., slaughter and deaths) of' beef' cows and beef' heifers, also lagged 1 year. Since the latter data are lacking, estimates of' federally inspected slaughter of' all cows and heifers serve as indicators of' the desired variables--total slaughter and total deaths of' beef' cows and heifers during the preceding year.
Two major considerations are involved in the estimation of' yearly variability in beef' cow numbers: the diversion of heifers for slaughter and the replacement rate for beef' cows. If' beef' heifers were kept only for breeding purposes, i.e., to replace beef cows, the cow-heifer ratio would equal unity. The cow-heifer coefficient during the 1949-1958 period was substantially more than unity--and quite appropriately in view of' the flexibility introduced into farm production planning by diverting a rather large potential number of' heifer calves from feeding to breeding, and by withholding older beef' cows from commercial slaughter. In the short run, therefore, changes in feeder calf prices and in cow and heifer slaughter,
rather than changes in the number of' beef' heifers, account for a substantial part of the variability in the number of' beef' cows on farms.
To further evaluate the make-up of the beef' cycle, the beef cow inventory equation was transformed into an equivalent equation including only lagged beef' cow inventories and feeder calf' prices. In its modified form, the beef' cow inventory equation in table 1 is represented by
zAH23t = 1,758.~5 0.117H13t1 + 0.719-H23-1 0.719&H23t-2 + 0.282aH 3 + 97.5894P + 40.4141P*
23t-3 2t-3 2t_4
where H =23tk = year-to-year change in total number of other cows and
Sheifers, 2 years and over, on farms, January 1, in
thousands of head, (t~,k)- th year;
H 13t-1 = total n xber of cows and heifers, 2 years and over, kept
mainly for milk, on farms, January 1, in thousands of
head, t-th year;
2t-k = year-to-year change in average price of feeder calves
sold at Kansas City, in dollars per 100 pounds, (t-k)-th
Appropriate reaction intervals are denoted by the subscript k.
As shown by the values of the above coefficients, an increase in
either group of lagged explanatory variables--beef cows or feeder calf prices-generally was associated with an increase in beef cow numbers on January 1. To obtain the beef cycle, therefore, the inverse price-quantity relationship at the primary demand level must be introduced into the causal chain of events. The use of the price.quantity coefficient is contingent, however, on an estimate of total disposition of cattle for commercial slaughter. Commercial cattle slaugter
Two sets of slaughter prediction equations were derived to show the
association between feeder calf prices, cattle on hand, and cattle slaughter (table 2). The first set of equations shows the association between the two critical cattle inventory variables--beef cows and steers--on the total federally inspected slaughter of specified classes of cattle. A change in the second difference value of the beef cow inventory variable, 4NH23t'
during the 1949-1958 period was associated with a somewhat saller inverse change in federally inspected slaughter of heifers. An increase in the annual rate of change of beef cows on hand involves the withholding of
calves, heifers and cows for breeding purposes rather than for slaughter, which accounts for the negative inventory-slaughter relationship. An increase in the number of steers on hand, however, offers only the single possibility of increased sales of steers for slaughter. Thus, a change in steers on hand during the 1949-1958 period was associated with an almost equal change in beef cows in federally inspected slaughter. In total, therefore, a +1 unit change in beef cows on January 1 was associated with a -3.020 unit change in federally inspected cattle slaughter. Year-to-year changes in the number of dairy cows and steers on January 1 accounted for most of the remaining explained variation in the slaughter variable.
Feeder calf prices
Average annual Kansas City feeder calf prices were related to
average annual slaughter steer prices, average annual corn prices, and the year-to-year change in steers on hand, January 1. Using annual data, 93 percent of the variation in feeder calf prices was explained. Only one regression coefficient--slaughter steer prices--however, was significant (at the 0.01 probability level). Moreover, variability in slaughter steer prices introduced substantial instability to the feeder cattle market, as shown by the regression relationship,
2t -2t -l497P4t 0.001H24t 0.930,
(0.238) (4.789) (0.001)
where P2t = average annual price, in dollars per 100 pounds, of U. S. Choice
and prime grade feeder calves sold at Kansas City during the
P2t = average annual price, in dollars per 100 pounds, of U. S.
Choice grade beef steers sold at selected markets during t-th
P4t = average annual price, in cents per bushel, of No. 3 yellow corn
sold at Chicago during t-th year;
24= year-to-year change in total steers on farms, January 1, in
millions of head, t-th year.
The potential instability in the feeder cattle market revealed by the feeder price equation contributes to short-term pricing errors, particularly when the major production changes lag price changes by 3 to 4 years. An initial output response is attained, however, by slight gains in weight of slaughter cattle, chiefly heifers and steers, and by short-term increases in the number of cattle on feed. But the major production response is not attained until the cows and heifers that were withheld from slaughter--as a result of an initial price increase--produce a calf crop and subsequently yield an increased supply of slaughter cattle. During the intervening period, the long-run historical pattern of increase in beef production must be consistent with the increase in aggregate demand; otherwise, further price changes can be expected in the primary livestock markets. '
If beef supplies increase without compensating increases in aggregate consumer demand, slaughter cattle prices decline and, consequently, feeder cattle prices also decline. Thus, yearly changes in the feeding margin are inversely associated with changes in beef production. Moreover, the
effect of a 1-unit change in beef production on feeder calf price is almost twice as large as the corresponding effect on slaughter steer price. Hence, the price elasticity of demand for feeder calves would be substantially less than the price elasticity of demand for slaughter steers. Specifically, if the latter were -0.6, the former would be about -0.4. A
A modified form of the slaughter price equation was represented merely by the price-quantity coefficient, -0522, to account for the inverse demand effect in consumption. This coefficient denotes the change in slaughter steer price associated with a +1 pound change in annual per capita beef production.
given price change thus appears as a less effective mechanism in changing production patterns than in changing consumption patterns (insofar as the criterion of effectiveness is specified in terms of the price elasticity of demand, which is about -0.8 for beef at the retail level). In terms of this presentation, moreover, the existence of an inverse margin-quantity relationship in cattle feeding represents a substantial source of shortterm instability in the beef economy.
From the available data, the time path of cattle inventories can be generated as a function of slaughter cattle, feeder calf and corn prices. Obviously, many other factors account for changes in cattle inventories, and these factors may differ in their impacts on cattle production in different geographical areas. For example, the 11 western states account for 1 of every 4 beef cows on hand, but during the upswing or downswing of the cattle cycle these states account for only 1 of every 6 beef cow accumulations or decumulations. In the seven west northcentral states, however, which account for approximately the same number of all beef cows, year-to-year changes in beef cow numbers are twice as large as in the 11 western states.6J Alternative production opportunities in these two areas differ and, hence, the production response to price will show corresponding area differences. Because the economic model shows market prices as the controlling influences on production, non-price factors presumably are included implicitly in the constant terms. A regionally differentiated
6 Only because of the inclusion of the 4 Plains StateE, North Dakota, South Dakota, Nebraska and Kansas, the West Northcentral States reveal greater variability on beef cow numbers than the 11 western sta'es.
model of the beef economy could involve additional production inputs as well as a different set of regression coefficients. In terms of the aggregate representation of the beef economy, the effective constraints on year-to-year variability in inventories, production and prices are established through the aggregate price-quantity relationships. Differential rates of change in these relationships, however, may contribute to short-term inconsistencies and instabilities in market behavior.
Feedback and market stability
The negative price-quantity relationship at the primary market demand level and the positive output response to price changes provide for market stability if the output response occurs simultaneously with the price changes. Because of the tendency to use current market prices in production planning and because of the rather long production period for beef cattle, however, the output response to price involves a substantial time lag and, thus, an output cycle of approximately 8 years duration. While the feedback of price information from the slaughter cattle markets to the feeder cattle markets is almost instantaneous, a corresponding feedback of price information from the feeder cattle markets to the rancher or producer is inadequate, therefore, from the standpoint of the latter simply because of the nature of the production process (as contrasted to the pricing process). To more adequately satisfy production
planning requirements, the feedback of market information should include prospective prices for both the feeder and slaughter cattle markets. If production decisions were based on estimates of future market prices-2 to 4 years ahead--then a higher degree of output stability would be achieved in calf and fat cattle production. In the aggregate model of
the beef economy, therefore, price information represents the primary means for controlling the yearly rate of change in beef cow inventories and cattle production. The long-run changes in production and consumption must be taken into account, however, in the preparation of annual and quarterly forecasts for effective long-run production.planning in the beef economy.
Causal Chains in Beef Production
To paraphrase Dr. Herman Wold, a dynamic model of the beef economy
should solve three problems in one stroke; namely, "(1) the existence of a limiting equilibrium between demand and supply, (2) the existence of stable prices and quantities in the limit, and (3) the path of the prices and quantities in their development towards the stable limit."Z A system of causal relations, moreover, requires that the direction of the causal influences must be specified for each relation of the system and that variables subject to equilibrium relations must be distinctly observable for the purpose of causal chain analysis.8 Finally, the several groups of decision-makers--producers, consumers and marketing firms--are "autonomous" in the sense that they are mutually free in their behavior patterns. With this orientation, the relevant data are now presented to show the internal mechanism of the beef output cycle.
The operation of the beef cycle can be presented quite simply by a
recursive chain of market and production variables. In this causal chain of events, feeder calf prices are linked to cattle inventories and, thence, to cattle slaughter and prices as follows:
Z/ Herman 0. A. Wold, Ends and means in econometric model building, In: Probability and Statistics, Ulf Grenander (ed.), Stockholm, Geber, 1959, p. 381.
8/ Herman 0. A. Wold, A case study of interdependent versus causal chain systems, Review of the Intern. Statist. Inst., 26:5-25, 1959.
production variable Year t-2 Year t-1 Year t Year t+l Year t+2
Feeder calf price r-n r-n
_ I__J u-- I.-.
Other cattle on farms,
Calves L-J 1_Heifers
Conmercial cattle slaughter
Slaughter cattle price
Feeder calf price
Each successive year the change in feeder calf price induces a series of changes that gradually modify the initial impact of the first price change in year t-2. Exogenous factors affect slaughter cattle prices and, thus, modify the rather simple pattern of generating the beef cycle described above.
As will be demonstrated later, changes in beef cow inventories perform an extremely critical role in accounting for both the period and the amplitude of the beef cycle. Because of the cumulative processes involved in the initial phase of the cycle, an overestimation of equilibrium requirements may be corrected quickly by an increase in the disposition of cows and heifers for slaughter. A small decrease in beef cow inventories on January 1, for example, would signal a much larger increase in cmercial slaughter during the forthcoming year. Moreover, beef cows on January 1 may decline in total number because of an increase in cow and heifer slaughter during the preceding year.
To achieve an increase in cow and heifer slaughter, beef cow inventories must have declined 2 years earlier, or atleast the variable,
AC2H23t-1 must have declined during year t-2. Thus, a small change in beef cow inventories generates a series of inventory adjustments of increasing magnitude, except for the restraining influence of the inverse pricequantity relationship. The lagged price-quantity coefficients ultimately, however, contribute to an increase in each component of cattle slaughter until a net increase is attained in the total slaughter variable and, hence, a net decrease is attained in the corresponding price variable. This decrease
- in price gradually induces a reduction in inventories and, subsequently, the volume of each component of commercial slaughter, until a net decrease in the total slaughter variable results in an increase in the price variable. By including both (1) the cow and heifer slaughter variable and (2) the feeder calf price variable as determinants of changes in the beef cow inventory level, additional sensitivity is introduced into the prediction procedures.
For the most part, the explanation of internal relationships (which was derived from highly aggregate time series data) in the beef economy has been formulated as a series of hypotheses that must be subject to rigorous investigation. To phrase these statements in the context of a modified stimulus-response causality increases the burden of investigation but also renders the task more fitting for an experimental approach in testing the relevant hypotheses. In the following sections, several experimental approaches are considered in relation to accumulation problems that are part of the beef economy and its internal mechanism.
Measurement of Causal Relations
The underlying behavioral process in the operation if the beef economy is that of human beings making choices. A change in the stotkinb rate on
some range land, for example, may be preceded by a period in which market reports, conversation with neighbors and other bits of information on future market prospects are acquired. This information may be organized in some manner and processed into alternative courses of action. Finally, a choice is made to change the existing stocking rate. Because of envirormiental conditions, however, the alternative choices may be quite limited; or the value system in operation may contribute to changes that appear inconsistent with economic objectives. Moreover, the uncertainties of nature are known to affect outcomes adversely and, hence, the choice is affected accordingly. Each decision-maker, finally, has a unique set of
rules or patterns of behavior that prescribes how information is used to attain or avoid values and objectives. Thus, the aggregation of the outcomes of producer decisions is quite",simple when compared with the aggregation of the variety of choice-making processes that can be expected to occur in the entire beef economy. Nevertheless, choices are being made with incomplete information regarding critical factors that have a known relation to the outcome and that are amenable to more precise estimation. The estimation of these factors is reviewed with reference to an experimental design framework, including industry simulation,
business gaming, longitudinal studies and learning theory.
The advent of the "computer age" makes possible experimentation with economic systems once the parameters and initial conditions of this system have been specified. In a simulation study, the behavior of the system is given (unlike a business game in which decision-makers act within
the simulated environment).2/ In this presentation, the model of the beef economy provides the necessary data for an example of industry simulation.
In the simulation of the beef economy, an increase in consumer demand equivalent to a $1 increase in feeder calf price is introduced as the stimulus to start the beef cycle. The estimated effects of the $1 increase in feeder calf price over a l0-year period, in terms of year-to-year changes in cattle inventories, slaughter and prices, are summarized in table 3 for the interested reader to examine and relate to the earlier discussion.
Because of secular growth in both supply and demand, and because of initial conditions affecting the level of beef production and prices, the predicted values for the period 1958-1965, corresponding with the data in table 3, yield a somewhat different pattern of variability. As in table 3, however, the cattle inventory series shows a period that L, roughly twice the period of the beef production and price cycles, Similarly, the potentially explosive nature of the over-all beef cycle, as revealed by the gradually increasing amplitude of oscillations, is evident in the predicted price and quantity series for the period 1958-1965.
An industry simulation problem, as suggested at the beginning of this discussion, is more readily solved by using computer language and flow diagramming than by using a verbal description of the beef economy and the related equations in tables 1 and 2.1- Moreover, the increasing flexibility of computer operations will make possible the use of representative firms on a regional basis in an aggregate analysis of the livestock and meat industries. Thus, the effects of changes in behavioral relationships
9/ Martin Shubik, Simulation of the indu.-stry and firn, Economic Review, 50:908-919, December, 196c0.
10/ International Business Machines Corporation, Programmer's Primehr for Fortran Automatic Coding System for the IBM 704l, 1957.
Table 3. Predicted change from base year (t 0) in specified cattle, in 1,000 head, associated with an initial
$1 increase in feeder calf price, by year
Other cattle on farms, January 1 Commercial slaughter
Calves, Heifers, Cows, Steers, Under federal inspection Feeder
Year under 1 to 2 2 years 1 year calf
t 1 year years and over and over Total Total Steers Other Total price
H21 HI H I
2 3 24 02 C24 7C2
0 0 0 0 0 0 0 0 0 0 1.00
1 0 0 0 76 76 125 76 0 76 0.63
2 95 54 0 lO4 253 171 103 0 103 0.50
3 60 56 98 132 346 -137 49 -214 -165 1.4o
4 112 41 168 187 508 51 131 -154 -23 0.85
5 245 101 122 166 634 440 207 101 308 -0.29
6 162 102 153 133 550 103 110 -69 41 0.70
7 74 22 208 174 478 88 131 -119 12 0.74
8 204 54 77 142 477 708 254 286 540 -1.07
9 122 87 11 56 276 331 115 144 259 0.03
10 -95 -29 114 107 97 -198 25 -225 -200 1.58
within firms and among firms, as well as changes in initial conditions, can be examined with respect to prospective developments among a specified group of firms.
A rapidly expanding literature on business games for teaching and experimental purposes is available in a wide variety of professional and trade journals.-/ The authors of a recent study in this area in which the experimental method was used concluded thusly: "By so doing, we have demonstrated that the amount of information available to a bargainer and
his level of aspiration are significant determinants of the price-quantity contract which will be reached. We aver that only the experimental method could have demonstrated the influence and importance of these determinants. 1,,l_ In the disaggregation of the beef economy into regions and firms, an accurate specification of the various behavioral relations would require new information about the decision-making process. Much of this information can be acquired most readily in the laboratory situation where those aspects of the problem which are irrelevant to the testing of, hypotheses can be strictly controlled. Longitudinal studies
Chapin cites two methods of controlled observation over time; namely, the classical pattern of "before" and "after" experiments and the ex post facto
_,j Martin Shubik, Bibliography on simulation, gaming, artificial intelligence and allied topics, Journal of the American Statistical Association, 55:736-751, December, 1960.
12/ Sidney Siegel and Lawrence E. Fouraker, Bargaining and Group Decision Making, McGraw-Hill Book Co., Inc., New York, 1960, p. 73.
experimental design.1-' The benefit-cost analyses accompanying new reclamation project proposals appropriately could use the projective form of experimental design. An ex post facto design could be applied in a study of two communities that at one time were alike in certain characteristics but now are different because, let us say, of the beneficial impact of an irrigation project on one of the two communities. Numerous other designs are available for economic research. Generally, however, longitudinal studies are not confined to the use of experimental designs.1-4
Control in longitudinal studies is achieved by selecting for observation two groups of like firms or households; for example, firms of the same size in animal units or households of the same income bracket. One group--the experimental group--may be provided with market information regarding prospective price changes of demonstrated reliability, while the other group--the control group--would not be provided this information. If these two groups were cattle ranchers, then the number of cattle and their disposition would be observed over a period of time. Meanwhile, other factors affecting choice-making within each group could be isolated. Later experiments could deal with the effects of each of these additional factors, or their relation to the treatment variables could be ascertained by covariance analysis.
With reference tothe aggregate model of the beef economy, each
autonomous group of decision-makers is conceived as a "quantity adjuster"
l Chapin, op. cit., pp. 29-33.
L_/ Nathan Goldfarb, An Introduction to Longitudinal Statistical Analysis, The Free Press of Glencoe, Illinois, 1960.
or a "price adjuster."~ The cattle rancher, for example, adjusts the level of cattle inventories as feeder calf prices change, while the feeder cattle market adjusts to changes in slaughter steer prices. In the aggregate behavioral relationships, the outcomes of countless numbers of adjustments to price or quantity changes occur with a high degree of regularity, on the average, for the entire population.
Underlying the notion of causal chains is a complementary notion of stimulus-response causality for each decision-making unit. This notion of causality can be phrased in terms of a statistical theory of learning.1 The latter, moreover, is amenable to experimental analysis,
In the context of learning theory, adjustments in cattle numbers can be viewed (paraphrasing Estes) as follows: L6
1. Initially, a rancher responds to each major environmental change
by random choice of one of the permissible responses (on an allor-none basis), with probability one-half for each.
2. Over a period of weeks, a learning process is established whereby
the responses become conditioned to the stimulus (environmental
change) pattern with probability c, the parameter c being assumed
constant over weeks for each rancher.
3. Once conditioned to a given stimulus pattern, the correct response
henceforth occurs to that pattern with probability one or approaching one.
These assumptions may be represented further by a mean error value for r alternative changes in cattle numbers; namely,
~/W. K. Estes, New Developments in statistical behavior theory:
differential tests of axioms for associative learning, Psychom _'rica, 26: 73-84, March, 1961.
L/ Ibid., pp. 82-83.
Sxn ) U -()1 (l c)N]
n=l i c
where X = random variable which equals 1 or 0 accordingly as an error or
a correct response, respectively, occurs to a given item (cattle
inventories) on trial n for a total of N trials.
Finally, the last of the three assumptions may be stated, following Estes, as a general matching law, which is "that, beginning at any point in a learning series, the cumulative proportions of a given response and corresponding reinforcing event tend to equality. ,lOne task of experimental design would be to obtain estimates of the parameter "c" for different groups of decision-making units with respect to specific objects of decision-making. Cumulative proportions of a particular response--for example, an increase in beef cow numbers-would be obtained over a period of time with reference to a particular environmental change. It is quite possible that the learning theory model offers an explanation for the persistent underestimation of future change in prices and other market factors on the part of livestock producers generally. In any event, the causal chains in the aggregate model of the beef economy thus could be verified in terms of the individual decision-making units of which the model is composed.
Research Strategy in Experimental Design
Because of the considerable progress in the application of experimental design to nutrition problems and production economics, and because of the ample source books on experimental design techniques, it seemed appropriate to deal essentially with the behavioral relations associated
I/ W. K. Estes, Of models and men, The American Psychologist, 12:609-617, October, 1957.
with problems of' changing numbers of livestock. To establish the role of' experimental. design in the estimation of' behavioral relationships, moreover, it seemed appropriate that we view the beef' economy as an economic system with an internal mechanism of' its own to account for year-to-year variability in its principal variables. In summary, therefore, elements of a research strategy are presented as follows:
1. Learning: theory to establish the quantitative characteristics of' the
choice-making processes in the beef' economy.
2. Longitudinal studies to identify and estimate changes over time of'
economic relations accounting for year-to-year variability in
livestock numbers and prices.
3. Business gaming to obtain fruitful hypotheses for investigation and
development with reference to improving existing chol-ce-making
4. Industry simulation to evaluate the probable impacts of changes
in specified variables and relationships on the over-all operation
of the beef economy.
DISCUSSION: EXPERIMENTAL DESIGN AND ACCUMULATION PROBLEMS
by Douglas D. Caton-1/
Dr. Maki argues that except for the unusual circumstances in which conditions can be controlled or safely assumed to be sufficiently stable, analysis of cross-section survey data and time-series data is usually insufficient to isolate and explain causal relations adequately. Understanding an economic process and how it works is-always difficult. We acquire knowledge in two different ways: as a result of direct experience and from theoretical and empirical propositions. Each has its own range of application and its own particular limitations. A concern about the "experience" explanation of economic processes is its dependence on the qualifications of the observer and the fact that the "error" of the estimate cannot be statistically established. But users of more objective methods who depend upon distinctly observable variables and formal analytical procedures frequently do not feel justified in making predictions or in making deductions about causal relations because the observed variables may be indirect indicators or the observed relations may be unstable.
Dr. Maki, therefore, argues for a more determinate theory of cause and effect relations. He holds that economic behavior cannot be inter-preted systematically without a thorough understanding of the underlying conditions. Various ways of getting at the underlying conditions are examined as to each method's possible contribution to data construction and utilization. The concluding section is tied back to a subsection of
Agricultural Economist, Farm Economics Division, Economic Research Service, U. S. Department of Agriculture
the introduction entitled "Control of a Multivariable System." "Control," as the word is used, does not mean control in the sense of constraint, but rather "conceptual control" to permit better visualization of the component associations and their interactions and isolation of the key factors. Among the key factors are prices, inventory patterns, and the distinctions that must be made between the short and the long run.
Before examining the possible uses of experimental design in dealing with accumulation problems, I shall review the case for time-series analysis, in this instance, a stimulus-response model. The equations identified are equations of condition. I intend to go beyond an explanation of livestock inventory behavior as a patterned sequence in time. The primary focus is on cause and effect. Causal analysis is concerned with two main questions. "What caused this result?" and "Given these conditions, what effect will follow?" In answering the first question, we reason from effect back to cause, and in answering the second question, from cause to effect.
Given the effect, time-series analysis can help in isolating the cause and, given the cause, can help in estimating the effect under stated conditions. In this regard, cause and effect can be determined only if a sufficient degree of uniformity and regularity between an occurrence and immediately connected variables can be isolated. Dr. Maki strengthened his argument by specifying the range of application, the rearrangement of variables necessary to account for interaction, and the change in inventory behavior from stage to stage. He gives primary attention to the fact that an event does not take place in complete isolation. It takes place in a real environment, and many factors contribute to its setting.-g/ In most instances it is not possible to make an
Z/ A condition is whatever factor in a situation that allows an event to occur.
absolute distinction between cause and condition. The selection of one factor as the cause is on the basis of immediate connection; -that is, price-stimulus-response, and on the basis of what is the particular interest. When we take one or more factors for the cause, we presume the presence of the others,2'
Production adjustments to drought conditions is an illustration of the importance of' determining "conditions." The immediate cause of a reduction in forage is lack of rainfall. Looking back, we can indicate wit~h some confidence whether what was done was the only thing that could have been done or whether something else would have been preferable-to preserve the grass, to minimize cost, or to give a desired distribution of income. But not being able to predict rainfall lessens the chances of guessing right. Consequently, each rancher does what he can, considering what he can foresee and what he can afford to do. A
reliable method of predicting rainfall is desirable before effective drought-adjustment procedures can be undertaken, It is necessary then to know what the conditions will be before the relevancy of an adjustment technique can be stated. It is also necessary to distinguish between relevant factors and factors present as mere background. The fact that something happens to be associated with something else in time does not mean that the one or the other is either a cause or an effect.
~A necessary condition is a factor situation when an event never occurs in its absence. If at the low point of inventories a build-up in inventory occurs as a result of a price increase, the price increase might be taken as a sufficient condition, but a build-up can also occur as a result of a decrease in the price of feed or an increase in soil moisture that favors forage production. In this illustration, price is a sufficient condition, but it is not necessary; some other factor situation will do. Then, it seems obvious, the selection of causal factors must always be done arbitrarily (on the basis of some interest) because, in its fullest sence, the cause is the complex of factors that has a direct or an indirect bearing on the event.
Reliance on association to mean that a cause-effect connection also exists is one of the troublesome features of inventory analysis. The inventory analysis of the livestock production cycles with which I am familiar have slanted their arguments one way or another: that either the inventories are self-generating, even though the necessity of the existence of an external shock variable is conceded; or that inventory changes are due to certain exogenous variables, such as price, demand shifts, and substitute product capetition. To a considerable extent, livestock inventories are self-generating, but at key points external variables become more important; for example, Dr. Maki's calf price at the low point of the cycle. Both the internal self-sustaining arguments and the external exogenous variable arguments need to recognize the emphasis that must be given to different variables and different conditions at different inventory stages.
The rate of growth of the livestock industry is subject to two main limitations: competition and the ecological balance of plant and animal life. To understand the process of growth, we must know the conditions for plant and animal growth and the factors in the competitive situation. The modified stimulus-response model of the paper explores possible ways to isolate and to specify the form of connective relationships in a causal sense. The model is partial, -onditions are given, and the equations are conditional equations. Each equation is a proposition to be believed or not, depending upon the weight of the evidence. The sustaining logic of a method of this kind is not so much how well it explains a single case but rather how well a principle of uniformity can be established. Can we expect the san~e Anventory behavior time after time and what is the degree of probability that certain events will be repeated? Regularity must have
been established and the conditions; that is, the principle that binds the variables of the prediction equation together, must have been understood.
Dr. Maki contends that the principle binding the components of the livestock inventory together is the multiplier effect, which is due to the reaction of certain inventory components to price. Prices affect calf inventories. Calf inventories eventually affect heifer inventories and a year later, cow inventories. However, partial independence of inventory stages can be argued, even though considerable evidence exists that overall time build-up sequence is self-generating~once it is started. Calves can be used as feeders as well as breeding-herd replacements; culling rates can be changed and do change with a change in replacement numbers; and slaughter rates change as do holding rates with changes in prospects for feed and forage.
The reason for examining beef-cattle inventory behavior is to
explain economic behavior by isolating the elements of the inventory th at most nearly follow the perceived time path. Should the course of events be repetitive, the specified variables may be sufficient indicators. However, as experience has indicated, they seldom are sufficient, even under the idealized data situation which, it is argued, would simplify the progress of keeping track of developments through the use of an accounting identity. Producer psychology, leakage in the indicator variables, and disturbance factors cause inventory patterns to deviate from expectations and, consequently, the indicator variables become unstable. The failure, for example, of a change in replacement rates to hold up will cause a graduated change in numbers, and allowance for
such an occurrence must be "built in" the production coefficients. In the short run, a change in slaughter cattle prices account for most of the year-to-year changes in cow numbers. In the long run, changes in cow numbers must come from the calf-heifer replacement ratio. Each inventory stage affects each succeeding stage, but beyond the first/ stage, inventory behavior is guided by both condition variables and prices of feeder and slaughter livestock. What this means is that the cycle has both selfgenerating and external-stimulus features and that the transition from one set of circumstances to the other is difficult to determine.
One limitation of estimates of time-series supply response analysis is that few variables and a limited number of relationships can be taken into account. A second limitation is that the relation of the unobserved variables to the observed variables may not be close. In these instances, whether the coefficients have any real structural interpretation may be questioned because in each equation the value of the expectations (prediction) is sensitive to the omission of relevant variables.3/
The low point in the cycle
"Other factor" conditions point up the desirability of not depending entirely upon deductions from secondary data to explain an economic process. Equally, it does not seem entirely realistic to presume that once the pattern is fixed no interaction takes place between the elements of the "constant" terms and the selected variables. This contention is difficult to support directly but, for example, the supply and price of feed can accent or limit year-to-year variability through their controlling influence on production. There is also some evidence to support the argument that it is easier to reason from price to secondary production points and back than from price to the primary production points. Production response to price at the primary production points has on occasion (during the war years) been a primary consideration, as has been argued by Breimyer; but production at the farm level has many self-generating elements. Explanation of inventory behavior, therefore, must depend upon examination of the relationship and interaction between the inventory components. See Brandon (2).
Because supply response is not a simple condition of the relationship of price to output, the interdependence of causal relations and predictive indicator analysis is stressed. This point has been emphasized in other papers and research reports. Bachman and Nerlove stated that the study of production functions on the firm level is both a necessary and desirable supplement to time-series analysis of supply. The reason is to help interpretation through an understanding of the problems that arise in the structural analysis of an industry because of complementarity and supplementarity of products and inputs, interfirm differences, multipleproduct interdependence, and identity and measurement. In this respect, various types of "constructed" expectation models have been used--Hicks, expectation model based on a study of behavior in situations involving price expectations held with certainty (5), and Nerlove's concept of expected normal price (10), Other approaches that follow these lines are the "statistical" method of aggregation suggested by Thiel (11); Henderson's short-run land use predictions (4) based on recursive analysis; and Wold's system of economic relations (14) based on two properties: (1) the development of the variables of a system up to time (t-l) determines the values taken by the variables at time (t), and (2) the variables at time
(t) may be obtained one by one in a definite order, That is, knowledge of p (t-1) enables us to determine q (t) from the supply relation, and then p (t) can be determined from the demand relation (1).
Various arguments have been developed for and against each of these approaches to an empirical explanation of supply response. Prices lagged one year may not be the prices farmers take into account, or the prices they choose to consider. Although the "expected normal price," seems to work, it has little theoretical justification. The statistical approaches have not as yet taken into account the fact that some macro-relations may differ from micro-relations. Bachman and Nerlove contend that because livestock production is of the "continuous input-continuous output type," it cannot be fitted into a recursive framework as long as the temporal net of observation periods is as coarse as at present. In a review of Nerlove's book (8),6J Ladd raised several questions about the applicability of simple dynamic models to livestock supply questions. Apparently the qualifications as to the applicability of predictive models to livestock response questions are based on the "continuance" of the production characteristic when current output depends upon decisions made in more than one period and upon expectations concerning present price that were formed over several periods, and also upon the complexity of both the physical properties and the price relations of the livestock industry. Breimyer (3) brings out many of these problems; and Kearl (6) brings out the diverse and complex relationships between price and the cattle cycle.
6/ See also Ladd (7, 9).
Maki's main interest in his analysis, as I see it, is to "net out" certain indicators which, in turn, can be used for initial establishment of the causal conditions. On the basis of the relationships he worked out, he selected the variables slaughter cattle, feeder calf prices, and corn prices as the primary indicators of the time path of cattle inventories. He points out, however, that these estimating aids need to be placed in the proper context. The context for interpretation of causal relations might be limited to a sector or an area analysis, depending on expected response differences. In this regard, the paper brings out clearly the importance of being able to specify the effect of the underlying behavior processes on supply response. In my opinion, the simulation technique he suggests and an even more extensive development of learning theory have considerable merit. Still another approach that can be added to the list of suggested experimental methods is the statistical decision function. The central idea of this approach is that we perform experiments or take observations as a basis for establishing hypotheses as to the probable results of further action. These hypotheses would be used to consider possible types of action, the risks involved in each course of action, and the probabilities that.the data and known statistical techniques will provide acceptable answers (12).
From an examination of the price change behavior in the Kansas City market for the period 1949-59, the price basis used by Dr. Maki, it is
difficult to contend that the inventory patterns can be explained by prices or their derivatives alone. During the 1949-59 period, six different trend situations occurred in the prices of stocker and feeder steers at Kansas City, Missouri. These trends were abrupt--2. to 35 percent of' the mid-range value. The price changes can be grouped as follows: (1) in 1943-45, 1949-51, and 1956-59, prices were moving upward; (2) in 1948-49 and 1953-56, prices were declining; and (3) in 1953-56 prices were stable.ZI' These price relationships indicate the frequency of occurrence, the abruptness of intermediate time-period price changes, and the considerable instability in year-to-year prices.J Complicating features are the sensitivity of livestock prices to outside influences at high inventory numbers regardless of the cycle phase, and the trend effect of changes in production technology and in management practices.
Professor Maki rightly states that the path of the cattle cycle is
dependent upon both price and inventory behavior. Prices of cattle affect most decisions, and prices and inventories including changes in the composition of inventories are mutually related. An answer to the question of the effect of price on producer decisions would seem to require examination of the anatomy of the cycle by means of the progressive balance sheet or inventory analysis suggested by Breiinyer and a comprehensive and
detailed analysis of beef cattle prices of the type developed in the paper, combined with an appropriate condition framework for analysis.
Z/1 Price data and related materials were provided by W. G. Kearl, Dept. of Agricultural. Economics, University of Wyoming, Laramie, Wyoming.
/ The instability of particular prices was emphasized by Maki, together with the probable contribution of such instability to short-term pricing errors.
(1) Bachman, K. L., and Nerlove, Marc, "Memorandum on the Analysis of Changes in Agricultural Supply," Mimeograph paper, ARS, FERD, USDA,
undated, p. 9.
(2) Brandon, G. E., "A Note on the Nerlove Estimate of Supply Elasticity."
Jour. Farm Econ. 40:719-722, 1958.
(3) Breimyer, H. F., "Observations on the Cattle Cycle," Agr. Econ. Res.
(4) Henderson, J. W., "The Utilization of Agricultural Land: A Theoretical and Empirical Inquiry," Rev. Econ. and Statis., 41:242-259, 1959.
(5) Hicks, J. R., Value and Capital, 2nd ed. (Oxford: Oxford Univ. Press, 1946).
(6) Kearl, W. G., "Beef Cattle Prices for Ranchers' Decision Making."
(7) Ladd, G. W., "Effects of Shocks and Errors in Estimation: An Empirical Comparison," Jour. Farm Econ., 38:485-495, 1956.
(8) Ladd, G. W., "The Dynamics of Supply: Estimation of Farmers' Response to Price, by Marc Nerlov," Jour. Farm Econ. 41:452-455, 1959.
(9) Ladd, G. W., and Tedford, J. R., "A Generalization of the Working Method for Estimating Long-run Elasticities," Jour. Farm Econ.,
(10) Nerlove, Marc, The Dynamics of Supply: Estimation of Farmers' Response
to Price. Baltimore, Md., Johns Hopkins Press, 1958.
(11) Thiel, H., Linear Aggregation of Economic Relations. Amsterdam, NorthHolland Publishing Co., 1954.
(12) Wald, A., Statistical Decision Functions. New York, John Wiley and
(13) Wald, A., and Kempthorne, 0. The Design and Ana]ysis of Experiments.
New York, John Wiley and Sons, 1952.
(14) Wold, H., and Jureen, L, Demand Analysis, New York, John Wiley and
ANALYSIS TECHNIQUES FOR INDUSTRY-WIDE ADJUSTMENTS by Don Bostwick J1
My direct experience with the range livestock industry consists largely of having been a practicing cowboy for a while in western Colorado. Applying a more recently acquired vocabulary, I believe that my efforts were devoted to maximizing the intake of grub and to minimizing the activity of being throwed from a horse. The first objective presented no problems, as I recall, but failure sufficiently to minimize the second led to my seeking other professional employment. An economist might argue that these objectives were poorly chosen or were perhaps more means than ends, but this wasn't the point at the time.
My research activity has been concerned with managerial problems of dryland grain farmers, particularly those that arise from uncertain weather and crop yields. In effect, I lack the background, training, and professional experience that would seem to be required for an adequate discussion of the assigned topic. But this doesn't prevent my talking about it; indeed, it constitutes a very interesting and challenging opportunity to try my hand at a somewhat alien activity. Having taken care of this necessary confessional, let me proceed to the business at hand.
The first order of business is a bit of explicit fencewbuilding. I assume that my job here is not to present data or research results, but to discuss techniques of analysis that might be appropriate to a study of adjustments in the range livestock industry. I shall include a
,1/ Agricultural Economist, Farm Economics Division, Economic Research Service, U. S. Dept. of Agriculture, Bozeman, Montana.
number of possibilities for your consideration, and leave it to you to decide which, if any, are pertinent to your problem.
I have organized the discussion around a series of basic models. I shall treat the assumptions that attach to each model and the analytical tools and data that I believe are required for the proper use of each model. I shan't worry over details, such as the mathematics that may be involved, or the specific sources of data, etc. I will only suggest the presence of these things and then pass on. I will try to be somewhat selective of techniques that might be appropriate to an aggregate model of the complexity of the range livestock industry. In short, this discussion will'be a broad-brush job; I leave the rest to you who are experts.
I want to define what I think are the necessary characteristics of a desirable model. A model is supposed to bear some recognizable resemblance to a segment of the real world. This requires both internal and external logical consistency and distinguishes a model from a paradigm, the latter of which requires only internal logical consistency.
We sometimes distinguish between descriptive and predictive models.
The difference is primarily one of time orientation. The descriptive model says, in effect, "these are the phenomena that have been observed, and the apparent relationships between them." Any uncertainty in a descriptive model lies in the cause-effect relationships; the observed events, being ex post, are certain, except for errors of observation. A predictive model is a series of if-then predications based generally on ex post descriptions, and causal relationships derived from them. Descriptive models are verified by historical data; predictive models may be checked against such data but are verified only by ex: ante or future events. Predictive
models therefore include probabilistic statements throughout, since both events and their relationships are uncertain. If we are working in a static framework, we may choose to assume that certain classes of events or relationships are certain within specified time limits, and still produce a predictive model within these limitations.
It is necessary to modify the requirement of logical consistence,
lest we try to build a model that reflects real events down to the relative minutia. One of the arts of the successful model builder is his ability to account for events and relationships just suffLcient for the application desired. It is impossible completely to specify everything involved in a very simple model. We must be content to specify the level of generality with which we are prepared to live, and then to select data and techniques that will satisfy just these conditions and possibly no more. We must be artists enough to select just those simplifying assumptions that allow for the desired results, being neither too general nor too specific.
It is generally agreed that, given the explicit purposes of the model, a simply conceived model is more desirable than an ornate one. We must bow first to our own limited powers of simultaneous comprehension. We must bow also to the restrictions of data processing and computation. In the end, we must also bow to the need for communication with people who have not our own experience of and interest in the particular problem with which the model deals. It is conceivable that members of this committee could successfully construct a model of the range livestock industry comprehensible by perhaps a dozen other people in the country, and no more. This might be desirable, but I doubt it. I think that you want a model that will be communicable to most oth -r researchers interested in the general problem area.
We must be able to acquire data and to devise analytical techniques by which the hypotheses of the model may be tested. This is a shoal on which much theoretically well-conceived research founders. I find it difficult to limit my theoretical constructs to the often pedestrian constraints imposed by available data and analytical tools. This accounts for a lot of what I prefer to call "creative abortions." A certain amount of these hopeful creations are exciting, but eventually one must still back up to modifications in the model which are susceptible to testing, assuming that the expected abortion does occur. I like to
make some allowance for this kind of activity in the work plan, but the allowance must be made in terms of the possible benefits, should the attenpt succeed, and the penalties in time, money, and human resources, should it fail. Such a determination is a probabilistic, expectations model in its own right. The probabilities might be estimated by the researcher, but the payoffs are set by the research administrator, who characteristically dislikes to lose, This sort of Cloud 9 activity should be considered before the research is started, not after it is underway and an abortion and salvage operation is imminent.
In summary, I would characterize a desirable model as follows:
it is logically consistent in its internal logic and its representation
of selected real-world phenomena; it is as simple as possible for the specified level of generality; it requires only data that can be obtained within the restraints of time and money; and it calls for the use of analytical tools that are available and that permit rigorous testing of the hypotheses of the model. The criterion of reasonableness is implied in all cases, allowing for the fun and games associated with a bit of research uncertainty. It is possible, of course, to build models
for the purpose of testing the adequacy of available data and/or the nature of the data needed but not available. This gets into the province of methodological research, one remove from the more mundane research on practical problems of the range livestock industry.
Constraints for industry-adjustment models
The purpose of an industrywide adjustments model is, I presume, to indicate possible innovations, ranked according to some scale of socio-politico-economic criteria, and probable results if given adjustments should take place. It would be necessary. explicitly to establish the goals of adjustment, then to list all possible means of adjusting toward these goals, and last, to apply acceptability criteria to these possible means, establishing a desirability continuum. The three processes operate as constraints on the activities of the adjustments model.
It is usual to assume the single-valued criterion of welfare
maximization in economic models, but this fails to represent the real world. I have never known a person, real or corporate, with such an uncomplicated goal structure. The range livestock industry is an abstraction, and as such does not have goals. It represents a gaggle of people who do have goals--multivalued, often poorly enunciated, and frequently conflicting, but withal, quite real. A practical adjustments model should reflect these characteristics, except perhaps for the "Poorly enunciated" bit. So much for this suggestion that a meansends framework is necessary; the job has been done so often now, that I shall only refer you back to the literature with which you are already familiar. Let me discuss some of the constraints more or less peculiar to the range livestock industry.
The industry is situate here and there over the western half of the United States. This leads to dissimilarities of topography; of rainfall both as to amount and pattern of occurrence; of soil structure, fertility level, and moisture-holding capacity; of temperature in terms of degree-day totals, or seasonal ranges; of dominant forage type; of association with areas of dryland or irrigated crop production, or with such other uses as recreation, forest products, watershed control, etc.; of relationships to primary markets, meaning feeder buyers, auctions, etc.; to population centers that influence demands; etc.
This suggests that the most acceptable industry adjustments model might well be an aggregate of models specific to the dozen or more disparate areas in which range livestock are produced. I can't imagine an equilibrium adjustment that would be equally suitable for such dissimilar areas as the Northern Plains, the plateau country of western Coloradoeastern Utah, and the Red Desert of Wyoming.
As an example, consider three bases of stratification which are, in effect, a definition of constraints on the area model, in relation to an area such as the Red Desert. Stratify the constraints first on the basis of such physical features as topography, climate, and forage associations. Second, consider the location of the area relative to major primary markets, transportation facilities, and demographic features. Third, consider the alternative use of the resources employed in the industry.
A range area like the Red Desert is exceptionally vulnerable to rather modest variations in the amount and timing of rainfall. The carrying capacity for 6 months grazing might range from 50 to 60 acres per cow unit in a "wet" year up to a section or so in a '.'dry" one. (I suggest that this latter figure is a practical definition of infinitely poor range,
excluding the Sahara). Range utilization is limited by the availability of stock water, drift fencing, and the ownership pattern of the land.
Land use may well be limited to the alternatives: range livestock or nonuse. A certain amount of oil extraction hardly competes, nor does antelope production which, if expanded, would put things in the nonuse category above for practical economic purposes. The combination of altitude (6,000 to 7,000 feet in the main), aridity somethingg like 8"1 to 12"1 of rainfal I per year), and latitude (taking Rock Springs, Wyoming, as a mean), has led to a pattern of heavy winter feeding requirements. Cattle are fed about 5 months on hay raised in the rare irrigated river bottoms, while sheep producers rely on rather scroungy winter range plus hay in reserve.
The nearest primary markets are the feeding areas along the Platte River in eastern Colorado and western Nebraska, several hundred miles away. In recent years, the feeder markets on the West Coast have developed as a primary market for range animals from this area, and this is considerably farther in miles, and a bit further in transit time.
Without going into any great detail, I suggest that an adjustments model must include these limitations; and that a model which does so would hardly be suitable f or other producing areas. Industrywide constraints
Some factors are more or less peculiar to the range livestock industry generally. These factors might enter as constraints on the
aggregate adjustments level, applying with only minor modifications to all of the area models. The first that occurs to me is the competitive situation of the industry. It seems reasonable to assume that no individual producer is able to affect his market significantly. This
might want some modification if the pooled marketing operations of wool growers are considered. One might consider the case for prices administered by buyers in primary markets, Cooperative effort by buyers may be evident in stockyards, etc., but they may still depend upon prices established in a proximate sense by a market beyond the significant control of local buyers. This matter deserves more than just speculation. But lacking the data of a research effort, the assumption of competitive markets might not be too far from reality.
The wool market is peculiar in that it is affected both by a
governmentally administered base price, and by well-developed marketing pools. This no doubt affects, or should affect, the production and marketing decisions of the range sheep producer. Again, these are intuitive statements which need the support or refutation of research
findings before incorporation into a model.
A second industrywide constraint has to do with the ability of producers to adjust through innovations; with the pressures toward adjustments of various kinds and with the aggregate of producers' desires to adopt what might be defined as desirable adjustments. Areas of possible innovation might include the technological, such as machinery, range improvement and feeding and breeding practices; economic organization, such as insurance, price controls, cooperative marketing, and integration and specialization of production; and effective political action, in the large sense, which is the means toward economic-technological innovationary goals.
It seems to me that innovations in these areas have had a more rapid rate of adoption among other groups of agricultural producers, for instance, dryland wheat growers, and specialized truck crop and fruit growers, than among range livestock producers. I dontt know for certain
whether this is so, why it is so, or even if' it is desirable. But I read the general subject of' this meeting as an explicit recognition that some kind of' adjustment is desirable. I suggest that the implied maladjustment might have to do with pressures toward innovation in the industry, and perhaps with a set of' attitudes toward innovation held by the dominant group of' range livestock producers. An effective adjustments model must include these pressures, limitations, and attitudes in
the set of' constraints. It does not simplify the methodology to admit that these. constraining factors are, in all likelihood, interrelated.
I suggest that the range livestock industry is still motivated largely by a philosophical remnant of' the 19th century. The public press maintained in the name of' the dryland wheat industry loudly proclaims the still politically virulent virtues of' agricultural fundamentalism. But dryland wheat producers, individually and in
bunches, have begun the adjustment to the somewhat unique milieu of' the 1940's and 1950's. The consumer and the centralized industries that have captivated him, are in the saddle. With all deliberate alacrity, dryland wheat producers have adopted technological and marketing innovations, along with rapid adjustments in scale.
I suggest that the range livestock industry has not shown an equal grasp of' current realities. This may be due to a permissive lag in individual motivational adjustments, in the pressures exerted by the entrepreneurial f'ew, or by the adjustment choices suggested by researchers in the field. In any event, I believe that the dryland grain producers, though not by any means up to date are ahead of' their largehatted and long-booted brethren in adjusting to nascent economic realities.
Techniques and Data
I come now to a discussion of various analytical techniques that
might be appropriate to an industry adjustments model. Ancillary to this emphasis, I shall discuss some of the types of data appropriate to the various techniques.
Budgeting is an old friend of all of us, I am sure. It is a static technique which we often use in comparing the results of alternative sets of assumptions. For instance, we might be concerned with aggregate production of certain classes of cattle, under a series of alternative stocking rates, holding price and management constant. A budget study is often useful in suggesting the most likely equilibria positions, given certain adjustments in resources, technology, etc. The technique can say little about the adjustment processes, the time required, or the path that would most likely be followed during adjustment.
Perhaps the greatest utility of budget analysis in an aggregate adjustments problem is to allow a comparison between assumed goals and those goals mostly likely to be achieved by a range of alternative modifications in the resources bundle. The data required for budget analysis are input-output coefficients for the activities involved in the range of alternatives to be considered.
Linear programing is a way of arriving at the same general conclusions possible with budgets, though not probable except with considerable luck. A linear programing solution guarantees an optimum if there is a solution at all. Budgeting is more of a hit or miss affair, with no tightly controlled
test for an optimum, and no procedure that ensures that an optimum will be recognized even if it is calculated.
The linear programing technique assumes linear and independent variables whose possible values are limited by a series of linear inequalities. Like budgets, linear programs provide point estimates of equilibrium; positions. The solution adjustment is innocent of time dimension and of data on the adjustment processes involved in reaching the final equilibrium position. One advantage of linear programing over budgeting is its simultaneous consideration of allowable activities and levels of activity. A, large number of variables (100 or more) can be included in the possibilities space, and the solution can be computed in a short time using numerous available electronic computer programs.
The data required for a linear program do not differ greatly from
those required for a budget solution. It is necessary to have input-output coefficients and a reasonable set of linear formulae describing the activities and constraints on them.
It is possible to replace the original values of the constraints
and recalculate the problem, noting the effect of these new values on the optimum solution each time. The next step is parametric linear programing, which treats the values of the constraints as parameters in the problem. These values are allowed to vary over continuous range, for the purpose of observing the transitions that occur in the system. The technique permits analysis of the optimal incremental behavior of the system, as well as of the effect-of changes in these parameters on the final solutions. Spatial equilibrium
Spatial equilibrium analyses look at price and demand interrelationships between. areas. The problem under attack is a price-demand equilibrium
solution on a geographical basis. This technique assumes: a perfectly competitive market (in space, time, and form); the maximization of net profits as the sole objective of the firms involved; supply sources and markets to be single points; transportation costs between any two points to be independent of volume; and the commodity produced and marketed to be homogenous. The quantity available from an area, population characteristics, and disposable income are taken to be exogenous variables within the assumed time period of one year. There is no allowance for inventory management between years. The market demand schedules for each area are known, but they are not necessarily the same.
The problem in a spatial equilibrium analysis is to maximize the profit at each shipping point, by minimizing the transportation and associated costs involved. The problem fits the general framework of a linear programing solution technique. The solution, if there is one, indicates a price for each shipping point and market, and the amount of the commodity that will be shipped over each path.
Varying the demand, price, or production limits for areas and resolving this new problem allows a prediction of the effects likely to flow from similar changes in the actual situation, if the assumptions of the technique are acceptable. The datarequired for this technique include aggregate production possibilities, price, amount, and paths of available transportation, for each area involved in the analysis. It is also necessary to have the demand schedule for the various markets to be considered, in terms of population levels, disposable income, and effective prices. Such an analysis might be useful in indicating the marginal or submarginal livestock-producing areas under specified price and productivity assumptions, indicating areas of possible adjustment.
Game theory might have some utility in an industry adjustments study, but utility would be limited. This technique assumes two or more rational opponents engaged in the selection of countervailing strategies, or modes of behavior, toward a profit-maximizing or loss-minimizing goal. If the losses in a game exactly equal the gains, the game is said to be zero-sum. This can be converted and solved in a linear programing format. If the losses do not exactly offset the gains, the game is non-zero-sum, and a rigorous solution technique may be hard to devise.
It is easy to visualize a game situation involving a livestock producer and a country buyer, quite possibly zero-sum in nature. It is also possible to visualize an aggregate game with the opposing interests represented on the one hand by large buyers or a market, and on the other by some aggregate of livestock producers. In this case, each strategy would represent a segment of the aggregate possibilities, the probability assigned to the strategy being derived from the frequency of individual sellers or buyers normally following the designated strategy.
The linear constraints and strategy sets and the necessary omission of a time variable seem to limit the applicability of game solutions to industrywide problems, A. complete list of available strategies is required for both game participants, as is a payoff function for each strategy combination. These data may well be available only as the result of preliminary research of a descriptive nature.. They are equivalent to the input-output data used in the budgeting or linear programing techniques. Decision theory
This is a technique often described as a game between nature and a rational player. The decision maker is assumed to be a rational animal,
with some range of choices to be made in the strategy he chooses. His opponent (Nature) also has a range of possible actions, but these occur according to some probability derived from a study of historical events.
The choice criteria are somewhat more flexible than the min-max required of a player in the game situation. These may include such criteria as maximum marginal net payoff, expected value of payoffs, the minimum opportunity loss, or expected loss, maximum likelihood, etc. The proper criterion is a function of the decision maker's concept of the problem involved, of his available choices under various probable events, and perhaps most critically, of the probabilities he assigns to the various possible actions of Nature.
Decision theory might be useful in the establishment of optimum
long-term stocking rates on extensive grazing land, of feeding and breeding practices, shipping, culling, and replacement practices, etc., for an aggregate representing all reasonable choices in a producing area. Markov chains
Markov chain analysis assumes that there is a probabilistic relationship between levels of a studied activity in two successive time periods, e.g., that successive paired observations are auto-correlated. This seems to be the case for many human as well as natural phenomena, including yields of grain on dry land, perhaps cattle prices on a central market, range capacities from year to year, support prices based on a moving average, etc.
The data required for a Markov chain analysis are paired sequential observations of the variable under study. From this, it is relatively simple to compute the probabilities of transition from a given activity state to any other in one period, or any number of periods in the future
up to a steady state, where the probabilities no longer change with increments of time. The process will not describe the course of events between the current activity state and any given future state. It will report the mean number of trials required to arrive at the selected state, the probability of being in any given state n trials in the the future, and the mean number of trials required to arrive for the first time back ~t the state from which the process took off.
Marko,~ chain analysis is a neat and computationally rather simple technique hat might be used to estimate probable events in a wide range of situations where there is reason to believe that the events are autocorrelated over successive time periods. Signal flow
Signal flow theory is an analytical tool that isn't entirely dependent on the researchers' ability to express salient relationships in mathematics II terms. It is permissible here to reason by analogy, so that this techno ue is probably a special case of simulation. This tool was developed for application in engineering research, especially circuitry, but I believe that it can be adapted to certain problems in economic research as well.
The procedure is one of constructing a network of activities
connected in various ways by relational propositions. One enters the system with a specified level of the studied activity and traces the effect on the final result, of modifications of activity level and perhaps type arising from the action of the network. It is possible to define interrelationships within the system to any degree of complication that the researcher's knowledge and computing ability will allow. This includes the possibility of feedback, or dampened oscillations. Any
infinite series oscillation prevents a solution (a constant loop feedback), and an exploding oscillation of course destroys the system.
Each activity node is defined in terms of its subject and limits. The relational propositions are generally rather straightforward mathematical formulae, but they needn't be. Mathematics may break down when it comes to structuring the network, leaving the researcher with a set of logical but nonarithmetic structural statements. These do not prevent computer solutions, although they may complicate the programing a bit.
The value of signal-flow analysis would lie in testing structural or relational hypotheses for exogenous logical consistency, prior to their inclusion (or exclusion) in an econometric model. Once a signal-flow model is operational, it is possible to change activity levels or hypothecate changes in the structure and to attempt to predict by analogy the results of similar changes in the real-world situation. This technique, of course, has all the built-in pitfalls associated with any argument by analogy, and it should be used with these limitations in mind. Attitudinal scaling techniques
Most formulations of economic relationships assume away such factors as attitudes, learning ability, and state of knowledge, and assorted "subjective" processes of evaluation and decision-making. I think that the basis for this is the difficulty encountered in earlier times of getting objective data in these areas. The difficulty is rapidly becoming less acute, so that we are in position to incorporate scme of the human variables explicitly in our economic analysis. This should lead to a fuller understanding of the economic processes we study and consequently to better predictive results.
The breakthrough in the provision of such data is due to the rapidly increasing kit of psycho-dynamic research techniques. One of the earliest of these techniques, and the one with which I am most familiar, is the Guttman scale. This technique allows for the placing of individuals, relative to a group, on an attitudinal continuum ranging from least to most favorable. Study attitudes may be anything about which it is possible to make statements that can be agreed or disagreed with by individual respondents. A Guttman scale may be used as one variable in correlation and regression studies. A scale that meets established tests for statistical validity may also be used to predict attitudes for the population from which the scale sample was drawn.
Statistical techniques, such as rank correlation and paired comparisons, may also be useful in establishing attitudes and preferences as objective data. These and related techniques are useful in studying some of the causal factors in consumer demand; the adoption of new technology; the participation in cooperative marketing or range livestock grazing such as pooled grazing permits; or cooperation with various aggregate programs sponsored by various governmental agencies. I am sure that a careful search of psychometric and sociological literature would turn up a number of techniques of this general kind that have interesting applications for an industry adjustments study. Leontief input-output systems
The Leontief system assumes a high degree of interdependence between the various production, processing, marketing, and service activities in an economy. There are certain primary factors, especially labor, which are required in all other activities, but are not themselves outputs from any other activity.
The system consists of a description of inputs used in the output of each studied activity, including the internal consumption of part of an output (some cows are required as inputs for the output of cows). A matrix format called the technology matrix, allows the summation of inputs to all studied activities, from each studied activity. This summation is the total output and the allocative consumption of that particular activity. Similarly, a summation of inputs to each activity from all studied activities is the total of resources used by that activity. The elements of the system may be expressed in value terms, so that marginal-value productivities, prices, profits, losses, etc., can be calculated.
In the simplest Leontief systems, final consumption is assumed to
be the only human good and labor the only human cost. The system can be fitted into a linear programing solution, maximizing consumption for a minimum level of labor use.
The system can be complicated with the inclusion of a time variable, thus becoming a dynamic but still linear system. Outputs are then characterized as additions to stocks required for current production; for maintenance of capital goods used in output activities; or held for input in the next, or some future, time period. This is essentially an economy flow model and allows for balanced growth within the system. Such a system is causally indeterminate. This forces exogenous choices of rate of growth, preferences for one use of a resource, or one activity over another, etc.
Leontief input-output systems might provide a way of estimating the current position of the range livestock industry in the larger economy. More important, such a technique might suggest possible adjustments that
could be expected in the economy at large that would impinge on the range livestock industry, forcing adjustments in one area or another. There adjustments could then be incorporated as constraints in an optimizing model for the industry.
I have talked about my idea of a proper industry adjustments
model, and of techniques and data that might go into one. I want to conclude with a few general remarks intended to fill some of the more obvious lacunae in this discussion. These are statements so obvious that they are usually ignored.
I believe that any approach to an adjustments model for the range livestock industry must begin with a carefully logical structuring of the problem. There must be an explicit definition of the goals, an exhaustive listing of the possible and appropriate means to them, and of constraints and limits that might apply. The logic of the structure must be consistent with external reality or the result is likely to be intellectualized gibberish. The logic of the structure must also be internally consistent, or there will be built-in errors that destroy the effectiveness and purpose of the research effort.
A model that assumes away or ignores institutional or attitudinal restraints on human action, for instance, is likely to contribute neither to our understanding of real events nor to our ability accurately to predict their consequences. The range livestock industry is not an extensive game of chess, an aggregation from model phenomena, or a living case study of linear mathematics. The industry is a loose gaggle of live people whom we cannot fully understand, whose goals and means are largely inarticulate, and with whom we can barely communicate at times.
My personal feeling is that a model built on probabilities, hunches,
and a careful observation of human actions, may be closer to the truth than a very neat and precise list of arithmetic equations based on a careful reading of extant economic treatises. I do not insist that you include the possibility of errant human behavior in an industry adjustments model-this would be both presumptuous and contrary to accepted practice. I only suggest that your results, whatever the quality of the methodological tinsel, will not be worth much if you do not do so.
Let me reiterate what I tried to say earlier about data. A model
depends upon data as a sheepherder depends upon his sheep. A county full of nice, high-quality sagebrush desert surrounding a faithful Basque and his dog is picturesque. But is is worthless without sheep. Similarly, a model without data is just a pretty picture. We can afford a few people, perhaps, who devote their entire efforts to the structuring of models. Bat we can afford these people only if there are others who can plug in the proper data, and crank out results that we can all examine and perforce improve upon. I have personally failed on this account more than on any other and it is not an especially pleasant way to abort.
I have suggested that the range livestock industry is especially infected with the image of the 19th century entrepreneur. We face the spectacle of some thousands of livestock producers in 1961, trying to emulate the philosophy of cattle companies that failed around 1890. Such rampant individualism may be admirable, but I suggest that its extension to current industry-operating procedure is not an equilibrium situation. Sooner or later the range livestock industry will adjust to the current economic and political realities, even as the wheat industry in the Northern Plains is doing.
I conceive the purpose of research to be one of suggesting adjustment processes that maximize the probability that this individualist will survive another generation or so, while still competing effectively in the rapidly coalescing milieu of the politically and economically powerful consumer. The analytical techniques and sources of data that I have observed (a limited sample) in research on the adjustments open to the range livestock industry are not adequate for this job.
My condolences to you who are charged with this research job, and to your constituents whom you may not know, but whose children may be foredoomed to a factory because of your and their joint failure to comprehend the adjustments and the choices still open, and those that the future portends.
Irving F. Fellows, Editor; Budgeting. Storrs Agric. Expt. Sta.,
U. of Conn., Bul. 357, Aug. 1961. Linear Programming:
Robert Dorfman, Paul A. Samuelson, & Robert M. Solow; Linear
Programming and Economic Analysis. New York, McGraw-Hill Book Co.
George C. Judge; A Spatial Equilibrium Model for Eggs, No. 7 of
the series, Competitive Position of the Connecticut Poultry
Industry, Storrs Agric. Expt. Sta., U. of Conn., Bul. 318, 1956. Game Theory:
R. Duncan Luce & Howard Raiffa; Games & Decisions, New York, John
Wiley & Sons, Inc., 1958.
Howard Raiffa & Robert Schlaifer; Applied Statistical Decision
Theory, Division of Research, Graduate School of Business Administration, Harvard University, Boston, 1961.
William J. Baumol, Economic Theory & Operations Analysis, New
York, Prentice-Hall, Inco., 1961.
Markov Chain Analysis:
John G. Kemeny & J. Lowrie Snell; Finite Markov Chains, Princeton,
N.J., D. Van Nostrand & Co., 1960.
A. T. Bharucha-Reid; Elements of the Theory of Markov Processes and
Their Application, New York, McGraI-Hill Book Co., Inc., 1960. Signal Flow:
T. R. Nisbet & W. W. Happ; Flow Graph Analysis, Technical Report,
LMSD 48357, Lockheed Missiles & Space Division, Sunnyvale, California,
M. G. Kendall; Rank Correlation Methods, Hafner Publishing Co., 1955.
Allen A. Edwards; Techniques of Attitude Scale Construction, New
York, Appleton-Century-Crofts, 1957.
J. P. Guildord: Psychometric Methods, New York, McGraw-Hill, 1954.
Don Bostwick, James Esmay, & Gordon Rodewald: Attitudinal Research Relating to Farmers Use of Short Term Credit. In process of publlcation by ERS, USDA, Washington, D. C. Leontief Input-Output Systems:
Robert Dorfman, et al., cit.
DISCUSSION OF "ANALYSIS TECHNIQUES IN INDUSTRY-WIDE ADJUSTMENTS"
by William G. Brown
Mr. Bostwick is to be commended for presenting his paper on
"Analysis Techniques in Industry-Wide Adjustments," in an inte resting and entertaining manner. Although I had thought that Mr. Bostwick's topic was too broad when first reading his paper, it is now apparent that his paper is very helpful in relating and integrating the other papers of the program. The program chairman has done well in obtaining a balance between depth, generality, and detail in the papers presented.
To briefly review the paper's format, after his introductory remarks, Mr. Bostwick discusses criteria for the selection of "1models."1 He then lists what he calls "constraints" for industry-adjustment models. Techniques and data are then presented and discussed in his interesting "rapid-fire" manner in the last major section.
In his paper, Mr. Bostwick made the following statements: "A model is supposed to bear some recognizable resemblence [sic] to a segment of the real world. This requires both internal and external logical consistency, and distinguishes a model from a paradigm, the latter requiring only internal logical consistency."
As discovered by Mr. Bostwick (on page 3 of my manuscript)
"external" logical consistency turns out to be a troublesome term to use. True "external" logical consistency would require perfect prediction and/or description of some part of the real world. Such a state of affairs is rare indeed, especially for economic models. Hence, it would seem preferable to substitute a term such as "predictive" or "descriptive" power for "external logical consistency" as a criterion for choosing among alternative models.
Mr. Bostwick's distinction between descriptive and predictive models is not so clear-cut as might be inferred. A "predictive" model is often used for describing as well as predicting. Similarly, many so-called descriptive analyses are of interest as far as the future outlook is concerned, at least by implication.
Returning to the problem of criteria in selecting among alternative models, Mr. Bostwick states, in effect, that it is generally agreed that
a simple model is often preferable to a more complicated one. The principle of parsimony or of Occam's Razor is indeed accepted by philosophers of science. However, some of the reasons given by Mr. Bostwick for preferring a simpler model are somewhat surprising. It is true that we must defer to general considerations of "cost," including data processing. But then the statement is made that, "In the end, we must also. bow to the need for communication with people who have not our own experience of and interest in the particular problem with which the model deals." This kind of idea has often been thrown around by economists and administrators but it is absolutely untenable, unless one is primarily a journalist rather than a researcher. Think of how Einstein would have had to have withheld his model because it was more complex in ma .ny respects than the classical theory. He had real difficulty in commrunicating his ideas to other researchers interested in the same problem area. However, because the predictive and explanatory power of Einstein's model was superior, his more complex model gained acceptance.
The following statements were made in Bostwick's paper:
"We must be able to acquire data and to devise analytical techniques by which the hypotheses of the model may be tested.
This is a shoal on which much theoretically well conceived
However, if the hypotheses of the model are not operationally testable, the research could not be considered as theoretically well conceived.
In Mr. Bostwick's next section on "Constraints for IndustryAdjustment Models," the word "constraint" was used fairly often rather than some other word such as "characteristic." A.s an example, consider the following statement: "Let me discuss some of the constraints more or less peculiar to the range livestock industry." Perhaps the IndustryAdjustment Model must take account of some of the characteristics noted, such as geographic dispersion, but I do not see how these can be entered into a model as simple "constraints" in the mathematical sense. If they are not constraints in the usual sense, then the model itself must be specially designed to somehow reflect the salient characteristics of the situation. I fear that much of our use of words such as "constraint" merely adds further to our professional kit of jargon.
It should be noted that the section on "Constraints" for IndustryAdjustment Models is about five typewritten pages long, yet in the next section on Techniques and Data, Bostwick fails, for the most part, to relate these so-called "constraints" to the various models discussed., Hence, the section on "constraints" is not very well integrated with the rest of the paper.
In the last major section, Techniques and Data, nine different
techniques are discussed. In my opinion, this section is the best of his paper as the techniques are presented in an interesting but concise manner. A possible shortcoming of this section is that in discussing this many techniques, there is insufficient time and space to relate in detail any one of the nine techniques to industry-wide adjustments in the range livestock industry. However, more detailed treatment of certain types of models is given by other papers on the program.
In Mr. Bostwickts conclusion he reiterates statements about data which, while true in themselves, tend to obscure an important point. Bostwick states that "A model depends on data like a sheepherder on his sheep.', Surely, we would all agree that nearly all our models are very dependent upon the data. However, a model may eventually be extremely useful even though we might not have data for the model at the time it is proposed. The reason is that the model itself specifies the type of data required. And contrary to the possible implication of Mr.-Bostwick's statements, data are not necessarily fixed or given for all time.
If a new model is proposed which promises to be logically superior, it may be possible to secure the new type of data specified by means of new surveys, experiments, or statistic collecting procedures. This important possibility must not be overlooked if we are to improve the reliability of our results.
Although many of my comments have been on the critical side, most of these comments have been concerned with minor aspects of the paper. I think that we are all in agreement with the major portion of Mr. Bostwick's paper and appreciate his considerable efforts in obtaining and presenting his material in an interesting and straightforward manner.
DECISION THEORY AND RANGE LIVESTOCK OPERATIONS
by R. J. McConnen, Montana State College
If the range livestock operator had perfect knowledge about the future levels of price, feed production, and performance of livestock, his decision-making would be a more simple task than it is today. If he also had perfect knowledge about how actions in one year would affect the feed production and livestock performance in future years, there would be precious little art left to the science of the management of range livestock operations. It is likely that the big "ifs" will remain with us. Range livestock operators must make decisions on the basis of less than perfect knowledge about future levels of prices, feed production and livestock performance.
In 1921, Professor Frank Fnight's Risk, Uncertainty and Profit was published.!/ Knight not only developed the basis for the modern theory of profits, he also distinguished between the knowledge situations of risk and uncertainty. Knight's risk involves situations where well defined probabilities can be attached to the alternative outcomes. Knight's uncertainty involves knowledge situations where it is not possible to attach quantitative probabilities to alternative outcomes. This classification of knowledge situations which will be referred to as classical risk and uncertainty, was often helpful in conceptualizing research problems and undoubtedly stimulated much thought. Now, when economists are faced with problems of less than perfect knowledge about future conditions, they could conveniently drop the problems into one
F. H. Knight, Risk, Uncertainty and Profit, Houghton-Mifflin, Boston, 1921.
of two baskets.Z" Knight's classification of knowledge situations could
certainly be used to characterize many of the problems of a range livestock
operation. Most of the situations would be classified under uncertainty.
While Knight's modern theory of profits was -extremely useful to the
economist, his classification of knowledge situations led, in my knowledge,
to no significant research in the area of range livestock operations.
Indeed, the concepts of risk and uncertainty, after being clarified by
Knight,'were sometimes confused and the issues were clouded rather than
clarified. This was the case in my own Master's thesis, which dealt with
Z/ Perfect knowledge is when a single future outcome would occur with certainty. If a future situation could have several outcomes and perfect knowledge existed about the probabilities attached to these outcomes (provided that the probability for any one outcome did not equal one),
less than perfect knowledge exists about the particular outcome occurring
at some future time. The phrase "less than perfect knowledge" is used
differently here than by Heady. See E. 0. Heady, Economics of Agricultural Production and Resource Use, Prentice Hall, New York, 1952 p. 4435. Knight states, "1. . it is unnecessary to perfect, profitless imputation that particular occurrences be foreseeable, if only all the alternative possibilities are known and the probability of the occurrence of each can be accurately ascertained. Even though the business man could not know in advance the results of individual ventures, he could operate and base his competitive offers upon accurate foreknowledge of the future if quantitative knowledge of the probability of every possible outcome can be had. For by figuring on the basis of a large number of ventures (whether in his own business alone or in that of business in general) the losses could be converted into fixed costs." (Knight op. cit., pp. 198-199). But in many cases, the occurrence takes place only once, and although the probability
distribution for the occurrences is known with certainty, an individual entrepreneur cannot properly analyze the case by considering the problem of risk as one of fixed costs. The case is one where, as Knight states,
1...the practical problem may relate to the degree of knowledge rather than to its presence or absence in toto . . The essence of the situation is action according to opinion, of greater or less foundation and value, neither entire ignorance nor complete and perfect information, but partial knowledge." Ibid., p. 199.
,2/ R. J. McConnen, Risk and Uncertainty in the Appraisal of Sunken 'Investments in Range Development, Master's Thesis, Department of Agricultural Economics, Montana State College, Bozeman, 1953, Mimeo.
With the publication of Value and Capital in 1939, economists were provided with a systematic outline of how to deal with problems of dynamic economics.4-/ In building these pioneer dynamic models, Hicks found himself confronted with situations where knowledge was less than perfect. Hicks restricted himself to dealing with the knowledge situation that Knight would classify as risk. Hicks determined equilibrium situations by using the value of the most probable, that is model, price and technical expectations./ Hicks' model has often been modified to the extent that the mathematical expectations of price and technical outcomes have been used to calculate equilibrium or optimum conditions6 Hicks' method of dealing with risk (along with certain modifications mentioned above), when combined with his methods of handling sunken investments and a flow of future incomes, has served as the basic model for most of the work published under the auspices of the W-16 Technical Committee.2I Economic research in the area of range livestock operations has been able to deal with the knowledge situation which is defined as the case of classical risk. Cases of knowledge situations which fall into the categories of either classical uncertainty or that crevice that exists between classical uncertainty and classical risk, are seldom explicit subjects for research. The researcher is often forced to deal with
4/ J. R. Hicks, Value and Capital, An Inquiry Into Some Fundamental Principles of Economic Theory, Second Edition, 1946, Oxford at the Clarendon Press, especially Part III and Part IV.
/ Ibid., pp. 124-127.
6/ For a discussion of these modifications, see Fredrick and Vera Lutz, The Theory of Investment of the Firm Princeton University Press, Princeton, 1951, Chapter XV, "Treatment of Risk and Uncertainty," p. 179.
7/ A good exposition of the economic theory is presented by the Lutzes.
these knowledge situations, however, Usually he deals with them, often after paying lip service to the problem of uncertainty, by either (1) ignoring the problem of uncertainty thereafter or (2) implicitly treating such knowledge situations as cases of classical risk. Later in this paper, I will treat such knowledge situations as risk. This risk will be defined somewhat differently than the classical risk, 'However, I maintain that the crime will not be as great because (1) this will be done
explicitly and (2) it will be done for a definite purpose.
One day economists started to hear about game theory. Some agricultural economists naively believed that game theory could be used to deal with problems of uncertainty. However, they soon found that after you advanced beyond the two-person zero.-sum game, they had reason to doubt the honesty
of the author who stated in the preface, "No knowledge of mathematics beyond high school algebra is required . ." Also, game theory could only be used when all players were "rational" and there were conflicts of interests. Few would regard the sources of uncertainty (price, climate, etc.) as being governed by a player who opposed us. Finally, game theory had been developed to deal with risk, not uncertainty anyway.8j
Now decision theory. Can it be used to deal with problems of uncertainty? "Decision theory has been developed to deal with problems of choice or decision-making under uncertainty, where the probability figures required for the utility calculus are not available. "21 Thus, decision
8V For a discussion of game theory see R. Duncan Luce and Howard Raiffa, Games-and Decisions, Introduction and Critical Survey, John Wiley and Sons, New York, 1957, Chapter 1.
2/ W. J. Baumol, Economic Theory and Operations Analysis, Prentice Hall, 1961, p. 368.
theory as defined by Baumol differs from the Hicksian analysis and from game theory. However, many of the terms used in decision theory are borrowed from game theory.
Several proposed criteria for decision-making will be outlined
shortly. The decision-making criterion used extensively in this paper is, however, closely related to the basic method of analysis outlined by Hicks. Why then refer to decision theory rather than the general model outlined by Hicks? First, some methods of analysis which cannot be considered as an outgrowth of Hicks' model will be considered. Secondly, most of the developments in the application of decision theory have been made in the general field referred to as operations research. The philosophy of operations research is encompassed in the definition of the field given by Saaty. "Operations research is the art of giving bad answers to problems to which otherwise worse answers are given."l;O The philosophy of operations research seems to correspond more closely to Samuel Gompers' philosophy of, "Each day, more and more." The philosophy of much economic research seems to hue more closely to the Marxist philosophy of Lenin, "All or nothing." When dealing with the problems of range livestock operations, the philosophy of Gompers seems more appropriate. Therefore, I intend to give no final answers in this paper. My purpose is to outline a method which I believe will give
bad answers to problems to which otherwise worse answers are
given." And in the spirit of the philosophy of this paper, I would prophesy that if you use the method outlined in this paper, each year your results will become, to paraphrase Gompers, "better and better."
10 Thomas L. Saaty, Mathematical Methods of Operations Research, McGraw-Hill Book Co., Inc., New York, 1959, p. 3.
Management plays a game" against nature. However, it must be assumed that nature is not a "diabolical Miss Nature." 11 If decision theory is to be used, what is required? First, the manager or "player" has to be capable of: (a) making a list of strategy alternatives which are available to his "opponent," Miss Nature (these strategy alternatives are referred to as "states of nature"), (b) making a list of strategy alternatives available to himself, 2 and (c) constructing a "pay-off matrix" on the basis of the possible states of nature and available strategies. Secondly, the player must have considerable information about himself. He must know what his attitude is towards taking chances in order to select an appropriate criterion for decision-making.
The pay-off matrix below will be used to illustrate the criteria presented below.
C D E
A YO 211
A and B are strategies for the player while C, D, and E are states of nature. The elements in the matrix are the "pay-offs5."' For instance, if the manager plays A and the state of nature C occurs, the pay-off will
j1/ Luce and Raiffa, op. cit., p. 279.
L2/ strategy alternatives are a reflection of the flexibility available to the decision-maker. For a discussion on flexibility, see Heady, op. cit., pp. 282-284, 524-525, and especially PP. 34+5-348 and 792-793.
Baumol lists six criteria as proposed decision rules.1-' (1) The maximim criterion defines the strategy with the "least worst" possible outcome as the "best." Using this criterion, strategy A would be the "best" strategy. (2) The maximax criterion defines the strategy with the best possible outcome as the "best." Again, strategy A would be the best strategy. (3) The Hurwicz O
B 1* 0LO1
12/ Baumol, OP. cit., Chapter 19, The discussion which follows is paraphrased from Baumol.
The maximum regret in each row is starred and that strategy with the minimum maximum regret is the "best" strategy. (6) Mixed strategies permit some combination of two or more strategies. For instance you could use half of your resources to play strategy A and the other half to play strategy B.
If meaningful probabilities could be attached to the states of nature, we have a knowledge situation which Knight would refer to as risk. If no such probabilities could be attached, the situation would be one of uncertainty. If the probabilities .2, .6, and .2 were attached to the states of nature C, D, and E in the pay-off matrix used above, it would be possible
to define a "Hicks criterion." D is the most probable state of nature. The "best" strategy for the decision-maker using this criterion would be strategy B.
The manager has the job of picking either one of these or some other criterion as the proper criterion. The proper criterion will change from manager to manager and for any one manager over time as his psychology, social position, and economic outlook and position change. Therefore, the economist can choose no "correct" criterion. However, with this in mind, I will make the following hypotheses. "The Bayes criterion will no prove to be the most appropriate criterion in outlining the approach for researchers working in the area of decision theory." Once the hypothesis has been stated in this form, I find it possible for me to put on my armor, designed by John Dewey, and strive to reject such a hypothesis.
As stated earlier, decision theory was developed to deal with decisionmaking under-uncertainty. Luce and Raiffa state,
"The field of decision-making is commonly partitioned according
to whether a decision is made by (i) an individual or (ii) a
group and according to whether it is effected under conditions
of (a) certainty, (b) risk, or (c) uncertainty. To this last we must add (d) a combination of uncertainty and risk in the
light of experimental evidence."l-4
This paper will be concerned with individual decision-making. "Any decision-maker--a single human being or an organization--which can be thought of as having a unitary interest motivating its decisions can be treated as an individual in the theory.'1lNow, lets look at the states of knowledge. The condition of
certainty requires a particular type of probability distribution and can be treated as a special case of risk. What is required for decisionmaking under risk?
"In general, if an a priori probability distribution over the
states of nature exists, or is assumed as meaningful by the
decision-maker, then the problem can be transformed into the
domain of decision-making under risk."l_/
In order for any element of a set of conceivable states of nature
to be possible, the probability of this state of nature occurring must be greater than zero. But this isn't enough. It is both conceivable and possible (though not at all very probable) that the annual precipitation at Fort Collins next year will exceed 100 inches. However, the probability at Fort Collins next year will exceed 100 inches. However, the probability of the occurrence of this state of nature, while greater than zero, is so small that we would not consider this state of nature as possible for pragmatic decision problems. This decision had to be made with at least some subjective guess about the quantitative nature of at least a portion of the probability distribution of unknown states of
,4/ Luce and Raiffa, OP. cit., p. 13.
I Ibid., p. 13.
16 Ibid., p. 277.
nature. Ignoring for a moment the condition (d) "a combination of uncertainty and risk in the light of experimental evidence," the two remaining conditions, (b) risk and (c) uncertainty, must be combined. The only remaining condition is that of risk. Risk in this case is a continuum from a well defined and stable probability distribution for the states of nature (the classical case of risk) to an ill-defined and unreliable probability distribution for the states of nature (an approach to the classical case of uncertainty).
Classical uncertainty corresponds closely to the "complete ignorance
case."1Z/ It's the contention of this paper that complete ignorance rarely exists. If the case of complete ignorance persists, the decision-maker makes the decision to make no decision (an inactive situation) until he is propelled into a forced action situation.18/ It appears that many range livestock operations needlessly go through this cycle when disastrous market conditions and/or drought occur. Cases of complete ignorance are often incorrectly labeled as cases of optimism. Complete ignorance and rational action are incompatible. We must know something about the future in order to act rationally. At least complete ignorance for the researcher shouldn't exist by the time a project statement is drawn up. Partial ignorance, or partial knowledge if you will, describes the area between complete ignorance and classical risk.12/ Risk as used above, includes both classical risk and partial ignorance. If the Von Neumann-Morgenstern utility theory is accepted, it may be argued that since probability distributions are available for
I/ Luce and Raiffa, op. cit., p. 295.
18/ L. A. Bradford and G. L. Johnson, Farm Management Analysis, John Wiley & Sons, New York, 1953, p. 29.
l_9 Luce and Raiffa, o_. cit., pp. 299-316.
the states of nature, even though they may be subjective and perhaps unreliable, the appropriate criterion to use is the Bayes criterion.L-' The rejection of the original hypotheses will not, however, hinge on such a sophisticated argument. The rejection is based on the following reasoning. If adequate knowledge is available to permit the construction of subjective probability distribution for the states of nature, it is possible to use the Bayes criterion by utilizing this distribution. If it is possible to use the Bayes criterion, and if the decision-maker
knows his own attitudes, there is enough information to use any of the other criteria. By basing research on the needs of the Bayes criterion, the researcher does not have to name the "right" criterion. If the researcher uses the Bayes criterion as the basis for research in the area of decision theory, he will be forced to attempt to improve the reliability of the subjective probability distributions. Instead of dealing with the case of "complete ignorance," the researcher deals with a case of "partial ignorance." The purpose of the research is to (a) adequately describe the pay-off matrix and (b) to decrease the degree of ignorance about the probability distribution of the states of nature. The economist is forced to deal with the cause-effect relationship and treat this
relationship as deterministic. The objective is to find out more about this relationship, The researcher can no longer shrug off his responsibilities merely by classifying knowledge situations. However, experimentation does have a cost. How much experimentation is of significant help is itself a problem for decision theory.-1
20/ Ibid., p. 304 and Baumol, op. cit., pp. 381-384.
2_/ Luce and Raiffa, .. cit., "13.8 Statistical Decision Theory, Experimentation Not Fixed," p. 313.
This does not mean that no criterion but the Bayes criterion has any meaning for the researcher. The other criteria can be of definite value, particularly in setting up "reasonable" criteria to establish rules for strategy dominance. Before discussing this point, a short discussion on the usual meaning of dominance will be given.
Assume there are two reasonable strategies, S1 and $2P available to
decision-maker. Say S1 dominates S2. Then the pay-offs of Sl and S2 for the difference states of nature are not all identical and the pay-off for S1 for each state of nature is either more desirable than or equally dedirable to the corresponding pay-off for S2. S2 would then be an inadmissible strategy.'2 Strategies which have identical pay-offs for all states of nature are equivalent strategies and may be considered as admissible strategies. Usually, only one of a number of equivalent strategies should be selected to use in the decision model. A side remark here. A
considerable increase in the understanding of a problem would probably occur merely from the construction of a pay-off matrix and the selection of admissible strategies.
For particular problems, some one or more criteria may be used to
augment the specifications to be met by admissible strategies. For instance, admissible strategies could be required to have a maximum loss of not more than some fixed amount.
All this may seem somewhat nebulous. However, it is important to (1) remember that the primary objective of decision theory should be to give .. bad answers to problems to which otherwise worse answers are given," and (2) believe "that each year your results will become, to paraphrase Compers 'better and better,'"
2/ Herman Chernoff and Lincoln E. Moses, Elementary Decision Theory, John Wiley and Sons, New York, 1959, Pp. 123-124.
Decision theory, leaning heavily on a variant of the Bayes criterion, will now be used to explore two problems in range livestock operations.
The first problem will be to select the "best" rate of stocking for a predominantly cow-calf operation. The second problem will be to select
the "best" time to sell yearlings grazed on leased land. If this paper were not an exploratory effort, I might be accused of having a disease
called quantophrenia, an uncritical devotion to faulty statistics. I must apologize for the fact that the first example is also used in a contributed paper that I will give during the American Farm Economics Association Meetings next week.
Selected rates of stocking
Cattle ranchers in the Northern Great Plains have relatively few
alternative strategies which can be used to minimize the costs associated
with climatic variability. The costs may be either direct consequences of unfavorable climatic conditions or opportunities not realized when favorable climatic conditions occur. It will be assumed in this paper that three different rates of stocking are the only admissible short-run strategies available to a particular rancher. The flexibility available to the rancher is described by these three strategies. The problem is
to pick the "best" of the three strategies. These strategies may in practice be dominated by other strategies.
The assumed goal of this hypothetical rancher is to select that strategy which will maximize the expected gross ranch profit for the current year.2 The impact of the present rate of use of this range resource on the rate of flow in future intervals has not been considered.
23/ It is assumed that the price of cattle will remain constant. Different expected price levels for livestock will affect the expected
The number of animal. unit days is used as a measure of range productivity. The results of a grazing intensity study were used as a basis for
establishing the relationship between range productivity and the level of
For the purposes of constructing budgets for each of the three levels
of stocking, range productivity is considered to fall within one of five
levels. The interval for each level of productivity is given in table 1.
The gross ranch profit for each level of stocking for five levels of range
productivity is given in table 2.2gross ranch profit for any one strategy. The impact of different expected prices on the choice of strategies could be considered. One method of handling expected prices would be to define the goal as that of maximizing expected net worth. A functional analytical model would have to be more sophisticated than the illustrative model used here.
2_/ The experiment was conducted at the U.S.D.A. Range-Livestock
Experiment Station at Miles City, Montana, from 1933 to 1959. The functional relation used to predict range productivity on the basis of precipitation was X1 = a + bI loge X3 + B2 (logeX3)2 + b4\f-. X1 is the level of range productivity,X5 is the precipitation in March, April and May. The term \I-is a modified trend variable. The heavy rate of stocking was the only level of stocking which could be used to measure range productivity. Cattle were taken off from all pastures when all forage was grazed in the heavily stocked pasture. The' .t variable recognized the decreased rate of flow from this resource in later intervals as the result of heavy grazing in the forecasting model and was used for predictive purposes only.
Z/ The basic data used to calculate these 15 gross ranch profits
were taken from R. 0. Wheeler and R. J. McConnen, Costs. Returns and Organizational Characteristics--Three Sizes of Commercial Family-Operated Cattle Ranches--Northern Great Plains-1959, Bulletin 557, Montana State College, Agricultural Experiment Station, Bozeman, Montana, 1961. The large size ranch with 309.2 animal units on hand January 1, 1959, was used as a basis for these budgets. The experimental data were used as a basis for adjusting the gross ranch profit as the stocking rate and the level of range productivity changed. The medium rate of stocking would be 309 animal units. In order to achieve the light rate of stocking, it is necessary to reduce the number of animal units to 210, This is approximated by selling all the cattle not in the producing breeding herd. The heavy rate of stocking required the purchase of 144 head of long yearling steers. These changes were made the last of May.
Table 1. Levels of range productivity in terms of animal unit days
for each 12 acres
productivity I I II III III,
Interval AUD AUD AUD AUD AUD
99 or less 100-149 150-199 200-249 250 or more
Table 2. Gross ranch profit associated with three different rates of
stocking and five different levels of range productivity Rate of Level of range productivity
stocking I' I II III III'
dollars dollars dollars dollars dollars
A. Heavy 4,000 605 7,645 11,389 11,389
B. Medium 200 2,833 7,165 8,527 8,527
C. Light 304 2,604 2,939 3,261 3,261
The prediction equation was used to estimate the expected level of range productivity for any observed level of precipitation in March, April and May., It was assumed that the deviations of the observed levels from any expected level of range productivity had a mean value of zero and were nonnally distributed. The standard error of estimate was used as a basis for attaching probabilities to the five levels of range productivity.-/ This was done for each expected level of range productivity by using a cumulative normal distribution table. The probabilities assigned to each level of range productivity for three different levels of precipitation are given in table 3.
2_ It would seem that the appropriate statistics to use in assigning probabilities to the levels of productivity would be the standard error of forecast and tolerance intervals. The probabilities for the levels of range productivity calculated using the standard error of forecast
Table 3. Probabilities assigned to each level of range productivity when
precipitation in March, April and May equals 4, 3 and 2 inches
Level of range
productivity Il I II I IIII
4 inches .0011 .0968 .5400 .3430 .0202
3 inches .0094 .2484 .5953 .1439 .0030
2 inches o0968 .5586 .3244 .0201 .0000
It is assumed that the probabilities assigned to each level of range
productivity can be assigned to the gross ranch profit for that level of
range productivity.!Z/' The expected gross ranch profit for each of the
three strategies was calculated by multiplying the five possible gross
ranch profits by the probability for each level of range productivity and
summing the products. Values of the expected gross ranch profit for each
strategy using the probabilities in table 3 are presented in table 4.
and confidence intervals were not acceptable as "good" subjective probabilities. The probabilities assigned to the levels of range productivities when precipitation in March, April, and May equaled four inches where, I' .15, I .18, 11 .23, 111 20, and III' .24. The probabilities assigned when precipitation in this period equaled three inches where, V' .19, I .24, 11 .36, III .22, and III' .06. The probability of the lowest level of range productivity is greater with four inches of precipitation than with three inches of precipitation. The oddity occurred because 11 and III' are open-end classifications and because in this case, of the rapid increase in the value of the standard error of forecast as the values of these independent variables deviate from their mean values.
L/ There is a certain weakness in this assumption. The gross ranch
profit for levels of range productivity were calculated by using the central value of each level. The central values will be the expected value in only a special case.
Table 4. Expected gross ranch profits for each of three rates of stocking
and three levels of precipitation
Rate of Expected gross ranch profit when precipitation equals
stocking 4 inches 3 inches 2 inches
dollars dollars dollars
A.Heavy *8,519 5,998 2,660
B. Medium 7,240 *6,249 *4,059
C. Light 3,024 2,878 2,503
Using the Bayes Criterion, the "best" strategy for this hypothetical rancher would be A when precipitation equals four inches, B when precipitation equals three inches and B when precipitation equals two inches. Sequential decisions--the "best" time for selling
This illustration is perhaps more naive than the first. It illustrates what essentially is a quasi-sequential decision-making model which is used to make the "best" decision with respect to time of selling. 8
The range livestock operator used in this case runs 100 head of
yearlings on rented pasture. This phase of his operation is assumed to be separate from any of his other activities. He pays a grazing fee in advance each month of one dollar per head per month. He feels he should have a six percent return on the value of the yearlings and his investments in grazing fees. The value of the yearlings at the end of a month are used as the value in the succeeding month for purposes of comaputing interest charges. Thaere are no other variable costs with respect to time associated with the operation.
L8/ For a discussion of sequential decision procedures see, Robert Schleifer, Probability and Statistics for Business Decision and Introduction to Managerial Economics Under Uncertainty, Mc~raw-Hill Book Co., Inc., New York, 1959 Chapter 38 and Luce and Raiffa op. cit., section 13.8.
The "rules of the game" are listed below. He can only sell all or
none of the yearlings. They are sold as feeder-stockers. He can only sell the yearlings on the last day of the month. If he sells the yearlings, he does not have to pay the grazing fees for the succeeding months. He owns the yearlings the last of April, Their average weight is 400 pounds. He can sell the cattle in any of the months of April through October, On the last day of October, "the game" terminates, if it hasn't been terminated earlier by the sale of the yearlings.
In order to escape some of the responsibility for this model, I will play reporter. Mr. Higgins operates a ranch not far from Fort Collins, Colorado, He knows something about decision theory and would like to use it to help him in his managerial chores, The "rules of the game" are a fairly reasonable description of one phase of his operation,
Higgins decides to use decision theory and the Bayes criterion to help him decide the "best" time of selling. He knows that the two major factors in determining "best" time of selling are (1) the market price, and (2) the weight of the yearlings,
Higgins feels that the major factor affecting animal gain is available feed, The amount of available feed on range is, in his mind, largely a function of physical features of the range site, the plant cover, and
the climatic conditions existing for any particular year, The range land Higgins rents is remarkedly similar to the range used in a grazing intensity study at the Central Plains Experiment Station located nearby. He has a publication reporting the result of this .grazing study.22/ Higgins feels
~2/G. E. Klipple and David F. Costello, "Vegetation and Cattle
Responses to Different Intensities of Grazing on Short-Grass Ranges of the Central Great Plains," U.S.D.A. Technical Bulletin 1216, United States Government Printing Office, Washington 25, D. C,, July 1960,
his rate of stocking corresponds closely to the assigned moderate use presented by Klipple and Costello. His animals also weigh about the same as those used in the experiments He then took the average monthly cattle gain per head for the pastures with an assigned treatment of moderate use from table 22 and constructed table 5 belowoaiTable 5 Average weight of yearlings by month Year, Aprila May June July August September October
1940 400 483 561 624 673 698 713
1941 400 491 541 601 651 696 682
1942 400 477 533 604 635 672 663
1943 400 470 539 597 656 683 697
1944 400 464 538 593 652 685 659
1945 400 464 531 573 635 663 663
1946 400 460 518 569 602 658 655
1947 400 479 538 590 637 676 672
1948 400 446 480 545 604 626 638
1949 400 461 524 591 644 672 676
a/ assumed constant
Higgins assumed the differences in the average gain could be explained by differences in accumulated precipitation. Therefore, he constructed table 6 from the information presented by Klipple and Costello in their table 1.2' He then constructed scatter diagrams by plotting
LO/ Ibid., p. 58.
L/ Ibid., p. 64.
2/ __d-, p. 7.
the average weight for each month against the accumulated precipitation by month. He didn't bother to plot, for instance, cases like accumulated precipitation for June against average weight for May.
Table 6. Accumulated precipitation by month
1 2 3 4 5 6
March + Col.,l + Col. 2 + Col. 3+ Col. 4 + Col.5
Year April MaT June July August Sept.
1940 1.2 3.9 4.8 7.6 8.5 13.0
1941 3.5 5.2 10.6 14.4 17.1 18.5
1942 1.6 3.9 6.3 7.2 7.4 7.8
1943 1.4 4.6 6.2 6.7 7.2 7.4
1944 3.3 4.2 4.9 7.1 7.5 7.8
1945 1.9 3.0 5.9 6.7 9.2 10.7
1946 .8 3.2 4.1 6.3 9.0 9.2
1947 1.6 3.5 7.5 lO.6 11.6 12.6
1948 .7 1.2 3.2 4.6 6.3 6.5
1949 1.6 5.3 9.0 10.3 11.4 11.6
Average 1.7 3.8 6.0 7.9 9.5 10.4
Next Higgins defined two climatic conditions, High Precipitation (above the 1939-53 average) and Low Precipitation (below the 1939-53 average). Average precipitation didn't occur between 1940 and 1949. Then, for each month, he classified the average weight into either a High, Medium, and Low ranges which are states of nature. Then, he divided each of the 28 scatter diagrams into six parts as indicated below.
He used the scatter diagrams to attach probabilities to the three stages of nature, High Weight, Medium Weight, and Low Weight. He found
that his model was too simple to use the added information provided by the accumulated precipitation after May. Therefore, he only used the relationship between average weights and accumulated precipitation in March April, and May. By using the mid-point of the ranges for average weight, Higgins calculated the expected average weight for each month for the climatic conditions of Low and High Precipitation.
States of nature Average weight
Low precipitation High precipitation precipitation Figure 1. States of nature related to accumulated precipitation
In the rest of the model, Higgins acted as if the expected did in fact occur. He realized the'danger of this, but had neither the time nor the data to modify his model. What Higgins should have done was to calculate conditional probabilities for average weights in future months based on the actual average weight in the present month.
Next Higgins turned to the question of price. On 30 April, when he starts to "play the game," the price is known with certainty. Higgins wants to know how this price will change. He sells the yearlings on the basis:of Kansas City prices for feeders and stockers.
Higgins claims he can, without error, classify market conditions on
the 30th of April, as either Weak or Strong. I asked him how he did this.
When pressed, he said he utilized U.S.D.A. market reports, the U.S.D.A. index on range feed condition for his area, and a tenacity index for ground squirrels. Then Mr. Higgins launched into quite a tirade. He was extremely critical of marketing people because they didn't give him the kind of information about price expectations that he needed for a decision model, I tried to quiet him down. I told him how busy marketing people were and how they've been heavily criticized for some of the price forecasting work they've done in the past. I tried to impress him with the fact that marketing people are a fine lot. In fact, I think I ended by saying, "Why some of my best friends are marketing people."
Well anyway, come to find out, a Weak Market happened to occur when the percent decrease between the April and October price for feeders and stockers, all weights, at Kansas City was 14.9% or more. Using monthly prices for the Kansas City market for 19.51-1960 (there were five years of Strong Market Conditions and .5 years of Weak Market Conditions), Higgins plotted first the percent change from April prices for each month, then the percent change from May prices and so forth. Prices showed a marked downward seasonal trdnd for both market conditions. The percent prices. changes were then classified into the three ranges for each month of Low, Medium and High, which are states of nature. The scatter diagrams were then used as a basis for establishing probabilities to attach to each state of nature. The mid-point of each range and the probabilities of each range were used to establish the expected percentage change in pric e. Once again, Higgins realized that he should have been dealing with conditional probabilities. What is the probability distribution of percentage changes in price for September and October given a 3% decrease in price from July to August? But Higgins didn't have the time.
Higgins then calculated the Gross Profits and Expected Gross Profits for two different April prices, 20 cents per pound and 30 cents per pound, for four possible situations. (1) Low Precipitation--Strong Market, (2) Low Precipitation--Weak Market, (3) High Precipitation--Strong Market,
(4) High Precipitation--Weak Market. In tables 7 and 8, the gross profits to the right of the dark line are expectations and to the left of this line the gross profits are known with certainty. The 30 April calculations are made on the basis of the information available on 30 April. If any one of the expected gross profits are greater than the 30 April gross profit, the decision is made not to sell on 30 April. If this decision is made, on 30 May another set of calculations are made using the information available on 30 May. Once again, if any one of the expected gross profits is greater than the 30 May gross profit, the "game" continues. In only one case, a 20 cent April price, Low Precipitation, and Weak Market, would the game terminate before 31 October. In this case, it would terminate on 30 September.
I criticized Mr. Higgins for using such a crude model. I told him he should have defined more states of nature for both percent price change and average weights and developed a more precise relationships between these states of nature and the climatic and market conditions. I also told him he should be more concerned about the concept of conditional probabilities. Higgins agreed and felt pretty badly about it. He said he would try to do better next year.
But Higgins is persistent. He wanted to take one more look at his data. He said, "Suppose it's July and I face the conditions of a Weak Market and High Precipitation. How could I use some of the other criteria I've heard about to help me make a decision?" The data is presented in table 9.
Table 7. Gross profits and expected gross profits with an April price of 20 cents
calcu- Climatic Market
lation condition condition April May June July August September October
30 April Low Strong 80.00 88.83 95.36 98.49 113.54 117.17 116.18
Weak 80,00 88.83 90.16 95.18 98.25 103.39 105.23
High Strong 80.00 90.10 97.84 103.40 11.29 118.98 117.17
Weak 80.00 90.10 92.51 99.92 99,76 105.09 106.01
106.92.5 10454 1393
30 May Low Strong 89.28 91.37 96.80 106.71 114.54 113.30
Weak 89.28 87.80 93,42 97.38 100.12 99.80
High Strong 92.85 97.76 101.99 111.97 117,71 118,14
Weak 92.85 93.94 98.43 102o20 102.90 104.10
30 June Low Strong 92.82 98.28 110.11 113.45 114.34
Weak 89.2.5 94o31 102.02 102.95 100.69
High Strong 99.23 103.50 115.49 116.58 119.17
Weak 95.41 99,32 107.02 105.78 104.95
31 July Low Strong 99.75 108.50 113.74 111.36
Weak 97.76 99-15 102.55 98.33
High Strong 105.00 113.75 116.86 116.03
Weak 100.80 103,.95 105o37 102.47
31 August Low Strong 110.00 114.64 112.32
Weak 10063 106.06 104.48
High Strong 115.28 117.77 116.98
Weak 105.46 108.97 108.83
30 Sep- Low Strong 116.20 116.55
tember Weak 107.57 103.14
High Strong 1119.35 121.34
Weak ("game" terminates) 11.0.48 109.01
31 October Low Strong 118.14
High Strong 121.94
Table 8. Gross profits and expected gross profits with an April price of 30 cents
calcu- Climatic Market
nation condition condition April May June July August September October
30 April Low Strong 120.00 133.75 143.81 149,83 170,74 176.69 175.71 Weak 120.00 133.75 136,53 144.28 149-73 158o45 160.09
High Strong 120.00 139.67 144.90 152-50 167,56 175.86 177,71 Weak 120.00 139.67 140.00 146.61 152.61 154,57 156-30
30 May Low Strong 133,92 137.05 146.53 161,59 173,19 171,52
Weak 133.92 132.46 140.87 147.29 152.23 151.93
High Strong 133.92 146.59 154.20 169.48 177,92 179.80
Weak 133.92 141.69 148,35 154.50 156.40 158,36
30 June Low Strong 138.72 147,07 165.26 170,36 173.24
Weak 134.13 141.94 154.06 156.61 153,72
High Strong 148.29 154.85 173.26 175.03 180.49
Weak 143.39 149.58 161.53 160,99 160.17
31 July Low Strong 148,77 162.63 170,99 167,92
Weak 143.64 149,52 154,52 149.02
High Strong 156.60 170,48 175.63 174.89
Weak 151,60 156,75 158,72 155.23
31 August Low Strong 164,38 172.14 172.48
Weak 151,25 152o95 149,57
High Strong 164,38 176,81 176.18
Weak 151,25 156.12 157.89
30 Sep- Low Strong 173,97 174.35
tember Weak 154.71 149.51
High Strong 173,97 181.48
Weak 154,71 157,54
31 October Low Strong 176.22
High Strong 183.38
Table 9. Future gross profits for possible states of nature and their probability--weak market and high precipitation
States of nature
1 2. 4 5 j6 7 8 9
decrease Low Low Low Med. Med. Med. High High High
weight High Med. Low High Med. Low High High Low
31 July $10,080
31 August $10,533 $10,048
probability .50 50
30 September $10,754 $10,279 $9,854 $9,517
probability .32 .48 08 .12
30 October $10,818 $10,184 $9,898 $9,313
probability .10 .50 .07 33
Higgins felt he would like to see what the results would be if he used the criteria titled (1) Hicks, (2) Maximim, (3) Maximax, (4) HurwiczX, and (5) Higgins. The Hicks criterion could not be used in August since there is no one most probable state of nature. However, this criteria would say do not sell now in favor of selling in either September or October. The maximim would consider state of nature 5 in August, 8 in September, and 8 in October. This criterion would say sell now. The maximax criterion would consider state of nature 4 in August, September, and October. This criterion would say do not sell now For the Hurwicz criterion, Higgins favors weighing the minimum values at o7 and the maximum values at .3. This criterion would give a value for August of $10,194, for September of $9,888 and $9,965 for October. This criterion would say do not sell now in favor of selling in August0 The Higgins criterion does not lend itself to a rigorous description. Higgins said, "There's a fifty percent chance I'll lose money
if I sell in August, a twenty percent chance if I sell in September and a forty percent chance if I sell in October. I don't like those kinds of odds. I'll sell now."
Even here, there was no answer. Except in this case, the Higgins criterion is the criterion that will be used. Mr. Higgins feels strongly about this.
Decision theory is designed to deal with the problem of uncertainty. Many of the most important problems faced by the managers of range livestock operations are problems associated with uncertainty. It seems appropriate to note that decision theory can be of considerable value as a research tool when dealing with the problems of range livestock operations. It seems likely that decision theory will also be of considerable value in extension work.
The definition of a problem within the decision theory framework requires (1) a definition of the states of nature, (2) a definition of the strategies that are available, and (3) the construction of a pay-off matrix. As in the case of linear programming, considerable insight into a problem is acquired just in the process of defining it in terms of a new analytical technique and getting the required data. We'll seldom be able to bet all the required data we need. This will require that we (1) advocate additional research of a particular kind and (2) use available
data in a more imaginative way.
In defining and discovering appropriate decision-making criterion, we will have to deviate from the classical economic models. In this process,
we may find out more about (1) the classical economic models we have dealt 9
with so long, and (2) the nature and peculiarities of the research area we have staked out.
It seems a certainty, if there is a future, that we will come to know more about the weather. Particularly about the predicting of the weather and maybe about controlling it. The knowledge of probability distributions about future states of nature with respect to weather will give us new parameters of knowledge. If this information can be combined with knowledge about the relationships between climate and agricultural production and adequate information is available about possible market performance, the very nature of agriculture could change. This is probably more true for crop production and certain livestock production than it is for range livestock production. I think that it is important that we look closely at this tool, New works are continually being published in this area, Recently, a new book came into my possession, Applied Statistical Decision
Thoy, by Raiffa and Sclaifer.221 On the basis of reading the lengthy
preface and introduction, I'd say that this book has much to offer despite the fact that some of its pages look like a collection of character brands. There are many other sources of help. The surface has just been scratched.
The purpose of this meeting was to explore possibilities of research in the area of range livestock industry. We need to explore in more detail both the available analytical techniques and the available data. We should not be satisfied with this. We also need to develop new analytical techniques and new sources of usable data, We have some of the analy-tical
3/Ho~ward Raiffa and Robert Sclaifer, Ap-plied Statistical Decision Theory, Division of Research, Graduate School of Business Administration,
Harvard University, Boston, 1961.
tools, some of~ the data we need. The purpose of~ this paper was to explore the possibilities of using decision theory as a research tool. The models I used were crude. It is possible to do better. Our initial answers may not be too good. But we should strive to give "...bad answers to problems to which otherwise worse answers are given,"' and believe that each year our answers will become to paraphrase Gompers, "better and better."
DISCUSSION OF PAPER
"DECISION THEORY AND RANGE LIVESTOCK OPERATIONS"1 by N. K. Roberts
McConnen has presented and illustrated decision theory as a technique for more adequately handling ranch management problems where uncertainty is an important aspect. He also traced briefly the development of' risk and uncertainty from Knight to Luce and Raiffa and Baumol. We are reminded "that the primary objective of decision theory is to give bad answers to problems to which otherwise worse answers are given,", and that, if we use decision theory "each year your results will become better and better." The requirements of decision theory were classified concerning nature, the player, and his abilities. Six criteria for making decisions within decision theory framework were discussed briefly. Except to illustrate how answers differ when using these decision making criteria, McConnen did not discuss the underlying differences among the criteria. He rather easily decides that the Bayes criterion is most applicable to ranching situations, though he does give a glimpse of what happens when the others are used.
Two important ranch problems involving uncertainty, selecting stocking rates and time of selling, were used to demonstrate how decision theory can be used. In the latter case McConnen introduced us to the imaginary Mr. Higgins, an uncommonly ordinary rancher, who seems to have all the qualifications necessary to use decision theory with a modified Bayes criterion. However, in the end, after working long and hard at his problem, he threw it all over and used his own criterion for deciding when to sell. Mr. Higgins is such a remarkable fellow and played such an important part in McConnen's paper that I feel Montana State College should award him an honorary degree.
All in all McConnen did a creditable job and achieved his purpose which was to introduce us to-a relatively new technique for range and ranch management research. I agree with him that one purpose of these meetings is to introduce and debate methods of solving range and ranch management problems. With this in mind I will ignore the temptation to dwell upon his examples, for, as he said, they served his purpose. Besides, they will get "better and better" in the future as method and data improve. I will spend the rest of my time raising questions about decision theory and McConnen's presentation of it. Possibly the questions I raise will stimulate discussion later.
Before I get too serious, let me take a semi-facetious crack at
those in our's and related professions who insist on congering up such
morbid and depressing terms as, for example, "least-worst" and "minimum regret." When an economist recommends to a friend in trouble that he select the "least-worst" alternative, he is immediately placed in the class with the undertaker who tries to sell a sick friend a cemetery lot.
I can agree with McConnen. when he implies that we should not wait for the time when we will be able to give perfect answers to range and ranch problems before we begin to work on them. The philosophy of doing our best even if it means "giving bad answers to problems to which otherwise worse answers are given" is sound, provided we do not misrepresent our answers as being perfect or use the philosophy as an excuse to stop looking for better answers. There is no doubt but that it is the philosophy we have to accept in our area of research if we hope to feel any satisfaction in the work.
McConnen did not draw a sharp enough distinction between decision theory as such and the use to which it is put in applied research. He
says, to quote again, that the primary objective of decision
theory is to give bad answers to problems to which otherwise worse answers are given." He seems to say decision theory is designed to give bad answers. I think what he means to say is that the data we have to plug into this problem solving model are imperfect; therefore, we get bad answers which are better than those obtained if the model were not used. The question that arises is this: If perfect data could be had, would the decision theory model yield better answers than any other known theoretical construct designed to solve the same problems?
In other words, a theoretical problem solving model need only
stand the fire test of pure logic to receive consideration irregardless of the imperfections in its application to real life problems.
At least five basic criteria must be met in testing a theoretical model for acceptance by applied researchers. First, it must resemble some phenomenon in the real world. Second, it must be able to withstand all external attacks on its logical form. Third, it must apply at the theoretical level to all cases in the problem class for which it was designed to solve. Fourth, it must be internally complete and explicit leaving nothing unsaid, Thus, a sound theoretical model lends itself to the precision of a mathematical expression. Though I am not a mathematician, I recognize the value of mathematics in expressing our economic concepts. As McConnen implies, art plays a big part in applied research on the dynamic problems of reality. Even so, our claim that economics as a science is justified because our body of theoretical laws are consistent though not complete, general, and can be expressed with the precision of mathematics or symbolic logic.
Does decision theory meet the criteria of logical soundness, or is it designed to give "bad" answers because of internal weaknesses in the theory? From what little I have read, I believe it is logically sound and does apply generally to the class of problems for which it was designed to solve. Thus, it is worthy of our attention.
Still, another question arises: If decision theory is not the only
model designed to solve the problems of uncertainty, how do we decide whether it should replace the old? There are some criteria to guide an applied researcher in his choice of concepts. First, a theoretical problem solving model must lend itself to modification so it will fit closely the conditions of the specific problem. Generally, the model which reflects most closely the real world without sacrificing logical soundness, generality of application, and preciseness is best. Second9 the model must be simple enough in its data and analytical requirements so that it can be used by the men and facilities available. Generally, the less complicated model will be least costly to use.
Is decision theory a simpler, more realistic model than game theory or one of the other logical systems designed to handle problems of uncertainty? McConnen seems to think so. I wish he had had time to compare it more fully with the competing theories in this respect.
McConnen raised another question in my mind: Is the Bayes criterion (or a variant) for making ranching decisipns given the "payoff" matrix always the appropriate one even for researchers? Could some of the others be useful for purposes other than selecting admissible strategies? He listed six criteria--(l) maximin, (2) maximax, (3) Hurwics, (4) Bayes,
(5) minimax regret, and (6) mixed case.
McConnen tells us that the answers to ranching problems involving uncertainty obtained from decision theory will apply only to the ranch
being studied. If this is so, it is an uncomfortable truth we face as researchers. Though the answer may be specific, the method is still general. It would be better if we could generalize both method and answers when dealing with uncertainty. If we are not to generalize our answers, isn't it possible that in some specific cases a criterion for selecting the strategy other than Bayes' is most appropriate to use with decision theory?
Baumol makes some pertinent observations about some of the criteria that McConnen didn't have time to discuss.!:/ Baumol would call a rancher who selects the maximin criterion a coward when he is dealing with unmotivated nature because he would select the "least-worst" strategy. I see three possible cases when this criterion might be most appropriate. The first is Baumol's c6ward or the person who just won't take a chance on losing. He is probably a small unimaginative rancher with a low income and a quarter of beef hanging in a sack in the garage and a wife with few economic demands.
The second is the rancher who has an average inclination to
gamble but runs on production credit and never seems to have any of his own money in the bank. He may not be able to chance losing on a gamble for high returns if the strategy requires more credit. If he loses two or three years in a row, he is out of credit opportunities and out of business. He continues to operate conservatively, hoping that someday he'll make a killing in spite of himself so he can get ahead of his creditors.
l_ W. J Baumol, Economic Theory and Operations Analysis, Prentice Hall, 1961, pp. 370-375.