An Experimental Investigation of the Incentives to Form Agricultural Marketing Pools

Journal of Mathematical Psychology 42, 287�304 (1998)

An Experimental Investigation of the Incentivesto Form Agricultural Marketing Pools

Elizabeth Hoffman

University of Illinois at Chicago

Gary Libecap

University of Arizona

and

Jason M. Shachat

University of California, San Diego

This paper presents theoretical extensions and laboratory tests of Hoffmanand Libecap's (1994) model of individual firms' incentives to form agriculturalmarketing pools. The key incentives are lower variance in output prices andeconomies in scale in marketing. This paper extends the model by formulatingthe pooling problem as a game of incomplete information in which firms haveheterogeneous and private risk attitudes. An experiment is conducted to testthe theoretical implications of this model. Statistical analysis of theexperimental data supports the model predictions of pooling rates, but alsoreveals that subjects form systematic probability biases and do not behave asstrategically as the model suggests. � 1998 Academic Press

INTRODUCTION

A marketing pool is an agreement between producers wherein participantsexchange their output for shares of the cooperative's profit. These cooperatives arequite prevalent in agricultural industries. For example, in 1995 U.S. agriculturalmarketing pools earned over sixty-nine billion dollars in net revenues and accountedfor thirty-one percent of total U.S. farm marketings (RBS, 1995). The fact that poolinghas been (and continues to be) a significant empirical phenomenon implies that itoffers participants advantages over independent activity. These advantages mayinclude economies in marketing, inventory control, and price stabilization forindividual producers. Furthermore, once firms form pools, it is conceivable that

Article No. MP981216

287 0022-2496�98 �25.00Copyright � 1998 by Academic Press

All rights of reproduction in any form reserved.

The authors thank Lester Taylor, Eric Von Dohlen, Jim Bradely, and two anonymous referees forproviding useful comments and suggestions. We also thank the University of Arizona for providingfinancial support.

they will attempt other types of cooperative behavior. For example, a pool ofproducers may be able to act as a monopsony in input markets or as a monopolyin output markets.

With potentially large returns from pooling, one may ask why producercooperatives are not more common in markets in which individual firms have littlemarket power.1 This paper argues that the incentive to pool depends on theindividual characteristics of firms (or individual farmers). And when theseindividual characteristics interact with market characteristics pools may becomemore or less likely. The roots of these conjectures lie in a historical case study,Hoffman and Libecap (1994). Currently we further develop these conjectures bymodeling how individuals with differing preferences over uncertain prospects formchoices in this class of economic group decision problems. Then we report on a setof experiments which evaluates these conjectures. The results of these experimentsconfirm Hoffman and Libecap's identification of key individual and industrycharacteristics which determine the success of attempts to form large pools. In addi-tion, these results also highlight the strong influence heterogeneous risk attitudesand individuals' probability biases exert on individuals' decisions to participate inmarketing pools.

Hoffman and Libecap (hereafter HL) explore the pooling question by examiningthe United States' orange industry from the late 1920s through the early 1940s. Atthat time, there were two major orange growing regions, Florida and California. InCalifornia, 90 percent of the growers participated in season-long pools, while at thesame time only limited pools formed in Florida. HL hypothesize that the drivingforces behind extensive pooling in California and the lack of pooling in Floridaresulted from differences in the risk and cost structures faced by orange growers inthe two regions. In both regions ``risk'' for an orange grower was characterized bythe random price received for output. By pooling, farmers reduce risk by reducingthe variance of the market price. We call this the insurance incentive. The secondindustry characteristic that differed across the two regions was the economies ofscale in marketing and shipping. We refer to this as the cost incentive.

Differences in the insurance incentive for Florida and California growers arosefrom the heterogeneity of price expectations. In California, there were only twovarieties of oranges harvested, homogeneous growing conditions, and the fruitcould be left on trees for a considerable length of time. These factors led to ahomogenous product for California growers and expected seasonal mean prices thatwere constant across growers (HL, p. 208). In Florida, five varieties of oranges weregrown, growing conditions varied across the region and the fruit could not bestored on the tree because of warm nights. Furthermore, with different sub-seasonsfor the different varieties, Florida oranges were a predictably heterogeneous productthroughout a given growing season. This led to predictable differences in mean

288 HOFFMAN, LIBECAP, AND SHACHAT

1 In this paper we attempt to answer this question from the perspective of individual firm incentives.Besides incentive compatibility, antitrust laws and the restrictions these present affect the number ofmarketing pools formed. For example, contemporary antitrust cases that have centered on the issues ofcartelization and marketing pools include U.S. vs Appalachian Coal (228 U.S. 344 (1933)) and U.S. vsSocony�Vacuum Oil Co. (310 U.S. 150 (1940)).

prices across sub-seasons in Florida.2 Thus, orange growers in Florida hadheterogeneous price expectations, in contrast to California growers.

Economies of scale in shipping and marketing led to cost differences between thetwo regions. First, the fact that California had fewer varieties of oranges madestoring and processing produce simple tasks. However, for a large marketingcooperative in Florida these same tasks required a more complicated technologybecause of the larger variety of oranges resulting in less economies of scale ofmarketing than in California. Second, in bargaining for shipping rates, Californiagrowers had an economy of scale which was not present for Florida growers. Theonly way for California growers to get their output to many major markets was totransport the fruit by rail. Hence, if large cooperatives had not existed, growerswould have had a difficult time in negotiating with the two main transcontinentalrailroads (Union Pacific and Southern Pacific) and in forming successful lobbieswith the I.C.C., which regulated the interstate fare structure. On the other hand,Florida growers could ship their fruit via railroad, trucks, and ships. This largerclass of alternatives made the shipping market for Florida oranges more com-petitive and large lobby groups were not needed to obtain competitive shippingrates.

Whether these two industries' environments generated strong differences in theincentives to pool depends crucially upon the individuals' preferences over uncer-tain earnings and the behavior they use to make choices and form probabilitybeliefs in this group decision making problem. A real possibility that one mustaccount for is the fact that individuals may possess heterogeneous risk attitudes. Inthis paper we theoretically model the impact heterogeneous risk attitudes haveupon pooling behavior by modeling different pooling scenarios as games of incom-plete information (i.e., individuals have differing risk attitudes which are privateinformation). The Bayes Nash equilibria of these games have strong testableimplications which include predictions of the comparative statics suggested by HLand that a diversity of risk attitudes can lead to a long term equilibrium in whichthere is only partial pooling participation within an industry. While this theoreticalmodeling suggests compelling reasons for large season long-pools in California, butfewer large season long-pools in Florida, there does not exist available individuallevel field data to evaluate these conjectures.

This paper evaluates the theoretical conjectures regarding growers' behavior inthe two industries through an economics experiment.3 Due to the applied nature ofthe pooling problem, we design and conduct an experiment that strives to possessas much parallelism4 as possible. The analysis of the experimental data reveals thatthe theory motivated by HL's hypotheses provides a strong predictor of differing

289INCENTIVE TO FORM MARKETING POOLS

2 Hoffman and Libecap (1994, p. 209) demonstrate that the mean price of Florida oranges followeda predictable U-shaped pattern in any given season. Thus growers whose fruit matured early or late inthe season possessed a higher expected price than a grower whose fruit matured in the middle of theseason.

3 For an extensive survey of the industrial organization experimental economics literature, we refer thereader to Holt's (1995) survey article.

4 According to Smith (1982), parallelism in a valid economics experiment implies that the experimen-tal design has captured the essential features of a naturally occurring institution being modeled.

pooling rates across different industries. However, analysis of the individuals' choicedynamics suggests that, in our repetitive environment, the subjects' decisions topool are strongly influenced by biases in their subjective probability assessments offuture prices and are not influenced by their co-players' past decisions. This isparticularly surprising in light of the fact that observations of past decisions are theonly information available for subjects to learn about each others risk attitudes.

2. EXPERIMENTAL DESIGN

The experiments reported in this paper5 are designed to capture the effects of costand insurance incentives on firms' decisions to join marketing pools that do notengage in price or quantity fixing. In all experiments, subjects are asked to makea repeated simple binary choice. For ten decision making periods, ten individualsare each given a single unit of a fictitious good which they must sell.6 Each subjectmust choose whether to sell their unit with other participants' units in a pool or tosell their unit individually. Prior to making this decision, the subjects can meet ina neutral place for up to five minutes and discuss their decisions, after which theymust return to a private decision making area. An individual's decision is alwaysprivate information and the only information the experimenter reveals is thenumber of individuals who decide to sell their units in the pool. Once this decisionis made, the cost of selling the unit and the revenue received (and hence the profit)are determined for each subject. At the end of the experiment, experimental dollarprofits are converted to US dollars at a ratio of five to one.

Four variations of this basic design are utilized. First, a set of experimentsdesigned to mimic the California scenario is conducted. These are collectivelyreferred to as the California treatment. The price a subject receives for a unit isdetermined by his or her choice. If a subject chooses to sell his unit in the pool, andat least one other person chooses the same, then the subject receives a fixed priceof 7.5 experimental dollars. Otherwise, the price received is a random variable thatplaces equal probability on each element of the set of prices, [2.50, 12.50].7 Thus,every participant in this environment has the same random price, i.e., there arehomogeneous price expectations. The cost a subject incurs for producing a unitdepends upon the size of the pool with which he sells his unit. These cost are givenin Fig. 1. Note that any unit sold by itself is considered to be a pool of size one.As in the case of the California growers, this cost is decreasing in the size of thepool. If these economies of scale are present, then we will call the environment ahigh cost environment.


5 All experiments were conducted at the Economic Science Laboratory (ESL) at the University ofArizona. All subjects were undergraduates enrolled at the University of Arizona during the summer orfall semesters of 1993. For a complete set of all instructions, please contact the authors.

6 By giving each subject a single unit we are hard wiring the choice that each producer produces atcapacity and that the pool does not attempt to exercise monopolistic power by quantity fixing.

7 A single draw from a bingo cage, with twenty balls numbered one through twenty, determines theprice realizations. If a number between one and ten is drawn the high price is realized for all non-poolingsubjects. Otherwise a low price is realized for all non-pooling subjects.

FIG. 1. Cost schedule for high cost environments.

A second variation conducted is an environment whose purpose is to mimic theconditions present in the Florida orange market. In this environment there are twotypes of experimental agents. These agent types differ in the support of the randomprice received for a unit. Five individuals receive a price of either 12.5 or 2.5experimental dollars with equal probability. These individuals are said to have alow price support. The other five individuals receive a price of either 12.5 or 7experimental dollars with equal probability, and these individuals have a high pricesupport.8 We refer to these differing random prices as a heterogeneous price expec-tation environment. If any subject chooses to sell a unit in the pool, and at leastone other subject chooses to do the same, then a fixed price of 7.5 experimentaldollars is received for the unit instead of the random price.9 The cost of producinga unit is 0.5 experimental dollars for each subject, irrespective of how the unit issold. This absence of economies of scale is referred to as a low cost environment.

Two more variations of the basic experimental design are conducted in order toobtain information on how the interaction of the cost and insurance incentives mayaffect pooling behavior. One set of experiments (or a treatment) has heterogeneousprice expectations as in the Florida treatment but also a high cost environment. A


8 These more advantageous price supports were awarded by the relative performance of subjects ona simultaneously administered computerized trivia quiz. The quiz was conducted after the instructionswere read but before the ten decision making periods started. Hoffman and Spitzer (1985) first used thistechnique to reinforce the sense of property rights for more advantageous positions or endowments inexperiments.

9 The procedure for determining random price realizations is the same as in the homogeneous priceexpectation environment.

TABLE 1

Experimental Treatments and Parameters

Low cost High cost

Homogeneous price T=10, N=10, and R=3 T=10, N=10, and R=3expectations PS=[2.50, 12.50] PS=[2.50, 12.50]

for all subjects for all subjectsCS=0.5 CS=see Fig. 1

Heterogeneous price T=10, N=10, and R=5 T=10, N=10, and R=5expectations PS=[2.50, 12.50] for 5 subjects PS=[2.50, 12.50] for 5 subjects

and [7, 12.50] for 5 subjects and [7, 12.50] for 5 subjectsCS=0.5 CS=see Fig. 1

second set of experiments utilizes the homogeneous price expectation environmentof the California treatment with the low cost environment of the Florida treatment.

Table 1 summarizes the experimental design used in this research. T is thenumber of periods per experiment. N is the number of subjects per experiment.R is the number of replications conducted for that treatment. PS is the price supportfor subjects' units. CS is the cost of producing a unit.

From now on we will refer to the treatment cells in Table 1 by name. The upperleft cell is the Homo�low treatment, the upper right cell is the California treatment,the lower left cell is the Florida treatment and the lower right cell is theHetero�high treatment. We also make the further distinction between individualswith different price supports in the Florida and Hetero�high treatments. If a subjecthas a ``low'' price support (i.e., their ``bad'' price is 2.50), then he or she isappropriately said to participate in either a Florida I or Hetero�high I treatment.On the other hand if a subject has a ``high'' price support (i.e., their ``bad'' price is7), then he or she is appropriately said to participate in either a Florida II orHetero�high II treatment.

Our experimental design generates six observationally distinct experimental agenttypes. In this paper we will frequently refer to agent types via an index e. The setof experimental agent types will be indexed as e=1, ..., 6 such that: e=1 whensubjects participate in the Homo�low treatment, e=2 for the California treatment,e=3 for the Florida I treatment, e=4 for the Florida II treatment, e=5 for theHetero�high I treatment, and e=6 for the Hetero�high II treatment.

3. A GAME THEORETIC MODEL OF THE POOLING EXPERIMENTS

In what follows, the structure of the observed experimental environment andconjectures on unobservable individual risk attitudes are analyzed as a game ofincomplete information. Individuals' attitudes toward uncertainty are central tothe economic question at hand. When recruiting subjects from a population toparticipate in an experiment, it is reasonable to expect that the subjects havedifferent preferences over uncertain outcomes. Likewise, risk attitudes may differwithin a population of orange growers. Consequently, in our strive for parallelism


we do not attempt to control the risk attitudes of the experimental subjects.10

However, in our experiment, as well as the orange industries of interest, there is noway to a priori observe attitudes towards risk. Hence we assume that our subjects'expected utility functions are

1&e?i +i if +i>0

U(?i ; +i)={6 i if + i=0

e?i+i&1 if +i<0,

where ? i is subject i 's monetary earnings from the experimental game and + i is asubject specific parameter.

There are several aspects of the assumed form of preferences worth noting andfurther elaboration. First, notice that U exhibits constant absolute risk aversion andthat +i is subject i 's coefficient of absolute risk aversion. Thus, an individual'sattitude towards risk is fully characterizes by his or her +i . One can easily showthat the degree of risk aversion is monotonic in +i , and risk neutrality occurs when+i=0. It is also worth noting that U is a reference dependent valuation functionwhose domain is the changes in wealth not terminal wealth. Consequently, since wedo not vary the level of payoffs within the experiment, the parametric form of U isnot as restrictive as it first appears. Specifically, one can not empirically distinguishbetween subjects who have expected utility functions with the same coefficient ofabsolute risk aversion for fixed alternative lotteries. Finally, we assume that +i is arandom variable which has an atomless distribution whose support is the realnumbers and that this distribution is the same and independent for each subject.Also, each subject is assumed to know their own +i but only know the distributionfrom which the others are drawn. In the formulation of the game of incompleteinformation, + i is player i 's type.

Our experimental environments and assumptions about the heterogeneity of sub-jects' risk attitudes fully define games of incomplete information. Pure strategies inthese games are functions that map (types) risk attitudes, +i , to (actions) choicesof joining the pool or not joining the pool. The symmetric Bayes�Nash solutions11

for each of the experimental environments consist of step functions that are bestresponses to one another. These step functions are of the following form: if aplayer's risk parameter is below a certain level, which we call a threshold, then heor she will choose not to pool. Likewise, he or she will join the pool if his or her+i is greater than or equal to the risk threshold. A threshold for experimental agenttype e will be denoted +*e . The predictions of this model are summarized in Fig. 2and by the following expressions.


10 For an example of experimental economic research that attempts to control subject risk attitude seeBerg, et al. (1986).

11 The formal game theoretic model, the derivation of equilibrium and the derivation of the testableimplications are fully presented in Appendix A of the working paper version of this paper (Hoffman,Libecap, and Shachat, 1997). The reader can download the working paper version at the URLhttp:��weber.ucsd.edu�Depts�Econ�Wpapers�dp97.html. The results are intuitive and will be presented herein a less rigorous manner.

FIG. 2. Theoretical implications. (*) The order of these two may be switched.

v +*2 <+*1 =+*3 <+*6 <+*4 , and

v +*5 <+*1 =+*3 <+*6 <+*4 .

These two statements have the following testable implications. The degree of riskaversion required to make joining the pool the best response in equilibrium is thegreatest for individuals who are Florida II experimental agents. The Hetero�high IIagents have then next greatest equilibrium thresholds. Florida I and Homo�lowagents have identical equilibrium threshold values, which are lower than the abovementioned agents. Finally, all four of the above mentioned agent types have higherthresholds than both California and Hetero�high I experimental agents. Withrespect to the proportion of subjects choosing to join the pool, the ranks of thesefrequencies will have the opposite ordering of the thresholds. In terms of orangegrowers, these predictions are consistent with the observations made in HL inregard to pooling rates across the two growing regions, namely that Californiagrowers are more likely to pool than Florida growers.

An additional result of the theoretical framework and experimental design is thattreatments incorporating low costs environments are weakly dominance solvable,but the high cost environments are only solvable by the more demanding solutionconcept of Bayes�Nash equilibrium. Low cost environments are weakly dominancesolvable because of the lack of variance in the pool's price and the fact that the sizeof the group that a subject sells his or her unit in does not affect the cost of the unit.Thus, in low cost environments a subject's belief about the other player's type doesnot influence the subject's expected utility for each action except in the case werehe or she believes with probability one that none of the other subjects will join the


pool. In this case, the expected utility of the two possible actions will be the sameand thus will not remove an action from the best response correspondence. Conse-quently, for three experimental agents in low cost environments we obtain explicitsolutions for the values of +*e and present them on Fig. 2.

4. AGGREGATE DATA AND POOLING PROPORTIONS

In this section of the paper, we present a discussion of the data in terms of theaggregated proportions of subjects choosing to pool. In the previous section, wepresented a model that makes specific predictions over the ranking of poolingparticipation rates for different experimental agent types. Next we present graphsthat provide visual evidence that these predictions hold true.

The phenomenon reported in HL of higher pooling frequencies amongstCalifornia growers is ``replicated'' in our experiment. The participation rates in theCalifornia treatment cell are much higher than those in the Florida treatment cell.This is easily seen by examining Figure 3. This result is certainly consistent withHL; however, we want to add a caveat to the conclusion. The parallelism in thisexperiment is based upon the qualitative nature of the induced incentives but noton the parametric form of these induced incentives. Still, the results are certainlyconsistent with the naturally occurring data in a qualitative sense.

FIG. 3. Pooling frequencies CA versus Fla treatment cells.


FIG. 4. Pooling frequencies for CA, Fla I, and Fla II.

FIG. 5. Pooling frequencies for low cost types.


FIG. 6. Pooling frequencies for high cost types.

Despite this lack of parametric parallelism, the consistency of the ordering ofpooling rates to those predicted in the model may provide a justification for usingthe model presented as a basis for making qualitative predictions about thisparticular naturally occurring phenomenon. This adherence to the theoreticalpredictions is seen by examining Figs. 4, 5, and 6. Figure 4 presents a slightlydisaggregated view of Fig. 1. Clearly, Florida II subjects pool very little, andFlorida I agents pool less than California subjects (except in period six). The poolingparticipation rates for low cost environment agents are presented in Fig. 5.Although Florida II and Homo�low agent types should have the same pooling rates,Homo�low agents participate at a slightly lower rate and the time trend appears toshow less variance. The pooling rates for the Hetero�high II agents are clearly thesecond lowest amongst agent types, California and Hetero�high I pooling frequen-cies are higher than all other types, and California agents pool at a slightly higherrate than Hetero�high I individuals according to the pooling rates presented inFig. 6. Almost all of the results are consistent with the predictions of our model.

5. INDIVIDUAL LEVEL DATA AND BEHAVIOR

The previous section's results show that our theoretical model adequatelypredicts the relative pooling participation rates of the different treatments. Recall


that these predictions were generated from a model which makes strong assump-tions regarding individuals' behavior. In this section, we analyze the individual leveldata asking what elements of individual's choice are consistent with our model'sassumptions. First, we use a random effects probit model to estimate how subjectsdetermine whether or not to join the pool. Two striking results emerge from thisexercise: Subjects do not condition their current decision to join the pool on thesize of past pools, but they do condition their decision on past price realizationseven though all realizations are independent. Next, we take a non-parametricapproach to analyze the stochastic process which drives the subjects' sequences ofpooling decisions. Here we find that, in many environments, we find reject theimplication of the Bayes�Nash equilibrium that subjects' choices follow aheterogeneous Bernoulli process.

5.1. Random Effects Probit Models

In our effort to identify certain dynamics in subject behavior, we present a seriesof random effects models for our discrete choice panel data set.12 Applying thesemodels, we obtain estimates of the theoretical threshold, +*e , for each experimentalagent type, the presence of state dependency (when a subject's past participation inthe pool affects his current likelihood of current participation in the pool), and theimpact of past participation rates on the pooling decision.

According to the theoretical model, the unconditional probability that anindividual joins a marketing pool is the probability that an individual ``draws'' arisk aversion parameter greater than the equilibrium threshold of the environmentin which he participates. Let yit be individual i's action choice in period t, for whichyit=1 is a choice to join the pool and yit=0 is a choice not to join the pool. Nowwe can define the probability that an individual i will choose to be in the pool forperiod t conditional upon experimental agent type, e, as follows

Pr ( yit=1 | Xit , ui)=Pr (+i+'it�+*Xit). (1)

Where Xit is a vector of dummy variables for experimental agent types and +* isa vector of experimental agents' risk aversion parameter thresholds. Assume thateach +2

i is normally distributed, denoted f, with mean +� and variance _2+ =1.13 We

also assume that for each i, +i is independent. Furthermore, for every t and i, 'it isan identical and independently distributed normal error term with mean zero andvariance _2

' , and is also independent of each +i . Also, Xit and +* will sometimes beexpanded to include other explanatory variables and their coefficients. Now we canrewrite (1) as

Pr( yit=1 | X it , ui)=Pr \'it

_'�

+*_'

Xit&+ i

_'+ . (2)


12 For a full discussion of the ability to identify dynamic characteristics in discrete choice panel datasets, we refer the reader to Heckman (1981).

13 This is not a restrictive assumption but a normalization.

Defining the interclass correlation coefficient \=_2+ �_2

++_2' , one can easily show

that _+ �_'=(\�1&\)1�2. Finally, let + be the 6x1 vector with typical element+e=+*e &+� �_' . Expression (2) is equivalent to

Pr( yit=1 | Xit , +i)=Pr \' it

_'�+$X it&+i \ \

1&\+1�2

+ (3)

Conditioning upon Xit and +i , the likelihood of a sequence of responses, denotedy(i), for an individual i for the ten experimental periods is expressed as follows

Pr( y(i) | Xit , + i)= `10

t=1

8 _\[(u$Xit&+ i \ \1&\+

1�2

+ (1&2yit)& , (4)

where 8( ) is cumulative distribution function for the standard normal.Recognizing that Xit is a fixed constant for all periods as is +i (\�1&\)1�2, there

is an identification problem. Therefore, in order to obtain estimates of the treatmentthresholds, we would like to maximize the likelihood in (4) unconditional upon +i ,or the expected likelihood,

Pr( y(i) | Xit , + i)=|�

&�`10

t=1

8 _\u$Xit&+ i \ \1&\+

1�2

+ (1&2yit)& f (u) d+ (5).

We can now write the joint log-likelihood function to be maximized for allindividuals who are experimental agent type e as

L= :N

i=1

ln |�

&�`10

t=1

8 _\u$Xit&+i \ \1&\+

1�2

+ (1&2yit)& f (u) d+. (6)

Expression (6) is a random effects probit model.14 As we noted above, one of ourprimary interest is the impact variables other than a players risk attitude has uponhis pooling decision. Consequently, we estimate a more general specification than(6). Specifically, we use the expression

L= :N

i=1

ln |�

&�`10

t=1

8[h( } )(1&2yit)] f (u) d+, where

h( } )=+e+#1y it&1+#2 yit&2+#3 laggpt&1

+#4hpt&1+#5mhp it&1+#6aeit&1&+iRho (7)

with the following definitions: laggpit is the number of individuals in the groupbesides i in period t, hpt is a dummy variable for a high price realization in periodt, mhpit is a dummy variable for a high price realization and a choice of i to be inthe pool in period t, and aeit is i 's accumulated earnings in U.S. dollars through


14 Efficient estimation of these models is discussed in Heckman (1978), Butler and Moffit (1982), andMaddala (1978). The small sample properties of this model are discussed in Guilkey and Murphy(1982).

period t, and Rho is shorthand for (\�1&\)1�2. We estimate this large specificationfor each experimental agent type, and then successively estimate more parsimoniousmodels until we were able to reject the restricted model with a likelihood ratio test.The simplest models not rejected by the likelihood ratio test are presented inTable 2.

The first striking result in Table 2 is that the estimated thresholds on the riskparameters (which are the constants in the regressions) for experimental agent typesare ordered exactly as the theory predicted. Specifically, California and Hetero�highI have the two lowest thresholds, Homo�low and Florida I have thresholds notsignificantly different from zero, Hetero�high II has the second highest estimatedthreshold, and Florida II has the highest estimated threshold. This is evidence infavor of the testable implications of the model presented in this paper. Further

TABLE 2

Random Effects Probit Estimations

Homo�low Treatment California Treatment

Parameter Estimate Std. Err. t-stat. p-value Parameter Estimate Std. Err. t-stat. p-valueConstant &.131 .165 &.799 .212 Constant &.742 .276 &2.69 .004HPt&1 &.408 .182 &2.243 .012 yit&2 &.150 .238 &.63 .264Rho .717 .107 6.70 .000 Rho .519 .135 3.86 .000

Log Likelihood Value &149.5 Log Likelihood Value &134.92L.R. Test Statistic .734 L.R. Test Statistic 2.69Degrees of Freedom 5 Degrees of Freedom 5p-value .981 p-value .747

Florida I Treatment Hetero�high I TreatmentParameter Estimate Std. Err. t-stat. p-value Parameter Estimate Std. Err. t-stat. p-valueConstant &.170 .238 &.712 .238 Constant &.596 .145 &4.098 .000yit&2 .621 .261 2.38 .009 HPt&1 .449 .164 2.74 .003HPt&1 &.825 .213 &3.874 .000 Rho .386 .079 4.885 .000Rho .514 .107 4.827 .000


Florida II Treatment Hetero�high II TreatmentParameter Estimate Std. Err. t-stat. p-value Parameter Estimate Std. Err. t-stat. p-valueConstant 2.307 .207 11.156 .000 Constant 1.268 .176 7.206 .000Rho 1.935 .1152 16.793 .000 HPt&1 &.452 .193 &2.349 .001

Rho .351 .107 3.289 .000



evidence in favor of the theoretical model is the general lack of state dependencyfound in the specifications. Especially since state dependency can lead to false sup-port of unobserved heterogeneity in panel data sets.15 While the estimates of the +e

are strikingly consistent with our theory, there are several results which are in factproblematic for the theory. One problem is the significant effect past but independ-ent price realizations have on the individuals' decisions to join the pool. For fourof the six agent types, the coefficient on hpt&1 is significantly different than zero inthe parsimonious specification. Interestingly, three of these estimates are negativeand reflect a belief that high prices are more like to be followed by low prices.A second negative result, in terms of supporting the model, is the complete lack ofinfluence past pool sizes have on individuals decisions. There is no agent type forwhich the variable laggpt&1 shows up in their parsimonious specification. Further-more, in all of the successive estimation of models the coefficient on laggpt&1 wasnever significant. Clearly, individual probability biases drive individual decisionsmore than strategic considerations in our experiment.

5.2. Nonparametric Analysis of the Individual Level Data

While the random effects probit models estimated earlier generated strikingresults we must still be leery of the associated strong distributional assumptions.Therefore, we choose to scrutinize the data for state dependence and heterogeneityin a framework that does not rely upon any of the assumptions made in theanalysis of the previous section. The framework adopted here is a nonparametricapproach for discrete panel data suggested by Lee (1987). This framework allowsus to distinguish among several stochastic processes that could generate the data.Our theoretical model makes a prediction that a heterogeneous Bernoulli modelshould characterize that data.

Lee argues that one can gain insight into the data generating process of a discretechoice panel data set by examining the sequences of choices from a finite data setfor run patterns. Lee's empirical model and procedure involve using a log-linearprobability model, much like an ANOVA, as a general specification. Next, Leeidentifies four potential discrete time stochastic processes that could generate therandom sequences of occupied states observed: the homogeneous Bernoulli, theheterogeneous Bernoulli, the Markov, and the mixed Markov models. Further-more, each of the four processes is indicative of whether heterogeneity and�or statedependency is present in the data. State dependency is inconsistent with eitherBernoulli process.

Each of these processes has simple implications for our experimental data. Thehomogeneous Bernoulli requires that the probability a given subject chooses to jointhe pool in a given decision period must be the same for all individuals and all timeperiods, or in other words the marginal probabilities of decisions are constantacross individuals and time. The heterogeneous Bernoulli model implies thatindividuals have differing marginal probabilities, but a given individual's marginalprobability must be constant across time. This process is indicative of heterogeneity


15 For a detailed discussion of this see Heckman (1978, 1981).

implied by our equilibrium model. The first order Markov process requires thatconditional probabilities over choices in a given period be completely determinedby the choices of the previous time period, and these are completely described bya Markov transition matrix. This process requires that every individual's behaviorfollows the same transition matrix while the mixed Markov model allows forindividuals to follow different transition matrices. The Markov model is consistentwith data characterized by only state dependency, while the mixed Markov modelis evidence of both heterogeneity and state dependency.

Lee demonstrates that each of these processes is nested within the log-linearprobability model by placing appropriate constraints upon the order terms. Onecan estimate these specifications by a multinomial logit procedure and then conductclassical hypothesis tests on the restrictions. In this section, we employ thelikelihood ratio test to test specific stochastic processes against the general model.Furthermore, due to our small data set and the possibility that the stochastic pro-cess may change we estimate two models for each experimental treatment; one forperiods two through six and another for periods seven through ten. We report theresults of the hypothesis test in Table 3.

In our discussion of the results in Table 3 we focus on the Markov andheterogeneous Bernoulli models. Unfortunately, in six out of twelve cases theheterogeneous Bernoulli model is rejected. Clearly the individual data is more com-plex than suggested by the theory. For instance, the Markov model is rejected inless than half the cases. While this is consistent with state dependency it may alsobe consistent with the probability biases noted in the previous section.

TABLE 3

Likelihood Ratio Test Comparisons within the Lee Framework

Homogeneous Heterogeneous MixedBernoulli Bernoulli Markov Markov14 D.O.F. 11 D.O.F. 8 D.O.F. 2 D.O.F.

Player Type T1 T2 T1 T2 T1 T2 T1 T2

Homo�low 25.73 35.82 18.71 22.58 14.38 6.61 0 0(.028) (.001) (.066) (.020) (.072) (.580) (1.000) (1.000)

California 35.71 38.07 20.22 20.14 27.68 23.53 0 0(.001) (.001) (.042) (.043) (.001) (.003) (1.000) (1.000)

Florida I 31.71 20.66 36.69 18.3 27.77 14.62 0 7.088(.004) (.111) (.000) (.075) (.001) (.067) (1.000) (.029)

Florida II 9.676 4.499 0 1.387 0 (.001) 0 0(.886) (.993) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000)

Hetero�high I 20.29 10.44 12.19 16.9 17.1 24.91 0 8.947(.121) (.729) (.350) (.111) (.028) (.002) (1.000) (.011)

Hetero�high II 22.76 35.05 21.08 23.51 17.21 9.501 0 0(.064) (.001) (.033) (.015) (.028) (.302) (1.000) (1.000)

Note. T1 = periods 3, 4, 5, and 6, and T2 = periods 7, 8, 9, and 10. Chi-square test statistics and(P-value). Bold face indicates a rejection at the 50 level of significance


6. CONCLUSION

Through the use of an economics experiment we attempted to explain whyCalifornia orange growers formed season-long pools, while Florida growers didnot.16 HL argued that this asymmetric pooling behavior was the result of differentinsurance and cost incentives. We constructed an experimental environment thatcontrols for the insurance incentive of the reduced variance in revenue offered bythe pool and the economies of scale in shipping rates that constitute the cost incen-tive. We also extend HL's model to allow for heterogeneous risk attitudes amongstproducers. This allows for individually rational behavior that is consistent with per-sistent partial participation in marketing cooperatives. After examination of theexperimental data, we find that the original insights provided by HL werequalitatively correct, and our model reasonably predicts the partial poolingbehavior observed and tracks the qualitative differences in participation rates acrosstreatments.

Our results imply the following four points. First, the experimental resultsreplicate the qualitative aggregate predictions of HL. Second, the game theoreticmodel of individual behavior we present makes strong predictions about partialpooling, and these predictions are consistent with results obtained from using dis-crete choice panel data techniques. Third, subjects are not as strategic as our modelsuggests as they do not utilize the information on the size of past pools in formingtheir decisions and furthermore they also form systematic probability biases.Finally, the nonparametric analysis of the data provides evidence that the staticmodels examined in this paper do not adequately explain the complex dynamicsfound in the data.

The results of this paper indicate several avenues for future research. For exam-ple, it is worthwhile to ask how heterogeneous producer attitudes towards uncer-tain profits affect cooperative and cartel behavior, especially when the cooperativeor cartel engages in market quantity restrictions. Furthermore, will partialcooperative or cartel participation be sustainable and persistent in this framework?Also, are other historical phenomena (for which there may be scant data) amenableto investigation by experimental methods? Finally, in terms of experimental dataanalysis, can we improve the econometric techniques commonly used in order tocontrol and evaluate dynamics imbedded in the data?

REFERENCES

Berg, J., Daley, L., Dickhaut, J., 6 O'brien, J. (1986). Controlling preferences for units of experimentalexchange. Quarterly Journal of Economics, 101, 281�306.

Binger, B., Hoffman, E., 6 Libecap, G. (1988), Experimental methods to advance historical investigation:

An examination of cartel compliance by large and small firms. University of Arizona, Discussion Paper.

Butler, J. S., 6 Moffit, R. (1982). A computationally efficient quadrature procedure for the one-factormultinomial probit model, Econometrica, 50(3), 761�764.


16 Note, that this is not the first research to examine an economic history topic with an economicexperiment. For an earlier example see Binger, Hoffman, and Libecap (1988).

Guilkey, D. K., 6 Murphy, J. L. (1993). Estimation and testing in the random effects probit model,Journal of Econometrics, 59, 301�317.

Heckman, J. J. (1978). Simple statistical models for discrete panel data developed and applied to test thehypothesis of true state dependence against the hypothesis of spurious state dependence, Annales deL'INSEE, 30�31, 227�269.

Heckman, J. J. (1981). Statistical models for discrete panel data. In C. F. Manski and Daniel McFadden,(Ed.), Structural analysis for discrete data with econometric applications, pp. 114�178. Cambridge,MA: MIT Press.

Hoffman, E., 6 Libecap, G. (1994). Political bargaining and new deal agricultural policies Citrusmarketing orders in the 1930's. In C. Goldin and G. Libecap (Eds.), The regulated economy: A histori-cal approach to political economy, pp. 189�221. Chicago: Univ. of Chicago Press.

Hoffman, E., Libecap, G., 6 Shachat, J. (1997). An experimental investigation of the incentives to formagricultural marketing pools, Working Paper 97-34, Department of Economics, UCSD, December.

Hoffman, E., 6 Spitzer, M. L. (1985). Entitlements, rights, and fairness: Some experimental evidence ofsubjects' concepts of distributive justice. The Journal of Legal Studies, 42(2), 258�298.

Holt, C. (1995). Industrial organization: A survey of laboratory research. In J. Kagel and A. Roth (Eds.),Handbook of experimental economics, pp. 114�178. Cambridge, MA: MIT Press.

Lee, L.-F. (1987), Nonparametric testing of discrete panel data models, Journal of Econometrics, 34,147�177.

Maddala, G. S. (1987), Limited dependent variable models using panel data, Journal of HumanResources, 22(3), 307�336.

Rural Business-Cooperative Service. (1995). Farmer Cooperative Statistics, RBS Service Report,52nd edition.

Smith, V. L. (1982). Microeconomic systems as an experimental science, American Economic Review, 72,923�955.

Received: February 10, 1998.


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An Experimental Investigation of the Incentives to Form Agricultural Marketing Pools