Laboratory Experiments with a Finite-Horizon Job-Search Model

In this article we explain the essential role of controlled experiments in testing job-search models. We derive the testable implications of a finite-horizon job-search model and layout the design of the controlled experiments that we use to test those implications. We present the results of several parametric and nonparametric tests, all conditional on the actual draws of the wage offers. Overall, we find close agreement between the predictions of the search model and observations of search duration and income for several experimental treatments. There is a voluminous literature on the theory of optimal job search.! Models have been developed for infinite and finite search horizons, costly and subsidized search, zero and positive discount rates, search with and without recall of past wage offers, and known and unknown wage-offer distributions. Much of the literature involves models of search by individual agents, although some articles embed job search in a market context. To date, this body of theory has been subjected to very little empirical testing. This article advances the process of testing the theory with controlled experiments. We report the results of experiments that are designed to test a finite horizon model of sequential search by an individual agent. The formal structure of the model is that of a stochastic dynamic programming model that incorporates the expected utility hypothesis. Because of the dynamic nature of the sequential search environment, the decision task faced by our subjects is much more complicated than those in most individual choice experiments. Consider, for example, the choice that must be made by a subject who receives an offer in soIIle period that is not the last period in an experimental trial. The offer is a certain amount of money. However, if the subject accepts the offer, then he must forego the opportunity to continue the search and possibly to receive a more remunerative offer. This opportunity cost of accepting an offer consists of the uncertain payoffs that JAMES C. COX AND RONALD L. OAXACA 302 are foregone by relinquishing the opportunity to draw from the wage-offers distribution in all of the periods that remain in the search horizon. The distribution of these foregone payoffs is complicated by the fact that the dollar value of a specific wage offer changes from one period to the next during an experiment trial because of the finite length of the (search and earnings) horizon. Before conducting the search experiments, it was our expectation thai the results would not be very consist~nt with the search model. This expectation was based on our observation that decision theory had performed rather poorly in previous individual choice experiments in both the simple decision environment of preference reversal experiments (Grether and Plott, 1979; Cox and Epstein, 1989) and the somewhat more complicated environment of Bayes' rule experiments (Grether, 1980). We were surprised to discover that our subjects' behavior was highly consistent with the finite-horizon search model that we tested. The remainder of this article contains the following. In section 1, we discuss the role of controlled experiments in testing job-search models. We explain that experiments are essential for testing these models, because several of the postulated determinants of search behavior are not observable in nonexperimental data sources. Section 2 contains a discussion of earlier experimental research on job-search models. Section 3 presents the finite-horizon search model that we test. This model differs from those in the literature because it specifies that economic variables are discrete (rather than continuous). This distinction is essential to the numerical solutions of the model that provide the basis of the most stringent tests of it. The numerical solutions are for the linear (risk-neutral) special case of the concave (risk-averse or risk-neutral) search model. They are used in two-sided tests of the risk-neutral special case of the model. The same numerical solutions are used in one-sided tests of the general concave (risk-neutral or risk-averse) model. The theore~cal basis for the one-sided tests is provided by the result derived in section 3 that the discrete reservation wages for a risk-averse agent never exceed those for a risk-neutral agent We explain our experimental design in section 4. In addition to the baseline trials, the experiments involve treatments that test for the effects on subject behavior of the interest rate, search costs and subsidies, riskiness of the wage-offers distribution, the probability of receiving an offer, and the length of the search horizon. In section 5 we present our analysis of the results of the experiments. Finally, in section 6 we make some concluding remarks. 1. The role of controlled experiments Job-search models are typically dynamic models of optimal search under conditions of uncertainty. The models incorporate the assumption that a searcher's only incentive in the search process is provided by the income stream that results from search. If such models are to be reasonably accurate predictors of job-search behavior in observable labor markets, then the behavior must be consistent with the following two behavioral hypotheses. EXPERIMENTS WITH FINITE-HORIZON JOB-SEARCH MODEL 303 FIND: Normally intelligent human beings are capable of making choices in a dynamic, uncertain decision environment as if they were finding the optimal solutions to stochastic dynamic decision problems. DaM: The income stream that results from search dominates other possible determinants of job search behavior. That hypothesis FIND is involved needs little explanation; if, using whatever heuristics they may, people do not make choices in these environments that are (appro~mately) optimal, then the models will not (reasonably) accurately predict their behavior. As for hypothesis DOM, our socialization may endow us with a much richer set of behavioral tendencies in job-search/job-acceptance choices than simple wealth maximization. In that case, the models might not predict behavior well, even if individuals behave as if they are good stochastic dynamic decision makers. The distinction between FIND and DOM, and the importance of both to empirical evaluation of job-search models, sheds light on the role of laboratory experiments in such research. Consider some of the difficulties in attempting to use nonexperimental data to test job-search theory. The models imply that the feasibility of recalling (inventorying) past wage offers, the length of the search horizon, and agent information on the distribution of wage offers are central determinants of an optimal search strategy. But possibilities of wage-offer ecall, the length of search horizons, and agent information on wage-offer distributions are not observable in nonexperimental data sources. How then can one use such data even to test hypothesis FIND, let alone to test the conjunction of FIND and DOM that would be the question in nonexperimental environments? In contrast, controlled experiments have some unique advantages for empirical evaluation of the models. The relative advantages of laboratory experiments and field experiments are somewhat different, and thus we will discuss both types. It is possible to design laboratory experiments that are intended to test the conjunction of hypotheses FIND and DOM. This can be done by incorporating in the experimental instructions such emotive terms as job, unemployment, income from working, etc., and asking the subjects to engage in job-market role-playing. Interpretation of the experimental results then requires the additional behavioral hypothesis that laboratory role-playing is equivalent to actual labor-market participation. If the theory fails the experimental test, it is then not clear whether this is due to the failure of hypothesis FIND or to the failure of hypothesis DOM. If the theory does not fail the experimental test, it is then not clear whether 1) the results support the conjunction of hypothesis FIND, hypothesis DOM, and the behavioral equivalence hypothesis, or 2) the subjects were not motivated by the roleplaying instructions, and hence hypothesis DOM was not really tested, and the results only support hypothesis FIND. In order to obtain results with an unambiguous interpretation, we have designed experiments to test only hypothesis FIND. This is done by carefully avoiding any use of possibly emotive terms such as job or employment in the experiments. The 304 JAMES C. COX AND RONALD L. OAXACA experimental subjects are given the opportunity to make sequential choices in a stochastic environment about accepting or not accepting points that have a known conversion rate into dollars. In addition, the experimenter can control, and thereby observe, the possibility of recalling past wage offers, the length of the search horizon, and agent information about the wage-offer distribution. Also under experimental control are theoretically hypothesized determinants of search behavior, such as the discounting rate of interest and the cost or subsidy to search. Thus laboratory experiments of the type reported below are well suited for yielding empirical information about hypothesis FIND. If the results of such experiments are inconsistent with FIND, then job-search models are called into question, if not rejected, as acceptable predictors of job-search behavior. If the results are consistent with FIND, then the research can proceed to examine DOM, or the conjunction of FIND and DOM. Field experiments can be used to test for the conjunction of hypotheses FIND and DOM. Such experiments could be done with offers in field labor markets in which the subject role-playing would be actual labor-market participation. One disadvantage of such experiments, relative to laboratory experiments, is that they would be expensive. Other disadvantages include'the researcher's inability to control the subjects' search horizons and difficulty in controlling their information about the wage-offer distribution and their discount rates. The reason for this is that the experimental field labor market could not be isolated from other uncontrolled markets. However, if laboratory experiments had previously found that subject behavior was consistent with hypothesis FIND, then the control problems in field experiments intended to incrementally test hypothesis DOM might not be prohibitive. 2. Previous experimental tests of job-search models Braunstein and Schotter (1981, 1982) present experimental tests of most of the hypotheses implied by the pre-1976 job-search theory surveyed in Lippman and McCall. (1976a, 1976b). With one prominent exception, the Braunstein-Schotter articles report results that are consistent with the theory. However, the one exception is central: it is a reported inconsistency between the observed decreasing reservation wages of the subjects and the predicted constant reservation wage path of the infinite-horizon search model that they use to interpret the data (Braunstein and Schotter, 1981, p. 20). Braunstein and Schotter did not (except in one trial) limit the number of searches that their subjects could undertake. They interpret this experimental design as corresponding to an infinite horizon search. But this interpretation can be questioned. After all, an infinite number of searches is clearly impossible for an individual in any experimental or field labor market. Did the subjects really believe that they could continue to search indefinitely? Braunstein and Schotter's data show decreasing reservation wages for their experiments where points had a one-for-one transformation into dollars (their risk-neutral experiments). Is this a EXPERIMENTS WITH FINITE-HORIZON JOB-SEARCH MODEL 305 result that is properly interpreted as being inconsistent with the constant reservation wage implication of the infinite-horizon search model? Or does it indicate that the subjects, in fact, realized that some finite limit would of necessity be imposed on the number of searches? In that case, if the subjects perceived the experiment as a finite-horizon search experiment, then the decreasing reservation wage results are consistent with finite-horizon search theory. In contrast, our approach makes possible an unambiguous interpretation of the experimental results, because we develop a finite-horizon search model and then run experiments that are clearly finite-horizon. The tests that Braunstein and Schotter (1981, 1982) apply to their data are relatively weak, and in many cases this approach favors acceptance of the theoretically predicted hypotheses. All their tests use only sample means. Furthermore, in most of their experimental trials they do not test for differences between observed search duration and theoretically predicted search duration, conditional on draws from the wage-offers distributions, although their experimental design would make such tests possible for all of their trials. In contrast, some of our tests are full distribution tests using theoretically predicted values conditional on actual draws of the random variables. Another feature of the Braunstein-Schotter experimental design that we will discuss is the way that they conveyed probability distribution information to the subjects. They informed the subjects that wage offers would be variously drawn by the computer from symmetric triangular, rectangular, truncated symmetric triangular, right triangular, and left triangular distributions! It is a common procedure in many experiments to have a computer draw values of a random variable from a distribution that is described to the subjects. There are possible problems with this approach. One is that the subjects may not understand the meaning of drawing values froJ]l at) abstractly represented distribution. Another is that they may not believe that the values they are assigned were actually drawn from the described distribution. We use a different approach in our experiments. We use physical devices (a container with white and black balls and a bingo cage) to generate values of random variables and a procedure where the subjects can inspect the devices and witness the draws. Therefore, an additional feature of our approach is that it provides a behavioral baseline that can be used to test the properties of abstract representation of probability distributions by considering that procedure to be an experimental treatment. 3. A simple finite-horizon search model Mortensen (1970) developed a basic search model that has achieved the status of a benchmark in job-search theory. That model assumes an infinite search horizon for an unemployed worker who knows the (differentiable) wage-offer cumulative distribution but does not know in advance which firm will be offering what wage. The worker is assumed to search one firm each period and must accept or reject an offer when it is received. The model predicts that a risk-neutral worker who seeks 306 JAMES C. COX AND RONALD L. OAXACA to maximize the expected net present value of income will select an optimal reservation wage that remains constant throughout the search. Among the implications of this model are that an increase in either the discounting rate of interest or the direct costs of search willi) lower the reservation wage and hence the expected acceptance wage, 2) lower the expected duration of search, and 3) raise the probability of accepting an offer in any given period. There are practical difficulties that arise with respect to the design of an experiment to test the"Mortenst:n model. One such problem is the matter of an infinite horizon. While perhaps not insurmountable, it is a complication that can be avoided by recasting the model in finite-horizon terms. Furthermore, it is the finite-horizon model that is empirically interesting because, after all, real workers have finite lives. An example of the finite-horizon version of Mortensen's model is found in Gronau (1971). The introduction of a finite horizon does lead to abandonment of the constant reservation wage property of the Mortensen model; but the qualitative implications of the model for changes in variables such as the discounting rate of interest and the direct costs of search are unchanged. Another difficulty with both the Mortensen and Gronau models is that the wage-offer distributions are not discrete. The use of wage-offer distributions with continuous densities is of course motivated by considerations of analytical convenience. Nevertheless, in an operational setting, wage-offer distributions are obviously discrete. This problem is easily remedied. The job-search model that we test is constructed as follows. We specify a search horizon of T periods. In each period, the probability that the job search will be rewarded with a job offer is p. If a job is offered, the (conditional) wage offer is a discrete random variable, W, with (conditional) discrete density function, for WI < w < Wh { prOb (W = w), g(w) = 0, otherwise. (1) If an offer is accepted in period t, wage payments begin in period t + 1 and continue through period T + 1. Any net subsidy to search (gross subsidy less search cost) in period t is paid in period t, whether or not a job is accepted. Let w, be the reservation wage for period t. Define l,(w,) as the time-period-one discounted value of the expected utility of income from the job search in period t. Define w7 as the optimal reservation wage for period t; that is,