Distributing scarce jobs and output: experimental evidence on the dynamic effects of rationing

Abstract

How does the allocation of scarce jobs and production influence their supply? We present the results of a macroeconomics laboratory experiment that investigates the effects of alternative rationing schemes on economic stability. Participants play the role of worker-consumers who interact in labor and output markets. All output, which yields a reward to participants, must be produced through costly labor. Automated firms hire workers to produce output so long as there is sufficient demand for all production. In every period either output or labor hours are rationed. Random queue, equitable, and priority (i.e., property rights) rationing schemes are compared. Production volatility is the lowest under a priority rationing rule and is significantly higher under a scheme that allocates the scarce resource through a random queue. Production converges toward the steady state under a priority rule, but can diverge to significantly lower levels under a random queue or equitable rule where there is the opportunity for and perception of free-riding. At the individual level, rationing in the output market leads consumer-workers to supply less labor in subsequent periods. A model of myopic decision-making is developed to rationalize the results.

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Notes

  1. 1.

    By contrast, evidence suggests that voluntary rationing of food during World War I was ineffective at ensuring equitable allocations: “While many better-educated and more affluent Americans did observe wheatless and meatless days, immigrants and those in the working class . . . increased their food intake; beef consumption . . . actually went up during the war” (Bentley 1998).

  2. 2.

    For an excellent survey of the macroeconomic disequilibrium theory literature, see Drazen (1980).

  3. 3.

    An alternative approach to rationing was developed by Clower (1965), Barro and Grossman (1971), and Benassy (1975, 1977), whereby the consumer maximizes demand for each good separately subject to her budget constraint. In forming the demand for a good, the agent disregards quantity rationing for the particular good, but optimizes as though all other demands for goods in her consumption set have faced rationing. Gale (1979) and Svensson (1980) explore the existence of disequilibria under stochastic manipulable and non-manipulable schemes.

  4. 4.

    Fenig et al. (2016) study household decisions in an environment with a priority rationing scheme. The data generated from their baseline environment is employed as one treatment in this paper.

  5. 5.

    There are macroeconomic experiments that involve utility for leisure and that individual household/consumers can sell their leisure for income: see Riedl and Van Winden (2007) and Lian and Plott (1998), while others focus on disutility from labor (Noussair et al. 2007; Bosch-Domènech and Silvestre 1997; Petersen 2015; Noussair et al. 2015). Macroeconomic models are often framed with supplying labor as a cost to the household. We can only speculate that endowing subjects with a stock of leisure which they can sell at a cost to themselves may encourage them to over-consume leisure due to an endowment-effect story. This was observed in Lian and Plott, but not in Riedl and Van Winden.

  6. 6.

    We intentionally avoided the inclusion of advanced production and inventories in our experimental design. First, the presence of inventories would alleviate the degree of rationing. Second, the underlying model of our economy assumes firms produce output made to order. Production economy experiments such as Lian and Plott (1998) and Noussair et al. (2014, 2015) allow for advanced production but do not allow firms to carry inventories from one period to the next. With advance-production, firms inevitably face the risk that their produced unit will not be sold. To buffer themselves, firms produce inefficiently low quantities. This is a plausible explanation for the low production levels in Lian and Plott (1998).

  7. 7.

    We use the median, rather than the average, of participants’ labor and consumption decisions because latter may be biased due to decisions that were not submitted on time or by extreme outliers.

  8. 8.

    This procedure was first implemented by Camerer and Weigelt (1993), and has been used by Lei and Noussair (2002) and Crockett and Duffy (2015) among others. Alternatively, one could shrink the utility points associated with consumption and labor as in Noussair et al. (2014).

  9. 9.

    Stationary repetition allows us to control for learning and is especially important in macroeconomic experiments. In our environment, subjects carry cash balances and debt from one period into the next. At the beginning of an experiment, it is not unreasonable for subjects to experiment with their decisions or make decision errors that will influence their bank account balances. Bank account balances, however, have important implications for optimal consumption and labor decision-making, and errors during learning can potentially bias subjects’ behavior.

  10. 10.

    We find little evidence that information about the steady state values biased subjects’ initial decisions. When we consider the first round of play, we find no subject selects the equilibrium decision or rounds up or down to the next 0.1 value. Moreover, a very small proportion of subjects are within 1 (0.5) unit of the equilibrium value for output demand (labor supply). Of those subjects that submitted a decision, 5/51 in the Random treatment, 2/62 in the Equitable treatment, and 0/54 in the Priority treatment chose a number in the range [21.37, 23.37]. When it comes to labor supply decisions, we observe 10/51 in the Random treatment, 10/62 in the Equitable treatment, and 6/54 in the Priority treatment chose values in the range [2, 2.5]. The full distribution of first-round decisions can be found in online Appendix E.

  11. 11.

    The intuition for excess labor supply follows a similar thought experiment.

  12. 12.

    Note that nominal wages and prices are more likely to respond minimally to rationing under an Equitable rule, as the median participant will also be changing her output demands and/or labor supplies. By contrast, under a Random Queue rule, the median participant in the initial stages of rationing will be unaffected by small amounts of labor shading. Under a Priority rule, wages and prices are unaffected by a single participant deviating from the representative agent prediction, regardless of the size of the deviation.

  13. 13.

    Screenshots of the computer interface can be found in Figures 4, 5 and 6 in online Appendix F.

  14. 14.

    The instructions can be found in online Appendix G and online Appendix H.

  15. 15.

    The frequency of subjects submitting the maximum levels of consumption and labor was extremely low. Only 0.6% (23/3928) of submitted decisions in the Random treatment, 0.1% (6/4723) in the Equitable treatment, and 0.3% (14/4177) in the Priority treatment were for \(c_{i,t}^D=100\) and \(l_{i,t}^S=10\).

  16. 16.

    We also compute a session-level measure of the likelihood of worsening output and labor rationing given past rationing. Wilcoxon signed-rank tests reject the null hypothesis that output rationing remains constant in favor of increased output rationing in all treatments (\(p<0.027\)). Only in the Random treatment does output rationing significantly worsens in the following period (\(p=0.06\)).

  17. 17.

    If at period t, \(\left| h_{t}^{med}-h_{ss}\right|>1/:(\left| c_{t}^{med}-c_{ss}\right| >10)\), where \(h_{t}^{med}\) and \(c_{t}^{med}\) are median labor supply and median output demand at period t, respectively, we still count it as a converging period only if convergence is restored in the following period, \(\left| h_{t+1}^{med}-h_{ss}\right|<1 /:(\left| c_{t+1}^{med}-c_{ss}\right| <10)\).

  18. 18.

    We consider the excess output demand case. Whenever there is excess labor supply, agents would find it profitable to deviate by cutting their hours of work, up to the point at which there would be excess output demand.

  19. 19.

    Given that this is the equilibrium solution for the static model, labor supply is higher than in the steady state. However, for the dynamic case, the Nash equilibrium labor supply and the implied consumption do not maximize individuals’ lifetime utility because they imply a positive level of indebtedness.

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Correspondence to Luba Petersen.

Additional information

We have benefited from the insightful comments of Katherine Anderson, David Freeman, Catherine Eckel, George Evans, Chloe Gibbs, Brit Grosskopf, Erik Kimbrough, Corrine Low, Charles Noussair, Rosemary Prentice, Alexandra van Geen, two anonymous referees as well as seminar and conference participants at University of British Columbia, University of Saskatchewan, the 2014 Canadian Economic Association Meetings, the 2015 Barcelona GSE Summer Forum in Theoretical and Experimental Macroeconomics, and the 2016 North American Economic Science Association. We also appreciate the insightful comments from two anonymous referees. Finally, we would like to thank the Sury Initiative for Global Finance and International Risk Management and the Social Sciences and Humanities Research Council of Canada for generous financial support and Camila Cordoba and Matthew Pentecost for excellent research assistance.

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Fenig, G., Petersen, L. Distributing scarce jobs and output: experimental evidence on the dynamic effects of rationing. Exp Econ 20, 707–735 (2017). https://doi.org/10.1007/s10683-016-9507-y

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Keywords

  • Rationing
  • Allocation rules
  • Unemployment
  • Experimental macroeconomics
  • Laboratory experiment
  • General equilibrium

JEL Classification

  • C92
  • E13
  • H31
  • H4
  • E62