Sorting into Contests: Evidence from Production Contracts

Zhen Wang; Tomislav Vukina

doi:10.1515/bejeap-2018-0049

Artikel

Sorting into Contests: Evidence from Production Contracts

Zhen Wang und Tomislav Vukina

Veröffentlicht/Copyright: 5. Januar 2019

Veröffentlicht von

Veröffentlichen auch Sie bei De Gruyter Brill

Manuskript einreichen Informationen für Autor*innen Erkunden Sie dieses Fachgebiet

Aus der Zeitschrift The B.E. Journal of Economic Analysis & Policy Band 19 Heft 1

Abstract

In this paper, we investigate sorting patterns among chicken producers who are offered a menu of contracts to choose from. We show that the sorting equilibrium reveals a positive sorting where higher ability producers self-select themselves into contracts to grow larger chickens and lower ability types self-select themselves into contracts to grow smaller birds. We also show that eliciting this type of sorting behavior is profit maximizing for the principal. In the empirical part of the paper, we first estimate growers’ abilities using a two-way fixed effects model and subsequently use these estimated abilities to estimate a random utility model of contract choice. Our empirical results are supportive of the developed theory.

Keywords: hiring; incentives; cardinal tournaments

JEL Classification: M52; J43; D86

Appendix

Proof of Proposition 1:

Proof. Suppose there are three contracts in the pool of contract alternatives with Q¯1<Q¯2<Q¯3. The threshold ability which equates the expected utility from contract Q¯2 and contract Q¯3,

(19)a23=−bNβ(N−1)+a¯3Q¯3−a¯2Q¯2Q¯3−Q¯2+β(N−1)(Q¯3+Q¯2)2γN

must be greater than a12 and smaller than amax. This is because when a23<a12, contract Q¯2 would be dominated by either contract Q¯1 or contract Q¯3 and would not be chosen by any grower, and when a23>amax, even the best grower would pick contract Q¯2 and no grower would choose contract Q¯3. Hence, it must be that amin<a12<a23<amax. With this condition, growers with abilities in (amin,a12) would choose contract Q¯1, growers with abilities in (a12,a23) would choose contract Q¯2 and growers with abilities in (a23,amax) would choose contract Q¯3. This sorting result for three contracts is illustrated in Figure 2b in the main text. The equilibrium in average abilities is calculated as the solution of the following system of equations:

(20)a¯1=∫amina12aig(ai)dai∫amina12g(ai)dai

(21)a¯2=∫a12a23aig(ai)dai∫a12a23g(ai)dai

(22)a¯3=∫a23amaxaig(ai)dai∫a23amaxg(ai)dai

with eqs. (9) and (19) used as the thresholds (integral limits). Same as in the two contracts case, here as well, the equilibrium average abilities are positively related to the contract expected outputs because a¯1<a12<a¯2<a23<a¯3, i. e.:

a¯1=∫amina12aig(ai)dai∫amina12g(ai)dai<∫amina12a12g(ai)dai∫amina12g(ai)dai=a12a¯2=∫a12a23aig(ai)dai∫a12a23g(ai)dai>∫a12a23a12g(ai)dai∫a12a23g(ai)dai=a12a¯2=∫a12a23aig(ai)dai∫a12a23g(ai)dai<∫a12a23a23g(ai)dai∫a12a23g(ai)dai=a23a¯3=∫a23amaxaig(ai)dai∫a23amaxg(ai)dai>∫a23amaxa23g(ai)dai∫a23amaxg(ai)dai=a23.

The same reasoning can be extended to K contract alternatives. Threshold abilities are expressed as

(23)ak−1,k=−bNβ(N−1)+a¯kQ¯k−a¯k−1Q¯k−1Q¯k−Q¯k−1+β(N−1)(Q¯k+Q¯k−1)2γN∀k=2,3,⋅⋅⋅,K

and growers with abilities between ak−1,kandak,k+1 would choose contract k. The equilibrium average abilities can be calculated from the following system of equations:

(24)a¯1=∫amina12aig(ai)dai∫amina12g(ai)dai⋅⋅⋅

(25)a¯k=∫ak−1,kak,k+1aig(ai)dai∫ak−1,kak,k+1g(ai)dai⋅⋅⋅

(26)a¯K=∫aK−1,Kamaxaig(ai)dai∫aK−1,Kamaxg(ai)dai

and, same as before, in equilibrium, contracted average abilities are increasing with contract expected output. □

Acknowledgement

We would like to thank Atsushi Inoue, Zheng Li, Walter Thurman, Xiaoyong Zheng and the participants of the Society of Labor Economists Conference in Raleigh, NC, May 5-6, 2017 for their helpful comments on an earlier version of this manuscript.

References

Azmat G., and M. Möller. 2009. “Competition Among Contests.” The RAND Journal of Economics 40 (4): 743–68.10.1111/j.1756-2171.2009.00087.xSuche in Google Scholar

Azmat, G., and M. Möller. 2013. “The Distribution of Talent across Contests.” Barcelona GSE Working paper Series, 600, May, 2013.10.1111/ecoj.12426Suche in Google Scholar

Bandiera, O., L. Guiso, A. Prat, and R. Sadun. 2015. “Matching Firms, Managers and Incentives.” Journal of Labor Economics 33 (3).10.3386/w16691Suche in Google Scholar

Barro, J., and N. Beaulieu. 2003. “Selection and Improvement: Physician Responses to Financial Incentives.” NBER Working Paper Series, No. 10017, 2003.10.3386/w10017Suche in Google Scholar

Bull, C., A. Schotter, and K. Weigelt. 1987. “Tournaments and Piece Rates: An Experimental Study.” Journal of Political Economy 95 (1): 1–33.10.1086/261439Suche in Google Scholar

Cadsby, C., F. Song, and F. Tapon. 2007. “Sorting and Incentive Effects of Pay for Performance: An Experimental Investigation.” Academy of Management Journal 50: 1–41.10.5465/amj.2007.24634448Suche in Google Scholar

Cameron, A. C., and D. L. Miller. 2015. “A Practitioners Guide to Cluster-Robust Inference.” Journal of Human Resources 50 (2): 317–72.10.3368/jhr.50.2.317Suche in Google Scholar

Dechenaux, E., D. Kovenock, and R. M. Sheremeta. 2015. “A Survey of Experimental Research on Contests, All-Pay Auctions and Tournaments.” Experimental Economics 18 (4): 609–69.10.1007/s10683-014-9421-0Suche in Google Scholar

Dohmen, T., and A. Falk. 2011. “Performance Pay and Multidimensional Sorting: Productivity, Preferences, and Gender.” American Economic Review 101 (2): 556–90.10.1257/aer.101.2.556Suche in Google Scholar

Ehrenberg, R. G., and M. L. Bognanno. 1990. “Do Tournaments Have Incentive Effects?” Journal of Political Economy 98 (6): 1307–24.10.1086/261736Suche in Google Scholar

Eriksson, T., and M. C. Villeval. 2008. “Performance-Pay, Sorting and Social Motivation.” Journal of Economic Behavior and Organization 68, no. 2 (November): 412–21.10.1016/j.jebo.2007.10.003Suche in Google Scholar

Freeman, R. B., and M. M. Kleiner. 2005. “The Last American Shoe Manufacturers: Decreasing Productivity and Increasing Profits in the Shift from Piece Rates to Continuous Flow Production.” Industrial Relations 44, no. 2 (March): 307–30.10.1111/j.0019-8676.2005.00385.xSuche in Google Scholar

Knoeber, C., and W. Thurman. 1994. “Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production.” Journal of Labor Economics 12 (2): 155–79.10.1086/298354Suche in Google Scholar

Lancaster, T. 2000. “The Incidental Parameter Problem Since 1948.” Journal of Econometrics 95 (2): 391–413.10.1016/S0304-4076(99)00044-5Suche in Google Scholar

Lazear, E. 2000. “Performance Pay and Productivity.” American Economic Review 90 (February): 1346–61.10.1257/aer.90.5.1346Suche in Google Scholar

Leuven, E., H. Oosterbeek, J. Sonnemans, and B. van der Klaauw. 2011. “Incentives versus Sorting in Tournaments: Evidence from a Field Experiment.” Journal of Labor Economics 29 (3): 637–58.10.1086/659345Suche in Google Scholar

Leuven, E., H. Oosterbeek, and B. van der Klaauw. 2011. Splitting contests. Working paper, mimeo.10.2139/ssrn.1682707Suche in Google Scholar

Levy, A., and T. Vukina. 2004. “The League Composition Effect in Tournaments with Heterogeneous Players: An Empirical Analysis of Broiler Contracts.” Journal of Labor Economics 22 (2): 353–77.10.1086/381253Suche in Google Scholar

Lynch, J. G., and J. S. Zax. 2000. “The Rewards to Running: Prize Structure and Performance in Professional Road Racing.” Journal of Sports Economics 1 (4): 323–40.10.1177/152700250000100401Suche in Google Scholar

Morgan, J., D. Sisak, and F. Várdy. 2014. “Self-selection into Contests.” Working paper, mimeo.Suche in Google Scholar

Nagin, D. S., J. B. Rebitzer, S. Sanders, and L. J. Taylor. 2002. “Monitoring, Motivation, and Management: The Determinants of Opportunistic Behavior in a Field Experiment.” American Economic Review 92: 850–78.10.1257/00028280260344498Suche in Google Scholar

Oyer, P., and S. Schaefer. 2011. “Personnel Economics: Hiring and Incentives.” Handbook of Labor Economics 4: 1769–823.10.1016/S0169-7218(11)02418-XSuche in Google Scholar

Tsoulouhas, T., and T. Vukina. 1999. “Integrator Contracts with Many Agents and Bankruptcy.” American Journal of Agricultural Economics 81 (1): 61–74.10.2307/1244450Suche in Google Scholar

Van der Sluis, J., M. Van Praag, and W. Vijverberg. 2008. “Education and Entrepreneurship Selection and Performance: A Review of the Empirical Literature.” Journal of Economic Surveys 22 (5): 795–841.10.1111/j.1467-6419.2008.00550.xSuche in Google Scholar

Vukina, T., and X. Zheng. 2011. “Homogenous and Heterogenous Contestants in Piece Rate Tournaments: Theory and Empirical Analysis.” Journal of Business and Economic Statistics 29, no. 4 (December): 506–17.10.1198/jbes.2010.08345Suche in Google Scholar

Wooldridge, J. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: The MIT Press, 2002.Suche in Google Scholar

Published Online: 2019-01-05

Sie haben derzeit keinen Zugang zu diesem Inhalt.

Artikel in diesem Heft

https://doi.org/10.1515/bejeap-2018-0049

Schlagwörter für diesen Artikel

hiring; incentives; cardinal tournaments