Abstract
We investigate a number of canonical predictions that arise from relational contract theory. Employing an experimental design with endogenous choice of contract type, we find considerable experimental support for several well-established predictions, including the importance of self-enforcement and individual rationality constraints for contractual performance; a preference for informal agreements when third-party verification of performance is coarse; and a tendency toward strategic ambiguity (Bernheim and Whinston Am Econ Rev 88(4):902–932, 1998). However, two findings that appear to be inconsistent with theory are that (1) contractually specified performance levels do not appear to respond to the discount factor though realized performance does; and (2) subjects often apply inefficient punishments following a deviation. By providing evidence on the strengths and weaknesses of standard relational contract theory, our study shows where there is room for improvement. We conjecture that incorporating social preferences and semi-grim strategies (Breitmoser Am Econ Rev 105(9):2882–2910, 2015) can potentially address the observed weaknesses.
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29 March 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10683-021-09712-z
Notes
For example, efficient punishments may mean contract continuation but with rents reallocated away from the deviator. One can conjecture that distributional social preferences combined with reciprocity may act as constraints because they may limit the amount of redistribution as well as the parties’ willingness to continue to contract.
See Aghion and Holden (2011). In their survey article, they point out that the “second generation” models of incomplete contracts tend to focus on relational contracting.
The interaction between explicit contracts and implicit incentives has also been studied in an one-shot interaction environment. See, for example, Fehr et al. (2007).
No other quality level is verifiable, so the agent will choose \(q=q^{d}\) even if a contract calls for \(Q>q^{d}\) and will choose \(q={\underline{q}}\) if the contract calls for \({\underline{q}}<Q<q^{d}\).
P is always third-party enforceable because it is not contingent on quality.
Under symmetric information, which pertains to our case, stationary contracts can be used to simplify the modeling of optimal contracts (Levin 2003). While stationary contracts refer to identical contracts across t on the equilibrium path, the contract must still specify what will happen off the equilibrium path. This may call for some type of punishment such as termination of the contract or a continuation of the contract with a redistribution of the surplus, but this does not imply non-stationary behavior. The specification of termination or a different type of contract off the equilibrium path, even under stationarity assumptions, is fairly conventional in the repeated game and relational contract literatures (e.g., Levin (2003)). Practically speaking, it is important to point out that nearly all experiments involve some dynamics simply because subjects learn how to play the game. Hence, researchers typically treat predictions from stationary symmetric information games as theoretical benchmarks that subjects should converge to after sufficient learning. The actual dynamics that lead to convergence is typically not of theoretical interest and early period departures from theoretical benchmarks are treated as noise which is likely to reduce with subject experience.
The agent’s self-enforcement constraint acts as an incentive compatibility condition for the agent to deliver on Q.
In principle, values of \(B({\tilde{Q}})\) that violate the l.h.s. of 7 should also increase shirking on the bonus by the principal. However, since the principal both sets \(B({\tilde{Q}})\) and makes the decision on actual bonus b, this is plagued by endogeneity problems. A principal who specifies a non-credible \(B({\tilde{Q}})\) may have no intention of paying the bonus in the first place so promised bonus and actual bonus are jointly determined.
We say weakly because if \(\alpha =0\), then the threshold does not change until the joint surplus with formal contracts exceeds the joint surplus under the reservation payoffs, triggering \(\alpha =1\).
It is also well known from the implementation literature that option contracts can achieve efficient outcomes even with non-verifiable performance factors and even in one-shot situations. However, this also raises complicated questions regarding the effectiveness of option contracts in the presence of renegotiation (e.g. see Edlin and Hermalin (2000) for one example). While these are interesting issues, they are not the focus of our study; instead, we focus on canonical assumption from the relational contracting literature rather than the implementation literature.
Despite random continuation being a widely used protocol, one might still be concerned that subjects might be confused. In an attempt to minimize confusion, at the end of each trading period, subjects were shown a screen that resembled a roulette wheel with ten numbers. In the PE0.80 treatment, for example, eight of the ten numbers were green to illustrate the probability of continuation. The full details and screenshot are given in Figure 23 in Online Appendix D. Another potential concern is that the experiment, taken as a whole, can seem complicated. In this regard, we have taken several steps to minimize confusion. First, we conducted two trial periods imposing no time limits to ensure that subjects had adequate time to become familiar with the procedures and screens. Second, the experiment is framed in terms of a buyer-seller transaction so the sequence of events does not depart very far from many transactions that occur naturally in the real world. Third, the transaction was sequential rather than simultaneous so each separate decision had its own relatively uncluttered decision screen that involve simply entering a number or clicking an option (see Online Appendix D for the screenshots). While there is no guarantee that these steps eliminated all confusion, there are clear systematic patterns in our data that seem intuitive and expected if subjects understood the nature of the transactions that they engaged in.
The expected number of periods is \(\frac{1}{1-\delta }\).
We recruited more subjects for the \(\delta =0.5\) treatments because the expected length of supergames are shorter. Thus, we would likely exhaust matches more frequently in the \(\delta =0.5\) sessions if we did not recruit more subjects. The differences in group size should not create an imbalance in group reputation effects since we implemented stranger matching.
Only one of the three PE0.50 sessions lasted longer than 20 periods, so the data from period 20 and beyond is from one session and may be more volatile.
Recall that buyers are not required to offer contracts. Thus, the number of contracts need not match total possible trading opportunities.
The data do not imply that the contract only satisfies the column constraint. For example, according to the Buyer Self-Enforcement column, 80 (29%) of offered contracts satisfied the buyer self-enforcement constraint for B. This does not mean that this is the only constraint that those 80 contracts satisfied. It could be that some of those satisfied one or more of the other constraints as well. We did not partition the data into finer detail because there were so many possible combinations that it would make the table unwieldy.
The volatility of the PE0.50 line reflects the fact that there were very few observations involving relational contracting after period 19 in the PE0.50 sessions.
There were no observations where \(B-B_h<-25\).
The Period variable is not a count of the number of periods in each supergame as there are multiple supergames within a session. Thus, Period does not restart after each supergame.
To further check for robustness, we also ran regressions with seller-session-buyer random effects, and separately estimated probit regressions. The qualitative results remain unchanged.
We also created the same figure using data after period 10 only to see whether subjects adjust their behavior after some learning takes place. The results were very similar, although there is a slight decrease in the use of relational contracts and increase in termination following shirking.
Breitmoser (2015) argues that controlling for unobserved heterogeneity is important since observations from cooperative states are more likely to come from cooperative types. Theoretically, there should be no correlation between unobserved buyer heterogeneity and the other independent variables so that random-effects can be used.
We discuss the impact of social preferences and semi-grim strategies in more detail in Online Appendix B.
In Online Appendix C, we provide a detailed discussion of why buyers may under-specify Q in PE0.80 and yet over-specify Q in PE0.50.
We also separately estimated fixed effects and probits, but the qualitative results are unchanged.
Pure bonus contracts are not included in the figure because they were not used in Treatment PE0.50 and there were only three used in Treatment PE0.80.
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Acknowledgements
We thank Klaus Abbink, Tim Cason, Vai-Lam Mui, Tom Wilkening, and seminar participants at Monash University and University of Sydney for helpful comments. Sharon Raszap and Amy Corman provided excellent research assistance. The experimental work was conducted under Purdue University IRB Protocol number 1103010650.
Funding
Funding from USDA-NIFA grant number 2010-65400-20430 and HATCH project IND010580 are gratefully acknowledged. Roe recognizes support from the McCormick Program at the Ohio State University. The financial sponsors of this research played no role in the study design, the collection and analysis/interpretation of the data, the writing of the article, and the decision to submit the article for publication. This research is not the result of a for-pay consulting relationship.
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Erkal, N., Wu, S.Y. & Roe, B.E. Putting relational contract theory to the test: experimental evidence. Exp Econ 25, 111–139 (2022). https://doi.org/10.1007/s10683-021-09707-w
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DOI: https://doi.org/10.1007/s10683-021-09707-w