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Managerial Payoff and Gift-Exchange in the Field

Abstract

We conduct a field experiment where we vary both the presence of a gift-exchange wage and the effect of the worker’s effort on the manager’s payoff. Results indicate a strong complementarity between the initial wage-gift and the agent’s ability to “repay the gift”. We control for differences in ability and reciprocal inclination and show that gift-exchange is more effective with more reciprocal agents. We present a principal-agent model with reciprocal subjects that motivates our findings. Our results help to reconcile the conflicting evidence on the efficacy of gift-exchange outside the lab.

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Fig. 1

Notes

  1. An extensive theoretical literature—e.g., Holmström (1979) or Grossman and Hart (1983)—has emphasized the importance of strong monetary incentives to induce effort.

  2. We were, in 2007, among the first to take seriously the documented heterogeneity in the population along the reciprocity dimension and to test a key tenet of reciprocity models: that treatment effects should be brought about by reciprocal subjects.

  3. On a more methodological level we think this paper was, at the time of writing in 2007, the first to recruit subjects for a natural field experiment via a temp worker agency and to exploit additional data that could be garnered from this specific subject pool.

  4. The “Big 5” personality factors capture five distinct aspects of an individual’s personality: extraversion; agreeablenes; conscientiousness; emotional stability; and imagination. These factors are typically measured by having subjects agree or disagree with an extensive series of statements.

  5. This result is akin to the findings that are summarized in Ichniowski and Shaw (2003) on the complementarities among various HR policy instruments.

  6. This is in contrast to Kim and Slonim (2009), who find gift-exchange mainly along the quality margin.

  7. For further reference see also Fehr and Gächter (2000) or Fehr and Schmidt (2003) and the references therein.

  8. Atrium Staffing of Boston, http://www.atriumstaff.com/, described (as of 2007) their services as follows: “Since 1995, Atrium’s Office Support Practice has been the firm’s stronghold. Our team of skilled recruiters, who themselves draw from diverse career backgrounds, are experts in identifying administrative talent and understanding client needs. Our thorough screening processes ensure that we know our Associates well. Our customized approach to client searches results in impressive hire retention rates of over 93%. We staff direct hire, temp-to-hire and temporary administrative roles in a variety of companies.”

  9. An example from the 1849 Prussian Census can be found in Fig. 2 in Appendix 1.

  10. Note that in principle this is a setting where effort could be motivated by paying a piece rate as suggested by the classic moral hazard literature; cf. Holmström (1979). However, this is not done by the temp agency we work with. Hence, also below in the model, we will treat effort as not contractible (due to constraints on the contracting space).

  11. In order to not deceive the subjects on this issue we arranged with one of the providers of the Prussian Census Data, Sascha Becker, to put such an incentive scheme in place. Our actual “completion bonus” came in the form of free lunch and was worth roughly $10.

  12. Rabin (1993), for simultaneous move games, and Dufwenberg and Kirchsteiger (2004) and Falk and Fischbacher (2006), for sequential games, have developed powerful and general models of reciprocal preferences.

  13. See Appendix 2 for the derivations and a parameterized example.

  14. The Prussian Census has two volumes that differ slightly in their content: in particular, in the number of cells/line and the average number of characters/cell. To control for these differences we convert the number of cells (which is our basic measure of performance) into characters entered by weighting cells by the average number of characters/cell in the respective volume. Alternatively, we can also directly control for the volume by adding a dummy variable and keeping cells as the measure. These results are quantitatively and qualitatively similar.

  15. To construct this measure we repeat the exercise used to construct the data entry rate, i.e. we convert the number of correctly entered cells into characters entered by weighing cells with the average number of characters/cell in the respective volume.

  16. Gneezy and List (2006) and Kim and Slonim (2009) use the same units of observation. Our performance measure is constructed from information when whole lines of the census were finished. These lines took several minutes to be completely entered. To smooth our data, we proceed as follows: If a line was started x minutes before the end of the n-th 10 min sub-period and finished in the y-th minute of the (n+1)-th 10 min sub-period, we account x/(x+y) of the characters of this line to the n-th and y/(x+y) of the characters of this line to the (n+1)-th 10 min sub-period.

  17. Relaxing our specification by allowing for non-linear effects of ability, we estimate a specification with separate dummy variables for the lowest, middle, and highest terciles of ability. In this analysis, we find very similar coefficients and present them in Table 7 in Appendix 3. Note that the results in Table 7 suggest non-linear effects of ability with the middle tercile not being different from the top tercile but the bottom tercile being significantly slower.

  18. The qualitative results are robust to using different cut offs for classifying subjects as highly agreeable. Directly interacting the continuous agreeableness score with the interactions of interests is somewhat too demanding given our sample size.

  19. E.g., performing an hourly based analysis gives similar results.

  20. Kessler (2013) and Esteves-Sorenson (2018) are two careful and comprehensive papers that explicitly try to explain the heterogeneous treatment effects in the various extant studies. Moreover, they examine other characteristics of the work setting that determine the effectiveness of reciprocity-based incentives.

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Acknowledgements

We thank Greg Baron, Gary Charness, Tore Ellingsen, Lena Greska, Al Roth, Carmit Segal, Caspar Siegert, Christina Strassmair, Victor Tremblay, Mo Xiao, and participants of the 2011 EWEBE meeting for their comments and suggestions. We also thank Sascha Becker and Ludger Wössmann for providing us with the Prussian Census materials for our field experiment. Florian Englmaier thanks the Harvard Business School for its hospitality and the German Science Foundation (DFG) for financial support via grants EN 784/2-1, SFB/TR-15, and SFB/TR-190. Steve Leider thanks the National Science Foundation and the Sperry Fund for financial support. The study received IRB approval by Harvard University’s Committee on the Use of Human Subjects in Research, Application Numer: F15221-101.

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Appendices

Appendix 1: Additional Material

See Fig. 2.

Fig. 2
figure 2

Example Page Prussian Census of 1849

Appendix 2: Derivations

Comparative Statics

On the assumption that the contract is generous, the worker’s optimal effort choice \(a^*\) for a given contract is implicitly defined by the first order condition

$$\begin{aligned} \frac{\partial U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a}= - c^{\prime }(a^*) + \eta \left( u({\tilde{w}}) - c({\hat{a}})- {\bar{u}}\right) M \cdot ER^{\prime }(a^*)=0 . \end{aligned}$$

Applying the implicit function theorem we can derive the relevant comparative statics w.r.t. \({\tilde{w}}\) and M:

$$\begin{aligned} \frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a^2}= & {} - c^{\prime \prime }(a^*) + \eta \left( u({\tilde{w}}) - c({\hat{a}})- {\bar{u}}\right) M \cdot ER^{\prime \prime }(a^*)<0\\ \frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a \partial M }= & {} \eta \left( u({\tilde{w}}) - c({\hat{a}})- {\bar{u}}\right) ER^{\prime }(a^*)>0\\ \frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a \partial {\tilde{w}}}= & {} \eta M \cdot u^\prime ({\tilde{w}}) \cdot ER^{\prime \prime }(a^*)>0\\ \end{aligned}$$

Hence it follows that

$$\begin{aligned} \frac{\partial a^*}{\partial M} = -\frac{\frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a \partial M }}{\frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a^2}}> 0 ; \qquad \frac{\partial a^*}{\partial {\tilde{w}}} = -\frac{\frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a \partial {\tilde{w}}}}{\frac{\partial ^2 U\left( {\tilde{w}}, a,{\hat{a}}\right) }{\partial a^2}}> 0 ; \qquad \text {and} \qquad \frac{\partial ^2 a^*}{\partial M \partial w} > 0. \end{aligned}$$

A Simple Example

To provide a concrete example assume that

$$\begin{aligned} ER(a)= a; \qquad u({\tilde{w}}) = {\tilde{w}}; \qquad \text {and} \qquad c(a) = \frac{a^2}{2} . \end{aligned}$$

Then the worker’s utility can be written as

$$\begin{aligned} U\left( {\tilde{w}}, a,{\hat{a}}\right) = {\tilde{w}}- \frac{a^2}{2} + \eta \left( {\tilde{w}}- \frac{{\hat{a}}^2}{2} - {\bar{u}}\right) M \left( a-{\tilde{w}}\right) , \end{aligned}$$

the first order condition is given by

$$\begin{aligned} -a + \eta \left( {\tilde{w}}- \frac{{\hat{a}}^2}{2} - {\bar{u}}\right) M =0, \end{aligned}$$

and can be rearranged to define explicitly \(a^*\)

$$\begin{aligned} a^* = \eta \left( {\tilde{w}}- \frac{{\hat{a}}^2}{2} - {\bar{u}}\right) M. \end{aligned}$$

Now taking explicit derivatives gives

$$\begin{aligned} \frac{\partial a^*}{\partial M} = \eta \left( {\tilde{w}}- \frac{{\hat{a}}^2}{2} - {\bar{u}}\right)> 0; \qquad \frac{\partial a^*}{\partial {\tilde{w}}} = \eta M> 0; \qquad \text {and} \qquad \frac{\partial ^2 a^*}{\partial M\partial {\tilde{w}}} = \eta > 0. \end{aligned}$$

Appendix 3: Additional Analysis

See Table 7.

Table 7 Regression: performance (10 min. Periods) incl.

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Englmaier, F., Leider, S. Managerial Payoff and Gift-Exchange in the Field. Rev Ind Organ 56, 259–280 (2020). https://doi.org/10.1007/s11151-019-09737-y

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Keywords

  • Incentives
  • Field experiments
  • Gift-exchange
  • Reciprocity