Efficiency wages in an experimental labor market Mary L. Rigdon† Department of Economics, University of Texas, Austin, TX 78712 Communicated by Vernon L. Smith, George Mason University, Arlington, VA, July 29, 2002 (received for review March 10, 2002)
There has been recent experimental support for efficiency wage theories of the labor market. This short paper initiates the larger process of evaluating the boundary conditions of the giftexchange phenomenon. In particular, we will see whether behavior consistent with the fair wage– effort hypothesis can emerge and be sustained under conditions in which there is (i) a nontrivial marginal cost to providing effort and (ii) increased social distance between subject and experimenter.
T
he competitive theory of the labor market predicts that in markets without information or contracting problems workers are paid according to their opportunity cost. Wages depend only on workers’ abilities. As firms bid for workers’ services, labor markets clear and involuntary unemployment falls to zero. However, empirical evidence suggests that wage determination does not always work this way. This fact has led to the development of efficiency wage theories. These theories posit that firms voluntarily pay supracompetitive wages. One view is that the labor contract is a form of ‘‘partial gift exchange’’ (1–3). That is, an employer’s gift to a worker is a wage above what the market bears, and the worker exchanges by offering aboveminimal productivity. This is also known as the fair wage–effort hypothesis. As intuitively plausible as efficiency wage theories are, they are difficult to test. There is a large empirical literature surrounding the fair wage–effort hypothesis, examining everything from the interindustry wage structure (4) to whether Henry Ford paid an efficiency wage at $5 per day (5). Case studies, including surveys, provide some insight (6–8), but as Raff and Summers note, ‘‘the very impediments to evaluating workers’ ability, motivation, and stability that might lead employers to pay efficiency wages make conventional testing of efficiency wage theories difficult’’ (ref. 5, pp. S58–S59). Testing these theories using econometric methods is hampered by the problem that variations in wages across workers or firms are not likely exogenous, which of course complicates the issue of identification in a model. The control and replicability of laboratory methods can allow unique insights into the robustness and boundary conditions of the fair wage– effort hypothesis. By using induced utilities, we can create an environment in which all workers are identical: They face the same costs to providing effort, and all provide the same return to the firm for any given level of effort. As a result, differences in workers’ abilities兾human capital are no longer an issue as they are in field data. Ernst Fehr and coworkers (9–11) have used the laboratory to test the fair wage–effort hypothesis. They report impressive support for efficiency wages in their initial experiments: laboratory ‘‘employers’’ offer wages above the competitive level, and laboratory ‘‘workers’’ reciprocate with high levels of effort. However, establishing the possible existence of efficiency wages in the laboratory constitutes only the first step of what we can learn from experimental labor markets. This short paper initiates the larger process of evaluating the boundary conditions of the gift-exchange phenomenon. In particular, we will see whether behavior consistent with the fair wage–effort hypothesis can emerge and be sustained under conditions in which there is (i) a nontrivial marginal cost to providing effort and (ii) increased social distance between subject and experimenter. 13348 –13351 兩 PNAS 兩 October 1, 2002 兩 vol. 99 兩 no. 20
Game Theoretic Environment Interactions between a firm and its prospective employees can be thought of as a two-stage game (9), and features of firm–worker relationships can be represented by restrictions placed on the structure of the game. The first stage in the game is a one-sided auction with an employer posting a single contract offer consisting of a wage to be paid (w) and a desired effort level (eˆ). Workers cannot make counteroffers. In a random order, workers then choose whether to accept an available contract offer or not. A worker’s acceptance of an offer creates a contract. In the second stage, employed workers choose their actual effort level, e, anonymously. Workers can choose a lower actual effort level than the desired level specified in their contract (e ⬍ ˆe), fulfill their contractual agreement (e ⫽ ˆe), or be more generous to their employer by working harder than specified in the contract (e ⬎ ˆe). Furthermore, the choice of e is unconstrained in the sense that an employer cannot punish or reward a worker following the choice. This restriction models the situation that faces large firms: Monitoring employees is too costly, and therefore punishing or rewarding them for their effort levels is infeasible. There are four further conditions.‡ First, there is an excess supply of workers, which is common information among firms and workers. This is an attempt to give competitive theory its ‘‘best shot.’’ It has been shown that one-sided auctions converge quickly and slightly above the competitive market-clearing level (13). Thus, by having more workers than employers we would expect to see further downward pressure on wages. Second, wages being offered are common information, but effort choices are relayed only to the workers’ particular employer, and thus effort levels are private information among the parties involved in the transaction. Third, the parties do not know the identity of their trading partners during or after the game. Finally, the experiments reported here that implement this institution are framed in market terms: Employers are called ‘‘buyers,’’ workers are called ‘‘sellers,’’ the wage is called ‘‘price,’’ and the effort level is called ‘‘quality level.’’ This avoids emotive terms such as ‘‘wage,’’ ‘‘effort’’ or ‘‘employment.’’ Consider the competitive equilibrium predictions. Assume all agents in the two-stage game are money maximizers, and this is common knowledge. Let W be the set of possible wage offers in a market if W is a set of nonnegative real numbers (W 傺 ᑬ⫹), and there is wi 僆 W such that wi ⬍ wj (for any wj 僆 W such that j ⫽ i). If wi is minimal in W, call it wmin. Similarly, let E be the set of possible effort level choices if E 傺 ᑬ⫹ and there is an ei in E such that ei ⬍ ej (for any ej 僆 E such that j ⫽ i). If ei is minimal in E, call it emin. Since effort is a costly enterprise, and workers cannot be punished for their choice of effort level, then workers will always choose e ⫽ emin. Hence, the competitive level of effort, e*, is emin. This is true regardless of what wage offer they receive from a prospective employer. Employers, being rational themselves, know this fact. Moreover, there is a known surplus of workers. These two facts entail that there is no incentive for employers to provide wages above the level that clears the market. Thus if wmin ⫽ 0, then wmin is the smallest wage that will be accepted. So w* ⫽ wmin. Otherwise, i.e., if wmin ⫽ 0, then w* ⫽ †E-mail: ‡These
[email protected].
particular features follow the protocols found in refs. 9 –11 (see also ref. 12).
www.pnas.org兾cgi兾doi兾10.1073兾pnas.152449999
Table 1. c(e) schedule for workers
Table 2. v(e) schedule for employers
1
2
3
4
5
6
0
2
4
6
8
10
wmin ⫹ 僐.§ Note that e* and w* are independent (neither is a function of the other). The fair wage–effort hypothesis, on the other hand, yields very different predictions. Instead of assuming that firms and workers each aim to maximize their own narrowly construed utilities, the gift-exchange model allows for the possibility that agents aim at maximizing the gains to be had from exchange and distributing that total in reasonable ways. Thus, the actual effort level provided by a worker correlates positively with the wage offered by firms. Employers with more productive workers have an opportunity for higher profits, and thus employers may have an incentive to pay a wage above that which is competitive. The higher the rent offered to the worker, the more trusting a contract is. Rent is the amount a worker receives in excess of the associated cost for the employer’s desired effort level. A reciprocating agent will be willing to increase the actual effort choice in response to increases in rent. It therefore will be to a firm’s advantage to trust workers by offering contracts with higher rents and correspondingly higher desired effort levels. The utilities to the workers (uj) and firms (i) in this environment are as follows. Let w be a wage offer (10 ⱕ w ⱕ 35) and e an actual effort-level choice by the worker (1 ⱕ e ⱕ 6). Worker j’s utility of the wage–effort bundle (w, e) is the wage received minus what it costs to provide that particular effort. Similarly, firm i’s utility of (w, e) is the value to i of that effort minus the wage paid out. More formally, define the utility to worker j of wage w at effort e as u j 共w, e兲 ⫽
再
w ⫺ c共e兲 0
if contract is accepted , otherwise
[1]
where c(e) is a schedule of effort cost to the worker. Similarly, the profit to firm i of (w, e) is given by
再
v共e兲 ⫺ w i 共w, e兲 ⫽ 0
if contract is accepted , otherwise
[2]
where v(e) is a schedule of the effort value to the firm. Let the values for c(e) and v(e) be as in the schedules shown in Tables 1 and 2, respectively. Under this parameterization, the competitive equilibrium prediction is that e* ⫽ 1, and thus w* ⫽ 10. The representative worker receives a utility of u*j (10, 1) ⫽ 10 ⫺ c(1) ⫽ 10, and each firm earns a profit of *i (10, 1) ⫽ v(1) ⫺ 10 ⫽ 25. The most efficient distribution, however, occurs when both wage and effort are at their maximal values: Workers receive a utility of uj(35, 6) ⫽ 35 ⫺ c(6) ⫽ 25, and firms receive a profit of i(35, 6) ⫽ v(6) ⫺ 35 ⫽ 40. The restrictions are such that if an employer offers the maximum wage but receives the minimum effort, then i(35, 1) ⫽ v(1) ⫺ 35 ⫽ 0; that is, this parameterization precludes the possibility of firm bankruptcy, which is useful for an experimental evaluation of the fair wage–effort hypothesis. Experimental Procedures Fehr’s early experimental results report evidence in favor of the efficiency wage hypothesis (9, 10). However, the initial environ§This
solution concentrates on the equilibrium where the workers are strictly better off if they accept the contract than if they remain unemployed.
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v(e), $
1
2
3
4
5
6
35
43
51
59
67
75
ments were highly restrictive, and hence the conclusions to be drawn are far from clear. In particular, these experiments use an environment in which (in real terms) the marginal cost of high levels of effort is low, and the procedures had high levels of experimenter–subject interaction. For instance, it costs only 0.24 (0.32 Swiss Francs) for a worker to provide an effort level equal to the observed average. But in situations facing real workers the marginal cost of effort (especially at high levels) is almost always nontrivial. Moreover, the fair wage–effort hypothesis is most interesting in cases in which there is no monitoring by the firm or other supervision of workers’ effort-level choices. Fehr’s design, on the other hand, requires experimenter supervision (single-blind protocol) and close experimenter–subject contact. But there is evidence from other experimental bargaining environments that the very presence of an observer—an experimenter—may influence behavior toward cooperative outcomes (14). Hoffman et al. (14) conducted double-blind experiments using dictator games in which the experimenter could not identify the decision makers based on their behavior in the game. They find that the further the experimenter is removed from the experiment (in terms of social distance), the more self-interested offers become. The design required to both strengthen any conclusions about the partial gift-exchange hypothesis and test the boundary conditions of the theory can be thought of as the result of manipulations of two design variables: experimenter participation and the monetary cost of effort. By removing the experimenter and other ‘‘supervisors’’ from the environment, we naturally give competitive theory its best shot at explaining the data. By increasing the costliness of effort we test a boundary condition to the partial gift-exchange model. The experiment reported here is computerized.¶ Employers have 2 min to submit sealed-bid contract offers consisting of a wage and a desired effort level. Recall that subjects see their task as trading between buyers and sellers with a price and desired quality being chosen by buyers and an actual quality being chosen by sellers. Once all offers are in or time expires, all offers are displayed in a queue on all participants’ computer screens. Workers then are chosen in a random order to decide whether to accept an offer.储 They can choose to accept an offer from those remaining or be voluntarily unemployed. Employed workers then choose their effort level, which is subsequently displayed only on their respective employer’s screen. An individual record is kept on their screen for each trading day, including the contract offer, the actual effort provided, and their own payoff. ¶In
Fehr’s experiments, the employers and the workers are located in separate rooms, and messages are communicated via telephone between the two rooms. To record the information either publicly on a blackboard (in the case of offers and acceptances) or privately between a firm and worker (in the case of effort) requires the help of four experimenters, two located in each room. Removing the experimenter does raise a question: How will employers communicate offers, and how will workers accept these offers and then choose their actual effort level? It is no longer feasible to have contract offers written on a board and acceptances called out verbally by buyers. Thus, we computerize the environment.
储The
choice to use a sealed-bid institution and random acceptance order was to keep the institutional environment consistent with that in ref. 9. One can imagine that the particular choice made regarding the institutional arrangement may matter to the outcome. For instance, one could use a real-time auction where employers enter bids and both sides of the market see the bids such that workers could begin accepting bids immediately. The dynamics of this market may be very different from those under a sealed-bid market.
PNAS 兩 October 1, 2002 兩 vol. 99 兩 no. 20 兩 13349
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c(e), $
e
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e
Table 3. Mean wage, desired effort, actual effort, and rent by trading day block Trading day 1–8 9–15 16
w
eˆ
e
r
20.11 (7.32) 14.20 (6.66) 12.10 (5.27)
4.16 (1.45) 3.52 (1.85) 3.31 (1.98)
1.92 (1.26) 1.42 (1.00) 1 (0)
13.78 (6.80) 9.16 (6.44) 7.14 (5.70)
Standard deviations are reported in parentheses.
The instructions state that there will be multiple trading days and one of the days will be selected randomly for money payoff.** The subjects actually participate in 16 trading days. After the completion of the 15th trading day, subjects’ computer screens alerted them that day 16 is the final trading day. At this point they are informed of the exact probabilities of payoff. Once the final trading day is over, we place 30 bingo balls, numbered 1–30, in a bingo cage. If a ball with number 16 or higher is drawn, then the final trading day, 16, is used for the money payoff. Otherwise, if the ball drawn has number n, 1 ⱕ n ⱕ 15, then trading day n is the one used for the money payoff. Therefore, there is a 0.5 probability that day 16 results will be used for money payoff and a 0.067 chance that any single previous trading day will be used for money payoff.†† The experimental protocol is double-blind. Each person chooses a key before entering the laboratory. The keys are in blank envelopes shuffled in a box. Each key is labeled with two numbers, a letter, and another number. Subjects then enter the laboratory, and once all of them enter their key code, the experiment begins. After the completion of the experiment, subjects privately retrieve their final earnings (including their show-up fee) from a mailbox with a letter matching the letter on their key. The experimenter does not know which subject has which letter. All workers in the experiments have the same induced utilities, and all firms have the same payoff function. As a result, the differences of workers’ abilities兾human capital are no longer an issue as they are in field data. Utilities and effort and value schedules are all public information. We can then test straightforwardly whether wage offers made by employers are higher than those predicted by competitive theory and whether workers, after receiving above-market wages, provide a higher effort level than predicted by competitive theory. Results The experiment was conducted at the University of Arizona (Tucson). A total of 68 undergraduates participated in a total of
Table 4. Rent, r ⴝ w ⴚ c(eˆ), at desired effort levels eˆ
Mean Median s r⫽0
1
2
3
4
5
6
10.55 10 1.82 0
12.47 10 4.65 0
11.06 9.5 5.41 0
14.43 14 7.15 0
16.38 13.5 6.90 0
8.96 5 8.99 49
five sessions: four with 6 buyers and 8 sellers, and one with 5 buyers and 7 sellers (due to 2 no-shows). Each session lasted 1.5 h. In addition to their $5 show-up fee, subjects earned on average $23 (employers) and $9 (workers). There were, of course, always two workers who left the session with only their show-up fee, because unemployed workers earn nothing on that particular trading day. The employers offered a total of 464 contracts, which were all accepted eventually.‡‡ Some descriptive statistics are reported by trading-day blocks in Table 3. The market dynamics across trading-day blocks reveal a consistent trend downward toward the competitive prediction for all the crucial variables: wages (w), desired effort (eˆ), actual effort (e), and rent (r), where r ⫽ w ⫺ c(eˆ).§§ A contract is more generous the higher the rent. If employers offer a competitive contract of (10, 1), then r ⫽ 10 ⫺ 0 ⫽ 10, whereas if they offer an efficient contact of (35, 6), then r ⫽ 35 ⫺ 10 ⫽ 25. It is worth examining the amount of rent offered at each of the possible effort levels (see Table 4). The mean rent offered by employers steadily increases as the desired effort level increases, until ˆe ⫽ 6. This drop in the mean (and median) at ˆe ⫽ 6 can be explained by the 49 offers (or 43.36%) of (10, 6); such maximum effort at minimum-wage contracts yield a rent and utility of zero for the workers. If one excludes these unreasonable contract offers from the analysis, then the mean rent offered at ˆe ⫽ 6 is much higher, 15.81. Given the rent levels, let us look at how many contracts were shirked on by the workers and how many fulfilled their contractual agreement. Out of the total number of contracts, workers shirk (e ⬍ ˆe) 367 times or 79.09%, they fulfill their contractual agreement (e ⫽ ˆe) 82 times or 17.68%, and they exceed their employer’s expectations (e ⬎ ˆe) 15 times or 3.23%. Workers chose the equilibrium effort level (e ⫽ 1) in 317 cases or 68.32% of the time. The distribution of desired effort and actual effort are displayed in Fig. 1. One can see the evolution of desired effort and actual effort in Fig. 2, which also plots the average ‡‡When given the chance to accept a bid from the available offers or to pass, a pass occurred
**The instructions and questionnaire used to check subjects’ understanding of the experiment before their participation are available upon request. ††The
use of the lottery payoff procedure was the result of funding constraints.
Fig. 1. 13350 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.152449999
15 times. These passes result in a worker voluntarily choosing to go unemployed for that day. Most passes occurred in the first several periods of a session, before the workers appreciated the effective surplus of workers. §§The
data are consistent in this respect across experimental sessions.
Distribution of desired and actual effort.
Rigdon
robustness of the gift-exchange phenomenon, since this is precisely the situation faced by workers in real labor markets. Previous experimental research in bargaining games can also give some insight into the data here. Dictator game data are highly sensitive to instructional variation and protocol, e.g., single- vs. double-blind (14). In dictator experiments, the controllers of the final distribution of the pie (the dictators) are far less ‘‘fair’’ when completely anonymous. In the experiments reported in refs. 9–11, however, workers had to report their actual effort choices directly to an experimenter. Real workers, under the assumed conditions of no monitoring, do not report their effort choices to anyone. The present design parallels real labor markets in this respect. Choices by firms and workers are made anonymously and under a double-blind protocol; that is, the subjects know that no one, not even the experimenter, will be able to identify who the shirkers are. Under these conditions we observe that employers initially attempt to reach a more efficient outcome but encounter more selfish behavior by the workers. Movers who have the final say about the distribution (the workers) are more self-interested under a double-blind payoff procedure. These results suggest that the level of cooperation achieved between an employer and a worker can be influenced also by subtle shifts in institutional arrangement, and that is an important boundary to the efficiency wage hypothesis. The environment for these experiments provides a labor market that parallels natural labor markets in important respects but in which high levels of reciprocal effort do not follow high wages. More experimental work on the efficiency wage hypothesis is needed.
wage in each trading day. The two effort distributions clearly are drawn from different populations; the whole distribution of actual effort is shifted to the left compared with the distribution of desired effort. A Kolmogrorov–Smirnov test for differences in distributions confirms this fact (p ⬍ 0.001). Furthermore, even though on the last trading day employers are stating an average desired effort of 3.31, they are only offering a mean wage of 12.1. And all workers in all five sessions respond with an actual effort choice of 1. Thus, by the final (known) trading day, the results have converged to the competitive equilibrium prediction (p ⫽ 1.0). If this convergence were simply the result of boundedly rational learning, we would expect e and ˆe to come from the same population. Employers begin the experiment with what seems to be moderate trusting behavior. This is seen most clearly on trading day 1 resulting in offers with an average wage of 21.48, an average desired effort of 4.07, and an average rent of 15.46. This is considerably higher than the rent of 10 predicted by the competitive outcome. The evidence here is moderate, although no (35, 6) contracts are offered in the first trading day, and only 12 are ever offered. However, these modest efforts of reaching a more efficient solution are thwarted by workers who do not reciprocate: The average actual effort level in the very first trading day is 2.66, by trading day 5 it is 1.72, and by trading day 10 it is 1.44. In fact, by the (known) final day, the behavior has converged to the competitive equilibrium. The above results stand in strong contrast with previous research, where workers respond to high wages with high effort levels (9, 10). Further, despite the use of largely parallel procedures, no market dynamics of the type illustrated in Fig. 2 were observed previously. So what are we to make of the differences? The experiments reported here are motivated by the need to explore the fair wage–effort hypothesis under conditions in which there is both a nontrivial marginal cost to the worker providing effort and increased social distance between subject and experimenter. A nontrivial marginal cost of effort is critical to examining the
Thanks are due to Jim Cox, Doug Davis, Anthony Gillies, Dan Houser, John List, Kevin McCabe, and Jan Potters for comments on design, treatments, and earlier versions of this article. Above all, thanks to Vernon Smith for his continued support and enthusiasm for this project. The work has been supported by a Department of Economics Dissertation grant from the University of Arizona and by the International Foundation for Research in Experimental Economics.
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9. Fehr, E., Kirchsteiger, G. & Riedl, A. (1993) Q. J. Econ. 108, 437–460. 10. Fehr, E., Ga¨ chter, S. & Kirchsteiger, G. (1997) Econometrica 65, 833– 860. 11. Fehr, E. & Ga¨chter, S. (2002) J. Econ. Perspect. 14, 159–181. 12. Charness, G. (2000) J. Econ. Behav. Organ. 42, 375–384. 13. Smith, V. L. (1964) Q. J. Econ. 78, 181–201. 14. Hoffman, E., McCabe, K., Shachat, K. & Smith, V. (1994) Games Econ. Behav. 7, 346–380.
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Desired effort and actual effort over time.
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Fig. 2.
