Do Co-Workers Wages Matter? Theory and Evidence on Wage Secrecy, Wage Compression and Effort Gary Charness and Peter Kuhn* Department of Economics University of California, Santa Barbara Santa Barbara CA 9306 January 7, 2004 Abstract: A central component of many efficiency wage models is the notion that workers will withdraw effort when they perceive that they have not been paid a fair wage. An equally influential notion has been that workers perceptions of fairness depend, at least in part, on the wages paid to their co-workers. We study worker and firm behavior in a labor market where each firm is paired with a high-productivity worker and a lowproductivity worker. Theoretically, we show that worker concerns with co-worker wages should lead profitmaximizing firms to compress wages under quite general conditions. However, firms should be harmed by such concerns, and such concerns can justify paying equal wages to differently-able workers only when those concerns are asymmetric (in the sense that only underpayment matters). In our laboratory experiments, we find that workers effort choices are highly sensitive to the wage assigned; little overall effect of co-worker wages on effort is found, but some weak evidence of a small asymmetric effect exists. We compare firm behavior in secret versus and public wage regimes, and find some evidence of (apparently unnecessary) wage compression when wages are public. Overall, our empirical results substantially weaken the case that co-worker comparisons among heterogeneous workers are important enough to justify either wage secrecy or substantial wage compression as profit-maximizing policies. *charness@econ.ucsb.edu and pjkuhn@econ.ucsb.edu respectively. This research was supported by a grant from the UCSB Academic Senate Committee on Research.
. Introduction A central component of many efficiency wage models is the notion that workers will withdraw effort when they perceive that they have not been paid a fair wage (e.g. Akerlof and Yellen 990; Bewley 999). An equally influential notion has been that workers perceptions of fairness depend, at least in part, on the wages paid to their co- workers in the same firm (e.g. Frank 984). Together, these two hypotheses have been invoked to explain two compensation practices in firms: wage compression (Akerlof and Yellen 990, p.265), and wage secrecy (Lawler 990, pp. 238-242). To the best of our knowledge, aside from the assertions of human resource managers, the only evidence supporting either of the above hypotheses is experimental in nature. Beginning with Fehr, Kirchsteiger, and Riedl (993) and continuing with studies such as Fehr, Kirchler, Weichbold and Gächter (998), Charness (forthcoming), and Fehr and Falk (999), experimental gift-exchange labor markets usually show that workers offered a gift (or wage) by firms tend to reciprocate with return gifts ( effort ). This occurs even in completely anonymous, oneshot situations when the dominant strategy is for workers to provide no effort at all. While this evidence suggests that effort decisions might respond to perceptions of fairness, it does not speak to the notion that wage comparisons among co-workers might influence compensation policy, thereby giving rise to such policies as wage compression or secrecy. If workers effort levels respond to co-worker wages, how would we expect a profitmaximizing firm to set wages? Do workers effort decisions in fact depend on their co-workers wages? And if so, are relative-wage effects strong enough to justify either a substantial degree Harris and Holmstrom (982) offer an alternative explanation of wage compression, based on an insurance argument. The only formal model of wage secrecy of which we are aware (Danziger and Katz 997) is also based on an insurance story. Clearly, our evidence only relates to equity - or morale-based explanations of these phenomena.
2 of wage compression, or wage secrecy as a profit-maximizing policy? In this paper we examine all of these questions, the first using a simple theoretical model; the latter two in a laboratory experiment. This experiment is designed: (a) to eliminate influences on worker behavior other than fairness considerations, and (b) to make it essentially costless for workers to punish firms quite severely for wage differentials that are perceived to be unfair. With a few modifications, our experiments thus extend gift-exchange labor market models to the case where two (differently-productive) workers are employed by each principal. 2 Our main results are as follows. Theoretically, we show that worker concerns with co-worker wages should lead profitmaximizing firms to compress wages under quite general conditions. However, firms should be harmed by such concerns, and such concerns can justify paying equal wages to differently-able workers only when those concerns are asymmetric (in the sense that underpayment affects effort but overpayment does not). In our laboratory experiment, however, we detect little or no concerns with co-worker wages in the sample as a whole; effort seems to be sensitive to own wages alone. Third, despite this lack of worker response, it appears that the subjects representing firms in our sample anticipated some sort of adverse reaction from an unequal-wage policy, as they were more likely to compress wages when wages were public information than when wages were private. In fact, the most commonly-selected wage policy when wages were public was an egalitarian one, even though a number of other (unequal) wage policies consistently yielded 2 While as noted-- there have been many experimental studies of labor markets, only a few allow for multiple workers per firm. Güth, Königstein, Kovács and Zala-Mezõ (200) consider a two-part contract in a principal-agent relationship and find that making work contracts observable leads to a greater degree of pay compression. On the other hand, Cabrales and Charness (999) find no evidence of one agent having much concern about the payoff of the other agent, although the principal s payoff was important for agent behavior. Importantly, neither of these studies involves gift exchange, as principals choose contract menus with take-it-or-leave-it options.
3 higher profits. This suggests that either that firms overestimated the role of social preferences in making wage offers, or were deliberately sacrificing their own profits in the interests of interworker equity. Results from an exit survey however lead us to prefer the first of these possibilities: most firms said they were motivated purely by profits, and the wage-compression result holds up when the sample is restricted to firms who indicated profits were their only motivation. Fourth, mandating that firms share wage information with all their workers does not significantly reduce firms profits. Firms profits are, however, reduced when they are forced to adopt an egalitarian wage policy. either of these results support the notion that concerns for wage equity among workers are sufficiently important in practice to make it in the interests of profit-maximizing firms to adopt a policy of wage secrecy, or of wage equality for differentlyproductive workers. Finally, while we detect no significant effects of co-worker wages on effort in our sample as a whole, we are able to identify modest, statistically significant co-worker wage effects for two subpopulations: male subjects assigned to the low-productivity worker role, and those subjects who reported in an exit survey that they took their co-worker s wage into account in making their effort decisions. Because it is confined to low-productivity workers, the former result provides some support for the notion that equity concerns, when present, are asymmetric (as defined above). In neither case, however, are these subgroups large enough, or the effects strong enough, to change our conclusion that neither wage secrecy, nor wage egalitarianism, is a profit-maximizing compensation policy.
4 2. A Model In this section we analyse the expected effects of workers concerns with co-worker equity on wage levels, wage compression, worker effort and profits. We consider two main cases: In the case of symmetric worker concerns with relative wages, workers effort decisions respond equally to an extra dollar of overpayment relative to their co-workers as they respond to a dollar less of underpayment. In the asymmetric case, workers effort decisions respond to underpayment only. Within both cases, we consider the effects of an increase in the responsiveness of workers effort supply functions to their co-workers wages (henceforth the parameter b ) on a variety of outcomes, assuming firms set wages to maximize profits. Our main results are as follows. First, in both the symmetric and asymmetric cases, an increase in workers concerns with co-worker equity should lead profit-maximizing firms to choose greater wage compression. In the symmetric case, however, we show that under quite general conditions these concerns do not harm firms: maximized profits are unaffected by the strength of workers concerns with relative wages. Further, in the symmetric case the amount of wage compression predicted by the model can be quantified under quite general conditions. For example, if workers care as much about relative wages as do about own wages (b=) which seems to us a plausible upper bound to equity concerns the profit-maximizing wage gap between differently-productive workers is reduced by half. Under no circumstances (in the symmetric case) is it ever optimal to pay equal wages to differently productive workers. In the asymmetric case, in contrast, firms are harmed by the fact that workers care about relative wages. Optimal wage compression is harder to quantify in general (for example the functional form of the production function now matters), but is greater than under symmetry in the
5 following sense: Above a theshold level of b, strictly egalitarian wage policies will now be profit-maximizing. a. The Symmetric Case Imagine two workers in a firm, each of whose effort is given by: () E = aw + b w w ) ( c where w is the worker s own wage, w c is his/her co-worker s wage, a > 0, and b 0. Workers care about co-worker wages when b > 0; we refer to the case b = 0 as egoistic behavior. The formulation in () has three noteworthy features. First, by assumption, when the two workers receive the same wage w = w ), a worker who cares about co-worker wages (b > 0) exerts the ( c same effort as a worker who does not care (b = 0). Second, when workers care about co-worker wages, they reduce their effort below the egoistic level if paid less than a co-worker, and raise effort above the egoistic level when paid more than a co-worker. These effects are equal in magnitude, their strength given by a single parameter b. This second assumption is our symmetry restriction and is relaxed later in this section. Third, our effort-supply functions are assumed to be linear, since it is easiest to define symmetry in this context. Also, as we shall see the linear case most dramatically illustrates the intuition of how firms are affected by b, especially in the symmetric case. Finally, since we allow output to be a general, nonlinear function of each worker s effort (see below), linearity of the effort-supply function is not as restrictive as it might seem. Let total revenues produced by a type- (low-productivity) worker be given by R(E), revenues from a type-2 worker by θr(e), where R > 0, R < 0, and θ >. Total profits earned by a firm employing one worker of each type are then: Π = R aw b( w w θ R aw b w w w w. + ) + + ( ) (2) ( 2 ) ( 2 2 ) 2
6 In this base case, first-order conditions for a maximum of profits with respect to w and w 2 can be written respectively as 3 : (3) ar ( E ) + b[ R ( E ) θ R ( E )] 2 = (4) θ ar ( E ) + b[ θ R ( E ) R ( E )] 2 2 = where E aw + b w ) and E aw + b w ) are worker s and worker 2 s effort respectively. ( w2 2 2 ( 2 w Result. When workers behave egoistically (b = 0), profit-maximizing firms will pay higher wages to their more-productive workers (w 2 > w ), who in turn supply greater effort than the less-productive workers (E 2 > E ). θ. Proof. When b = 0, (3) and (4) simplify respectively to a R ( E ) = and ar ( E ) 2 = It follows directly (from R < 0 ) that E 2 > E. Since, in the egoistic case, each worker s effort is proportional to his/her own wage only ( E = aw ; E2 = aw2 ) it also follows that w 2 > w. Result 2. When workers care about relative wages (b > 0), profit-maximizing effort levels for each worker (E and E 2 ) are identical to the egoistic levels identified in Result, regardless of the value of b. Wages, however, are not identical to the egoistic case: profit-maximizing firms compress wages relative to the egoistic equilibrium; i.e. e w w > and e w2 < w2, where e e w, w2 denote wages under egoism. As b rises, w rises and w 2 falls, but workers wage rankings are never reversed, i.e. w < w2 regardless of b. Further, regardless of the level of b, the total wage bill (w + w 2 ), and total profits are identical to the egoistic case. 3 For consistency with the standard formulation and for ease of presentation, we model firms decisions as not subject to any constraints on the total wage bill, w + w 2. Such a constraint is imposed for practical reasons in our experiment. In our base case model, the profit-maximizing wage bill is in fact invariant to the degree of worker concerns with equity (b); as a consequence the model s predictions are identical to the case of a fixed budget for wages.
7 Proof. Suppose that R ( E ) < R ( ) θ in the non-egoistical equilibrium. It then follows from (3) E 2 that a R ( E ) >, and from (4) that ar ( E 2 ) < parallel argument rules out the possibility that R ( E ) > R ( ) θ. Together these contradict the supposition. A θ. The only remaining possibility E 2 that satisfies both (3) and (4) equates effort levels to those in the egoistical equilibrium, i.e. E e E E = and e E2 = E2. ext, recall that wages are related to efforts via the system of linear equations = aw + b( w 2 ) and E = aw + b w ). Solving these for w and w 2 yields: w 2 2 ( 2 w (5) (6) be2 + ( a + b) E w = 2 a + 2ab w 2 be + ( a + b) E = 2 a + 2ab 2 From previous results we know that e E E = < e E2 = E2, and that E and E 2 in (5) and (6) are invariant to b. Since both w and w 2 are weighted averages of E and E 2, but the latter assigns a higher weight to E 2, it follows that w < w 2. Summing (5) and (6) yields w + w 2 = (E + E 2 )/a, which is independent of b. Independence of profits from b follows from this plus the independence of effort levels from b. Finally, differentiating (5) and (6) with respect to b (and using de = de 0 ) yields: 2 = (7) (8) dw dw ( w2 w ) a db = > 0 a + 2ab / 2 ( w w2 ) a db = < 0. a + 2ab 2 / 2 A key implication of Result 2 is that firms are not hurt by the presence of concerns with co-worker equity among their workers. The generality of this result is also noteworthy: it holds regardless of the strength of workers concerns with equity (b), regardless of the form of the
8 production function (R), and regardless of the slope of the own labor-supply function (a). To see the intuition for this result recall that in equilibrium total costs are given by w + w 2 = (E + E 2 )/a; thus because of symmetry the marginal cost to the firm of inducing an extra unit of effort from either worker is independent of b. The other key implication of Result 2 is that, despite the invariance of effort, some wage compression is in the interests of a profit-maximizing firm. To see why, consider the effects of a small increase in b, beginning at the egoistic (b = 0) equilibrium. If after this increase we kept wages at their egoistic levels, low-productivity (type ) workers will now work less than before; their effort is reduced by the fact they are underpaid (w < w 2 ). By the same argument, type-2 workers will work harder. But we have just shown that because the marginal cost of both E and E 2 are independent of b--, profits are maximized by keeping effort levels unchanged. To achieve this, firms must raise w and cut w 2 ; i.e. compress wages. In sum, wages are compressed because, when workers care symmetrically about each others wages, a smaller wage gap is needed to elicit profit-maximizing effort levels from both workers. It is perhaps noteworthy that this intuition differs somewhat from that in popular discussions, perhaps because the latter discussions seem to focus only on the effects of wage discounts on low-ability workers, ignoring the potential for wage premia to motivate highability workers. Result 3. When workers care about relative wages, the optimal amount of wage compression relative to the egoistic case is given by: (9) w2 w a = = e e w w a + 2b + 2 2( b / a) Proof. Subtracting (5) from (6) for the cases b>0 and b=0 respectively, noting (from Result 2) that effort levels are identical in the two cases, then taking the ratio of the two cases and simplifying yields the result shown.
9 Equation (9) implies a very specific relation between the strength of workers concerns with wage equity and the profit-maximizing degree of wage compression. This relation is true for any production function R. For example, if workers effort is one-tenth as sensitive to relative wages as to their own wage (b/a =.), the wage gap should be reduced by 6.7 percent, to 83.3% of its value under egoism. If workers care equally about own and relative wages (b=a), the wage gap should be 50% of its egoistic level. Finally, note that (9) approaches zero from above as b grows without bound. Even in the most extreme case imaginable, it is therefore never optimal to pay equal wages to workers of differing ability. Because of its relative simplicity, extensions to the symmetric case are relatively easy to explore. A key question (not addressed empirically in this paper) allows for an arbitrary number () of workers instead of two, and considers the effects of changing the relative numbers of high- and low- productivity workers. These questions are explored in Appendix, which shows that the invariance of effort and profits to b extends to the -worker case as well. Interestingly, we can also show that profit-maximizing wages offered to workers of both types of workers must rise when a low-productivity worker is replaced by a high-productivity worker. This rent-sharing among workers within firms may help explain why firms choose to hire more-productive workers. 4 b. The Asymmetric Case Suppose now that workers only respond to relative wages when they are paid less than their co-workers. Specifically, let E = aw + bδ w w ) where the function δ ( x ) = x for x > 0, δ ( x) = 0 for x 0. ( c
0 Result 3. When workers concerns with relative wages are asymmetric in the sense described above, profit-maximizing effort levels deviate from the egoistic levels. In particular, and e E2 E2 e E > E <, i.e. low-ability workers provide more effort than in the egoistic equilibrium, while high-ability workers provide less. E is monotonically increasing in b; E 2 monotonically decreasing. Proof. Returning for simplicity to the two-worker case, the first-order conditions for a profit maximum ((3) and (4)) now become: a + b R E (0) ( ) ( ) = θ ar E br E () ( ) ( ) 2 = The result for E follows directly from monotonicity of R in (0). For E 2, solve (0) for R and substitute into (), yielding: (2) θ ar ( E ) 2 a + 2b = a + b Since the RHS of (2) is increasing in b, E 2 must be decreasing in b. Result 4. When workers concerns with relative wages are asymmetric, profit-maximizing firms pay high-ability workers less than their egoistic wage, i.e. the wage ratio, w 2 / w, must be below its egoistic level. e w2 w2 <. Also, for positive b, Proof. Solving for wages as a function of effort, equations (5) and (6) now become: (3) ae + be2 w = a( a + b) 4 In a strict neoclassical model where wages equal marginal products, firms (and workers) would of course be indifferent to the quality of workers hired.
(4) E2 w2 = a as long as w < w2. Since E 2 declines with b, w 2 must do so as well. Taking the ratio of (4) to (3) yields: (5) w w 2 E + ( b / a) E E + ( b / a) E 2 2 =. 2 e e e e Recall that under egoism (b=0), the wage ratio is given by w w = E / E. According to 2 / 2 > Result 3, e E E > and e E2 < E2, for b > 0, which in turn implies that e e w2 / w < w2 / w. Result 9. In contrast to the symmetric case, for high-enough values of b a firm s profitmaximizing wage policy in the asymmetric case could involve equal wages for differentlyproductive workers ( w = w2 ). Proof. By example. Let R(E)= E.5, choose units of effort so that a = and let worker 2 be twice as productive as worker, i.e. θ = 2. Computing profit-maximizing effort and wage levels using (0) and (2)-(4) generates values of w 2 < w for any b in excess of about.355. Since firms will never wish to reduce w 2 below w (note that (0)-(4) no longer apply when w 2 < w since they are predicated on the low-ability worker receiving the lower wage), we conclude that there is a critical value of b above which a strict egalitarian wage policy maximizes profits. Result 0. When workers concerns with co-worker wages are asymmetric, maximized profits are strictly declining in the strength of those concerns (b). Proof. Applying the envelope theorem to the expression for profits yields: dπ db Π b R E ( w w2 (6) = = ( ) ) which is strictly negative in the relevant region (w 2 > w ).
2 3. The Experiment Following Fehr, Kirchsteiger, and Riedl (993), we model the labor market as a simple gift exchange. The firm moves first, by offering the worker a salary, S, which can depend on the worker s type. The worker then selects an effort level, E. Payoffs are then: Principal s payoff ( Profits ): Π = Q S = Q(E) S Agent s payoff ( Utility ): U = S V(E). Clearly, the perfect equilibrium to this game is not efficient. According to standard reasoning, agents should expend no effort and (anticipating this) the principal will pay no salary. In practice, however, it is well known that much more cooperation than this occurs. As noted, our question in this paper is whether the amount of cooperation (and the surplus generated) is influenced by pay comparisons made between two types of workers (highproductivity and low-productivity) employed by the same firm. In each period, each firm is therefore matched with one worker of each type. We vary whether wages are public (both workers know both wages) or private (each worker knows only his or her own wage). When wages are private, we also impose a 50% chance (with a new realization in each period of this regime) that the firm must choose identical wages for the two workers. A facsimile of the experimental instructions is provided in Appendix 2. Each firm is endowed with $4 (lab dollars) in each period, and can pay total wages (in integer amounts) in each period that do not exceed the $4 endowment. If a firm chooses not to spend the entire endowment, it keeps the unspent money, but cannot use any such savings to pay higher wages in later periods. The wages chosen are subtracted from the $4 endowment, and the firm receives the benefits of any revenues produced by the workers. Earnings accumulate over the course of the session, and are then converted from lab dollars to real dollars. There were different
3 conversion rates for different types, and participants knew that there were different conversion rates across types. Each player-type knew only the conversion rate for his or her type. Thus, firms were allowed to choose from among five salary levels (zero, one, two, three or four lab dollars), and workers could respond with one of four effort levels (zero, low, medium or high). The Q(E) and V(E) functions for both worker types are shown in Table. [Table about here] As can be seen, increasing effort is increasingly costly for the workers receive no direct benefit from providing costly effort, while the firms profits depend critically on the effort levels chosen. All sessions were conducted at the University of California at Santa Barbara. Eighteen undergraduate students participated in each of seven sessions; fifteen in another session, for a total of 4 subjects. Each subject participated in only one session. Average earnings were about $5 for the one-hour sessions. At the beginning of each session the students were randomly divided into three groups of equal size: firms, low-productivity (Type ) workers, and high-productivity (Type 2) workers. Each person stayed in his or her assigned role for the duration of the session. There were 30 periods in each session; after every period, the firms and workers were randomly re-matched (with no 3-person group remaining the same from one period to the next). All of this was common information. Within each period, play proceeds as follows. First, each firm makes a salary payment to both of his or her agents. After these payments are entered in the workers accounts, all workers decide on how much of a transfer ( effort ) to make to the firm, given the costs shown in Table. ote that each worker saw only his or her own productivity schedule, while being aware that the other worker s schedule was different.
4 Different information structures were implemented at different times during the various sessions. With private wages each worker is told only his or her own wage in the period, while with public wages, each worker learns both wages chosen by the firm. othing else is changed. During the public-wage regime, the experimenter randomly (50% probability) imposes the constraint that firms must pay the same wage to both affiliated workers. Participants knew that there would be regime changes during the session, but were not told in advance the nature of these changes. Workers were not informed about the possibility of the same-wage constraint. In our first four sessions, we had public wages during periods -25 and private wages in all other periods. In the remaining four sessions, we had private wages during periods 6-25 and public wages in all other periods. Our calibration was chosen (based on past experience) to generate non-zero effort levels from the majority of workers in a simple gift-exchange game, to exhibit diminishing marginal returns to effort, and to embody large productivity differences between the workers. The surplus-maximizing effort level (Q(E) - V(E)) is medium for the low-productivity worker and high for the high-productivity worker. A low effort level by type workers in the presence of a $.00 wage results in equal sharing of the $.80 surplus from production between the worker (et Receipts = $.00 - $0.0 = $0.90) and the firm (Profit = $.90 - $.00 = $0.90). Similarly, a high effort level by type 2 workers when assigned a $3.00 wage results in equal sharing of the $4.80 surplus that occurs in that event. 4. Worker Behavior a) Means In this section we analyze how workers effort decisions responded to the wage they were offered, and to the wage that was offered to the other worker employed by their firm. We do this
5 separately for two information regimes: wage secrecy (where workers were informed only of their own wage); and public wages (where they are informed of their own wage and that received by their co-worker). 5 As we do not expect co-workers wages to affect effort in the wage secrecy regime, this serves as a useful specification check for our experimental design and econometric procedures. Unadjusted counts of all possible wage offer combinations and the mean effort levels of both worker types for each combination are presented in Table 2: [Table 2 about here] The table shows, for example, that the most common wage-offer pair chosen by firms when wages were secret was a wage of to their low-productivity worker and 3 to their highproductivity worker. This combination, which fully exhausts firms budget constraint, was chosen 6 times; when it was chosen, the average effort level chosen by type workers (with possible choices ranging from zero to 3) was 0.93; the average effort chosen by type 2 workers was.87. Part A of Table 2 shows two results very clearly. First, workers effort decisions respond very strongly to their own wage: reading down the columns for type- workers, or across the rows for type-2 workers, mean effort levels rise monotonically, and precipitously, with own wages. There is only one exception to these monotonic increases, involving a cell with only 4 observations in it. Second, no such pattern is visible for co-workers wages (going across rows for type- workers or down columns for type-2 workers). Since workers were not informed of their co-worker s wage in this wage-setting regime, this is exactly what we expect. 5 The reader may recall that, within the public wage regime, firms were subject to two distinct treatments: either they were free to choose any wage combination they wanted (subject only to their budget constraint), or they were forced to pay equal wages to both their workers. Since workers were never informed about whether the latter restriction on firms behavior was in place, throughout this section on worker behavior we simply combine both
6 Part B of Table 2 presents results in exactly the same format for all the experimental rounds in which workers were informed of the wage their co-worker was offered before choosing their own effort levels. In our view, the most striking aspect of Part B is its similarity to Part A: own wages matter (a lot), but no strong or consistent pattern emerges for the effect of co-worker wages. Holding type s wage fixed at $, and focusing on those cases with the largest sample size, (203, 79 and 6) there is a small increase in type s effort as 2 s wage rises from to 2, then a decline when 2 s wage rises further, from 2 to 3. There is also a small decline in type 2 s effort with type s wage holding type 2 s wage fixed at $2 (sample sizes 79 and 328) or at $3 (= 33 and 6). At the same time, many other comparisons, though based on smaller samples, show effects in the both directions. While we try to combine all this information by parameterizing the effects of wages in the following table, our main impression from Table 2 is the lack of a robust effect of co-workers wages on effort. b) Regressions Table 3 summarizes the information in Table 2 in a regression context. This serves several purposes, one of which is to control for period effects that could bias the Table 2 results. While we changed the order of the public versus secret wage treatments across sessions, these changes were not completely balanced 6 ; further, examination of the data reveals significant unraveling in the sense of declining effort levels across rounds even within treatments. The regression context also lets us parameterize the effect of other workers wages in simple ways and conduct significance tests for co-worker wage effects that (a) treat every round as a separate observation, but (b) allow for correlated error terms within subjects by clustering on these treatments in the public wage regime. They must of course be distinguished in the following section on firm behavior. 6 This was intentional; we wanted more observations in total from the public wage regime, in part because of a special interest in phenomena, such as the response of effort to other workers wages, that take place within that
7 individuals. Finally, the regression context allows us to ask whether estimated effects of offered wages are different when we look only within subjects (i.e. allowing each subject his/her own effort intercept and examining the effects of different wage offers to the same person). [Table 3 about here] All of Table 3 includes data from the public wage regime only, i.e. from those rounds in which workers were informed of, and thus able to respond to their co-worker s wage. Part A of the table focuses on type- (low-productivity) workers, presenting estimated coefficients from regressions in which effort is the dependent variable. In column we simply allow for a linear effect of the worker s own wage on effort. The effects of own wages on effort are very strong, and statistically highly significant (with a t-ratio in excess of 3). 7 Columns 2 and 3 add two alternative measures of the co-worker s wage to the column regression; coefficients on both of these are small and statistically insignificant. 8 Columns 4 and 5 replicate columns 2 and 3 with a more flexible measure of the worker s own wage; while own wage effects remain strong and monotonic, there is essentially no change in the estimated co-worker wage effect. Finally, columns 6 and 7 add worker and period fixed effects in turn. Overall, in all specifications the estimated effect on a low-productivity worker s effort of being paid less than his/her co-worker is negative --as one might expect from a jealousy hypothesis--, but is statistically insignificant and economically very small. To see this last point, consider the effect in column 7 of being underpaid by at least one lab dollar on effort of -.077. This effect is less than one tenth the effect of having one s own wage raised from one to two lab regime; in part because we impose two distinct treatments on firms (freely-chosen wages versus forced wage equality) within that regime. 7 Since effort decisions are likely correlated within workers indeed our fixed-effect models show this very strongly the standard errors presented in Table 3 (and throughout this paper) are adjusted for clustering on individual workers. Without this adjustment the t statistic in column would be around 20, rather than 3. 8 A variety of other formulations were estimated, including effects of being paid equally, of being paid more than one s co-worker, etc. o robust effects were found in these instances either.
8 dollars. Clearly, effects of this size do not suggest there will be strong beneficial effects on profits of wage policies that accommodate workers concerns for inter-worker equity. We shall, however, address the effects of wage compression on profits more directly in Section 4 of the paper. Part B of Table 3 focuses on type-2 (high productivity) workers. Overall the results are very similar, with strong and monotonic own-wage effects and insignificant co-worker wage effects. Interestingly, columns 3 and 5-7 now show a positive, though statistically insignificant effect of being paid less than one s co-worker on effort. In our model (as in most principal-agent models), disutility of effort is a convex monotonic function of effort, while output is a concave monotonic function of effort. Perhaps effects of other workers wages on a worker s performance would be more apparent if we focus on one of these other metrics. This question is addressed in Appendix 3, which replicates Table 2B for effort costs (Table A) and revenues produced by the worker (Table A2). It also replicates selected regressions from Table 3 specifically columns 2 and 7 for both of these alternative measures of worker performance (Tables A3 and A4). o substantial difference in the results is observed, though in one specification (involving type-2 workers and effort cost, with no period or worker fixed effects), a small, negative, and statistically significant co-worker wage effect is observed. 5. Firm Behavior a) Comparisons Across Regimes Even if our examination of worker behavior suggests that relative wages did not affect worker behavior, it does not follow that firms in our experiment behaved as though this were the case. If the undergraduate firms in our experiment had priors that were similar to ours, they
9 would have entered the experiment with a belief that within-firm wage equity does matter and behaved accordingly. Did they? Descriptive statistics concerning firms wage offer behavior across the three wage-setting regimes in our experiment are provided in Table 4. ote that, since we are now interested in firms wage-setting choices, Table 4 disaggregates the public wage regime into those cases where firms could choose any wage pair satisfying their budget constraint and those where firms were forced to offer equal wages to their two workers. Recall also that the latter equal-wage restriction was randomly imposed on firms throughout those rounds in which wages were public. The detailed counts of wage-offer pairs underlying Table 4 are reported in Appendix 4. [Table 4 about here] According to Table 4, on average, type workers were offered the lowest wage under wage secrecy, higher wages when wages were public but unconstrained, and the highest wages when wages were public and forced to be equal. Exactly the reverse is true for type 2 workers. Thus it appears that firms wanted to offer higher wages to the more-productive workers when unconstrained by co-worker equity considerations. But firms voluntarily reduce this wage ratio when they know that workers will observe both wages. Comparing columns and 2, where firms faced no experimenter-imposed restrictions on wage setting (aside from the budget constraint), a particularly striking result is the difference in the share of cases in which equal wages were offered to the two workers, from 30 percent when wages were secret to 43 percent when wages were made public. While most of this difference is due to a reduction in cases where less-productive workers were paid less, Table 4 indicates that a reduction in the number of cases where more-productive workers were paid less also took place. Looking at the total wage bill, however, it is almost identical in the secret and public
20 unconstrained regimes. In contrast, comparing the equal-wage regime to the public unconstrained regime, firms paid lower total wages when forced to offer equal wages to both their employees. The remainder of Table 4 presents means of other outcome variables by regime. Comparing the secret and public unconstrained regimes, essentially all these outcomes, including total profits, are very similar. The only exceptions are that overall profits are slightly higher when wages are public information, and that firms earn a larger share of their profits from their more-productive workers when wages are public. While this might suggest a subtle way in which co-worker wages could affect effort (that would not be detected in the comparisons made in Table 3), 9 the regressions reported in Table 5 show that unlike the wage-compression results discussed above these differences are not statistically significant. Further, pooled regressions of effort on regime and wages (not reported) show no significant effect of regime on effort, holding wages fixed. In contrast to making wages public, forcing firms to adopt egalitarian wage policies reduces profits, almost cutting them in half. Although low-ability workers respond to the higher wages they receive under egalitarianism by producing more revenue, this response is swamped by the reduction in revenue from high-ability workers. Clearly, workers social preferences for wage equality within firms cannot justify egalitarian wage policies on the basis of profits. Overall, Table 4 thus suggests that, in the public-wage regime, firms anticipated an adverse response from paying different wages to their two, differently-productive workers. This resulted in a narrowing of within-firm wage differentials when wage information became public, 9 The argument goes like this: In the private-wage regime, type- workers are not aware that they are paid, on average, less than type-2 workers. In the public-wage regime, they are. Even though workers do not respond to coworker wages offered by any particular firm within the public-wage regime Tables 2B and 3 show this very clearly for any given own wage they might work less on average in the public wage regime because of the
2 with the total wage bill unaffected by this reduction in wage differentials. Despite firms apparent expectations, however, Table 3 also shows that firms pay no penalty in profits when they are forced to make their wages public (but remain free to set wages as they wish). In contrast, firms profits did suffer if they were forced to offer equal wages to workers with different levels of productivity. [Table 5 about here] As noted, Table 5 examines the same effects as Table 4 but in a regression context that controls for period and firm effects. Columns through 3 present coefficients measuring differences between the private and public unconstrained wage regimes; columns 4 through 6 focus on the effect of forced wage equality within the public wage regime. The regressions without covariates in columns and 4 provide significance tests for differences between the means reported in Table 4; by construction these coefficients are exactly equal to the differences between columns in Table 4. The remaining columns of Table 5 control for period and firm effects in turn. As expected, essentially all the differences observed in the raw data are replicated in these regressions, though not all are statistically significant. By several measures, the increase in voluntary wage compression when wages are made public is substantial and statistically significant, as is the reduction in the total wage bill when wages are forced to be equal. Profit effects of making wages public are small and statistically insignificant; profit effects of forced wage equality are larger, and marginally statistically significant in some specifications. b) Effects of Wage Policies on Firms Outcomes Within Regimes. knowledge that, on average, they are paid less than their co-workers. A parallel argument can be made to explain higher type-2 effort in the public wage regime.
22 The second question we address in this section is the impact of specific pay structures on profits within each compensation regime. The goal here is to match firms perceptions with reality: within each regime, which exact wage pair maximized firms profits, and did firms disproportionately choose wage pairs that yielded higher profits? Did firms decisions to compress wages in the public-wage regime, documented above, reduce their profits given the lack of evident worker concern with co-worker equity? Table 6 presents mean profits earned by each possible wage-offer combination, separately for the wage-secrecy (Part A) and public wage regime (Part B). [Table 6 about here] According to Part A, the wage structure that maximized firms profits under wage secrecy was a wage of for the low-productivity worker and a wage of 3 for the high-productivity worker, yielding a total profit of $.4 (in lab dollars) per period. Interestingly, this was also the most prevalent wage package, suggesting a rough correspondence between firms perceptions and reality. The second-highest level of profits was earned by the package (w, w 2 ) = (,2), which also involved higher pay for the more-productive worker but a smaller pay differential. Interestingly, this pay package was chosen slightly less frequently than the second-most-popular pay package, the egalitarian (2,2), even though the latter generated significantly lower profits. Significance tests on these differences, formulated identically to those in columns and 4 of Table 5, show that profits under both (,2) and (,3) were significantly different from (2,2), with t-ratios of 2.43 and 2.94 respectively. 0 It is worth noting that Part B of Table 6, focusing on the public-wage regime, reports two sample sizes for each cell. Of these, (total) gives the sample size from which mean profits 0 Adding period effects changes these t-ratios to.52 and 2.92 respectively; adding both period and firm effects changes them to.58 and 2.54. All t ratios adjust for correlation of disturbances within firms.
23 were computed. This includes both cases where firms were constrained to offer equal wages and ones where they were not: since workers had no way of knowing whether firms were constrained it seems appropriate to include constrained observations when measuring workers responses to wage offers). (unconstrained only) gives the count of instances in which firms voluntarily chose that pay combination; this tells us about firms choices when they are free to choose. Within the public-wage regime, Table 6 shows that high profits were made by a number of wage packages that were rarely chosen and involved a zero wage (specifically (0,), (0,2), (,0), and (2,0)). If we discounting these as one-time punishments, the highest profit earned by a wage strategy that was selected more than six times was.252, earned by (0,3), closely followed by.028 (,2), and then by.679 (,3). Importantly, all three of these strategies give higher wages to the more-productive worker. The most commonly chosen pay structure (when firms were free to choose wages), however, was an egalitarian one, (2,2), by quite a wide margin (08 times versus 79 for its nearest rival). Further, (2,2) yielded significantly lower profits than (,2) (t=2.59), though the differential between (2,2) and (,3) is not significant (t=0.80). Taken together, these results reinforce our suspicion that firms incorrect anticipation of an adverse worker response explains the greater prevalence of wage compression under the public wage regime. 6. Results for Subpopulations In this section we ask whether the results for the entire sample presented so far in the paper hold up for certain subsamples based on (a) gender, and (b) participants self-reported Adding period effects changes these t-ratios to 2.44 and 0.90 respectively; adding both period and firm effects changes them to 2.00 and.8.
24 motivations for their own behavior, taken from an exit survey. 2 Results from both these exercises bolster our confidence that our design would, in fact, be capable of detecting a coworker wage effect should one truly exist, because we do detect small effects of this kind among subgroups where, arguably, one might most expect to see them. Results from the latter exercise also help clarify why firms equalized wages in the public wage regime. a. Gender Table 7 replicates the worker effort regressions in column 6 of Table 3, separately by gender and worker type. As for the population as a whole, effects of co-worker wages on effort are small, statistically insignificant, and generally positive in sign, for three of the four subsamples examined. A negative co-worker wage effect is however detected for male subjects who were assigned the low-productivity worker role, and this effect is (marginally) statistically significant in one of the two specifications examined. [Table 7 about here] The possibility that men --when cast in situations where their productivity is low-- are more likely to withdraw effort when paid less than their more-productive co-workers strikes us as plausible: men, on average, are paid more in the real world and might therefore be more likely to protest this unfamiliar outcome. In our opinion, however, this finding has two more important implications: first, it indicates that our experimental design is capable of detecting coworker wage effects: there is nothing inherent in our parameterization or information structure that prevents this. The second point involves magnitudes: compared to the own-wage effect, the co-worker wage effect is small in magnitude even in the one subsample where it appears to be 2 We also collected information on the subjects college major. In fairly detailed exploratory analysis, no robust correlations between major and either worker or firm behavior were detected.
25 present, and thus seems very unlikely to justify either a wage compression or wage secrecy policy. 3 We also examined our data for any gender differences in the wage-setting behavior of firms. For most outcomes, for example overall wage levels, no significant differences were found. Interestingly, the only significant gender difference we were able to detect in firm behavior was confined to the wage secrecy regime: when wages were secret, female firms actually chose less-egalitarian wage policies (i.e. women favored the more-productive worker more); a difference that disappeared when wages became public. While it is interesting to speculate on explanations for such a difference, we leave this to the reader s imagination. b. Reported Motivations In the last six of our eight sessions, we administered an exit survey to participants. In the survey, workers were asked, In the periods where you saw the wage the firm offered its other worker, to what extent did you consider the other worker's wage when deciding how much effort to supply? Responses to this question were coded on a five-point scale with indicating not at all and 5 indicating that the other worker s wage was the respondent s primary consideration in choosing [his/her] effort. In all, 44 of 72 (6%) workers chose a value of 3 or greater, indicating a moderate influence or greater of co-worker wages on their choices. Are estimated responses to co-worker wages larger for the subsample of workers who said they cared about them? Columns 2 and 4 of Table 8 replicate the regressions in column 6 of 3 To explore this notion somewhat more formally, we re-ran the regressions in Table 7A with revenues produced by each worker as the dependent variable, then computed the predicted profits of an all-male firm under two wage policies: (,3) and (2,2). These were.69 and.44 lab dollars respectively under the specification in columns and 3, and.69 and.42 under the other specification. Thus, even in an all-male firm where according to our estimates co-worker jealousy effects are the strongest, profits would be cut by more than a third if an egalitarian wage policy was implemented.
26 Table 3 for the subsample of workers who indicated that their co-worker s wage had at least a moderate effect on their effort decision (columns and 3 consider a similar specification). [Table 8 about here] Effects of co-worker wages on own effort are now negative in all specifications and marginally statistically significant in two of the four specifications presented. Once again, however, they are small in magnitude, especially in comparison with the effects of own wages on effort. It is thus, apparently not the case that our experimental procedure is simply incapable of detecting coworker wage effects when they are in fact present. or is it the case that workers claims that they care about co-workers wages are rare, erroneous, or disingenuous. It is simply the case that not enough workers care about their co-workers wages, and that those workers who do care don t care enough, for wage compression to be a profitable compensation policy. Some indication of firms subjective motivations can be gleaned from two additional exitsurvey questions. All told, only seven of 36 firms (9 percent) answered yes to the question, I wanted to offer equal wages to the two workers, independently of their ability, because this is the fair thing to do. In contrast, 26 of the 36 firms (72%) answered yes to: I wanted to offer higher wages to the high-productivity workers in order to maximize my profits. Of the latter group, however, four also answered yes to the previous question, leaving a group of 22 firms (6% of the total, whose reported motivation was in a sense purely driven by profits. While the preponderance of reported profit motivations over reported equity motivations among firms certainly suggests that firms voluntary wage-compression behavior was primarily instrumental rather than equity-driven, a more nuanced test of this hypothesis involves replicating the firm behavior regressions in Table 5 for the firms who said that they were motivated only by profits. If these firms reduce wage differentials when wages become