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Can reference points explain wage rigidity? Experimental evidence

Can reference points explain wage rigidity? Experimental evidence I examine whether reference points can provide an explanation for rigid wages in recessions. Even though a recession provides a good reason to adjust wages downward, workers’ perception of a “fair wage” may depend on their previ‑ ous wage, their reference point. Using a laboratory experiment, I test this idea by varying whether initially concluded contracts—and their stipulated wages—can serve as reference points. My experimental results show that with initial contracts workers punish wage cuts even in recessions, leading to considerable more rigid wages. Surprisingly, this is even true without an “objective” justification to feel entitled to initial contracts. Keywords: Wage rigidity, Reference points, Gift exchange, Labor contracts, Experiments JEL classification: C9, J3, M5 concerns. Wage cuts are, however, perceived as unfair by 1 Introduction workers and lead to a decrease in work morale. In antici- A long-standing question in economics is why wages do pation, firms do not cut wages. not fall in recessions (Fehr and Goette 2005; Bauer et al. But why do workers perceive wage cuts as unfair 2007; Dickens et  al. 2007). Understanding this phenom- even though a recession seems to provide an appropri- enon of (downward) wage rigidity is important as it has ate reason to cut wages since it limits firms’ abilities to been shown empirically to be associated with unfavora- pay high wages? Even standard outcome-based fairness ble labor market outcomes, in particular unemployment models (e.g. Fehr and Schmidt 1999; Charness and Rabin (Barwell and Schweitzer 2007; Devicienti et  al. 2007; 2002) predict moderate wage cuts since they enable fair- Elsby et al. 2016). A number of explanations of why firms minded workers to share the recession’s burden that oth- pay wages that are above the market clearing wage and erwise only the firm would have to bear. Already Akerlof that cannot be easily adjusted downward has been put (1982) and Akerlof and Yellen (1990) have suggested, forward, including e.g. insider-outsider theories (Lind- however, that what workers perceive as a “fair wage” beck and Snower 1988, Calmfors and Driffill 1988) or might depend—among other things —on the wage they (disciplining versions of) the efficiency wage hypothesis previously received, their reference point (Goette et  al. (Gintis 1976; Shapiro and Stiglitz 1984). 2007; Shafir et al. 1997). While this seems very plausible This study’s focus will be on a fairness explanation of the wage rigidity puzzle that has found support by ques- Other theories of wage rigidity include the implicit contract theory (as tionnaire studies interviewing managers (e.g. Blinder and developed by Baily 1974; Gordon 1974; Azariadis 1975) or job search models Choi 1990; Campbell and Kamlani 1997; Bewley 1999): as reviewed in Mortensen (1986). When contracts are incomplete, firms partly have to Akerlof (1982) have also highlighted the importance of social compari- sons for the “fair wage”, namely what co-workers earn. This study focuses on rely on workers’ intrinsic motivation and their fairness past wages, but other work has already explored the social comparisons (see e.g. Charness and Kuhn 2007; Abeler et al. 2010; Bartling and von Siemens 2011; Cohn et  al. 2014). Recent studies (Charness et  al. 2012; Franke et  al. *Correspondence: chris.koch@univie.ac.at 2016) have also explored workers’ participation in wage setting as an influ- Department of Economics, University of Vienna, Oskar‑Morgenstern‑Platz ence on workers’ fairness perceptions and effort provision. 1, 1090 Vienna, Austria © The Author(s) 2021. 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To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. 5 Page 2 of 17 C. Koch under stable conditions, it is less clear whether it is also fairness explanation (potentially in combination with ref- true in a recession. erence points)—is valid even in times of recession. This is In this study, I experimentally manipulate whether my paper’s core contribution. The main innovation of my (previous) out-of-recession wages can serve as a refer- design is to manipulate whether out-of-recession wages ence point, influence what workers perceive as a “fair can serve as reference points inspired by the idea of Hart wage” in recession and, thereby, provide an explanation and Moore (2008) that contracts serve as reference points for rigid wages. In an informative field experiment, Kube (see also Herweg and Schmidt 2015). In “real-world” et  al. (2013) have already shown that exogenous wage labor markets, contractual arrangements often have to cuts have a negative impact on participants’ work morale. be revised before wage cuts can be implemented. In such Crucially, the authors deliberately cut wages without a revision, existing contract conditions might be salient providing a “good reason” (e.g. recession), and Chen and and, thus, serve as reference points. Horton (2014)—although using a fairly different setting— I model the labor market as a simple gift-exchange do not find a negative effect when providing such an (Fehr et al. 1993). Firms sometimes face a ‘recession’—in explanation. Since significant company-wide wage cuts terms of a negative profit shock—that ceteris paribus only are rarely observed, empirical evidence is scarce. For the reduces their profits. Two different treatments manipu - airline industry, Lee and Rupp (2007) find only limited late whether (previous) out-of-recession wages can serve support that wage cuts lower employee effort. A potential as reference points. In the Contracts as Reference Points explanation is that most of the wage cuts they observe (CasRP) treatment, workers and firms first conclude a occur under the threat of bankruptcy, providing a justifi - contract before they are informed about whether a reces- cation for the cut. Finally, Bracha et al. (2015, p. 312) have sion has occurred in this period. In the recession case, experimentally shown that making a given wage high (or the concluded contract can be revised. Otherwise, initial low) relative to past or other wages increases (decreases) contract conditions determine payoffs. In this treatment, labor supply. Crucially, the authors find that providing the initial contract’s wage—which workers explicitly “even a flimsy rationale” for these differences make the agreed to when accepting a contract offer—potentially effect disappear. serves as a reference point for the revision stage. Imple- Although there is, thus, evidence that previous wages menting such a contract-revision structure deviates from can serve as reference points, precisely this evidence much of the prior literature but provides out-of-recession cast doubts on whether this is actually true under all cir- wages with a realistic shot at serving as reference points. cumstances, questioning whether a fairness explanation This is not possible in the Baseline (BASE) treatment. of wage rigidty is valid for the recession case. Question- Here, firms and workers are first informed about whether naire and survey studies (Kahneman et  al. 1986; Char- a recession has occurred and only afterwards have the ness and Levine 2002; Kaur 2018) might be consistent ability to conclude a contract. Hence, firms’ contract with this idea but cannot—due to a lack of control treat- offers can already take the state of the world into account ments—rule out that wage cuts are rejected for reasons and no initial contracts exist. unrelated to reference points: If workers believe that it The data suggests that wages are neither completely is the firm that mostly benefits from a boom, they might rigid in CasRP nor in BASE. Wage cuts are, however, be generally unwilling to share the burden of the bust significantly higher in BASE than in CasRP. Compared to because they might perceive the recession as part of the the out-of-recession case, the average wage is reduced by firm’s entrepreneurial risk, completely independent of 13.1 points (or 21 percent) in recession in BASE but less reference points. Utilizing the strength of the experimen- than half this amount (6.0 points or 10 percent) in CasRP. tal analysis, I test, under tightly controlled conditions, In the latter treatment, there is evidence of a reference- whether one particular explanation of wage rigidity—a point effect: Controlling for the wage level, workers’ effort is lower for wages below the reference wage compared to those at or above this level. This, reference-point effect There is additional evidence that reference points and previous wages influ - leads to significant treatment differences: In case wages ence current wages, which is, however, not directly related to rigid wages in recessions. Abeler et  al. (2011) have experimentally shown that expectations are cut in CasRP, workers do not share the recession’s affect workers’ reference points. Accordingly, Mas (2006) find empirical evi - burden (as much) as they do in BASE, explaining why dence that wage increases that do not meet workers’ expectations can lead to firms pay more rigid wages in CasRP. a decline in performance. Similarly, Ockenfels et al. (2015) show that manag- ers’ performance is reduced when their bonus payment falls behind a refer- ence point (see also Cohn et al. 2015). Notably, these papers do not illuminate whether a “good” reason (recession) provides a justification for wage cuts. Falk et al. (2006) have shown experimentally that reservation wages are influenced by the introduction of minimum wages (see also Owens and Kagel 2010). It seems reasonable to use the terms rigid wages and wage cuts also for Finally, Greenberg (1990) and Greenberg (1993) find evidence that underpay - BASE. Crucially, due to construction, they can, however, only refer to a com- ment can lead to theft. parison of average wages in and out of recession in BASE. Can reference points explain wage rigidity? Experimental evidence Page 3 of 17 5 On the basis of these results, I implemented two converse effect in my setting: they encourage workers control treatments. First, the Wages as Reference Points not to share a part of the recession’s burden by refus- (WasRP) treatment shows that an “objective” justifica- ing to accept wage cuts and, thus, actually behave less tion for feelings of entitlement—an explicit contract fair-minded than otherwise agreement—is surprisingly not necessary to induce more rigid wages, highlighting a strength of reference 2 Experimental design and procedures points that has not been observed in previous stud- 2.1 Main Treatments: BASE vs. CasRP ies. Second, the Contract as Reference Points treat- I consider an experimental labor market in which firms ment with Feedback (CasRP-F) manipulates the firm’s can be hit by a ‘recession’ (see Kocher and Strasser 2011 information condition by providing better feedback and Gerhards and Heinz 2017). More precisely, following but does not lead to significant differences, at least on Fehr et  al. (1993), I model the labor market as a simple average. gift-exchange but modify the standard setting by using Overall, this study provides evidence that is con- a non-static version in which firms can be randomly hit sistent with the idea that reference points shape what by a negative profit shock (which is called a “bad mar - workers perceive as a “fair” recession wage in a con- ket situation” in the instructions). Notably, for the ease trolled experimental labor market, providing one of exposition, I use the terms ‘negative profit shock’ explanation for more rigid wages in this setting. My and ‘recession’ interchangeably in the following, but the paper may also help to reconcile conflicting results reader should always bear in mind the stylized nature in the experimental literature linked to wage rigidity. of the ‘recession’ in my setting, as outlined below. The As noted before, my study focuses on the revision of game proceeds as follows: Firms make a contract offer by contractual arrangements that make reference points choosing a wage, an integer w ∈{30, . . . , 100} , and work- salient. In contrast, the earlier literature was primar- ers who accept a contract offer have to choose how much ily concerned with reactions to wage changes relative effort to exert, e ∈{1, . . . , 10}. to earlier periods, where every period featured a “new As usual in a gift-exchange setting, contracts are contract”. In the latter setting, earlier contracts seemed incomplete since workers’ effort levels are not contracta - not serve as reference points and Burda et  al. (2005), ble. I implemented a slightly modified version of the pay - Kocher and Strasser (2011), and Gerhards and Heinz off functions used by Riedl and Tyran (2005). Firms have (2017) find that wages are flexible. In contrast, Hannan the following payoff function: (2005) uses a setting in which initial wages are revised 10 × e − w + 50, if no profit shock occurs (p = ), in recession and workers at least partly seem to pun- � = 10 × e − w + 30, otherwise (p = ). ish wage cuts. Notably, since her study does not focus (1) on wage rigidity, it misses control treatments, and it is Workers’ payoffs are given by even unclear how rigid wages overall are in her setting. Finally, Buchanan and Houser (2020) investigate wage � = w − c(e). (2) rigidity in a setting in which contracts can serve as ref- erence points but do not provide a control treatment in Here, F denotes the firm, W denotes the worker, and c(e) which this is not the case as they focus on employers’ is the cost of effort that is an increasing function of e. In beliefs about workers’ work morale and the distinction my experiment, I used a standard cost-of-effort function between nominal and real wage cuts. My study, thus, shown in Table 1. Workers who reject their contract offer complements their research. get a payoff of  = 20 whereas their assigned firms This study also informs the literature about contracts get a zero profit,  = 0 . Additionally, firms earn zero as reference points, starting with Hart and Moore profits if their contract offers have been accepted, but (2008). Unrelated to wage rigidity, their model mainly effort levels had resulted in a negative payoff for the firm. analyzes why people write long-term employment con- Notably, firms do not state a desired effort level. For clean tracts by looking at the implications of reference points identification, only one variable—the wage—will poten - for different contract types. Fehr et  al. (2009, 2011, tially serve as a potential reference point in my setting. 2015) experimentally test these implications compar- My payoff functions capture the following core idea: In ing the performance of different contract types. Bar- a recession, first of all only firms suffer. The question then tling and Schmidt (2014) are the first that analyze how is whether workers are willing to share a part of the reces- initially concluded contracts affect renegotiation via sion’s burden. More particularly, these functions were reference-point formation in a buyer-seller relation- chosen to meet two objectives: The impact of a recession ship. While reference points in their setting constrain should be substantial enough such that firms consider sellers to be fair and not to exploit buyers, they have a cutting wages, but at the same time firms that do not cut 5 Page 4 of 17 C. Koch Table 1 Eor ff t levels and cost of effort e 1 2 3 4 5 6 7 8 9 10 c(e) 0 1 2 4 6 8 10 12 15 18 wages should still make a small profit or at least avoid do not find significant differences between a bilateral ver - losses. The underlying idea is that questionnaire studies sion of the game and gift-exchange markets. (see e.g. Bewley 1999, Kahneman et al. 1986) suggest that losses legitimize wage cuts: They find that firms that face 2.1.1 CasRP treatment losses in the field are able to reduce wages substantially and that the general wage-rigidity finding is driven by • Stage 1: Firms make a contract offer to their workers those firms that are not threatened in their existence. My by choosing a wage, w ∈{30, . . . , 100} . Af ter w ards , design focuses on the latter situation. To avoid that losses these workers have to decide whether they want to legitimize wage cuts, firms are provided with some extra accept their offer. If they accept, workers have to money (50 points) and it is ruled out that firms make choose their effort level, e ∈{1, . . . , 10} . This effort negative earnings. level is first of all not communicated to firms. If they In this setting, I implemented two main treatments reject, subjects are informed about payoffs in stage 3. that are designed to test whether out-of-recession wages • Stage 2: At the beginning of the second stage, two out can serve as reference points and, thus, influence what of six firms are randomly selected and hit by a nega - workers perceive as a fair wage in recession. My design tive profit shock. Only these two firms are allowed is (loosely) based on the idea of Hart and Moore (2008) to change the initial contract conditions by choosing that contracts serve as reference points because they a new wage, w ∈{30, . . . , 100} . Although affected create feelings of entitlement. Wage cuts in “real-world” workers cannot reject wage changes, they are allowed labor markets might require a revision of the contractual to adjust their initial effort by choosing a new effort arrangements between workers and firms simply because level, e ∈{1, . . . , 10}. these arrangements already exist before the recession. In • Stage 3: Firms and workers get to know their payoffs, particular, in the Contracts as Reference Points (CasRP) and firms are informed about their workers’ relevant treatment, contracts concluded initially before reces- effort if their contract offer has not been rejected. sions—or more precisely the initial out-of-recession wage This means that firms only learn about e in case a they stipulate—can potentially serve as reference points negative shock does not occur, and in case such a for workers’ feelings of entitlement regarding the reces- shock occurs, firms only learn about e , ensuring sion wage. In the Baseline (BASE) treatment, no such comparability with BASE. initial contracts exist. For reasons of treatment compa- rability, a bilateral version of the gift-exchange game is In case that no profit shock occurs, wages and effort lev - implemented in both treatments: Subjects play in groups els of stage 1, w and e , determine payoffs. Otherwise, 1 1 of 12 (6 firms and 6 workers) for 18 periods. One firm wages and effort levels of stage 2, w and e , determine 2 2 is matched with one worker and pairs are randomly payoffs. In BASE, no initial contracts that could serve rematched every period. This rematching is implemented as a reference point exist and, thus, firms are informed to minimize the importance of reference points other upfront whether a negative profit shock has occurred. than those induced by initially concluded contracts (e.g. previous periods). This allows for a clean identification of 2.1.2 BASE tr eatmentBASE treatment the impact reference points induced by initial contracts and their stipulated wages. Moreover, Fehr et  al. (1998) • Stage 1: At the beginning of the first stage, two out of six firms are randomly selected. These two firms are hit by a negative profit shock. Knowing whether Implementing the ‘recession’ by a reduction of the extra money by 20 points ensures that both objectives are met in a simple, feasible way for all wage lev- els: Independent of the out-of-recession wage level, firms experience a notice - able decrease of their profits in recession. This decrease is, however, still small In my design, only some firms have to face a negative profit shock in each enough not to inevitably lead to zero profits when wages are not reduced. period and not all firms in some periods. Due to the bilateral structure, no Alternatively reducing the productivity parameter might be considered more qualitative differences should be observed. In both situations, workers and realistic but has the drawback that both objectives cannot be easily ensured firms only have information about their wage and effort, not about other for all wage levels. wages or effort levels. The outlined implementation was chosen because it is Occassionally, there were also groups of 10 with 5 firms and 5 workers. more appropriate for a potential follow-up study. Can reference points explain wage rigidity? Experimental evidence Page 5 of 17 5 they have been hit by such a shock or not, firms implementations that allow for rejections in recession make a contract offer to workers by choosing a wage, are experimentally less feasible. w ∈{30, . . . , 100}. Nonetheless, three concerns may arise. First, workers • Stage 2: This stage depends on the previous one. In may perceive the revision procedure as especially aver- case the assigned firm is not hit by a negative profit sive in CasRP because firms can change an established shock, workers first have to decide whether they contract. Second, one may also fear that the asymmetry want to accept their contract offer or not. If they between the recession and the no-recession case is more accept, workers have to choose their effort level, salient and less natural in BASE (as there is no initial con- e ∈{1, . . . , 10} . In case the assigned firm is actually tract), creating an experimenter demand effect to lower hit by a negative profit shock, workers only have to wages in this treatment. Finally, providing an opportunity choose their effort but cannot reject the contract to reject a contract out-of-recession but not in recession offer. This difference is implemented in order to might raise the concern that firms have to pay higher ensure comparability with the CasRP treatment. wages in case workers can reject. Crucially, my first con - • Stage 3: Firms and workers get to know their payoffs, trol treatment, WasRP, has a structure that resembles and firms are informed about their workers’ effort if BASE more closely—not featuring established contracts their contract offer has not been rejected. for example—and, hence, allows me to control for the first two concerns. The last concern, however, even biases In both treatments, subjects are informed about the exact against observing rigid wages in recession, suggesting sequence of events in advance. The fundamental idea of that my analysis provides a conservative test for wage the two treatments is that in one of them initial contracts rigidity. exist while this not true in the other. Notably, this implies that CasRP has two important features: First, even in case 2.2 Control treatments, discussion & procedures there is a profit shock, subjects know the wage without In case a difference between BASE and CasRP is observed, such a shock, which is not true in BASE. Second, they the two control treatments try to illuminate why such a explicitly agreed to this latter wage. Although this seems treatment difference is observed. The first control treat - to realistically capture field labor contracts, it also repre - ment is the Wages as Reference Points (WasRP) treatment. sents a change of two things at the same time. I conjec- This treatment tries to disentangle which of the two main tured that the acceptance decision would be necessary aspects changed from BASE to CasRP potentially provides for contracts to serve as reference points and, hence, a channel that leads to rigid wages. Is an explicit con- for observing wage rigidity. The underlying idea was tract conclusion necessary to create workers’ resistance that only an explicit agreement might sufficiently trig - against wage cuts or do contracts already serve as refer- ger workers’ self-serving biases because only when such ence points just by determining the out-of-recession wage an agreement exists wage cuts can constitute a violation and conveying this information to workers? Concerning of it. My first control treatment (WasRP) will disentangle the sequence of events, this treatment is a combination of whether an acceptance is really necessary, allowing for a BASE and CasRP. Workers know the payoff-relevant out- clean identification of the impact and the channel of ref - of-recession wage also in recession (and that this wage erence points. Surprisingly, it will show that the accept- ance decision is actually not necessary. The contract revision in recession is implemented fol - First, a real renegotiation stage in which the initial contract is valid in case workers reject wage changes would require a baseline treatment compara- lowing Fehr et  al. (2015). Firms can revise their work- ble to Bartling and Schmidt (2014): the same initial participants’ behavior as er’s wage as they like and workers cannot get out of in CasRP would have to be exogenously imposed in this baseline treatment. an agreed-upon contract and reject the new wage— This would, of course, undermine the ability to analyze whether firms antici - pate resistance against wage cuts in CasRP and already adjust out-of-recession although they can change their effort level. This extreme wages downward compared to the baseline. By construction, initial behavior implementation is not intended to capture field nego - would be the same in both treatments. Second, when workers’ rejection leads tiations realistically but tries to provide “stress test” for to outside-option payments, rejecting would only provide a reasonable expen- sive punishment opportunity for wage cuts that lead to very low but not to contractual reference points. Previous studies’ suggest medium/high wage levels since outside-option payments are not too high. that the impact of reference points can be limited by Rejecting e.g. a wage cut from 90 to 75 would lead to outside option payments design specifics and Fehr et  al. (2015,  p. 4) have argued of 30, resulting in a cost of up to 45 points. The result of the first control treatment—that an explicit acceptance is not that “the easier it is to change a contract the less likely it necessary—suggests that a design without an acceptance decision at any is to serve as a reference point,” biasing against observ- point would also have led to rigid wages. Notably, due to its simplicity, this ing any effect of reference points. In addition, alternative alternative design might be considered preferable to the implemented one. Crucially, this insight was, of course, only gained in hindsight: it material- ized as a consequence of my more complex design and can, thus, be seen as a result of my analysis. 5 Page 6 of 17 C. Koch Table 2 Summary of treatments Treatments Information about out-of-recession Initial contracts (explicit Extended Sessions Number wage in recession agreement) feedback of subjects BASE No No No 6 68 CasRP Yes Yes No 6 70 WasRP Yes No No 6 68 CasRP‑F Yes Yes Yes 6 72 Notes: While all treatments except BASE inform workers about the out-of-recession wage also in recession, initial contracts and, thus, an explicit agreement about the out-of-recession wage is only given in CasRP/CasRP-F but not in WasRP. Finally, firms are only provided with extended feedback in CasRP-F potentially has been cut) although they have not explicitly cuts and firms are not fully aware of this behavior, the concluded a contract with their firm before the recession. difference between the BASE and the CasRP treatment Because there is no explicit contract conclusion, WasRP might underestimate the real difference caused by ini - is, however, structurally closer to BASE avoiding potential tial contracts. In CasRP-F, however, firms in recession concerns outlined before. are informed not only about the relevant but about both effort levels in stage 3. Table  2 provides an overview over all four treatments, summarizing the key differences. • Stage 1: Firms choose a contract offer (by specify - Sessions lasted on average between 75 and 90 minutes ing a wage) for the case that no negative profit shock and took place at the mLab at the University of Mannheim. occurs. Then, the computer selects two out of six Overall, 278 (undergraduate and master) student subjects firms. These firms are hit by a negative profit shock (six session per treatment with 10-12 subjects) of any field and are allowed to adjust their contract offer for the participated in the experiment and earned on average 20 recession. EUR, where final payoffs are the sum of all 18 periods’ pay - • Stage 2: If the assigned firm is not hit by a negative offs. Recruitment was done by ORSEE, Greiner (2004), and profit shock, workers first have to decide whether the experiment was programmed in z-Tree (Fischbacher they want to accept their (out-of-recession) contract 2007). Experimental instructions—that had a labor-market offer or not. If they accept, they have to choose their framing to facilitate understanding—for all treatments can effort. If the assigned firm is hit by a negative profit be found in the Additional file 1 : Appendix E. shock, workers only have to choose their effort but cannot reject their (recession) contract offer. Impor - 3 Hypotheses tantly, in the second case, workers are also informed In this section, I discuss two hypotheses. These hypoth - about the out-of-recession contract offer (wage) that eses are based on the model of inequity aversion by is irrelevant for payoffs. Fehr and Schmidt (1999). I provide a simple extension • Stage 3: Firms and workers get to know their pay- of this model—inspired by the idea of Hart and Moore offs, and the firms are informed about their work - (2008)—that incorporates that workers’ behavior might ers’ relevant effort if their contract offer has not been be reference-dependent with respect to the previous rejected. out-of-recession wage. In the text, I focus on provid- ing intuitions, whereas Appendix A outlines more for- My second control treatment is the Contracts as Refer- mal arguments. Crucially, the gift-exchange literature has ence Points treatment with Feedback (CasRP-F). This shown that the standard game theoretic solution is not a treatment is very similar to CasRP and only slightly var- good predictor for this game. Whether wage cuts hap- ies the information condition of the firm. To ensure pen in such an equilibrium is not really an empirically comparability between BASE and CasRP, firms are only interesting question, and for this reason my design was informed about their workers’ relevant effort levels not tailored to allow for such equilibrium wage cuts. (not about effort level adjustments) in stage 3 in CasRP. Hence, it is not straightforward for firms to infer how workers react to wage cuts. But if workers punish wage See also Dickson and Fongoni (2019) for a more elaborated approach. 10 12 This treatment also controls for a small difference between the two main Assuming common knowledge of perfectly rational and selfish agents: treatments: In CasRP, an out-of-recession wage offer can be rejected and in Workers do not have an incentive to provide more than minimal effort, this case a potential recession cannot even occur, potentially creating a selec- e = 1 (even though the highest feasible effort level would maximize the joint tion problem since this is not true for BASE. Although this type of rejection is surplus). Firms anticipate this and choose the minimum wage for workers, empirically very rare (10 out of 630 cases) and would potentially bias against w = 30 . In recession, firms’ and workers’ behavior does not change because observing a treatment difference, it does not even exist in WasRP. firms already pay the minimum wage. This outcome is the same for all treat - ments because material incentives do not change between treatments. Can reference points explain wage rigidity? Experimental evidence Page 7 of 17 5 Fairness models, however, predict participants’ behavior however, contracts are not concluded before recessions in the gift-exchange game more accurately. If workers are and firms cut wages. Although we may not expect such a sufficiently fair-minded/inequity-averse, they will recipro - clear-cut result, we should at least expect: cate high wages by high effort levels, (ideally) splitting the surplus with their firm equally to avoid harming inequality. Hypothesis 2 [Contracts as Reference Points]: Wages are Since only the firm but not the worker is hit by a negative more rigid in CasRP than in BASE. In CasRP, a reference- profit shock in recession, the inequality between both par - point effect is observed: controlling for the wage level, effort ties ceteris paribus increases in a recession. Thus, the split is lower for wage cuts than for stable (or increased) wages. of surplus has to be adjusted. A moderate wage cut that is accompanied by an unchanged effort level allows workers Notably, firms with standard preferences will also not and firms to (equally) share the recession’s burden. Since lower out-of-recession wages in CasRP (compared to wages, thus, go down in recession, workers—when con- BASE) to preemptively mitigate the rigidity problem. The trolling for the wage level—exert more effort in than out of underlying idea is following: Under the parameters of recession. Since monetary incentives do not vary between the experiment, cutting wages already out-of-recession treatments, no differences between treatments occur. to allow for lower wages in recession leads to losses out- of-recession that outweigh the gains in recession. When Hypothesis 1 [Outcome-Based Social Preferences]: firms, however, are somewhat inequity-averse (see Appen - In both main treatments, BASE and CasRP, firms mod - dix A), they may have an incentive to lower wages out-of- erately adjust their wages downward if they are hit by a recession to avoid the higher inequality associated with negative profit shock. This adjustment is not different rigid wages in recession. Notably, this potential behavioral between treatments. pattern also originates from workers’ resistance against wage cuts, could contribute to the overall rigidity of wages Notably, with the standard inequity-aversion model, and might also be relevant in the field. As the theoretical it cannot be rationalized as equilibrium behavior that analysis is, however, somewhat inconclusive on this point, workers share the recession’s burden by increasing effort i.e., the prediction depends on what one assumes about for constant wages. This is naturally true for workers that the firms’ preferences, I do not offer a prediction here, but already exert the maximum effort but also holds for other state an open question. Finally, following the motivation of workers (as is outlined in more detail in Appendix A). the two control treatments, I have two conjectures. When workers also care for reference points, the predic- tion changes: If a firm cuts wages in recession in CasRP, Open question: Do firms adjust the out-of-recession workers feel entitled to the wage of the initial contract. wage downward in CasRP? While stable wages can lead to a loss in utility due to risen Conjecture 1 [Wages as reference points]: An explicit inequality, wage cuts decrease workers’ utility since they contract conclusion is necessary to generate resistance are perceived as reference-point violation. If workers suf- against wage cuts. ficiently care for reference points, they punish wage cuts Conjecture 2 [Contracts as reference points with feed- by lowering effort to offset the reference-point violation. back]: Due to the better information conditions, wage By how much workers have to punish wage cuts to make cuts in CasRP-F are less pronounced than in CasRP. them unprofitable, depends on their relative reaction to stable wages. If workers reciprocate stable wages only by constant effort—as predicted by inequality aversion (see 4 Results and discussion Appendix A)—their effort reduction has to overcompen - 4.1 Firms’ Behavior—BASE vs. CasRP sate the wage cut (| w|= 10 leads to |�e| > 1 ). If stable Table  3 and Fig.  1 summarize firms’ behavior. Table  3 wages are reciprocated by higher effort, a proportional provides average wages in and out of recession as well as effort reduction is already sufficient. In both cases, when two measures of the wage difference in and out of reces - controlling for the wage level, effort is lower for wage cuts sion: the (raw) wage cut and the relative wage cut. The than for stable wages. This implies that firms—with stand - later measure is provided as a complementary measure ard preferences—do not cut wages in recession. In BASE, Due to the construction of the treatments, the term wage cut can have two different meanings: Both in BASE and in CasRP, an indirect wage cut can be observed insofar as one can compare average wages of firms in recession with average wages of firms out of recession. In CasRP, also a direct wage cut can Intention-based fairness models (e.g. Charness and Rabin 2002—with the be observed by comparing wages from stage 1 and stage 2 in case a recession reciprocity parameter θ ) potentially predict wage rigidity if one assumes that occurs. Since there is no reason to expect a difference between the two meas - wage cuts are considered as unkind actions. The question, however, remains ures, I report indirect wage cuts unless otherwise stated. Reporting direct why a moderate wage cut should be considered unfair although a recession wage cuts would lead to very similar results limits firms’ abilities to pay high wages (see also Rabin 1993). 5 Page 8 of 17 C. Koch Table 3 Average wages: BASE vs. CasRP relative wage cut measure (21 percent vs. 10 percent). Hence, a treatment difference in line with hypothesis Wage Wage cut Relative 2 is observed: initial contracts that potentially serve as No-recession Recession Wage cut reference points reduce wage cuts in CasRP to less than half their size in BASE. The difference between treat - BASE 60.1 47.0 13.1 21% ments is significant both for (raw) wage cuts (rank-sum CasRP 57.9 51.9 6.0 10% test: p = 0.038) and for relative wage cuts (rank-sum test: p = 0.026). In addition, a difference of 7.1 points is non-negligible and economically meaningful in the sense since firms paying high wages have much more scope to that the predicted treatment difference would even only (absolutely) adjust their wages downward. Since my two be 10 points when making the unrealistic assumption of hypotheses make predictions about how rigid wages are, completely rigid wages in the CasRP treatment (whereas the two wage-cut measures are the main variables to test workers and firms share the profit shock of 20 points this prediction. Notably, since 98% of all wage offers are equally in BASE—Appendix A). accepted, my analysis below is based on accepted wage Figure  1 shows wages over time. In support of the offers. previous findings, firms seem to pay even more rigid Wages are cut in both treatments: average wages wages over time in CasRP. While wages are also cut by are significantly lower in recession than out of reces - 13.1 points in BASE in the last six rounds, they are only sion. While pay is, however, cut by 13.1 points in BASE 15 reduced by 1.6 points in the last third of the experiment (signed-rank test: p = 0.028 ), it is only reduced by 6.0 in CasRP. Although non-parametric tests cannot confirm points (signed-rank test: p = 0.023) in CasRP. This dif - that wage cuts are getting smaller in CasRP (signed-rank ference translates to a comparable discrepancy in the BASE CasRP 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 Period Period No Recession Recession No Recession Recession Fig. 1 Average wages—BASE vs. CasRP Tests in this paper are two-sided and since my observations are strictly only independent at the session level, non-parametric tests conservatively treat one session as one independent observation. Only when reporting power results for important null results, I also use more powerful individual observations and perform one-tailed tests in case of a directed hypothesis. Wage 35 40 45 50 55 60 65 70 Wage 35 40 45 50 55 60 65 70 Can reference points explain wage rigidity? Experimental evidence Page 9 of 17 5 Table 4 Panel regressions on wages test, p = 0.173), they do show that wages actually become fully rigid in CasRP: wages are not significantly different (1) (2) (3) (4) in and out-of recession in the last rounds (signed-rank RE RE RE FE test, p = 0.345). These findings clearly indicate that firms − − CasRP‑ dummy 0.257 1.659 3.285∗ seem to learn over time to pay even more rigid wages in (4.046) (4.138) (1.913) CasRP. − − CasRP‑F‑ dummy 1.388 0.834 3.347 As indicated before, out-of-recession wages could vary (3.408) (3.825) (2.104) between treatments when inequity-averse subjects who WasRP‑ dummy 3.000 1.159 1.471 represent a firm anticipate workers’ resistance against (4.420) (4.453) (1.818) wage cuts in CasRP, potentially contributing to the over- − − − − Recession‑ 6.832∗ ∗ ∗ 11.51∗ ∗ ∗ 10.65∗ ∗ ∗ 11.11∗ ∗ ∗ all rigidity of wages in this treatment. In line with this dummy (1.135) (1.550) (2.002) (1.759) idea, these wages are slightly lower in CasRP (57.9) than Rec × CasRP 5.822∗ ∗ ∗ 6.985∗ ∗ ∗ 5.879∗∗ in BASE (60.1). A non-parametric test is, however, unable (2.250) (2.477) (2.413) to detect a significant difference (rank sum test: p> 0.20) Rec × CasRP‑F 7.051∗∗ 8.287∗∗ 7.340∗ although this test is arguably underpowered. Potentially (3.247) (3.879) (3.634) because of the slight initial differences, recession wages Rec × WasRP 5.307 6.073 5.251 ∗∗ ∗∗ ∗∗ (47.0 vs. 51.9) are also only different with at best weak (2.153) (2.362) (2.176) significance (rank sum test: p = 0.075). Wage (No‑Rec) 0.438∗ ∗ ∗ 0.0885∗ ∗ ∗ To further validate the non-parametric analysis pre- t−1 (0.0529) (0.0289) sented so far, Table  4 shows panel random effects (RE) Wage (Rec) 0.561∗ ∗ ∗ 0.145∗ ∗ ∗ and fixed effects (FE) regressions with wages as the t−1 (0.0677) (0.0383) dependent variable and different specifications. All speci - Effort (No‑Rec) 1.723∗ ∗ ∗ 1.148∗ ∗ ∗ fications control for time trends, use data from all four t−1 (0.203) (0.147) treatments and include a recession dummy. Interact- Effort (Rec) 0.756∗ 0.633∗∗ ing the recession dummy with treatment dummies in t−1 (0.408) (0.241) specification (2) confirms that wage cuts are significantly First wage 0.0838 smaller in CasRP than in BASE. This result is robust to ∗∗ adding past-period information and using fixed instead (0.0271) of random effects (specification 3 and 4). Interestingly, in Period & Period one specification, out-of-recession wages are— with mar - Constant 57.83∗ ∗ ∗ 59.46∗ ∗ ∗ 23.98∗ ∗ ∗ 49.13∗ ∗ ∗ ginal significance—lower in CasRP compared to BASE, (3.280) (3.343) (3.854) (2.274) indicating that some firms seem to anticipate resistance Observations 2858 2858 2696 2696 against wage cuts and try to circumvent it by lowering 0.0329 0.0384 0.0984 0.120 wages already out of recession. This result is, however, Notes: Panel random effects (RE) and fixed effects (FE) regressions on wages neither robust across specifications nor across the other for all treatments. Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within control treatments. session. ∗∗∗ indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at the 10 percent level Result 1 In both treatments, wages are cut in recession. Importantly, however, wages are more rigid in CasRP than in BASE (and become fully rigid at the end of the that rigid wages are due to out-of-recession wage adjust- experiment). This supports hypothesis 2. Regarding the ments in CasRP is found. open question, no conclusive evidence in favor of the idea Power calculations based on observed standard deviations suggest that 38 4.2 Workers’ Behavior—BASE vs. CasRP (instead of 6) sessions per treatment would be needed to detect the small, Is there a reference-point effect present in CasRP that observed difference in wages as statistically significant at the 5% level 80% of the time. Alternatively, one could ask with what probability a true change in could explain why wages are more rigid in this treatment? behavior of 5 or 10 points would be detected (which would account either Table  5 provides a first average measure of workers’ for half of or the full theoretically predicted wage reduction in BASE). Such behavior in the two different treatments. In both treat - differences would be detected as significant at the 5% level with 25% or 61% probability (or 38% or 76% using individual data). Notably, power calcula- ments, average effort seems to be cut. While this reduc - tions for the associated regression analysis in Table  4—based on how much tion is, however, significant in BASE (signed-rank test: p the CasRP-dummy adds to the R —reveal a power of up to 92% even for the = 0.028), this is not true for CasRP (signed-rank test: p observed effect. Indeed, one specification finds some evidence for a small effect. 5 Page 10 of 17 C. Koch Table 5 Average effort: BASE vs. CasRP Effort Eor ff t cut No-Recession Recession BASE 4.0 3.3 0.7 CasRP 4.1 3.8 0.3 = 0.248). Of course, workers’ effort choices can only be fully understood when analyzing them accounting for their dependence on wages. Figure  2 gives a first impression why a treatment dif - [-70,-20) [-20,-10) [-10,-5) [-5,0) 0 (0,5] (0,10] (10,20] (20,70] (8) (34) (44) (15) (66) (17) (14) (6) (3) ference in wage-setting behavior might be observed. This Wage change (number of observations) figure reports workers’ reaction, their effort change, to dif - Fig. 2 Workers’ reaction to wage changes—CasRP ferent wage changes of firms for CasRP, for which direct wage-cut data is available (see footnote  14). While wages are cut roughly half of the time and remain exactly con- stant in one-third of the cases, firms somewhat surprisingly Table  6 supports the notion of a punishment reward also increase the recession wage sometimes. A potential pattern, at least in relative terms: Unpredicted by my rationale is that increasing the wage in a recession may be model of inequality aversion, stable or increased wages perceived as a particular strong gift that may not even be are—controlling for the wage level—reciprocated with that costly, at least for the more frequent moderate wage significantly higher effort (0.41) in recession. If pay increases. Indeed, the graph shows a punishment-reward is instead cut, average effort is 0.26 points lower and pattern of workers’ behavior: workers punish wage cuts by the resulting effort is statistically not different from decreasing effort, and they reward stable or increased wages zero (F-test: p = 0.324). Put differently, since stable (or by increasing effort (both in absolute terms). Notably, as increased) wages are already rewarded, workers do not discussed before, lower (higher) wages are generally recip- have to overcompensate the initial wage decrease to ren- rocated with lower (higher) effort in gift-exchange games, der wage cuts unprofitable. Even a less severe reaction completely independent of wage cuts. This positive wage- leads to the predicted reference-point effect: controlling effort relationship could in principle explain the observed for the wage level, effort is lower for wage cuts than for pattern. To fully understand the implications of workers’ stable wages, providing an incentive not to cut wages. behavior one has to analyze workers’ reactions to wage cuts Does the observed reference-point effect lead to behav - accounting for this relationship. ioral differences across treatments? Table  7 provides an To provide such an analysis, Table  6 reports fixed extended regression analysis for all treatments. While effects regressions for CasRP that explain effort and con - specification (2) disentangles the recession dummy by trol for the wage level (as well as a quadratic wage term adding treatment-specific recession dummies, specifica - and a quadratic time trend). While specification (2) tion (3) implements separate dummies for wage cuts and adds a simple recession dummy, specification (3) adds a stable (or increased) wages for all treatments with ref- dummy, Rec × Wage cut, that only has value one if a reces- erence points (CasRP, WasRP, CasRP-F). In these treat- sion occurs and the firm cuts wages. Finally, specification ments, this separation is meaningful since wage cuts can (4) provides an alternative way to control for the wage be perceived as reference-point violations. Finally, speci- level, namely by including 14 wage-dummies for wage fication (4), (5) and (6) look at further controls and fixed intervals with length of 5 ([ 30, 35], (35, 40], . . . , (95, 100]). effects specifications. Specification (3) shows that the reference-point effect observed before leads to meaningful treatment differ - ences: When controlling for the wage level, average To control for the fact that effort is discrete, e ∈{1, 10} , I also run ran- effort in recession increases by 0.63 points in BASE, dom-effects ordered probit and ordered legit regressions. Moreover, instead reflecting that workers share (an unequal) part of the of wages one could also use the wage-effort ratio as the dependent variable. Standard errors are clustered at the session level (as the level of independent recession’s burden even though wages are on average observations) because observations within session may heavily depend on adjusted downwards. This increase does not change sig - each other. To control for the dependence of observations both at the session nificantly for stable (or increased) wages in CasRP. It is, and the individual level, I also run hierarchical linear regressions with random intercepts on subjects nested in sessions. All these regressions lead to very however, significantly lower for wage cuts (0.55 points). similar results. Effort change -5 -4 -3 -2 -1 0 1 2 3 4 5 Can reference points explain wage rigidity? Experimental evidence Page 11 of 17 5 Table 6 Panel regressions on effort - CasRP on wages. The appendix also shows that workers seem— if anything—to earn slightly more in recession in treat- (1) (2) (3) (4) ments with reference points, increasing the inequality FE FE FE FE between firms and workers and, hence, suggesting that Wage 0.110∗∗ 0.113∗∗ 0.113∗∗ workers behave less fair-minded. (0.0316) (0.0308) (0.0315) Recession‑ dummy 0.285 0.408 0.379 ∗ ∗∗ ∗ 4.3 Control treatments (0.132) (0.150) (0.150) Is an explicit conclusion of a contract between firms Rec × Wage cut ‑0.257 ∗∗ ‑0.176 ∗∗ and workers necessary to create resistance against wage (0.0852) (0.0648) cuts? Does more information lead to more rigid wages? Wage Table 8 shows average wages and the two wage cut meas- Wage‑ dummies  ures for all treatments. Even without an explicit contract conclusion (WasRP), wage cuts of similar magnitude Period & Period − − − are observed than the one in CasRP. This finding is Constant 2.601∗∗ 2.779∗∗ 2.764∗∗ 8.301∗ ∗ ∗ also supported by the regression analysis of Table  4. It (0.892) (0.837) (0.846) (0.696) shows that in WasRP wages are adjusted downward but Observations 827 827 827 827 2 to significantly lesser extent than in BASE, as in CasRP. 0.669 0.672 0.672 0.683 Moreover, Additional file  1: Appendix B provides a Notes: Panel fixed effects (FE) regressions on effort, only for the CasRP treatment. more detailed analysis along the lines of the two main Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within session. ∗∗∗ treatments. The upshot is that a similar—if anything indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at intensified—reference-point effect is observed: workers the 10 percent level (relatively) punish wage cuts. Table  8 also shows that the average wage cut in The implication of this observation is that workers seem CasRP-F is roughly of the same size as in CasRP. less willing to accept wage cuts—reference-point viola- Table  4 corroborates this finding. Hence, at least on tions—in CasRP compared to BASE: they do not share average, additional feedback for firms seems not to alter the recession’s burden as much in this treatment as they the results and does not lead to completely rigid wages. do in BASE where wages are on average substantially Notably, the average results, however, mask non-neg- cut but this cut cannot be perceived as a reference-point ligible differences between CasRP and CasRP-F. Firms violation. While workers in BASE provide firms with an are slightly more likely to pay stable (or increased) extra of 6.3 points (controlling for the wage level), they wages in CasRP-F (CasRP-F: 60.3% vs. CasRP: 51.2% – only provide 0.8 points for wage cuts in CasRP. In other Z = 1.84, p = 0.065), as predicted by conjecture 2. This words, the observed reference-point effect in CasRP effect, however, appears to be negated by an increase implies that wage cuts in CasRP are punished compared in the very strong wage cuts above 20 points (CasRP-F: to average behavior in BASE. This provides an explana - 6.5% vs. CasRP: 2.9% – Z = 1.73, p = 0.083). Additional tion for the treatment difference in firms’ behavior. file  1: Appendix B further illuminates these findings by showing that not only firms but also workers change Result 2 In line with hypothesis 2, workers in CasRP their behavior in response to the change in informa- have established a reference point: controlling for the tion: workers in CasRP-F do not (significantly) punish wage level, effort is lower for wage cuts than for stable (or wage cuts compared to stable (or increased) wages such increased) wages. This effect leads to a significant treat - that there is no reference-point effect. Overall, changes ment difference that explains why wages are more rigid in both in workers’ and firms’ behavior imply that there is CasRP: compared to BASE, wage cuts are punished. no average effect. A concern could be that average differences between Result 3 In contrast to conjecture 2, more informa- wage cuts and stable wages are fairly small in CasRP tion does on average not lead to more rigid wages. In (0.18–0.26 effort units). Reassuringly, although by far not always significant, profit differences for firms are in line with the idea that firms that pay stable (or increased) CasRP vs. WasRP - (raw) wage cut: p = 0.424; relative wage cut: p = 0.424; wages earn more in CasRP (see Additional file  1: Appen- Base vs. WasRP - (raw) wage cut: p = 0.006; relative wage cut: p = 0.006. dix C). In addition and as discussed below, the difference p-values based on rank-sum tests. CasRP vs. CasRP-F - (raw) wage cut: p = 0.424, relative wage cut: p = between wage cuts and stable wages also seems to be 0.212; Base vs. CasRP-F - (raw) wage cut: p = 0.054, relative wage cut: p = more pronounced in WasRP with a similar overall effect 0.008. p-values based on rank-sum tests. 5 Page 12 of 17 C. Koch Table 7 Panel Regressions on effort (1) (2) (3) (4) (5) (6) RE RE RE RE FE FE Wage 0.132∗ ∗ ∗ 0.132∗ ∗ ∗ 0.132∗ ∗ ∗ 0.162∗ ∗ ∗ 0.131∗ ∗ ∗ 0.161∗ ∗ ∗ (0.0183) (0.0184) (0.0185) (0.0341) (0.0186) (0.0336) CasRP‑ dummy 0.219 0.345 0.343 1.217 (0.281) (0.264) (0.265) (1.143) CasRP‑F‑ dummy 0.0701 0.257 0.255 0.530 (0.331) (0.306) (0.307) (0.973) WasRP‑ dummy 0.0460 0.0948 0.0950 1.242 (0.333) (0.331) (0.333) (1.032) Recession‑ dummy 0.334∗ ∗ ∗ 0.640∗ ∗ ∗ 0.630∗ ∗ ∗ 0.556∗ ∗ ∗ 0.624∗ ∗ ∗ 0.548∗ ∗ ∗ (0.0905) (0.128) (0.128) (0.170) (0.122) (0.165) Rec × CasRP 0.386∗ ∗ ∗ (0.143) Rec × CasRP‑F 0.637 ∗ ∗ ∗ (0.195) Rec × WasRP 0.137 (0.184) − − − − Rec × CasRP × Wage cut 0.548∗ ∗ ∗ 0.407∗ 0.547∗ ∗ ∗ 0.402∗ (0.141) (0.213) (0.137) (0.209) − − − − Rec × CasRP × No wage cut 0.222 0.148 0.214 0.137 (0.172) (0.223) (0.168) (0.219) − − − − Rec × CasRP‑F × Wage cut 0.798∗ ∗ ∗ 0.623∗ ∗ ∗ 0.789∗ ∗ ∗ 0.606∗∗ (0.167) (0.241) (0.163) (0.236) − − − − Rec × CasRP‑F × No Wage cut 0.519 0.468 0.527 0.472 ∗∗ ∗∗ (0.253) (0.285) (0.251) (0.281) − − − − Rec × WasRP × Wage cut 0.378∗∗ 0.401∗ 0.379∗∗ 0.404∗ (0.156) (0.210) (0.154) (0.211) Rec × WasRP × No Wage cut 0.106 0.177 0.111 0.184 (0.212) (0.242) (0.209) (0.240) Wage Wage*CasRP & Wage *CasRP Wage*CasRP‑F & Wage *CasRP‑F Wage*WasRP & Wage *WasRP Period & Period − − − − − − Constant 3.004∗ ∗ ∗ 3.128∗ ∗ ∗ 3.082∗ ∗ ∗ 3.626∗ ∗ ∗ 2.856∗ ∗ ∗ 2.816∗ ∗ ∗ (0.503) (0.495) (0.494) (0.863) (0.499) (0.401) Observations 2858 2858 2858 2858 2858 2858 0.517 0.518 0.519 0.520 0.622 0.627 Notes: Panel random effects (RE) and fixed effects (FE) regressions on effort for all treatments. Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within session. ∗∗∗ indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at the 10 percent level addition, in contrast to conjecture 1, an explicit violation because of the explicit agreement but simply because of an agreed upon contract is surprisingly not necessary they determine the out-of-recession wage and convey to generate resistance against wage cuts. this information to the worker, which is sufficient to cre - ate feelings of entitlement. Notably, while it is conceiv- Overall, this study’s findings are in line with idea that able that initial contracts in CasRP influence subjects reference points motivate resistance against wage cuts expectations in a way not feasible in BASE, no such initial even though there is no violation of an explicit agree- contracts exist in WasRP. The result is, however, in line ment. Contracts seem to serve as reference points not with findings that entitlements could constitute a “moral Can reference points explain wage rigidity? Experimental evidence Page 13 of 17 5 Table 8 Average wages: BASE vs. CasRP/ WasRP/ CasRP-F be fired and firms have only one worker. Having said this, reference points are surprisingly strong in my set- Wage Wage cut Relative ting. Unlike in other studies, a good reason—the reces- No-Recession Recession Wage cut sion—does not mitigate their effect. A key feature of my design is that existing contractual arrangements have to BASE 60.1 47.0 13.1 0.21 be revised, providing initial wages with a realistic shot at CasRP 57.9 51.9 6.0 0.10 serving as reference points. In contrast, wage cuts e.g. in WasRP 60.4 53.8 6.6 0.11 Chen and Horton (2014) and Bracha et  al. (2015) were CasRP‑F 58.8 53.4 5.4 0.09 implemented by a new contract offer that simply stipu - lated a lower wage, not by a revision of an existing con- tract. Moreover, it seems likely that reference points also property right” that is independent of players’ legal prop- play a crucial role in the field since important real-world erty rights (GÄchter and Riedl 2005; Bolton and Karagö- features that reinforce them are even missing in my set- zoglu 2015). ting: workers in the field “associate pay with self-worth” On a more general level, I cannot rule out that other and also punish wage cuts because they want to maintain motivational forces, apart from reference points, might their standard of living (Bewley 1999, p.432). contribute to the observed results. Findings are for exam- One abstraction of my design is to deliberately disre- ple consistent with the idea of an anchoring effect (see gard the role of reputational concerns by implementing Furnham and Boo 2011 for a recent review). Even though stranger matching. As outlined before, this is done to the out-of-recession wage has no relevance in WasRP in allow for a clean identification of the effects of the par - case a recession occurs, it still influences the outcome. ticular reference point under investigation. Moreover, Relatedly, since workers seem to earn slightly more in implementing partner matching in my setting would recession when reference points are present, self-serving capture that field labor relationships are not one-shot biases (Babcock and Loewenstein 1997) could also be a but also seems to emphasize reputational concerns too driving force. Of course, these different motivations may strongly. Experimental rounds are very short—thereby not be mutually exclusive: Self-serving biases may simply making future periods very salient—compared to field reinforce reference points. labor-market contract periods. Workers’ resistance against wage cuts in the field seems likely to be driven 5 Conclusion by emotions triggered by cuts when the importance of In this paper, I examine whether reference points affect future contract periods is fairly inconspicuous due to the workers’ perception of a “fair” recession wage and, thus, longer time horizon. Stranger matching seems to reflect cause wage rigidity. In a controlled experimental labora- this to a better extent than partner matching. For this tory market, I manipulate whether workers’ fairness per- reason, I leave it for future research to analyze the inter- ceptions can be shaped by initially concluded contracts action of reputational concerns and wage rigidity. and the wage they stipulate. I find that wages are consider - Another open question is the effect of booms. One the able more rigid with these initial contracts than without. one hand, one could argue that if workers believe that When initial out-of-recession wages can serve as a refer- firms mostly benefit from booms, this may create an addi - ence point, workers punish wage cuts relative to stable tional mechanism for rigid wages because workers might wages, providing a reason for firms’ wage-setting behav - then perceive recessions as entrepreneurial risk and, thus, ior. Interestingly, workers still reward stable wages. Thus, not be willing to share the recession’s burden. This would rigid wages are observed despite the fact that a recession be completely independent of whether initial contracts provides a good reason to adjust the wage level. Unexpect- have been concluded or not. One the other hand, if work- edly, they even emerge when workers have not agreed to ers’ fairness perceptions are really driven by self-serving an initial contract and, thus, arguably have no “objective” biases, the rationale of the former statement is not so clear. justification to feel entitled to their reference wage. This Workers might—contrarily to what we observe for busts— highlights the strength of reference points in my setting. not perceive initially concluded contracts as a constraint What do my findings imply about reference points and demand their share of the boom’s surplus, e.g. in form and wage rigidity outside the lab? Do reference points of bonuses or other flexible pay components. Whatever provide one explanation for wage rigidity in the field? Like with all empirical studies, such statements should be made with great care. My results are obtained in a A real-effort experiment with partner matching in which providing effort takes some time—making future period less salient—could capture reputa- specific environment, one that—in order to isolate one tional concerns, emotional reactions, and their interactions with reference plausible explanation of wage rigidity—abstracts from points more adequately. Naturally, this kind of setting is more complex and many aspects of field labor markets, e.g. workers cannot does not allow for as much repetition and learning as my simpler setting does. 5 Page 14 of 17 C. Koch the answers to those questions may be, this paper shows U (x ,x ) =x − α · max[x − x ,0] W W F W F W (3) that reference points alone already provide an explanation − β · max[x − x ,0] W F for more rigid wages in recession in a controlled labora- where x and x are the monetary payoff of the worker tory environment, independent of other explanations that W F (W) and the firm (F) and α ( β ) reflects how much work - may or may not reinforce this phenomenon. ers suffer from disadvantageous (advantageous) inequal - ity. FS assume that β ≤ α and that 0 ≤ β< 1. Supplementary Information Crucially, if workers are sufficiently inequity-averse The online version contains supplementary material available at https ://doi. 18 11 3 org/10.1186/s1265 1‑021‑00284 ‑2. or fair-minded (β> ≈ 0.243 ; α> β − ), firms 74 2 2 offer a high wage and workers reciprocate by a high effort Additional file 1. Online Appendix. (w = 84, e = 10) . In recession, the negative profit shock is Additional file 2. “Readme” file for dataset. equally split (w = 74, e = 10) . More precisely: Out-of- Rec Rec Additional file 3. Dataset. recession, firms offer the highest possible wage that equal - izes payoffs and to which workers can react with the highest Acknowledgements possible effort ( w = 84, e = 10, x = x = 66 ). W or k ers W F For helpful suggestions, I would like to thank Andreas Bernecker, Dirk Engel‑ reciprocate the high wage with the highest effort level if mann, Urs Fischbacher, Leonie Gerhards, Botond Kőszegi, Nikos Nikiforakis, Jörg Oechsler, Henrik Orzen, Alexander Paul, Stefan Penczynski, Clemens Puppe, they are sufficiently averse against advantageous inequality, Klaus Schmidt, and Sigrid Suetens. I also received helpful comments from partic‑ 3 in this case β> ≈ 0.230 . Providing one unit less effort ipants at seminars in Abu Dhabi, Hamburg, Heidelberg, Mannheim, Munich, the will save the worker (at most) 3 points but advantageous Thurgau Experimental Economics Meeting 2013 ( Theem), the Florence Work‑ shop on Experimental and Behavioral Economics 2013, the ESA World Meeting inequality will rise from 0 to 13 points. Additionally, work- 2013 (Zurich), the 8th Nordic Conference on Behavioral and Experimental ers have to be sufficiently averse against disadvantageous Economics 2013 (Stockholm), the Gesellschaft für experimentelle Wirtschafts‑ 11 3 22 inequality ( α> β − ). This ensures that firms do not forschung 2013 (Helmstedt), the EEA annual meeting 2014 ( Toulouse). 2 2 have an incentive to pay less than the payoff-equalizing Authors’ contributions wage, w = 84 . In recession, firms again offer the highest Not applicable. No research assistants were used. wage that equalizes payoffs (accounting for the negative Funding profit shock) and to which workers respond with the high - Funding from the DGF is gratefully acknowledged. Rec Rec Rec Rec est possible effort ( w = 74, e = 10, x = x = 56 ). W F Note however, that in recession workers have to be slightly Avaiability of data and materials The dataset used during the current study is available as Additional files 2 and more fair-minded, β> ≈ 0.243 : Firms cannot make losses in my setting which restricts the degree of advanta- geous inequality. Receiving a wage of 74 and providing e = 1 Ethics approval and consent to participate No IRB approval was obtained as the University of Mannheim did not have instead of e = 10 saves the worker 18 points and increases IRBs at the time the study was implemented. For this reason (and since advantageous inequality only by 74 points. the study involved only minimal risk), solely the approval of the director of In a similar fashion as before, one can show that mLab at the University of Mannheim (at which the experiment was run) was obtained. In order to participate in the experiment, subjects had to register if workers are only fair-minded to a very low degree in advance for the mLab database. During this registration process a general 1 (β < ≈ 0.090) , workers exert minimal effort ( e = 1 ). consent to participate was obtained. The underlying idea is that workers can always save Consent for publication (at least) 1 point by lowering effort by one unit which Not applicable. The study does not include details, images, or videos relating would increase advantageous inequality by 11 points. to an individual person. Thus, no consent for publication was obtained. Firms should anticipate workers’ behavior and only Competing interests offer the minimum wage ( w = 30 ), both in and out of The authors declare that they have no competing interests. recession. If workers are fair-minded to an intermedi- 1 18 ate degree ( ≤ β ≤ ), intermediate equilibria arise 11 74 Appendix A Theory and hypotheses in which intermediate wage offers are reciprocated by Hypothesis 1 I formalize the first hypothesis using preferences of ineq - uity-aversion as introduced by Fehr and Schmidt (1999) (henceforth FS). I assume that workers have FS-prefer- ences, whereas firms have standard preferences. The condition for α arises from the comparison of the two situations U (w = 83, e = 10) = 65 − 2α< 68 − 11β = U (w = 83, e = 9) . If the W W condition is not met, an equilibrium with a slightly lower wage, e.g. w= 83 Importantly, the derived predictions are not specific to inequity-aversion. or w=82, arises in case firms have standard preferences. In case firms are also Social welfare preferences (Charness and Rabin 2002) would lead to qualita- (sufficiently) inequity averse, the outlined equilibrium persist, because firms tively similar results. avoid inequality. Can reference points explain wage rigidity? Experimental evidence Page 15 of 17 5 intermediate effort levels (see example below). In reces - the fraction of fair-minded workers is high enough: In my sion, wages are cut by (at least) 10 points. case, µ> 0.46. Notably, the adjustment of the split of surplus cannot Overall it holds that if workers are sufficiently fair- be done through increased effort and constant wages, at minded, the negative profit-shock is equally shared least not in equilibrium. Sufficiently fair-minded work - between workers and firms by a moderate wage cut of ers already exert the maximum effort. But the statement 10 points. Naturally, one might not expect such a clear- is even true for less fair-minded workers. This is trivial cut result, but controlling for the wage level, workers for workers that are only fair-minded to a very limited should at least provide more effort in recession than out degree because they will always provide minimal effort of recession. in and out-of-recession, as argued above. For workers with intermediate degrees of fairness, rational firms in Hypothesis 2 equilibrium already choose their out-of-recession wage I extend the model of FS (by a fourth term) to incorpo- such that it induces the highest effort level that is possi - rate that workers behavior might be reference-dependent ble when taking the limited degree of the worker’s fair- with respect to the previous out-of-recession wage. This ness into account. With constant wages, the recession extension is inspired by the general idea of Hart and increases the level of inequality. But since the utility func- Moore (2008) (henceforth HM) that contracts serve as tion is linear in inequity aversion, one unit more effort reference point because they create feelings of entitle- is still associated with the same costs and benefits (of ment. Although HM do not explicitly deal with renego- reduced inequality) as out of recession. tiations, the implication of their analysis is that wages As an example, consider the case that workers are suf- should be more rigid in recession with initial contracts ficiently inequity averse such that saving 2 points and than without. In  situations without initial contracts increasing inequality by 12 points is not attractive to (BASE), I assume that FS-preferences govern the rela- them ( β ≥ ) but saving three points and increasing tionship between workers and firms. inequality by 13 points is ( β< ). Due to the increas- In the CasRP treatment, contracts can serve as refer- ing cost function, this implies that firms cannot induce ence points and workers’ preferences as described in an effort of 9 or 10 but only 8. Thus, out-of-recession, equation (3) can be modified: firms will pay w = 71 to induce workers to exert an effort U (x , x ) =x − α · max[x − x ,0]− β · max[x − x ,0] W W F W F W W F of e = 8 , equalizing payoffs at x = x = 59 . Ke eping W F − γ · I max[θ · (w − w ) − 10 · (e − e ),0] [w2<w1] 1 2 1 2 this wage (as well as the effort) constant in recession, will (4) Rec Rec increase inequality considerably ( x = 59, x = 39 ). W F The basic idea of the fourth term is the following: But the cost of reducing this inequality stays the same as The weighted difference between the reference-point out of recession: Increasing effort beyond 8 to 9 still has wage out of recession and the actual wage in recession, a cost 3 and a benefit in reduced inequality of 13, which θ · (w − w ) can be interpreted as the worker’s aggrieve- 1 2 a worker with an intermediate aversion to inequality is ment caused by getting less than what you are entitled not willing to take. Anticipating this outcome, the firm Red to and θ represents a weighting parameter. Workers can will reduce the wage to w = 61 such that payoffs can offset their aggrievement, θ · (w − w ) , by adjusting 1 2 be equalized. Finally, it is noteworthy that constant wages their effort downward and hence punishing the firm by and increased effort are not an equilibrium phenomenon, 10 · (e − e ). 1 2 but sufficiently inequality averse player may well increase 23 Notably, as outlined before for hypothesis 1, stable effort for constant wages in recession off-equilibrium . wages cannot be reciprocated with higher effort levels To accommodate that laboratory subjects are fair- in recession since the highest (feasible) effort level has minded to different degrees, the literature often consid - already been induced out of recession. This may be all ers two-type models (see Kocher and Strasser 2011 and the more true since my approach—following HM— FS). Firms in my setting could e.g. assume that a fraction 18 only models a negative impact of a reference-point µ of workers is sufficiently fair-minded ( β> ), wherea s 1 violation but not a positive effect when a reference 1 − µ is (quasi-)selfish ( β< ). The intuition of these point is met. Thus, to establish that firms lose more by kind of models is quite clear: It is rational both for selfish and fair-minded firms to propose a high wage ( w = 84 ) if μ · U (w = 84, e = 10) + (1 − μ) · U (w = 84, e = 1)> U (w = 30, e = 1) W W W A sufficiently inequity-averse worker will reciprocate a wage of 71 with 8 ⇔ μ66 + (1 − μ)0 > 30. In recession, this fraction is even lower: μ · U (w = 74, out of recession but provide an effort of 10 in recession (both to equalize pay - (w = 74, e = 10) + (1 − μ) · U (w = 74, e = 1)> μ · U (w = 30, e = 3) + (1 − μ) W W offs). Notably, this cannot be an equilibrium outcome as the firm will benefit ·U (w = 30, e = 1) ⇔ μ56 + (1 − μ)0 >μ20 + 10. from deviating and paying the worker a higher wage out-of-recession. 5 Page 16 of 17 C. Koch reduced effort than they gain by paying lower wages, recession. Firms could react by paying lower wages (and workers have to overcompensate the wage decrease by hence foregoing earnings) out of recession and hence a relatively larger effort decrease. In other words, one being able to pay lower wages (and hence gain earn- has to assume that θ> 1 , deviating from HM. ings) also in recession. This kind of strategy is, however, Whether workers, however, really want to offset suboptimal given the parameters of the experiment. their aggrievement depends on the weighting param- Crucially, however, these strategies may become opti- eter γ : Only when workers weigh the negative impact mal for firms that also have preferences of the FS-type. of a reference-point violation high enough ( γ> 10 ) , In equilibrium, not cutting wages leads to disadvanta- they punish wage cuts by lowering effort although geous inequality, lowering firms’s utility compared to this also leads to higher inequality associated with standard preferences. Lowering, however, the out-of- lower utility. More precisely: Assume that firms and recession wage leads to less disadvantageous inequality workers act according to the FS-considerations of in recession. I do not make specific assumptions about hypothesis 1 ( w = 84, e = 10, x = x = 66 ) and that the parameters for the inequity averse firms, but con - W F workers are sufficiently fair-minded ( β> ≈ 0.243 ) . sider it as an open question whether out-of-recession Consider the case that firms cut wages in reces- wages in CasRP are already lower than in BASE. Addi- Rec sion by one unit, w = 83 . If γ> 10 , then even the tionally, the theory does not provide a clear-cut pre- smallest wage reduction will lead to a loss of utility of diction under which circumstances initially concluded more than 10. This is due to the reference-point vio- contracts serve as reference points, whether an explicit lation. Reducing effort by one unit will, however, off- contract conclusion is necessary or not, or whether set this negative effect and will lead to a utility loss better information lead to more rigid wages or not. that is strictly smaller than 10. A one-point decrease of effort increases advantageous inequality by 13 Received: 30 October 2019 Accepted: 12 January 2021 points but workers still saves 3 points of cost of effort. Hence, if workers weight the negative impact of vio- lating their reference point to a sufficient degree, firms with standard preferences will not cut wages References Rec Rec Rec Rec ( w = 84, e = 10, x = 46, x = 66 ). This is due F W Abeler, J., Altmann, S., Kube, S., Wibral, M.: Gift exchange and workers’ fairness to the fact that a wage reduction is always followed by concerns: when equality is unfair. J. Eur. Econ. 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Regarding effort: In case stable (or increased) wages are not reciprocated by higher effort, as predicted, workers overcompensate wage cuts by effort decreases (θ> 1 ), leading to an effort decrease even when controlling Paying w = 84 out of and in recession leads to earnings of x = 66 and Rec x = 46 with a probability of 2/3 and 1/3 respectively. The best strategies for the wage level. But even when stable wages are rewarded, available, in which the out of recession payment is reduced, lead to payoffs a reference-point effect is observed in CasRP since workers below this result. Paying w = 78 out of and in recession (in order to (almost) render wage cuts unprofitable in any case: Controlling for equalize payoffs with an effort level of 9 with a slight worker’s advantage) Rec leads to earnings of x = 62 and x = 52 : A loss of 4 out of recession with the wage level, wage cuts should be accompanied with rela- F a probability of 2/3 and a gain of 6 in recession with a probability of 1/3. 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Can reference points explain wage rigidity? Experimental evidence

Journal for Labour Market Research , Volume 55 (1) – Mar 10, 2021

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Abstract

I examine whether reference points can provide an explanation for rigid wages in recessions. Even though a recession provides a good reason to adjust wages downward, workers’ perception of a “fair wage” may depend on their previ‑ ous wage, their reference point. Using a laboratory experiment, I test this idea by varying whether initially concluded contracts—and their stipulated wages—can serve as reference points. My experimental results show that with initial contracts workers punish wage cuts even in recessions, leading to considerable more rigid wages. Surprisingly, this is even true without an “objective” justification to feel entitled to initial contracts. Keywords: Wage rigidity, Reference points, Gift exchange, Labor contracts, Experiments JEL classification: C9, J3, M5 concerns. Wage cuts are, however, perceived as unfair by 1 Introduction workers and lead to a decrease in work morale. In antici- A long-standing question in economics is why wages do pation, firms do not cut wages. not fall in recessions (Fehr and Goette 2005; Bauer et al. But why do workers perceive wage cuts as unfair 2007; Dickens et  al. 2007). Understanding this phenom- even though a recession seems to provide an appropri- enon of (downward) wage rigidity is important as it has ate reason to cut wages since it limits firms’ abilities to been shown empirically to be associated with unfavora- pay high wages? Even standard outcome-based fairness ble labor market outcomes, in particular unemployment models (e.g. Fehr and Schmidt 1999; Charness and Rabin (Barwell and Schweitzer 2007; Devicienti et  al. 2007; 2002) predict moderate wage cuts since they enable fair- Elsby et al. 2016). A number of explanations of why firms minded workers to share the recession’s burden that oth- pay wages that are above the market clearing wage and erwise only the firm would have to bear. Already Akerlof that cannot be easily adjusted downward has been put (1982) and Akerlof and Yellen (1990) have suggested, forward, including e.g. insider-outsider theories (Lind- however, that what workers perceive as a “fair wage” beck and Snower 1988, Calmfors and Driffill 1988) or might depend—among other things —on the wage they (disciplining versions of) the efficiency wage hypothesis previously received, their reference point (Goette et  al. (Gintis 1976; Shapiro and Stiglitz 1984). 2007; Shafir et al. 1997). While this seems very plausible This study’s focus will be on a fairness explanation of the wage rigidity puzzle that has found support by ques- Other theories of wage rigidity include the implicit contract theory (as tionnaire studies interviewing managers (e.g. Blinder and developed by Baily 1974; Gordon 1974; Azariadis 1975) or job search models Choi 1990; Campbell and Kamlani 1997; Bewley 1999): as reviewed in Mortensen (1986). When contracts are incomplete, firms partly have to Akerlof (1982) have also highlighted the importance of social compari- sons for the “fair wage”, namely what co-workers earn. This study focuses on rely on workers’ intrinsic motivation and their fairness past wages, but other work has already explored the social comparisons (see e.g. Charness and Kuhn 2007; Abeler et al. 2010; Bartling and von Siemens 2011; Cohn et  al. 2014). Recent studies (Charness et  al. 2012; Franke et  al. *Correspondence: chris.koch@univie.ac.at 2016) have also explored workers’ participation in wage setting as an influ- Department of Economics, University of Vienna, Oskar‑Morgenstern‑Platz ence on workers’ fairness perceptions and effort provision. 1, 1090 Vienna, Austria © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. 5 Page 2 of 17 C. Koch under stable conditions, it is less clear whether it is also fairness explanation (potentially in combination with ref- true in a recession. erence points)—is valid even in times of recession. This is In this study, I experimentally manipulate whether my paper’s core contribution. The main innovation of my (previous) out-of-recession wages can serve as a refer- design is to manipulate whether out-of-recession wages ence point, influence what workers perceive as a “fair can serve as reference points inspired by the idea of Hart wage” in recession and, thereby, provide an explanation and Moore (2008) that contracts serve as reference points for rigid wages. In an informative field experiment, Kube (see also Herweg and Schmidt 2015). In “real-world” et  al. (2013) have already shown that exogenous wage labor markets, contractual arrangements often have to cuts have a negative impact on participants’ work morale. be revised before wage cuts can be implemented. In such Crucially, the authors deliberately cut wages without a revision, existing contract conditions might be salient providing a “good reason” (e.g. recession), and Chen and and, thus, serve as reference points. Horton (2014)—although using a fairly different setting— I model the labor market as a simple gift-exchange do not find a negative effect when providing such an (Fehr et al. 1993). Firms sometimes face a ‘recession’—in explanation. Since significant company-wide wage cuts terms of a negative profit shock—that ceteris paribus only are rarely observed, empirical evidence is scarce. For the reduces their profits. Two different treatments manipu - airline industry, Lee and Rupp (2007) find only limited late whether (previous) out-of-recession wages can serve support that wage cuts lower employee effort. A potential as reference points. In the Contracts as Reference Points explanation is that most of the wage cuts they observe (CasRP) treatment, workers and firms first conclude a occur under the threat of bankruptcy, providing a justifi - contract before they are informed about whether a reces- cation for the cut. Finally, Bracha et al. (2015, p. 312) have sion has occurred in this period. In the recession case, experimentally shown that making a given wage high (or the concluded contract can be revised. Otherwise, initial low) relative to past or other wages increases (decreases) contract conditions determine payoffs. In this treatment, labor supply. Crucially, the authors find that providing the initial contract’s wage—which workers explicitly “even a flimsy rationale” for these differences make the agreed to when accepting a contract offer—potentially effect disappear. serves as a reference point for the revision stage. Imple- Although there is, thus, evidence that previous wages menting such a contract-revision structure deviates from can serve as reference points, precisely this evidence much of the prior literature but provides out-of-recession cast doubts on whether this is actually true under all cir- wages with a realistic shot at serving as reference points. cumstances, questioning whether a fairness explanation This is not possible in the Baseline (BASE) treatment. of wage rigidty is valid for the recession case. Question- Here, firms and workers are first informed about whether naire and survey studies (Kahneman et  al. 1986; Char- a recession has occurred and only afterwards have the ness and Levine 2002; Kaur 2018) might be consistent ability to conclude a contract. Hence, firms’ contract with this idea but cannot—due to a lack of control treat- offers can already take the state of the world into account ments—rule out that wage cuts are rejected for reasons and no initial contracts exist. unrelated to reference points: If workers believe that it The data suggests that wages are neither completely is the firm that mostly benefits from a boom, they might rigid in CasRP nor in BASE. Wage cuts are, however, be generally unwilling to share the burden of the bust significantly higher in BASE than in CasRP. Compared to because they might perceive the recession as part of the the out-of-recession case, the average wage is reduced by firm’s entrepreneurial risk, completely independent of 13.1 points (or 21 percent) in recession in BASE but less reference points. Utilizing the strength of the experimen- than half this amount (6.0 points or 10 percent) in CasRP. tal analysis, I test, under tightly controlled conditions, In the latter treatment, there is evidence of a reference- whether one particular explanation of wage rigidity—a point effect: Controlling for the wage level, workers’ effort is lower for wages below the reference wage compared to those at or above this level. This, reference-point effect There is additional evidence that reference points and previous wages influ - leads to significant treatment differences: In case wages ence current wages, which is, however, not directly related to rigid wages in recessions. Abeler et  al. (2011) have experimentally shown that expectations are cut in CasRP, workers do not share the recession’s affect workers’ reference points. Accordingly, Mas (2006) find empirical evi - burden (as much) as they do in BASE, explaining why dence that wage increases that do not meet workers’ expectations can lead to firms pay more rigid wages in CasRP. a decline in performance. Similarly, Ockenfels et al. (2015) show that manag- ers’ performance is reduced when their bonus payment falls behind a refer- ence point (see also Cohn et al. 2015). Notably, these papers do not illuminate whether a “good” reason (recession) provides a justification for wage cuts. Falk et al. (2006) have shown experimentally that reservation wages are influenced by the introduction of minimum wages (see also Owens and Kagel 2010). It seems reasonable to use the terms rigid wages and wage cuts also for Finally, Greenberg (1990) and Greenberg (1993) find evidence that underpay - BASE. Crucially, due to construction, they can, however, only refer to a com- ment can lead to theft. parison of average wages in and out of recession in BASE. Can reference points explain wage rigidity? Experimental evidence Page 3 of 17 5 On the basis of these results, I implemented two converse effect in my setting: they encourage workers control treatments. First, the Wages as Reference Points not to share a part of the recession’s burden by refus- (WasRP) treatment shows that an “objective” justifica- ing to accept wage cuts and, thus, actually behave less tion for feelings of entitlement—an explicit contract fair-minded than otherwise agreement—is surprisingly not necessary to induce more rigid wages, highlighting a strength of reference 2 Experimental design and procedures points that has not been observed in previous stud- 2.1 Main Treatments: BASE vs. CasRP ies. Second, the Contract as Reference Points treat- I consider an experimental labor market in which firms ment with Feedback (CasRP-F) manipulates the firm’s can be hit by a ‘recession’ (see Kocher and Strasser 2011 information condition by providing better feedback and Gerhards and Heinz 2017). More precisely, following but does not lead to significant differences, at least on Fehr et  al. (1993), I model the labor market as a simple average. gift-exchange but modify the standard setting by using Overall, this study provides evidence that is con- a non-static version in which firms can be randomly hit sistent with the idea that reference points shape what by a negative profit shock (which is called a “bad mar - workers perceive as a “fair” recession wage in a con- ket situation” in the instructions). Notably, for the ease trolled experimental labor market, providing one of exposition, I use the terms ‘negative profit shock’ explanation for more rigid wages in this setting. My and ‘recession’ interchangeably in the following, but the paper may also help to reconcile conflicting results reader should always bear in mind the stylized nature in the experimental literature linked to wage rigidity. of the ‘recession’ in my setting, as outlined below. The As noted before, my study focuses on the revision of game proceeds as follows: Firms make a contract offer by contractual arrangements that make reference points choosing a wage, an integer w ∈{30, . . . , 100} , and work- salient. In contrast, the earlier literature was primar- ers who accept a contract offer have to choose how much ily concerned with reactions to wage changes relative effort to exert, e ∈{1, . . . , 10}. to earlier periods, where every period featured a “new As usual in a gift-exchange setting, contracts are contract”. In the latter setting, earlier contracts seemed incomplete since workers’ effort levels are not contracta - not serve as reference points and Burda et  al. (2005), ble. I implemented a slightly modified version of the pay - Kocher and Strasser (2011), and Gerhards and Heinz off functions used by Riedl and Tyran (2005). Firms have (2017) find that wages are flexible. In contrast, Hannan the following payoff function: (2005) uses a setting in which initial wages are revised 10 × e − w + 50, if no profit shock occurs (p = ), in recession and workers at least partly seem to pun- � = 10 × e − w + 30, otherwise (p = ). ish wage cuts. Notably, since her study does not focus (1) on wage rigidity, it misses control treatments, and it is Workers’ payoffs are given by even unclear how rigid wages overall are in her setting. Finally, Buchanan and Houser (2020) investigate wage � = w − c(e). (2) rigidity in a setting in which contracts can serve as ref- erence points but do not provide a control treatment in Here, F denotes the firm, W denotes the worker, and c(e) which this is not the case as they focus on employers’ is the cost of effort that is an increasing function of e. In beliefs about workers’ work morale and the distinction my experiment, I used a standard cost-of-effort function between nominal and real wage cuts. My study, thus, shown in Table 1. Workers who reject their contract offer complements their research. get a payoff of  = 20 whereas their assigned firms This study also informs the literature about contracts get a zero profit,  = 0 . Additionally, firms earn zero as reference points, starting with Hart and Moore profits if their contract offers have been accepted, but (2008). Unrelated to wage rigidity, their model mainly effort levels had resulted in a negative payoff for the firm. analyzes why people write long-term employment con- Notably, firms do not state a desired effort level. For clean tracts by looking at the implications of reference points identification, only one variable—the wage—will poten - for different contract types. Fehr et  al. (2009, 2011, tially serve as a potential reference point in my setting. 2015) experimentally test these implications compar- My payoff functions capture the following core idea: In ing the performance of different contract types. Bar- a recession, first of all only firms suffer. The question then tling and Schmidt (2014) are the first that analyze how is whether workers are willing to share a part of the reces- initially concluded contracts affect renegotiation via sion’s burden. More particularly, these functions were reference-point formation in a buyer-seller relation- chosen to meet two objectives: The impact of a recession ship. While reference points in their setting constrain should be substantial enough such that firms consider sellers to be fair and not to exploit buyers, they have a cutting wages, but at the same time firms that do not cut 5 Page 4 of 17 C. Koch Table 1 Eor ff t levels and cost of effort e 1 2 3 4 5 6 7 8 9 10 c(e) 0 1 2 4 6 8 10 12 15 18 wages should still make a small profit or at least avoid do not find significant differences between a bilateral ver - losses. The underlying idea is that questionnaire studies sion of the game and gift-exchange markets. (see e.g. Bewley 1999, Kahneman et al. 1986) suggest that losses legitimize wage cuts: They find that firms that face 2.1.1 CasRP treatment losses in the field are able to reduce wages substantially and that the general wage-rigidity finding is driven by • Stage 1: Firms make a contract offer to their workers those firms that are not threatened in their existence. My by choosing a wage, w ∈{30, . . . , 100} . Af ter w ards , design focuses on the latter situation. To avoid that losses these workers have to decide whether they want to legitimize wage cuts, firms are provided with some extra accept their offer. If they accept, workers have to money (50 points) and it is ruled out that firms make choose their effort level, e ∈{1, . . . , 10} . This effort negative earnings. level is first of all not communicated to firms. If they In this setting, I implemented two main treatments reject, subjects are informed about payoffs in stage 3. that are designed to test whether out-of-recession wages • Stage 2: At the beginning of the second stage, two out can serve as reference points and, thus, influence what of six firms are randomly selected and hit by a nega - workers perceive as a fair wage in recession. My design tive profit shock. Only these two firms are allowed is (loosely) based on the idea of Hart and Moore (2008) to change the initial contract conditions by choosing that contracts serve as reference points because they a new wage, w ∈{30, . . . , 100} . Although affected create feelings of entitlement. Wage cuts in “real-world” workers cannot reject wage changes, they are allowed labor markets might require a revision of the contractual to adjust their initial effort by choosing a new effort arrangements between workers and firms simply because level, e ∈{1, . . . , 10}. these arrangements already exist before the recession. In • Stage 3: Firms and workers get to know their payoffs, particular, in the Contracts as Reference Points (CasRP) and firms are informed about their workers’ relevant treatment, contracts concluded initially before reces- effort if their contract offer has not been rejected. sions—or more precisely the initial out-of-recession wage This means that firms only learn about e in case a they stipulate—can potentially serve as reference points negative shock does not occur, and in case such a for workers’ feelings of entitlement regarding the reces- shock occurs, firms only learn about e , ensuring sion wage. In the Baseline (BASE) treatment, no such comparability with BASE. initial contracts exist. For reasons of treatment compa- rability, a bilateral version of the gift-exchange game is In case that no profit shock occurs, wages and effort lev - implemented in both treatments: Subjects play in groups els of stage 1, w and e , determine payoffs. Otherwise, 1 1 of 12 (6 firms and 6 workers) for 18 periods. One firm wages and effort levels of stage 2, w and e , determine 2 2 is matched with one worker and pairs are randomly payoffs. In BASE, no initial contracts that could serve rematched every period. This rematching is implemented as a reference point exist and, thus, firms are informed to minimize the importance of reference points other upfront whether a negative profit shock has occurred. than those induced by initially concluded contracts (e.g. previous periods). This allows for a clean identification of 2.1.2 BASE tr eatmentBASE treatment the impact reference points induced by initial contracts and their stipulated wages. Moreover, Fehr et  al. (1998) • Stage 1: At the beginning of the first stage, two out of six firms are randomly selected. These two firms are hit by a negative profit shock. Knowing whether Implementing the ‘recession’ by a reduction of the extra money by 20 points ensures that both objectives are met in a simple, feasible way for all wage lev- els: Independent of the out-of-recession wage level, firms experience a notice - able decrease of their profits in recession. This decrease is, however, still small In my design, only some firms have to face a negative profit shock in each enough not to inevitably lead to zero profits when wages are not reduced. period and not all firms in some periods. Due to the bilateral structure, no Alternatively reducing the productivity parameter might be considered more qualitative differences should be observed. In both situations, workers and realistic but has the drawback that both objectives cannot be easily ensured firms only have information about their wage and effort, not about other for all wage levels. wages or effort levels. The outlined implementation was chosen because it is Occassionally, there were also groups of 10 with 5 firms and 5 workers. more appropriate for a potential follow-up study. Can reference points explain wage rigidity? Experimental evidence Page 5 of 17 5 they have been hit by such a shock or not, firms implementations that allow for rejections in recession make a contract offer to workers by choosing a wage, are experimentally less feasible. w ∈{30, . . . , 100}. Nonetheless, three concerns may arise. First, workers • Stage 2: This stage depends on the previous one. In may perceive the revision procedure as especially aver- case the assigned firm is not hit by a negative profit sive in CasRP because firms can change an established shock, workers first have to decide whether they contract. Second, one may also fear that the asymmetry want to accept their contract offer or not. If they between the recession and the no-recession case is more accept, workers have to choose their effort level, salient and less natural in BASE (as there is no initial con- e ∈{1, . . . , 10} . In case the assigned firm is actually tract), creating an experimenter demand effect to lower hit by a negative profit shock, workers only have to wages in this treatment. Finally, providing an opportunity choose their effort but cannot reject the contract to reject a contract out-of-recession but not in recession offer. This difference is implemented in order to might raise the concern that firms have to pay higher ensure comparability with the CasRP treatment. wages in case workers can reject. Crucially, my first con - • Stage 3: Firms and workers get to know their payoffs, trol treatment, WasRP, has a structure that resembles and firms are informed about their workers’ effort if BASE more closely—not featuring established contracts their contract offer has not been rejected. for example—and, hence, allows me to control for the first two concerns. The last concern, however, even biases In both treatments, subjects are informed about the exact against observing rigid wages in recession, suggesting sequence of events in advance. The fundamental idea of that my analysis provides a conservative test for wage the two treatments is that in one of them initial contracts rigidity. exist while this not true in the other. Notably, this implies that CasRP has two important features: First, even in case 2.2 Control treatments, discussion & procedures there is a profit shock, subjects know the wage without In case a difference between BASE and CasRP is observed, such a shock, which is not true in BASE. Second, they the two control treatments try to illuminate why such a explicitly agreed to this latter wage. Although this seems treatment difference is observed. The first control treat - to realistically capture field labor contracts, it also repre - ment is the Wages as Reference Points (WasRP) treatment. sents a change of two things at the same time. I conjec- This treatment tries to disentangle which of the two main tured that the acceptance decision would be necessary aspects changed from BASE to CasRP potentially provides for contracts to serve as reference points and, hence, a channel that leads to rigid wages. Is an explicit con- for observing wage rigidity. The underlying idea was tract conclusion necessary to create workers’ resistance that only an explicit agreement might sufficiently trig - against wage cuts or do contracts already serve as refer- ger workers’ self-serving biases because only when such ence points just by determining the out-of-recession wage an agreement exists wage cuts can constitute a violation and conveying this information to workers? Concerning of it. My first control treatment (WasRP) will disentangle the sequence of events, this treatment is a combination of whether an acceptance is really necessary, allowing for a BASE and CasRP. Workers know the payoff-relevant out- clean identification of the impact and the channel of ref - of-recession wage also in recession (and that this wage erence points. Surprisingly, it will show that the accept- ance decision is actually not necessary. The contract revision in recession is implemented fol - First, a real renegotiation stage in which the initial contract is valid in case workers reject wage changes would require a baseline treatment compara- lowing Fehr et  al. (2015). Firms can revise their work- ble to Bartling and Schmidt (2014): the same initial participants’ behavior as er’s wage as they like and workers cannot get out of in CasRP would have to be exogenously imposed in this baseline treatment. an agreed-upon contract and reject the new wage— This would, of course, undermine the ability to analyze whether firms antici - pate resistance against wage cuts in CasRP and already adjust out-of-recession although they can change their effort level. This extreme wages downward compared to the baseline. By construction, initial behavior implementation is not intended to capture field nego - would be the same in both treatments. Second, when workers’ rejection leads tiations realistically but tries to provide “stress test” for to outside-option payments, rejecting would only provide a reasonable expen- sive punishment opportunity for wage cuts that lead to very low but not to contractual reference points. Previous studies’ suggest medium/high wage levels since outside-option payments are not too high. that the impact of reference points can be limited by Rejecting e.g. a wage cut from 90 to 75 would lead to outside option payments design specifics and Fehr et  al. (2015,  p. 4) have argued of 30, resulting in a cost of up to 45 points. The result of the first control treatment—that an explicit acceptance is not that “the easier it is to change a contract the less likely it necessary—suggests that a design without an acceptance decision at any is to serve as a reference point,” biasing against observ- point would also have led to rigid wages. Notably, due to its simplicity, this ing any effect of reference points. In addition, alternative alternative design might be considered preferable to the implemented one. Crucially, this insight was, of course, only gained in hindsight: it material- ized as a consequence of my more complex design and can, thus, be seen as a result of my analysis. 5 Page 6 of 17 C. Koch Table 2 Summary of treatments Treatments Information about out-of-recession Initial contracts (explicit Extended Sessions Number wage in recession agreement) feedback of subjects BASE No No No 6 68 CasRP Yes Yes No 6 70 WasRP Yes No No 6 68 CasRP‑F Yes Yes Yes 6 72 Notes: While all treatments except BASE inform workers about the out-of-recession wage also in recession, initial contracts and, thus, an explicit agreement about the out-of-recession wage is only given in CasRP/CasRP-F but not in WasRP. Finally, firms are only provided with extended feedback in CasRP-F potentially has been cut) although they have not explicitly cuts and firms are not fully aware of this behavior, the concluded a contract with their firm before the recession. difference between the BASE and the CasRP treatment Because there is no explicit contract conclusion, WasRP might underestimate the real difference caused by ini - is, however, structurally closer to BASE avoiding potential tial contracts. In CasRP-F, however, firms in recession concerns outlined before. are informed not only about the relevant but about both effort levels in stage 3. Table  2 provides an overview over all four treatments, summarizing the key differences. • Stage 1: Firms choose a contract offer (by specify - Sessions lasted on average between 75 and 90 minutes ing a wage) for the case that no negative profit shock and took place at the mLab at the University of Mannheim. occurs. Then, the computer selects two out of six Overall, 278 (undergraduate and master) student subjects firms. These firms are hit by a negative profit shock (six session per treatment with 10-12 subjects) of any field and are allowed to adjust their contract offer for the participated in the experiment and earned on average 20 recession. EUR, where final payoffs are the sum of all 18 periods’ pay - • Stage 2: If the assigned firm is not hit by a negative offs. Recruitment was done by ORSEE, Greiner (2004), and profit shock, workers first have to decide whether the experiment was programmed in z-Tree (Fischbacher they want to accept their (out-of-recession) contract 2007). Experimental instructions—that had a labor-market offer or not. If they accept, they have to choose their framing to facilitate understanding—for all treatments can effort. If the assigned firm is hit by a negative profit be found in the Additional file 1 : Appendix E. shock, workers only have to choose their effort but cannot reject their (recession) contract offer. Impor - 3 Hypotheses tantly, in the second case, workers are also informed In this section, I discuss two hypotheses. These hypoth - about the out-of-recession contract offer (wage) that eses are based on the model of inequity aversion by is irrelevant for payoffs. Fehr and Schmidt (1999). I provide a simple extension • Stage 3: Firms and workers get to know their pay- of this model—inspired by the idea of Hart and Moore offs, and the firms are informed about their work - (2008)—that incorporates that workers’ behavior might ers’ relevant effort if their contract offer has not been be reference-dependent with respect to the previous rejected. out-of-recession wage. In the text, I focus on provid- ing intuitions, whereas Appendix A outlines more for- My second control treatment is the Contracts as Refer- mal arguments. Crucially, the gift-exchange literature has ence Points treatment with Feedback (CasRP-F). This shown that the standard game theoretic solution is not a treatment is very similar to CasRP and only slightly var- good predictor for this game. Whether wage cuts hap- ies the information condition of the firm. To ensure pen in such an equilibrium is not really an empirically comparability between BASE and CasRP, firms are only interesting question, and for this reason my design was informed about their workers’ relevant effort levels not tailored to allow for such equilibrium wage cuts. (not about effort level adjustments) in stage 3 in CasRP. Hence, it is not straightforward for firms to infer how workers react to wage cuts. But if workers punish wage See also Dickson and Fongoni (2019) for a more elaborated approach. 10 12 This treatment also controls for a small difference between the two main Assuming common knowledge of perfectly rational and selfish agents: treatments: In CasRP, an out-of-recession wage offer can be rejected and in Workers do not have an incentive to provide more than minimal effort, this case a potential recession cannot even occur, potentially creating a selec- e = 1 (even though the highest feasible effort level would maximize the joint tion problem since this is not true for BASE. Although this type of rejection is surplus). Firms anticipate this and choose the minimum wage for workers, empirically very rare (10 out of 630 cases) and would potentially bias against w = 30 . In recession, firms’ and workers’ behavior does not change because observing a treatment difference, it does not even exist in WasRP. firms already pay the minimum wage. This outcome is the same for all treat - ments because material incentives do not change between treatments. Can reference points explain wage rigidity? Experimental evidence Page 7 of 17 5 Fairness models, however, predict participants’ behavior however, contracts are not concluded before recessions in the gift-exchange game more accurately. If workers are and firms cut wages. Although we may not expect such a sufficiently fair-minded/inequity-averse, they will recipro - clear-cut result, we should at least expect: cate high wages by high effort levels, (ideally) splitting the surplus with their firm equally to avoid harming inequality. Hypothesis 2 [Contracts as Reference Points]: Wages are Since only the firm but not the worker is hit by a negative more rigid in CasRP than in BASE. In CasRP, a reference- profit shock in recession, the inequality between both par - point effect is observed: controlling for the wage level, effort ties ceteris paribus increases in a recession. Thus, the split is lower for wage cuts than for stable (or increased) wages. of surplus has to be adjusted. A moderate wage cut that is accompanied by an unchanged effort level allows workers Notably, firms with standard preferences will also not and firms to (equally) share the recession’s burden. Since lower out-of-recession wages in CasRP (compared to wages, thus, go down in recession, workers—when con- BASE) to preemptively mitigate the rigidity problem. The trolling for the wage level—exert more effort in than out of underlying idea is following: Under the parameters of recession. Since monetary incentives do not vary between the experiment, cutting wages already out-of-recession treatments, no differences between treatments occur. to allow for lower wages in recession leads to losses out- of-recession that outweigh the gains in recession. When Hypothesis 1 [Outcome-Based Social Preferences]: firms, however, are somewhat inequity-averse (see Appen - In both main treatments, BASE and CasRP, firms mod - dix A), they may have an incentive to lower wages out-of- erately adjust their wages downward if they are hit by a recession to avoid the higher inequality associated with negative profit shock. This adjustment is not different rigid wages in recession. Notably, this potential behavioral between treatments. pattern also originates from workers’ resistance against wage cuts, could contribute to the overall rigidity of wages Notably, with the standard inequity-aversion model, and might also be relevant in the field. As the theoretical it cannot be rationalized as equilibrium behavior that analysis is, however, somewhat inconclusive on this point, workers share the recession’s burden by increasing effort i.e., the prediction depends on what one assumes about for constant wages. This is naturally true for workers that the firms’ preferences, I do not offer a prediction here, but already exert the maximum effort but also holds for other state an open question. Finally, following the motivation of workers (as is outlined in more detail in Appendix A). the two control treatments, I have two conjectures. When workers also care for reference points, the predic- tion changes: If a firm cuts wages in recession in CasRP, Open question: Do firms adjust the out-of-recession workers feel entitled to the wage of the initial contract. wage downward in CasRP? While stable wages can lead to a loss in utility due to risen Conjecture 1 [Wages as reference points]: An explicit inequality, wage cuts decrease workers’ utility since they contract conclusion is necessary to generate resistance are perceived as reference-point violation. If workers suf- against wage cuts. ficiently care for reference points, they punish wage cuts Conjecture 2 [Contracts as reference points with feed- by lowering effort to offset the reference-point violation. back]: Due to the better information conditions, wage By how much workers have to punish wage cuts to make cuts in CasRP-F are less pronounced than in CasRP. them unprofitable, depends on their relative reaction to stable wages. If workers reciprocate stable wages only by constant effort—as predicted by inequality aversion (see 4 Results and discussion Appendix A)—their effort reduction has to overcompen - 4.1 Firms’ Behavior—BASE vs. CasRP sate the wage cut (| w|= 10 leads to |�e| > 1 ). If stable Table  3 and Fig.  1 summarize firms’ behavior. Table  3 wages are reciprocated by higher effort, a proportional provides average wages in and out of recession as well as effort reduction is already sufficient. In both cases, when two measures of the wage difference in and out of reces - controlling for the wage level, effort is lower for wage cuts sion: the (raw) wage cut and the relative wage cut. The than for stable wages. This implies that firms—with stand - later measure is provided as a complementary measure ard preferences—do not cut wages in recession. In BASE, Due to the construction of the treatments, the term wage cut can have two different meanings: Both in BASE and in CasRP, an indirect wage cut can be observed insofar as one can compare average wages of firms in recession with average wages of firms out of recession. In CasRP, also a direct wage cut can Intention-based fairness models (e.g. Charness and Rabin 2002—with the be observed by comparing wages from stage 1 and stage 2 in case a recession reciprocity parameter θ ) potentially predict wage rigidity if one assumes that occurs. Since there is no reason to expect a difference between the two meas - wage cuts are considered as unkind actions. The question, however, remains ures, I report indirect wage cuts unless otherwise stated. Reporting direct why a moderate wage cut should be considered unfair although a recession wage cuts would lead to very similar results limits firms’ abilities to pay high wages (see also Rabin 1993). 5 Page 8 of 17 C. Koch Table 3 Average wages: BASE vs. CasRP relative wage cut measure (21 percent vs. 10 percent). Hence, a treatment difference in line with hypothesis Wage Wage cut Relative 2 is observed: initial contracts that potentially serve as No-recession Recession Wage cut reference points reduce wage cuts in CasRP to less than half their size in BASE. The difference between treat - BASE 60.1 47.0 13.1 21% ments is significant both for (raw) wage cuts (rank-sum CasRP 57.9 51.9 6.0 10% test: p = 0.038) and for relative wage cuts (rank-sum test: p = 0.026). In addition, a difference of 7.1 points is non-negligible and economically meaningful in the sense since firms paying high wages have much more scope to that the predicted treatment difference would even only (absolutely) adjust their wages downward. Since my two be 10 points when making the unrealistic assumption of hypotheses make predictions about how rigid wages are, completely rigid wages in the CasRP treatment (whereas the two wage-cut measures are the main variables to test workers and firms share the profit shock of 20 points this prediction. Notably, since 98% of all wage offers are equally in BASE—Appendix A). accepted, my analysis below is based on accepted wage Figure  1 shows wages over time. In support of the offers. previous findings, firms seem to pay even more rigid Wages are cut in both treatments: average wages wages over time in CasRP. While wages are also cut by are significantly lower in recession than out of reces - 13.1 points in BASE in the last six rounds, they are only sion. While pay is, however, cut by 13.1 points in BASE 15 reduced by 1.6 points in the last third of the experiment (signed-rank test: p = 0.028 ), it is only reduced by 6.0 in CasRP. Although non-parametric tests cannot confirm points (signed-rank test: p = 0.023) in CasRP. This dif - that wage cuts are getting smaller in CasRP (signed-rank ference translates to a comparable discrepancy in the BASE CasRP 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 Period Period No Recession Recession No Recession Recession Fig. 1 Average wages—BASE vs. CasRP Tests in this paper are two-sided and since my observations are strictly only independent at the session level, non-parametric tests conservatively treat one session as one independent observation. Only when reporting power results for important null results, I also use more powerful individual observations and perform one-tailed tests in case of a directed hypothesis. Wage 35 40 45 50 55 60 65 70 Wage 35 40 45 50 55 60 65 70 Can reference points explain wage rigidity? Experimental evidence Page 9 of 17 5 Table 4 Panel regressions on wages test, p = 0.173), they do show that wages actually become fully rigid in CasRP: wages are not significantly different (1) (2) (3) (4) in and out-of recession in the last rounds (signed-rank RE RE RE FE test, p = 0.345). These findings clearly indicate that firms − − CasRP‑ dummy 0.257 1.659 3.285∗ seem to learn over time to pay even more rigid wages in (4.046) (4.138) (1.913) CasRP. − − CasRP‑F‑ dummy 1.388 0.834 3.347 As indicated before, out-of-recession wages could vary (3.408) (3.825) (2.104) between treatments when inequity-averse subjects who WasRP‑ dummy 3.000 1.159 1.471 represent a firm anticipate workers’ resistance against (4.420) (4.453) (1.818) wage cuts in CasRP, potentially contributing to the over- − − − − Recession‑ 6.832∗ ∗ ∗ 11.51∗ ∗ ∗ 10.65∗ ∗ ∗ 11.11∗ ∗ ∗ all rigidity of wages in this treatment. In line with this dummy (1.135) (1.550) (2.002) (1.759) idea, these wages are slightly lower in CasRP (57.9) than Rec × CasRP 5.822∗ ∗ ∗ 6.985∗ ∗ ∗ 5.879∗∗ in BASE (60.1). A non-parametric test is, however, unable (2.250) (2.477) (2.413) to detect a significant difference (rank sum test: p> 0.20) Rec × CasRP‑F 7.051∗∗ 8.287∗∗ 7.340∗ although this test is arguably underpowered. Potentially (3.247) (3.879) (3.634) because of the slight initial differences, recession wages Rec × WasRP 5.307 6.073 5.251 ∗∗ ∗∗ ∗∗ (47.0 vs. 51.9) are also only different with at best weak (2.153) (2.362) (2.176) significance (rank sum test: p = 0.075). Wage (No‑Rec) 0.438∗ ∗ ∗ 0.0885∗ ∗ ∗ To further validate the non-parametric analysis pre- t−1 (0.0529) (0.0289) sented so far, Table  4 shows panel random effects (RE) Wage (Rec) 0.561∗ ∗ ∗ 0.145∗ ∗ ∗ and fixed effects (FE) regressions with wages as the t−1 (0.0677) (0.0383) dependent variable and different specifications. All speci - Effort (No‑Rec) 1.723∗ ∗ ∗ 1.148∗ ∗ ∗ fications control for time trends, use data from all four t−1 (0.203) (0.147) treatments and include a recession dummy. Interact- Effort (Rec) 0.756∗ 0.633∗∗ ing the recession dummy with treatment dummies in t−1 (0.408) (0.241) specification (2) confirms that wage cuts are significantly First wage 0.0838 smaller in CasRP than in BASE. This result is robust to ∗∗ adding past-period information and using fixed instead (0.0271) of random effects (specification 3 and 4). Interestingly, in Period & Period one specification, out-of-recession wages are— with mar - Constant 57.83∗ ∗ ∗ 59.46∗ ∗ ∗ 23.98∗ ∗ ∗ 49.13∗ ∗ ∗ ginal significance—lower in CasRP compared to BASE, (3.280) (3.343) (3.854) (2.274) indicating that some firms seem to anticipate resistance Observations 2858 2858 2696 2696 against wage cuts and try to circumvent it by lowering 0.0329 0.0384 0.0984 0.120 wages already out of recession. This result is, however, Notes: Panel random effects (RE) and fixed effects (FE) regressions on wages neither robust across specifications nor across the other for all treatments. Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within control treatments. session. ∗∗∗ indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at the 10 percent level Result 1 In both treatments, wages are cut in recession. Importantly, however, wages are more rigid in CasRP than in BASE (and become fully rigid at the end of the that rigid wages are due to out-of-recession wage adjust- experiment). This supports hypothesis 2. Regarding the ments in CasRP is found. open question, no conclusive evidence in favor of the idea Power calculations based on observed standard deviations suggest that 38 4.2 Workers’ Behavior—BASE vs. CasRP (instead of 6) sessions per treatment would be needed to detect the small, Is there a reference-point effect present in CasRP that observed difference in wages as statistically significant at the 5% level 80% of the time. Alternatively, one could ask with what probability a true change in could explain why wages are more rigid in this treatment? behavior of 5 or 10 points would be detected (which would account either Table  5 provides a first average measure of workers’ for half of or the full theoretically predicted wage reduction in BASE). Such behavior in the two different treatments. In both treat - differences would be detected as significant at the 5% level with 25% or 61% probability (or 38% or 76% using individual data). Notably, power calcula- ments, average effort seems to be cut. While this reduc - tions for the associated regression analysis in Table  4—based on how much tion is, however, significant in BASE (signed-rank test: p the CasRP-dummy adds to the R —reveal a power of up to 92% even for the = 0.028), this is not true for CasRP (signed-rank test: p observed effect. Indeed, one specification finds some evidence for a small effect. 5 Page 10 of 17 C. Koch Table 5 Average effort: BASE vs. CasRP Effort Eor ff t cut No-Recession Recession BASE 4.0 3.3 0.7 CasRP 4.1 3.8 0.3 = 0.248). Of course, workers’ effort choices can only be fully understood when analyzing them accounting for their dependence on wages. Figure  2 gives a first impression why a treatment dif - [-70,-20) [-20,-10) [-10,-5) [-5,0) 0 (0,5] (0,10] (10,20] (20,70] (8) (34) (44) (15) (66) (17) (14) (6) (3) ference in wage-setting behavior might be observed. This Wage change (number of observations) figure reports workers’ reaction, their effort change, to dif - Fig. 2 Workers’ reaction to wage changes—CasRP ferent wage changes of firms for CasRP, for which direct wage-cut data is available (see footnote  14). While wages are cut roughly half of the time and remain exactly con- stant in one-third of the cases, firms somewhat surprisingly Table  6 supports the notion of a punishment reward also increase the recession wage sometimes. A potential pattern, at least in relative terms: Unpredicted by my rationale is that increasing the wage in a recession may be model of inequality aversion, stable or increased wages perceived as a particular strong gift that may not even be are—controlling for the wage level—reciprocated with that costly, at least for the more frequent moderate wage significantly higher effort (0.41) in recession. If pay increases. Indeed, the graph shows a punishment-reward is instead cut, average effort is 0.26 points lower and pattern of workers’ behavior: workers punish wage cuts by the resulting effort is statistically not different from decreasing effort, and they reward stable or increased wages zero (F-test: p = 0.324). Put differently, since stable (or by increasing effort (both in absolute terms). Notably, as increased) wages are already rewarded, workers do not discussed before, lower (higher) wages are generally recip- have to overcompensate the initial wage decrease to ren- rocated with lower (higher) effort in gift-exchange games, der wage cuts unprofitable. Even a less severe reaction completely independent of wage cuts. This positive wage- leads to the predicted reference-point effect: controlling effort relationship could in principle explain the observed for the wage level, effort is lower for wage cuts than for pattern. To fully understand the implications of workers’ stable wages, providing an incentive not to cut wages. behavior one has to analyze workers’ reactions to wage cuts Does the observed reference-point effect lead to behav - accounting for this relationship. ioral differences across treatments? Table  7 provides an To provide such an analysis, Table  6 reports fixed extended regression analysis for all treatments. While effects regressions for CasRP that explain effort and con - specification (2) disentangles the recession dummy by trol for the wage level (as well as a quadratic wage term adding treatment-specific recession dummies, specifica - and a quadratic time trend). While specification (2) tion (3) implements separate dummies for wage cuts and adds a simple recession dummy, specification (3) adds a stable (or increased) wages for all treatments with ref- dummy, Rec × Wage cut, that only has value one if a reces- erence points (CasRP, WasRP, CasRP-F). In these treat- sion occurs and the firm cuts wages. Finally, specification ments, this separation is meaningful since wage cuts can (4) provides an alternative way to control for the wage be perceived as reference-point violations. Finally, speci- level, namely by including 14 wage-dummies for wage fication (4), (5) and (6) look at further controls and fixed intervals with length of 5 ([ 30, 35], (35, 40], . . . , (95, 100]). effects specifications. Specification (3) shows that the reference-point effect observed before leads to meaningful treatment differ - ences: When controlling for the wage level, average To control for the fact that effort is discrete, e ∈{1, 10} , I also run ran- effort in recession increases by 0.63 points in BASE, dom-effects ordered probit and ordered legit regressions. Moreover, instead reflecting that workers share (an unequal) part of the of wages one could also use the wage-effort ratio as the dependent variable. Standard errors are clustered at the session level (as the level of independent recession’s burden even though wages are on average observations) because observations within session may heavily depend on adjusted downwards. This increase does not change sig - each other. To control for the dependence of observations both at the session nificantly for stable (or increased) wages in CasRP. It is, and the individual level, I also run hierarchical linear regressions with random intercepts on subjects nested in sessions. All these regressions lead to very however, significantly lower for wage cuts (0.55 points). similar results. Effort change -5 -4 -3 -2 -1 0 1 2 3 4 5 Can reference points explain wage rigidity? Experimental evidence Page 11 of 17 5 Table 6 Panel regressions on effort - CasRP on wages. The appendix also shows that workers seem— if anything—to earn slightly more in recession in treat- (1) (2) (3) (4) ments with reference points, increasing the inequality FE FE FE FE between firms and workers and, hence, suggesting that Wage 0.110∗∗ 0.113∗∗ 0.113∗∗ workers behave less fair-minded. (0.0316) (0.0308) (0.0315) Recession‑ dummy 0.285 0.408 0.379 ∗ ∗∗ ∗ 4.3 Control treatments (0.132) (0.150) (0.150) Is an explicit conclusion of a contract between firms Rec × Wage cut ‑0.257 ∗∗ ‑0.176 ∗∗ and workers necessary to create resistance against wage (0.0852) (0.0648) cuts? Does more information lead to more rigid wages? Wage Table 8 shows average wages and the two wage cut meas- Wage‑ dummies  ures for all treatments. Even without an explicit contract conclusion (WasRP), wage cuts of similar magnitude Period & Period − − − are observed than the one in CasRP. This finding is Constant 2.601∗∗ 2.779∗∗ 2.764∗∗ 8.301∗ ∗ ∗ also supported by the regression analysis of Table  4. It (0.892) (0.837) (0.846) (0.696) shows that in WasRP wages are adjusted downward but Observations 827 827 827 827 2 to significantly lesser extent than in BASE, as in CasRP. 0.669 0.672 0.672 0.683 Moreover, Additional file  1: Appendix B provides a Notes: Panel fixed effects (FE) regressions on effort, only for the CasRP treatment. more detailed analysis along the lines of the two main Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within session. ∗∗∗ treatments. The upshot is that a similar—if anything indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at intensified—reference-point effect is observed: workers the 10 percent level (relatively) punish wage cuts. Table  8 also shows that the average wage cut in The implication of this observation is that workers seem CasRP-F is roughly of the same size as in CasRP. less willing to accept wage cuts—reference-point viola- Table  4 corroborates this finding. Hence, at least on tions—in CasRP compared to BASE: they do not share average, additional feedback for firms seems not to alter the recession’s burden as much in this treatment as they the results and does not lead to completely rigid wages. do in BASE where wages are on average substantially Notably, the average results, however, mask non-neg- cut but this cut cannot be perceived as a reference-point ligible differences between CasRP and CasRP-F. Firms violation. While workers in BASE provide firms with an are slightly more likely to pay stable (or increased) extra of 6.3 points (controlling for the wage level), they wages in CasRP-F (CasRP-F: 60.3% vs. CasRP: 51.2% – only provide 0.8 points for wage cuts in CasRP. In other Z = 1.84, p = 0.065), as predicted by conjecture 2. This words, the observed reference-point effect in CasRP effect, however, appears to be negated by an increase implies that wage cuts in CasRP are punished compared in the very strong wage cuts above 20 points (CasRP-F: to average behavior in BASE. This provides an explana - 6.5% vs. CasRP: 2.9% – Z = 1.73, p = 0.083). Additional tion for the treatment difference in firms’ behavior. file  1: Appendix B further illuminates these findings by showing that not only firms but also workers change Result 2 In line with hypothesis 2, workers in CasRP their behavior in response to the change in informa- have established a reference point: controlling for the tion: workers in CasRP-F do not (significantly) punish wage level, effort is lower for wage cuts than for stable (or wage cuts compared to stable (or increased) wages such increased) wages. This effect leads to a significant treat - that there is no reference-point effect. Overall, changes ment difference that explains why wages are more rigid in both in workers’ and firms’ behavior imply that there is CasRP: compared to BASE, wage cuts are punished. no average effect. A concern could be that average differences between Result 3 In contrast to conjecture 2, more informa- wage cuts and stable wages are fairly small in CasRP tion does on average not lead to more rigid wages. In (0.18–0.26 effort units). Reassuringly, although by far not always significant, profit differences for firms are in line with the idea that firms that pay stable (or increased) CasRP vs. WasRP - (raw) wage cut: p = 0.424; relative wage cut: p = 0.424; wages earn more in CasRP (see Additional file  1: Appen- Base vs. WasRP - (raw) wage cut: p = 0.006; relative wage cut: p = 0.006. dix C). In addition and as discussed below, the difference p-values based on rank-sum tests. CasRP vs. CasRP-F - (raw) wage cut: p = 0.424, relative wage cut: p = between wage cuts and stable wages also seems to be 0.212; Base vs. CasRP-F - (raw) wage cut: p = 0.054, relative wage cut: p = more pronounced in WasRP with a similar overall effect 0.008. p-values based on rank-sum tests. 5 Page 12 of 17 C. Koch Table 7 Panel Regressions on effort (1) (2) (3) (4) (5) (6) RE RE RE RE FE FE Wage 0.132∗ ∗ ∗ 0.132∗ ∗ ∗ 0.132∗ ∗ ∗ 0.162∗ ∗ ∗ 0.131∗ ∗ ∗ 0.161∗ ∗ ∗ (0.0183) (0.0184) (0.0185) (0.0341) (0.0186) (0.0336) CasRP‑ dummy 0.219 0.345 0.343 1.217 (0.281) (0.264) (0.265) (1.143) CasRP‑F‑ dummy 0.0701 0.257 0.255 0.530 (0.331) (0.306) (0.307) (0.973) WasRP‑ dummy 0.0460 0.0948 0.0950 1.242 (0.333) (0.331) (0.333) (1.032) Recession‑ dummy 0.334∗ ∗ ∗ 0.640∗ ∗ ∗ 0.630∗ ∗ ∗ 0.556∗ ∗ ∗ 0.624∗ ∗ ∗ 0.548∗ ∗ ∗ (0.0905) (0.128) (0.128) (0.170) (0.122) (0.165) Rec × CasRP 0.386∗ ∗ ∗ (0.143) Rec × CasRP‑F 0.637 ∗ ∗ ∗ (0.195) Rec × WasRP 0.137 (0.184) − − − − Rec × CasRP × Wage cut 0.548∗ ∗ ∗ 0.407∗ 0.547∗ ∗ ∗ 0.402∗ (0.141) (0.213) (0.137) (0.209) − − − − Rec × CasRP × No wage cut 0.222 0.148 0.214 0.137 (0.172) (0.223) (0.168) (0.219) − − − − Rec × CasRP‑F × Wage cut 0.798∗ ∗ ∗ 0.623∗ ∗ ∗ 0.789∗ ∗ ∗ 0.606∗∗ (0.167) (0.241) (0.163) (0.236) − − − − Rec × CasRP‑F × No Wage cut 0.519 0.468 0.527 0.472 ∗∗ ∗∗ (0.253) (0.285) (0.251) (0.281) − − − − Rec × WasRP × Wage cut 0.378∗∗ 0.401∗ 0.379∗∗ 0.404∗ (0.156) (0.210) (0.154) (0.211) Rec × WasRP × No Wage cut 0.106 0.177 0.111 0.184 (0.212) (0.242) (0.209) (0.240) Wage Wage*CasRP & Wage *CasRP Wage*CasRP‑F & Wage *CasRP‑F Wage*WasRP & Wage *WasRP Period & Period − − − − − − Constant 3.004∗ ∗ ∗ 3.128∗ ∗ ∗ 3.082∗ ∗ ∗ 3.626∗ ∗ ∗ 2.856∗ ∗ ∗ 2.816∗ ∗ ∗ (0.503) (0.495) (0.494) (0.863) (0.499) (0.401) Observations 2858 2858 2858 2858 2858 2858 0.517 0.518 0.519 0.520 0.622 0.627 Notes: Panel random effects (RE) and fixed effects (FE) regressions on effort for all treatments. Standard errors are reported in parentheses, adjusted for clustering at the session level since observations may be dependent within session. ∗∗∗ indicates significance at the 1 percent level, ∗∗ at the 5 percent level, and ∗ at the 10 percent level addition, in contrast to conjecture 1, an explicit violation because of the explicit agreement but simply because of an agreed upon contract is surprisingly not necessary they determine the out-of-recession wage and convey to generate resistance against wage cuts. this information to the worker, which is sufficient to cre - ate feelings of entitlement. Notably, while it is conceiv- Overall, this study’s findings are in line with idea that able that initial contracts in CasRP influence subjects reference points motivate resistance against wage cuts expectations in a way not feasible in BASE, no such initial even though there is no violation of an explicit agree- contracts exist in WasRP. The result is, however, in line ment. Contracts seem to serve as reference points not with findings that entitlements could constitute a “moral Can reference points explain wage rigidity? Experimental evidence Page 13 of 17 5 Table 8 Average wages: BASE vs. CasRP/ WasRP/ CasRP-F be fired and firms have only one worker. Having said this, reference points are surprisingly strong in my set- Wage Wage cut Relative ting. Unlike in other studies, a good reason—the reces- No-Recession Recession Wage cut sion—does not mitigate their effect. A key feature of my design is that existing contractual arrangements have to BASE 60.1 47.0 13.1 0.21 be revised, providing initial wages with a realistic shot at CasRP 57.9 51.9 6.0 0.10 serving as reference points. In contrast, wage cuts e.g. in WasRP 60.4 53.8 6.6 0.11 Chen and Horton (2014) and Bracha et  al. (2015) were CasRP‑F 58.8 53.4 5.4 0.09 implemented by a new contract offer that simply stipu - lated a lower wage, not by a revision of an existing con- tract. Moreover, it seems likely that reference points also property right” that is independent of players’ legal prop- play a crucial role in the field since important real-world erty rights (GÄchter and Riedl 2005; Bolton and Karagö- features that reinforce them are even missing in my set- zoglu 2015). ting: workers in the field “associate pay with self-worth” On a more general level, I cannot rule out that other and also punish wage cuts because they want to maintain motivational forces, apart from reference points, might their standard of living (Bewley 1999, p.432). contribute to the observed results. Findings are for exam- One abstraction of my design is to deliberately disre- ple consistent with the idea of an anchoring effect (see gard the role of reputational concerns by implementing Furnham and Boo 2011 for a recent review). Even though stranger matching. As outlined before, this is done to the out-of-recession wage has no relevance in WasRP in allow for a clean identification of the effects of the par - case a recession occurs, it still influences the outcome. ticular reference point under investigation. Moreover, Relatedly, since workers seem to earn slightly more in implementing partner matching in my setting would recession when reference points are present, self-serving capture that field labor relationships are not one-shot biases (Babcock and Loewenstein 1997) could also be a but also seems to emphasize reputational concerns too driving force. Of course, these different motivations may strongly. Experimental rounds are very short—thereby not be mutually exclusive: Self-serving biases may simply making future periods very salient—compared to field reinforce reference points. labor-market contract periods. Workers’ resistance against wage cuts in the field seems likely to be driven 5 Conclusion by emotions triggered by cuts when the importance of In this paper, I examine whether reference points affect future contract periods is fairly inconspicuous due to the workers’ perception of a “fair” recession wage and, thus, longer time horizon. Stranger matching seems to reflect cause wage rigidity. In a controlled experimental labora- this to a better extent than partner matching. For this tory market, I manipulate whether workers’ fairness per- reason, I leave it for future research to analyze the inter- ceptions can be shaped by initially concluded contracts action of reputational concerns and wage rigidity. and the wage they stipulate. I find that wages are consider - Another open question is the effect of booms. One the able more rigid with these initial contracts than without. one hand, one could argue that if workers believe that When initial out-of-recession wages can serve as a refer- firms mostly benefit from booms, this may create an addi - ence point, workers punish wage cuts relative to stable tional mechanism for rigid wages because workers might wages, providing a reason for firms’ wage-setting behav - then perceive recessions as entrepreneurial risk and, thus, ior. Interestingly, workers still reward stable wages. Thus, not be willing to share the recession’s burden. This would rigid wages are observed despite the fact that a recession be completely independent of whether initial contracts provides a good reason to adjust the wage level. Unexpect- have been concluded or not. One the other hand, if work- edly, they even emerge when workers have not agreed to ers’ fairness perceptions are really driven by self-serving an initial contract and, thus, arguably have no “objective” biases, the rationale of the former statement is not so clear. justification to feel entitled to their reference wage. This Workers might—contrarily to what we observe for busts— highlights the strength of reference points in my setting. not perceive initially concluded contracts as a constraint What do my findings imply about reference points and demand their share of the boom’s surplus, e.g. in form and wage rigidity outside the lab? Do reference points of bonuses or other flexible pay components. Whatever provide one explanation for wage rigidity in the field? Like with all empirical studies, such statements should be made with great care. My results are obtained in a A real-effort experiment with partner matching in which providing effort takes some time—making future period less salient—could capture reputa- specific environment, one that—in order to isolate one tional concerns, emotional reactions, and their interactions with reference plausible explanation of wage rigidity—abstracts from points more adequately. Naturally, this kind of setting is more complex and many aspects of field labor markets, e.g. workers cannot does not allow for as much repetition and learning as my simpler setting does. 5 Page 14 of 17 C. Koch the answers to those questions may be, this paper shows U (x ,x ) =x − α · max[x − x ,0] W W F W F W (3) that reference points alone already provide an explanation − β · max[x − x ,0] W F for more rigid wages in recession in a controlled labora- where x and x are the monetary payoff of the worker tory environment, independent of other explanations that W F (W) and the firm (F) and α ( β ) reflects how much work - may or may not reinforce this phenomenon. ers suffer from disadvantageous (advantageous) inequal - ity. FS assume that β ≤ α and that 0 ≤ β< 1. Supplementary Information Crucially, if workers are sufficiently inequity-averse The online version contains supplementary material available at https ://doi. 18 11 3 org/10.1186/s1265 1‑021‑00284 ‑2. or fair-minded (β> ≈ 0.243 ; α> β − ), firms 74 2 2 offer a high wage and workers reciprocate by a high effort Additional file 1. Online Appendix. (w = 84, e = 10) . In recession, the negative profit shock is Additional file 2. “Readme” file for dataset. equally split (w = 74, e = 10) . More precisely: Out-of- Rec Rec Additional file 3. Dataset. recession, firms offer the highest possible wage that equal - izes payoffs and to which workers can react with the highest Acknowledgements possible effort ( w = 84, e = 10, x = x = 66 ). W or k ers W F For helpful suggestions, I would like to thank Andreas Bernecker, Dirk Engel‑ reciprocate the high wage with the highest effort level if mann, Urs Fischbacher, Leonie Gerhards, Botond Kőszegi, Nikos Nikiforakis, Jörg Oechsler, Henrik Orzen, Alexander Paul, Stefan Penczynski, Clemens Puppe, they are sufficiently averse against advantageous inequality, Klaus Schmidt, and Sigrid Suetens. I also received helpful comments from partic‑ 3 in this case β> ≈ 0.230 . Providing one unit less effort ipants at seminars in Abu Dhabi, Hamburg, Heidelberg, Mannheim, Munich, the will save the worker (at most) 3 points but advantageous Thurgau Experimental Economics Meeting 2013 ( Theem), the Florence Work‑ shop on Experimental and Behavioral Economics 2013, the ESA World Meeting inequality will rise from 0 to 13 points. Additionally, work- 2013 (Zurich), the 8th Nordic Conference on Behavioral and Experimental ers have to be sufficiently averse against disadvantageous Economics 2013 (Stockholm), the Gesellschaft für experimentelle Wirtschafts‑ 11 3 22 inequality ( α> β − ). This ensures that firms do not forschung 2013 (Helmstedt), the EEA annual meeting 2014 ( Toulouse). 2 2 have an incentive to pay less than the payoff-equalizing Authors’ contributions wage, w = 84 . In recession, firms again offer the highest Not applicable. No research assistants were used. wage that equalizes payoffs (accounting for the negative Funding profit shock) and to which workers respond with the high - Funding from the DGF is gratefully acknowledged. Rec Rec Rec Rec est possible effort ( w = 74, e = 10, x = x = 56 ). W F Note however, that in recession workers have to be slightly Avaiability of data and materials The dataset used during the current study is available as Additional files 2 and more fair-minded, β> ≈ 0.243 : Firms cannot make losses in my setting which restricts the degree of advanta- geous inequality. Receiving a wage of 74 and providing e = 1 Ethics approval and consent to participate No IRB approval was obtained as the University of Mannheim did not have instead of e = 10 saves the worker 18 points and increases IRBs at the time the study was implemented. For this reason (and since advantageous inequality only by 74 points. the study involved only minimal risk), solely the approval of the director of In a similar fashion as before, one can show that mLab at the University of Mannheim (at which the experiment was run) was obtained. In order to participate in the experiment, subjects had to register if workers are only fair-minded to a very low degree in advance for the mLab database. During this registration process a general 1 (β < ≈ 0.090) , workers exert minimal effort ( e = 1 ). consent to participate was obtained. The underlying idea is that workers can always save Consent for publication (at least) 1 point by lowering effort by one unit which Not applicable. The study does not include details, images, or videos relating would increase advantageous inequality by 11 points. to an individual person. Thus, no consent for publication was obtained. Firms should anticipate workers’ behavior and only Competing interests offer the minimum wage ( w = 30 ), both in and out of The authors declare that they have no competing interests. recession. If workers are fair-minded to an intermedi- 1 18 ate degree ( ≤ β ≤ ), intermediate equilibria arise 11 74 Appendix A Theory and hypotheses in which intermediate wage offers are reciprocated by Hypothesis 1 I formalize the first hypothesis using preferences of ineq - uity-aversion as introduced by Fehr and Schmidt (1999) (henceforth FS). I assume that workers have FS-prefer- ences, whereas firms have standard preferences. The condition for α arises from the comparison of the two situations U (w = 83, e = 10) = 65 − 2α< 68 − 11β = U (w = 83, e = 9) . If the W W condition is not met, an equilibrium with a slightly lower wage, e.g. w= 83 Importantly, the derived predictions are not specific to inequity-aversion. or w=82, arises in case firms have standard preferences. In case firms are also Social welfare preferences (Charness and Rabin 2002) would lead to qualita- (sufficiently) inequity averse, the outlined equilibrium persist, because firms tively similar results. avoid inequality. Can reference points explain wage rigidity? Experimental evidence Page 15 of 17 5 intermediate effort levels (see example below). In reces - the fraction of fair-minded workers is high enough: In my sion, wages are cut by (at least) 10 points. case, µ> 0.46. Notably, the adjustment of the split of surplus cannot Overall it holds that if workers are sufficiently fair- be done through increased effort and constant wages, at minded, the negative profit-shock is equally shared least not in equilibrium. Sufficiently fair-minded work - between workers and firms by a moderate wage cut of ers already exert the maximum effort. But the statement 10 points. Naturally, one might not expect such a clear- is even true for less fair-minded workers. This is trivial cut result, but controlling for the wage level, workers for workers that are only fair-minded to a very limited should at least provide more effort in recession than out degree because they will always provide minimal effort of recession. in and out-of-recession, as argued above. For workers with intermediate degrees of fairness, rational firms in Hypothesis 2 equilibrium already choose their out-of-recession wage I extend the model of FS (by a fourth term) to incorpo- such that it induces the highest effort level that is possi - rate that workers behavior might be reference-dependent ble when taking the limited degree of the worker’s fair- with respect to the previous out-of-recession wage. This ness into account. With constant wages, the recession extension is inspired by the general idea of Hart and increases the level of inequality. But since the utility func- Moore (2008) (henceforth HM) that contracts serve as tion is linear in inequity aversion, one unit more effort reference point because they create feelings of entitle- is still associated with the same costs and benefits (of ment. Although HM do not explicitly deal with renego- reduced inequality) as out of recession. tiations, the implication of their analysis is that wages As an example, consider the case that workers are suf- should be more rigid in recession with initial contracts ficiently inequity averse such that saving 2 points and than without. In  situations without initial contracts increasing inequality by 12 points is not attractive to (BASE), I assume that FS-preferences govern the rela- them ( β ≥ ) but saving three points and increasing tionship between workers and firms. inequality by 13 points is ( β< ). Due to the increas- In the CasRP treatment, contracts can serve as refer- ing cost function, this implies that firms cannot induce ence points and workers’ preferences as described in an effort of 9 or 10 but only 8. Thus, out-of-recession, equation (3) can be modified: firms will pay w = 71 to induce workers to exert an effort U (x , x ) =x − α · max[x − x ,0]− β · max[x − x ,0] W W F W F W W F of e = 8 , equalizing payoffs at x = x = 59 . Ke eping W F − γ · I max[θ · (w − w ) − 10 · (e − e ),0] [w2<w1] 1 2 1 2 this wage (as well as the effort) constant in recession, will (4) Rec Rec increase inequality considerably ( x = 59, x = 39 ). W F The basic idea of the fourth term is the following: But the cost of reducing this inequality stays the same as The weighted difference between the reference-point out of recession: Increasing effort beyond 8 to 9 still has wage out of recession and the actual wage in recession, a cost 3 and a benefit in reduced inequality of 13, which θ · (w − w ) can be interpreted as the worker’s aggrieve- 1 2 a worker with an intermediate aversion to inequality is ment caused by getting less than what you are entitled not willing to take. Anticipating this outcome, the firm Red to and θ represents a weighting parameter. Workers can will reduce the wage to w = 61 such that payoffs can offset their aggrievement, θ · (w − w ) , by adjusting 1 2 be equalized. Finally, it is noteworthy that constant wages their effort downward and hence punishing the firm by and increased effort are not an equilibrium phenomenon, 10 · (e − e ). 1 2 but sufficiently inequality averse player may well increase 23 Notably, as outlined before for hypothesis 1, stable effort for constant wages in recession off-equilibrium . wages cannot be reciprocated with higher effort levels To accommodate that laboratory subjects are fair- in recession since the highest (feasible) effort level has minded to different degrees, the literature often consid - already been induced out of recession. This may be all ers two-type models (see Kocher and Strasser 2011 and the more true since my approach—following HM— FS). Firms in my setting could e.g. assume that a fraction 18 only models a negative impact of a reference-point µ of workers is sufficiently fair-minded ( β> ), wherea s 1 violation but not a positive effect when a reference 1 − µ is (quasi-)selfish ( β< ). The intuition of these point is met. Thus, to establish that firms lose more by kind of models is quite clear: It is rational both for selfish and fair-minded firms to propose a high wage ( w = 84 ) if μ · U (w = 84, e = 10) + (1 − μ) · U (w = 84, e = 1)> U (w = 30, e = 1) W W W A sufficiently inequity-averse worker will reciprocate a wage of 71 with 8 ⇔ μ66 + (1 − μ)0 > 30. In recession, this fraction is even lower: μ · U (w = 74, out of recession but provide an effort of 10 in recession (both to equalize pay - (w = 74, e = 10) + (1 − μ) · U (w = 74, e = 1)> μ · U (w = 30, e = 3) + (1 − μ) W W offs). Notably, this cannot be an equilibrium outcome as the firm will benefit ·U (w = 30, e = 1) ⇔ μ56 + (1 − μ)0 >μ20 + 10. from deviating and paying the worker a higher wage out-of-recession. 5 Page 16 of 17 C. Koch reduced effort than they gain by paying lower wages, recession. Firms could react by paying lower wages (and workers have to overcompensate the wage decrease by hence foregoing earnings) out of recession and hence a relatively larger effort decrease. In other words, one being able to pay lower wages (and hence gain earn- has to assume that θ> 1 , deviating from HM. ings) also in recession. This kind of strategy is, however, Whether workers, however, really want to offset suboptimal given the parameters of the experiment. their aggrievement depends on the weighting param- Crucially, however, these strategies may become opti- eter γ : Only when workers weigh the negative impact mal for firms that also have preferences of the FS-type. of a reference-point violation high enough ( γ> 10 ) , In equilibrium, not cutting wages leads to disadvanta- they punish wage cuts by lowering effort although geous inequality, lowering firms’s utility compared to this also leads to higher inequality associated with standard preferences. Lowering, however, the out-of- lower utility. More precisely: Assume that firms and recession wage leads to less disadvantageous inequality workers act according to the FS-considerations of in recession. I do not make specific assumptions about hypothesis 1 ( w = 84, e = 10, x = x = 66 ) and that the parameters for the inequity averse firms, but con - W F workers are sufficiently fair-minded ( β> ≈ 0.243 ) . sider it as an open question whether out-of-recession Consider the case that firms cut wages in reces- wages in CasRP are already lower than in BASE. Addi- Rec sion by one unit, w = 83 . If γ> 10 , then even the tionally, the theory does not provide a clear-cut pre- smallest wage reduction will lead to a loss of utility of diction under which circumstances initially concluded more than 10. This is due to the reference-point vio- contracts serve as reference points, whether an explicit lation. Reducing effort by one unit will, however, off- contract conclusion is necessary or not, or whether set this negative effect and will lead to a utility loss better information lead to more rigid wages or not. that is strictly smaller than 10. A one-point decrease of effort increases advantageous inequality by 13 Received: 30 October 2019 Accepted: 12 January 2021 points but workers still saves 3 points of cost of effort. Hence, if workers weight the negative impact of vio- lating their reference point to a sufficient degree, firms with standard preferences will not cut wages References Rec Rec Rec Rec ( w = 84, e = 10, x = 46, x = 66 ). This is due F W Abeler, J., Altmann, S., Kube, S., Wibral, M.: Gift exchange and workers’ fairness to the fact that a wage reduction is always followed by concerns: when equality is unfair. J. Eur. Econ. 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Regarding effort: In case stable (or increased) wages are not reciprocated by higher effort, as predicted, workers overcompensate wage cuts by effort decreases (θ> 1 ), leading to an effort decrease even when controlling Paying w = 84 out of and in recession leads to earnings of x = 66 and Rec x = 46 with a probability of 2/3 and 1/3 respectively. The best strategies for the wage level. But even when stable wages are rewarded, available, in which the out of recession payment is reduced, lead to payoffs a reference-point effect is observed in CasRP since workers below this result. Paying w = 78 out of and in recession (in order to (almost) render wage cuts unprofitable in any case: Controlling for equalize payoffs with an effort level of 9 with a slight worker’s advantage) Rec leads to earnings of x = 62 and x = 52 : A loss of 4 out of recession with the wage level, wage cuts should be accompanied with rela- F a probability of 2/3 and a gain of 6 in recession with a probability of 1/3. 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