The Incentive E¤ects of Inequality: An ExperimentalInvestigation�

Hyejin Kuy

Florida State UniversityTimothy C. Salmonz

Florida State University

November 2009

Abstract

The e¤ect of inequality on individual behavior is often debated in various literaturesincluding the development literature with many �nding that inequality among di¤erentgroups in a society has a negative impact on economic growth while others �nd theopposite result. Our study investigates a behavioral phenomenon which may contributeto any adverse consequences of inequality for growth. In particular we investigatewhether or not individuals exhibit a discouragement e¤ect in the face of inequality thatleads to lower work e¤ort. If such an e¤ect exists it provides a mechanism for convertingeven idiosyncratic inequality into sustained inequality with adverse consequences for theindividuals being a¤ected by the inequality and the economy as a whole. We investigatethis phenomenon using an economic experiment to allow us to cleanly vary the nature ofinequality and to allow us to directly observe several characteristics of the workers. We�nd robust support for the existence of a discouragement e¤ect lending credibility to theclaims that such an e¤ect would exist in external situations among workers confrontedwith disadvantageous inequality.JEL Codes: C90, D61, D63, O15, O40Key Words: inequality, e¢ ciency, productivity, experiment

�The authors would like to thank the National Science Foundation for research support in funding theseexperiments. We also thank participants at the Cornell-Edinburgh Conference on Relativity, Inequalityand Public Policy, International ESA Meeting in DC and the European ESA Meeting in Innsbruck as wellparticipants in seminars at Virginia Tech and Goethe University in Frankfurt.

yFlorida State University, Department of Economics, 113 Collegiate Loop, Room 263, PO Box 3062180,Tallahassee, FL 32306-2180, hku@fsu.edu. Phone: 850-644-7208 Fax: 850-644-4535.

zFlorida State University, Department of Economics, 113 Collegiate Loop, Room 263, PO Box 3062180,Tallahassee, FL 32306-2180, tsalmon@fsu.edu. Phone: 850-644-7207 Fax: 850-644-4535.

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1 Introduction

Economists have established many ways in which initial inequality may in�uence the pathsof economic development. In a series of historical studies, Engerman and Sokolo¤ (1997,2002 and 2005) argue that the initial di¤erences in factor endowments between the Northand South America contributed to the emergence of di¤erent institutions between the tworegions, which in turn led to the divergence in the rates of growth. Persson and Tabellini(1994) examine more recent data and argue that there is a signi�cant and large negativerelation between inequality and growth while Banerjee and Du�o (2003) argue that the re-lationship between growth and inequality is an inverted U-shaped function. Understandingthe relationship between inequality and economic growth is important in the design of abroad range of economic development policies and there is a substantial literature which in-vestigates the mechanics behind the linkages between growth and inequality. Loury (1981),Galor and Zeira (1993), Banerjee and Newman (1993), Durlauf (1996), Benabou (1996,2000) and Mookherjee and Ray (2003) are well-established studies in the literature and thetypical nature of the proposed linkage between inequality and either growth or persistentinequality in these papers is di¤erential endowment or investment opportunities of agentsoften in the form of human capital and occupational choice.

We propose a new possible linkage between inequality and growth which may also beuseful in explaining the persistence of inequality. The linkage we propose is the incentivee¤ects of inequality from a behavioral perspective. Speci�cally, we argue that individualsmay respond not just to the absolute return on their e¤ort but also to their return relativeto that of others. If present, this behavioral e¤ect of inequality leads to inequality havinga direct impact on the decisions of individuals unlike in the existing literature in whichinequality has no e¤ect on individual behavior though it does alter aggregate societal out-comes. To explain the nature of the e¤ect we investigate, suppose that due to her identitymarks such as gender, caste, or race, an individual receives lesser rewards than others in hersociety for the same amount of e¤ort provided. Then, one can envision this individual be-coming discouraged by the disadvantageous inequality and exhibiting a variety of responsesranging from decreased on the job work e¤ort to decreased human capital acquisition andto decreased contributions to public goods.

If such a behavioral response to inequality exists then there are a number of importantconsequences associated with it. First, this e¤ect ceteris paribus would generate a nega-tive relationship between inequality and economic growth. There are a number of forcesat play in an aggregate economy so this is not to claim that the overall relationship be-tween inequality and growth must be negative if this e¤ect exists but the partial e¤ect ofinequality on growth due to this behavioral e¤ect would be negative. Second, separatelyor in addition to the theoretical models cited above, this e¤ect could generate persistentinequality from initial idiosyncratic inequality. The reason is that even if the initial in-equality were idiosyncratic, if a worker responds by exerting lesser e¤ort or investing less inhuman capital, then this response has the potential to legitimize and then perpetuate theinitially low rewards for that individual or group. Thus initial idiosyncratic inequality canbe converted into longer term inequality. Any potential discouragement e¤ect is, of course,likely to be worsened if the inequality in rewards is not idiosyncratic but rather related to amore generalized social phenomenon of racial, ethnic, gender or caste based discrimination

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in which individuals from these disadvantaged groups expect to be confronted with unequaltreatment in many aspects of their lives.

There is of course also the possibility of a counter e¤ect which we might refer to asan �encouragement e¤ect�in which those who are subject to advantageous inequality maybene�t from the inequality and therefore work harder. The ultimate question of empiri-cal interest is if either of these two e¤ects exist and if both do what the net e¤ect is onoverall productivity. The goal of the present study is to examine exactly this issue in or-der to determine the likely e¤ect on overall productivity due to the existence of inequality.We present the results of a laboratory based experimental study designed to allow cleaninference on whether or not individuals become discouraged or encouraged in the face ofinequality. The environment we construct in our experiment should be a very strong test ofthe discouragement e¤ect in particular because many of the aspects of discrimination andlong run experience with inequality will not be present in the experiment. Consequently,if we �nd a discouragement e¤ect in our simpli�ed laboratory environment then it will berobust evidence that such an e¤ect could exist in a broader context in which the inequality isbased on overt discrimination and individuals would have long term experience with feelingthe e¤ects of inequality.

There is prior evidence on this issue but both the sign and robustness of any e¤ectis unclear. Akerlof and Yellen (1990) propose a similar e¤ect to what we refer to as adiscouragement e¤ect in the form of their �fair wage-e¤ort hypothesis� but provide rela-tively weak support for its existence. Ho¤ and Pandey (2006) come substantially closer todemonstrating a discouragement e¤ect as they provide evidence that low caste children inIndia decrease their performance when their caste identity is made salient. This perfor-mance drop is argued to be due to the anticipation of disadvantageous treatment leadingto discouragement once the caste information is revealed, but actual treatment was in factunchanged. While this is suggestive of a discouragement e¤ect due to unequal treatment,there are also other plausible explanations such as stereotype threat (Steele and Aronson,1995). There are a range of other studies which attempt to identify e¤ects like this in nat-urally occurring data typically focusing on wage inequality in workplaces. However, datalimitations in these studies lead to substantial inference problems. While there may beunfairness in naturally occurring wage schedules it is di¢ cult to separate cleanly between awage that is unfairly low and one that is deservedly low due to skill di¤erences or to traitswhich would be unobserved by a researcher.1 Proper inference on the e¤ects of inequalityon e¤ort though requires cleanly severing the link between wages and characteristics of aworker to �nd situations in which it is clear that �unfair inequality� is present. Were weable to �nd situations in which wages clearly satisfy this criteria there is also an empiricaldi¢ culty in observing work e¤ort. E¤ort itself is rarely observable and the measurementof most proxies for work e¤ort in common use such as the rate of promotion or turnoverare potentially related to any discrimination that generated the wage inequality. Even werea viable proxy for e¤ort to be available, there is still a problem of separating out e¤ortdi¤erences due to a pure wage e¤ect and e¤ort di¤erences due to the existence of inequal-ity. Separating these e¤ects requires observing workers exerting e¤ort when faced with thesame wage in similar environments that di¤er only in regard to whether or not wage in-

1Heckman, Lyons, and Todd (2000) summarizes the literature on identifying race based discriminationin wages against blacks in the US and explains many of the inherent problems in such attempts.

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equality is present. Due to these di¢ culties in inference from naturally occurring data, wepresent evidence from a laboratory experiment in which we will be able to observe e¤ortdirectly while implementing exogenously set wage schedules with and without inequality toovercome these limits on inference.

In our experiment equally quali�ed individuals engage in a real-e¤ort task (encodingrandom sequences of letters into numerical code) for piece rate earnings. The wage ratesare exogenously assigned and they are a proxy for general opportunity or rewards for e¤ort.2

Our design includes control sessions in which all subjects receive equal wages so that wecan identify the inequality e¤ect by comparing the performance of workers receiving aparticular wage in sessions with no inequality to that of workers receiving the same wagein the presence of inequality. Our experimental design will also address a less commonlyinvestigated issue regarding how the response to inequality might vary with the relativesizes of the advantaged and disadvantaged groups. Relative group size may be importantbecause the existence of an incentive e¤ect hinges on workers perceiving a low wage asbeing unfair. That perception of unfairness may be diminished if the majority of workersare receiving the same low wage and may be heightened if only a small number do. Toexamine this possibility our experiments will vary the size of the high and low wage groupsto determine if there is a systematic response of individuals to the status of their groups asbeing a numerical minority or majority.

In the end we do �nd that a discouragement e¤ect exists and it is of non-trivial size.We do not �nd evidence in favor of an encouragement e¤ect. This pair of �ndings are quiteimportant because they provide a demonstration of one channel through which inequalitycan lead to a decrease in economic e¢ ciency. We also �nd results suggesting that the sourceof the inequality can be an important factor, at least for some individuals. Previous researchin Bolton, Brandts, and Ockenfels (2005) shows that some individuals will judge the fairnessof an allocation based on the procedure used to generate it rather than just the allocationitself. We use what is sometimes considered a procedurally fair procedure for generating theinequality in our experiment (i.e. pure randomization) and �nd that subjects who we canmeasure separately as being more likely to view the allocation as unfair generate a muchstronger response.

In section 2 we will provide an overview of our experiment design. Section 3 will presenta series of hypotheses regarding what one might expect to observe in the experiments basedon prior literature. In section 4 we will present our results and we will provide a concludingdiscussion in section 5.

2 Experimental Design

The base task in this experiment involves subjects taking random strings of 4-letter �words�and using a code key to translate those letters into a numerical code. The subjects wereshown the encoding key and the string of letters on a screen and would enter the encoded

2An important detail about the e¤ect we propose is that we deal with the notion of inequality in �rewards�as opposed to �endowments.�This distinction between di¤erent types of inequality is discussed in Hopkinsand Kornienko (2009) in which it is pointed out that the term �inequality�means many di¤erent things inthe vast literature discussing it and often the di¤erential consquences of the two are overlooked. We agreethat the distinction is important and we will discuss the issue further in section 3.

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Table 1: Summary of experimental design.Common Common Disadvantaged Disadvantaged

Group Low High Minority MajorityBlue (6 Persons) $0.03 $0.09 $0.09 $0.03Green (2 Persons) $0.03 $0.09 $0.03 $0.09Sets of 8 Persons 4 2 8 8

version below the word. The same code key was used for the entire session. They hada button which would allow them to submit a word and after doing so they would beimmediately given a new word. For every word they encoded correctly they were paida piece rate wage which was exogenously set by the experimenters at the beginning ofthe session. This production task is very similar to the one used in Erkal, Gangadharan,and Nikiforakis (2008). We use a real e¤ort production task rather than a stylized e¤ortdesign in which subjects choose e¤ort numbers on a given range because the e¤ect we areinvestigating involves an emotional response to the stimulus and it seems more likely toemerge out of real e¤ort than out of a stylized e¤ort experiment.

Each session consisted of 16 subjects and these 16 subjects were divided into two setsof 8 at random. Inside of those sets of 8, subjects were further randomly assigned intowhat we labeled �blue� and �green� groups. The subjects were informed of the color oftheir group before anything else happened in the experiment as an attempt to make itclear that group assignment was exogenous. The meaning of the group assignment wasonly explained later to the subjects and the actual meaning referred to the wage rate theywould be assigned. Table 1 provides a summary of the experimental treatments as well asthe number of observations of sets of 8 subjects for each treatment. There are a total offour treatments contained in this design. There are two control treatments called CommonWage - Low and Common Wage - High in which all subjects received the same commonwage regardless of group assignment.3 For consistency with the other treatments subjectswere still divided such that there were 6 members of the blue group and 2 of the green ineach treatment but the wages across groups were constant. The high wage was $0.09 percorrectly encoded word while the low wage was $0.03. The other two treatments will becalled the Disadvantaged Minority treatment (Disad Min) and the Disadvantaged Majoritytreatment (Disad Maj). These two treatments introduce inequality by having one grouppossess the high wage and the other the low such that in the Minority treatment, themembers of the 2-person group are assigned the low wage while in the Majority treatmentthe members of the 6-person group are assigned the low wage.

The experiment was programmed using z-Tree, Fischbacher (2007). After subjects sawan initial screen indicating the color of the group to which they were assigned, they werepresented with a sample of the main screen for the experiment showing them the encodingtask. In the course of explaining this screen to the subjects, they were explicitly informedof the wage rates that would be in e¤ect for both groups. Also, before each round of

3We have fewer observations of the Common High treatment than the Common Low treatment becauseas our hypothesis section will make clear, our main interest is in the behavior of low wage workers and madethe choice to obtain a larger sample of those subjects. We do engage in some analysis of the response by thehigh wage subjects but our main focus is on the low wage subjects.

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production, subjects would see a screen which included a table showing them a columnfor each subject in their 8-subject set indicating their group color and corresponding wagerate. The idea of stating this information to them repeatedly was to ensure that they clearlyunderstood both the wage rate di¤erential as well as the relative size of both groups. Afterthe �rst round, this screen also showed them information on their own past earnings. Theywere not shown the earnings or production levels of other individuals in the experiment atany time. The only information they see about other subjects is their wage rates. As suchthere are no interactions between members of a group or members of a set making eachsubject independent of the others. This choice of feedback was made so that the only thingsthat should be salient to the subjects that might a¤ect their behavior are the treatmentvariables themselves and any session or group e¤ects should be minimal.

In order to give subjects an outside option should they wish to avoid the productiontask, we included another task on their screen. This other task was the option of playingTic-Tac-Toe (TTT) against the computer, which might be very loosely interpreted as a�shirking�option. The computerized opponent was programmed to be moderately di¢ cultbut beat-able. This task was only minimally incentivized in that it paid a subject $0.01 perwin. Due to the di¤erence between this wage rate as well as the time it would take to win agame and the wage rate and time to correctly encode a word for the encoding task, it shouldhave been quite clear to subjects that TTT would never compete in �nancial terms withthe main task. It was designed mainly to be at least mildly more �fun�than the encodingtask and allow subjects who did not want to engage in encoding another activity so thatthey would not just have to stare at the screen in boredom.

There were 12 rounds of production in each session with each round lasting for fourminutes. Subjects were not instructed on which task to engage in but rather they were toldhow both worked, the wage rates of both and then told they were free to allocate their timebetween the two tasks as they wished.4 At the end of each of the 12 rounds, each subjectwas presented with the screen summarizing her output in the encoding task, earnings fromthe encoding task, earnings from TTT, and cumulative earnings. On the practice screenthey were also allowed to practice TTT as well as the encoding task for a few times beforemoving on to the �rst paying round.

At the end of the 12 rounds we had subjects �ll out a short demographic questionnaireand complete two short sets of questions intended to measure various aspects of cognitivedecision making. The �rst of these is the Cognitive Re�ection Test (CRT) described inFrederick (2005). This three question test is designed to determine the degree to whichsubjects engage in thoughtful and re�ective versus quick and impulsive decision making.For example, one of the questions is:

�A bat and a ball cost $1.10. The bat costs $1.00 more than the ball. Howmuch does the ball cost?�

The most common quick answer one might come up with is $0.10 but this is clearly wrong asupon further re�ection the correct answer is $0.05. We used this measure because those whoscore low on it may be more inclined to make impulsive decisions and that impulsiveness

4Full instruction scripts are available from the authors upon request.

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might well lead to exhibiting greater e¤ects due to the treatments.5

We also used a second set of questions involving pattern matching problems in whichwe asked subjects to �ll in the number that �ts best in sequences such as: 3 6 9 12 (_). Wehad 10 sequences of this sort that varied in di¢ culty. This structure of these questions weredrawn from standard IQ tests and, while certainly not a complete version of such a test,the results on it should correlate with the results on a standard IQ test. More speci�callyit should measure a general facility with numerate tasks and so we will refer to this asmeasuring �numeracy.�Our interest in this measure is that highly numerate subjects maybe �overachievers�on tasks outside the lab and therefore might respond di¤erently to thepresence of inequality. Subjects received no payment for completing these questions and wegave them 100 seconds per test to complete as many of the questions as they could in thetime frame.6

We have conducted 11 sessions with 176 subjects generating the number of sets pertreatment as noted in Table 1. All subjects received $10 for showing up to the session andsessions last a little over an hour. Subjects earned on average $28.89 ($39.72 for high wageworkers and $19.86 for low wage workers) including their show-up fee.

3 Hypotheses

As a way of providing a framework for evaluating the results of the experiment we willpresent a simple but �exible theoretical framework to describe the potential e¤ects of in-equality on behavior. From this model we will then derive a series of hypotheses that willhelp to organize the presentation of the results.

Consider the utility function for an individual i as speci�ed in equation (1). Let wi bethe wage received by individual i, ni the productivity level chosen by individual i while wealso de�ne w = 1

I

PIj=1wj ; W = (w1; :::; wI) and N = (n1; :::; nI): We will let c(ni) be the

direct cost associated with the level of productivity ni. We will use a standard assumptionabout c(�) which is that c0 > 0 and c

00> 0: This utility function includes two additional

terms to account for two di¤erent ways that wage inequality could impact the behavior ofan individual. We will refer to the two e¤ects as the response to unequal wages (i.e. ratesof return on e¤ort) and the response to unequal income (i.e. �nal earnings). We mustdi¤erentiate these two similar sounding e¤ects because they turn out to have substantiallydi¤erent e¤ects on behavior.

ui(W;N) = wini � c(ni)� �i�(ni;W )� �i (w1n1; w2n2; :::; wInI) (1)

5Oechssler, Roider, and Schmitz (2009) investigate whether the CRT is a good overall measure of cognitiveability and �nd that it is correlated with other aspects of decision making such as risk and time preferencesas well as likelihood of making certain types of reasoning mistakes. While they do �nd some correlationwith these other elements of decision making, our focus is on using the CRT for the purpose it was designedwhich is to discriminate between impulsive and re�ective decision makers.

6For the CRT the majority of the subjects �nished well before the time limit while for the patternmatching test the time constraint was binding. Since speed was an issue in the main production task thefact that the constraint was binding for the pattern recognition task is not a problem since our goal wasto measure performance under time pressure. For the CRT one could imagine that a time constraint couldgenerate even less re�ective thinking than normal but since the constraint was so rarely even close to bindingthis should not be a problem.

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An individual�s response to unequal wages is represented by the function �(�) which accountsfor the possibility that the individual experiences some additional psychic cost from engagingin a level of e¤ort ni that is associated with wage inequality. The parameter �i � 0 indicatesthe degree to which individual i is concerned about the existence of wage inequality. Theform of �(�) or the magnitude of �i could be constructed to account for many di¤erentaspects of the judgement about the fairness of the wage pro�le and a general model mighttake into account the mechanism delivering the inequality into determining the importanceof its unfairness. For the purposes of constructing an initial model which is as simple aspossible we will assume that �(�) satis�es two properties, �ni = 0 if wi = w and �niwi < 0;which together imply that �ni > 0 if wi < w and �ni < 0 if wi > w. To see the implicationsof these properties we can set �i = 0 and examine the �rst order condition associatedwith the optimization of (1) with respect to ni which is wi = c

0(n�i ) + �i�ni(n

�i ;W ). This

condition simply states that the optimal e¤ort level is found where the wage is equal to themarginal cost of e¤ort. Here the marginal cost is composed of the standard marginal cost,c0; and an additional element that arises due to wage inequality, �ni : Given the propertiesof �ni it should be clear that an individual with a given wage will face higher (lower)marginal costs of e¤ort when facing disadvantageous (advantageous) inequality than whenfacing no inequality. This implies a lower (higher) e¤ort by those facing disadvantageous(advantagenous) inequality than by those who face no wage inequality. Further, these e¤ectsare stronger the farther is wi away from the average wage. For expositional simplicity, wewill refer to the motivations behind these di¤erential responses in e¤ort as �aversion�and�a¢ nity�to wage inequality, respectively. Of course the strength of these two e¤ects neednot be symmetric.

The last term in (1) captures an individual�s response to unequal income. The function (�) is a measure of the level of inequality in �nal income among all the relevant agents and�i � 0 is a parameter indicating the degree to which agent i is averse to this inequality.Again, we could construct a complex function for (�) to account for a number of di¤erentaspects of the e¤ect of income inequality but for the purposes of this exercise we just assumethat (�) is increasing in the variance of the income distribution. The e¤ect of aversion toincome inequality on e¤ort is quite di¤erent from how preferences over wage inequality af-fect e¤ort. The important di¤erence is that a worker�s e¤ort can impact the inequality in�nal income but not wage inequality. Any individual whose earnings are below the aver-age can decrease (�) by increasing their own production and thereby increase their utility,while anyone with above average earnings will do so by decreasing their own production.Consequently, a worker facing disadvantageous inequality will be able to decrease the neg-ative impact on his utility from the presence of inequality in the �nal wealth distributionby increasing his work e¤ort. A worker facing advantageous inequality will do the same bydecreasing her work e¤ort.

The end result is that these two di¤erent ways in which wage inequality could a¤ect util-ity lead to exactly opposite behavioral predictions. The aversion/a¢ nity to wage inequalitycan be thought of as an extension of the model in Torgler, Scha¤ner, Frey, Schmidt, andDulleck (2008) which proposed that for disadvantaged workers the cost of e¤ort is an in-creasing function of the degree of inequality.7 This assumption can be motivated in this

7We also note that the model of the e¤ect of inequality of rewards presented in Hopkins and Kornienko(2009) generates similar predictions for tournament competitions even though it does not directly contain

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context by arguing that a person�s happiness is likely connected to how they see their wagesor general reward to e¤ort relative to others. If an individual perceives others as being un-fairly advantaged compared to themselves then that person may well experience a greaterpsychic cost for a given level of e¤ort than if they perceived their position as being equalto or greater than that of others. The aversion to income inequality element in the abovemodel is a direct extension of standard models of inequality aversion such as those in Fehrand Schmidt (1999) and Bolton and Ockenfels (2000) to this environment. The importantdi¤erence between this environment and the ones for which standard models of inequalityaversion were developed is that the prior models have been most often investigated in con-texts without wealth production. In this context, those prior notions of inequality aversionare then best re�ected in what we have termed aversion to unequal income as that representsan aversion to inequality over �nal wealth allocations as posited in the prior models. It isquite interesting to see that these two di¤erent ways of modeling preferences over inequality,i.e. at the intermediate wage level versus �nal earnings level, which might seem a prioriquite similar lead to divergent predictions. The key reason for that di¤erence is that anindividual can reduce the degree of income inequality through their own actions but theycan not alter the degree of wage inequality.

Since these two e¤ects work in opposite directions it is not possible to separately identifythe magnitude of either in our data. The empirical question we can address is whether or noteither of the forms of preferences over inequality are strong enough in this task to overcomethe other. For convenience we will refer to the predictions based on the assumption thataversion/a¢ nity to wage inequality dominates and so low wage workers exhibit less e¤ort inthe presence of inequality as the Discouragement Hypothesis and the prediction that highwage workers work harder in the presence of inequality as the Encouragement Hypothesis.We will refer to the alternative set of predictions based on the dominance of the aversionto income inequality as the Income Inequality Aversion Hypothesis.8

This structure is also helpful in clarifying the di¤erence between the e¤ects we arediscussing here and the well known gift-exchange e¤ect. The gift-exchange e¤ect (Fehr,Kirchsteiger, and Riedl, 1993) deals with the choice of e¤ort level by agents depending onthe wages (as total �xed earnings) they receive from a principal. A gift-exchange e¤ectoccurs when an employer gives the worker a high �xed wage and the worker respondswith high e¤ort as a reciprocal response to that gift. If a worker exerts low e¤ort it isconsidered to be a way of punishing an employer who has given the worker a payment theworker perceives to be too low. This punishment is costly to the principal but since theagent receives a �xed wage, it is not costly to the agent. There are many reasons why theencouragement/discouragement hypotheses we describe here are substantially di¤erent andshould not be confused with the gift-exchange e¤ect. The most important is that there isno principal-agent structure in our design and the only person hurt when one of our workers

an inequality aversion component.8We note that the information structure in the experiment may be expected to minimize the impact of

the Income Inequality Aversion e¤ect since we did not report total income of other subjects, only their wagerates. This was intentional as our goal was to determine if subjects would respond to only the wage rate andby eliminating this additional information it increases our ability to attribute any di¤erences in behavior tothis one stimulus. Subjects could certainly envision the e¤ect on total earnings anyway and respond to thatexpectation but this is certainly a weaker e¤ect. Since our goal though was not to understand how subjectsmight respond to the total earnings though, we do not view this as a substantial problem.

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decreases his e¤ort in response to a low wage or the existence of inequality is himself asthe lower e¤ort level yields lower total earnings to him. Thus the mechanism that mightproduce the encouragement/discouragement response will be very di¤erent from the typicalgift-exchange e¤ect. Further, if a subject seeks to punish someone for receiving an unfairlylow wage, then the only option for punhishment is the experimenter who assigned the wageto him. The only avenue for punishing would then be to work harder to extract more moneyfrom the experimenter. Thus if the inequality of wages leads to a punishment act by thesubjects then it would work against the Discouragement Hypothesis.

There are two recent papers that address issues related to what we investigate. Charnessand Kuhn (2007) is a study based on the gift exchange game that involves a principalcontracting with multiple agents and the authors include treatments to determine whetheror not making the potentially unequal wages public a¤ects e¤ort levels of the agents. Theauthors observe no di¤erences in e¤ort levels between those treatments. However, the lackof a di¤erence here is not necessarily conclusive in regard to the hypotheses we propose.In that study, the wages of the workers were set endogenously by a subject in the roleof employer and the workers were heterogeneous with respect to the earnings their e¤ortgenerated to the employer. Therefore, if another subject were receiving a higher wage, thatmight have been justi�ed based on the di¤erential earnings generated to the employer. Incontrast, there is no employer-employee interaction in our design and any inequality in wagerates that our subjects observe is the result of a pure randomization, which is likely to leadsome of our subjects to perceive the wage inequality as �unfair.� If we �nd evidence fordiscouragement e¤ect, then it will be an indication that the reason for the inequality, notsimply the existence of inequality, is likely to be important to the judgement of unfairness.9

A study closer to our design is Burchett and Willoughby (2004) which presents datafrom a di¤erent experiment which also tests whether or not publicly announced and di¤erentcompensation rates matter. The authors had subjects engage in a real e¤ort task and thesubjects received randomly assigned wage structures for performing the same task. Whilethe researchers found clear evidence that public knowledge of the compensation schemes hadan impact on e¤ort, it is not certain to what the impacts can be attributed. The confoundis due to the fact that some of the subjects received �xed wages while others received piecerate wages which causes any judgement of unfairly unequal compensation among the piecerate earners to be unclear.

With a few simple extensions, this model can provide two additional hypotheses. The�rst concerns the e¤ect of the di¤erential group sizes across treatments. Our intention withthe group size treatments was to provide di¤erent contexts through which subjects mightview the inequality. From the point of view of the low wage subjects, one might think thatif they were almost singled out to be in the minority of the subjects in the experiment toreceive a low wage that this might be viewed as less fair than were they just one amongmany who received the low wage. In the context of the model above, this set of e¤ects ispredicated on the aversion to wage inequality dominating the aversion to income inequality.Based on the assumptions made on �(�); in particular the assumption that �niwi < 0; ifthere are a minority of low wage subjects in a group then the average wage in the group

9There is a growing literature on this issue of the perceived fairness of di¤erent allocation procedures andsee, e.g. Bolton, Brandts, and Ockenfels (2005), Karni, Salmon, and Sopher (2008), and Trautmann (2009)for details.

10

will be relatively high and so this should lead to a higher psychic cost of e¤ort for thelow wage earners due to the inequality than when the majority of the subjects possessthe low wage since the average wage will be lower and closer to their own wage. For thehigh wage earners, their wage is farther above the average when there are a minority ofhigh wage earners as in the Disadvantaged Majority treatment and thus might experiencea stronger encouragement e¤ect in that treatment. This leads to what we will refer to asthe Group Status Hypothesis which involves a prediction that the productivity of the lowwage subjects will be more responsive to the existence of inequality in the DisadvantagedMinority Treatment than the Disadvantaged Majority Treatment while the opposite shouldbe true for the high wage workers.

Our �nal hypothesis is related to the performance on the CRT measure of the degree towhich our subjects engage in re�ective versus impulsive decision making. The tendency of aperson to think deeply about matters related to the experiment is important to the potentialjudgement of whether or not the wage assignment is unfair. The wage rate assignments areunequal which could lead to an initial response by impulsive decision makers of judgingthat inequality to be �unfair.�More re�ective decision makers though might think moredeeply about the procedure used to assign those wage rates, pure randomization, and viewthe procedure itself as fair and then judge the outcome of that procedure to also be fair.The notion that individuals might judge the fairness of a �nal outcome on the basis ofthe procedure which generated it is discussed in detail in Bolton, Brandts, and Ockenfels(2005) in which the authors provide evidence that some individuals will view the outcomeof a procedurally fair process as fair even if the outcome of the process is inherently unfairwhile others will judge the fairness solely on the basis of the outcome itself. Since lookingpast the allocation itself to the process requires a more re�ective thought process, it isa reasonable claim that subjects exhibiting more re�ective decision making tendencies asmeasured by the CRT will be less likely to view the unequal wage allocations as unfair whilethose measured to be more impulsive will be more likely to see the allocation as unfair. Inthe context of the model presented above, the speci�c hypothesis we generate from this isbased on the notion that those classi�ed as more impulsive thinkers by the CRT will bemore likely to judge the wage allocation as unfair which could be seen to either increase �i;the parameter indicating the degree to which an individual is concerned about the existenceof wage inequality or it could e¤ect the shape of �(�): Either is observationally equivalentand leads to what we will refer to as the CRT Hypothesis with the prediction being thatsubjects who score lower on the CRT and are therefore measured to be more impulsiveshould exhibit a stronger discouragement e¤ect than the subjects scoring higher on theCRT.

4 Results

4.1 Data Overview

As an initial look at the data from the experiment, Table 2 displays some raw summary sta-tistics regarding average per round output and average number of times per round workerschose to play TTT by treatment with low wage and high wage workers broken out sepa-rately. At this level of aggregation it appears that the general directional e¤ects predicted

11

Table 2: Summary StatisticsCommon Disadvantaged DisadvantagedWage Minority Majority

Low Wage Workers Output 28:05(8:65)

27:54(8:37)

26:59(8:36)

TTT 1:58(4:62)

1:35(3:95)

1:31(4:06)

Individuals 32 16 48

High Wage Workers Output 26:39(9:25)

27:58(8:16)

28:27(6:56)

TTT 1:49(2:66)

0:99(2:52)

0:43(1:55)

Individuals 16 48 16

Standard errors in parentheses.

by the discouragement and encouragement hypotheses are present in that for low (high)wage workers the average productivity is lower (higher) in the two sessions with inequality.There does not appear to be a substantial impact on productivity due solely to the wagerate which might be unexpected but our chief concern is how subjects respond to inequal-ity, not wage rates alone.10 We can also note that while neither low nor high wage workersplay TTT with great frequency, there is some tendency for low wage workers to play moreoften (though with high variance) and high wage workers to play less when confronted withinequality.

In addition to the basic summary statistics we can examine Figures 1 - 4 for a lookat any di¤erences over time and whether subjects receiving di¤erent scores on the CRTor numeracy measures respond di¤erently to the treatments. Figure 1 shows the averageoutput per round separated out by treatment and by high wage versus low wage earners forthe entire sample while Figure 2 similarly shows the average propensity of subjects to playTTT per round. The �rst characteristic to note in the productivity data is that there is astrong learning trend by the subjects as output increases over time due to subjects gaininggreater facility with the task and perhaps memorizing portions of the code key. Further,we also see that for low wage earners, the increase in productivity appears to be less inthe treatments with inequality than in the control treatment without inequality while thereverse is true for the high wage workers. In examining �gure 2, we see that there is alsoa noticeable increase in the propensity of low wage subjects in the Disadvantaged Minoritytreatment playing TTT over the second half of the experiment which is consistent withtheir drop in productivity in the encoding task.

Figures 3 and 4 display similar looks at the productivity data but with the subjectsseparated into groups by CRT and Numeracy scores. A subject is placed in the Low CRTcategory if he gave 0 correct answers on the CRT instrument. If he had any correct answershe is placed in the High CRT category. Out of our 176 subjects 57 got at least 1 answer

10We note that we have conducted additional sessions with higher wage rates for a related study and itappears that there may be a U-shaped response to the wage rate in our data in which very low and veryhigh wage subjects work hard while intermediate wage subjects may work less though these e¤ects are notstrong.

12

Figure 1: Average production per round.

correct on the CRT and the other 119 had 0 correct answers.11 For Numeracy, we haveput those scoring below the median on that measure in the low category and those abovethe median are in the high category. In examining these �gures we see that of course thesame general learning trend is observed in the di¤erent groups as in the overall sample butthere is a substantial di¤erence between the low and high CRT groups and the low andhigh Numeracy groups in terms of the response to the introduction of inequality. The LowWage-Low CRT/Numeracy groups in the inequality treatments exhibit a more substantialperformance di¤erential relative to the Low Wage - Low CRT/Numeracy subjects in thetreatment without inequality than observed for the overall sample. The Low Wage - HighCRT/Numeracy subjects exhibit either no response or perhaps a response consistent withthe Income Inequality Aversion Hypothesis as their performance increases slightly in thepresence of inequality. This di¤erential response by these di¤erent groups suggests thatdi¤erent groups may well respond di¤erently to inequality based on personal characteristics.We of course can not draw hard conclusions from these visual inspections though so wewill refrain from further discussion of any particular e¤ects until we provide the statisticalanalysis in the next section.

Prior to engaging in the more careful tests of the hypotheses though it is useful to

11We note that this is lower performance than found in Frederick (2005), but in our case this test wasadministered after a long and tedious experiment and so some performance drop is to be expected. Since allwe really wish to do is separate out the most deliberate thinkers from the others, this should not be muchof a problem.

13

Figure 2: Average propensity to play TTT per round.

examine some baseline results on the determinants of productivity that will be importantfor framing the later analysis. Table 3 contains OLS regressions using as the dependentvariable the average output per period of a subject. The dependent variables we use referto characteristics of the individuals including a dummy variable for the wage rate, a dummyvariable for whether or not the subject is in the small group and then a set of demographicand cognitive control measures. We also include a similar set of regressions with the depen-dent variable being the fraction of periods in which a subject chose to play TTT. The onlydata considered in these regressions is derived from subjects in the common wage controltreatments as our goal here is to obtain some baseline measures on the determinants ofoverall performance and do not want the confound with any e¤ects that might be due tothe presence of inequality. The question these regressions are intended to address is whetherany of the demographic and cognitive measures we are using have any substantial impacton productivity or propensity to play TTT. For the cognitive measures we will be usingbinary measures to indicate whether or not a subject has been categorized as a member ofthe low group on each measure. Thus L-CRT is equal to 1 if a subject has been sorted intothe low CRT group and the same for L-Numeracy.

The results from the regressions in Table 3 demonstrate that for the most part, thedemographic and cognitive measures have little impact on the performance of our subjectsin the production task and in their propensity to play TTT.12 There is evidence that

12 In an appendix we have also provided a breakdown of average subject charactaristics across treatmentsalong with a brief analysis to demonstrate that there is little in the way of di¤erences in demographics across

14

Table 3: Determinants of productivity and probability of playing TTT in common wage treatments.Dependent variable:

Average Output Average DTTT(1) (2) (3) (4) (5) (6) (7) (8)

High wage -1.669 -2.270 -1.758 -2.111 0.086 0.068 0.091 0.072(2.066) (2.170) (2.036) (2.157) (0.086) (0.087) (0.087) (0.091)

Small group 3.826** 3.520* 3.315 2.837 -0.125 -0.092 -0.134 -0.101(1.751) (1.915) (1.994) (2.154) (0.080) (0.086) (0.093) (0.105)

L-CRT 1.697 0.502 -0.014 -0.015(1.858) (2.252) (0.079) (0.090)

L-Numeracy -0.747 -1.845 -0.037 -0.035(1.950) (2.203) (0.084) (0.099)

Female 1.534 1.117 0.073 0.072(2.081) (2.420) (0.079) (0.092)

Age 3.430 4.505 -0.105 -0.074(3.229) (3.272) (0.117) (0.131)

Age squared -0.079 -0.101 0.002 0.002(0.062) (0.064) (0.002) (0.003)

NonWhite 1.234 1.369 -0.173** -0.169**(1.795) (1.814) (0.075) (0.078)

Upperclass 0.491 -0.154 -0.118 -0.130(1.934) (2.248) (0.081) (0.085)

Constant 27.098*** -10.852 26.615*** -21.946 0.305*** 1.555 0.335*** 1.233(1.206) (39.301) (2.366) (38.952) (0.053) (1.431) (0.086) (1.545)

Observations 48 48 48 48 48 48 48 48R2 0.084 0.161 0.101 0.175 0.063 0.200 0.068 0.204

Robust standard errors are in parentheses.

*** p<0.01, ** p<0.05, * p<0.1

15

Figure 3: Average production over time by CRT.

NonWhite subjects may have been less likely to play TTT than White subjects but thisdi¤erence had no signi�cant impact on productivity. In particular we note that the CRTand Numeracy variables that we will use to separate subjects according to in subsequentanalysis are both uncorrelated with productivity. This demonstrate that none of thesecharacteristics can be seen as proxies for ability on this speci�c task. To reinforce thispoint for these two key cognitive measures we have constructed two additional measures ofproductivity in this task: Ability A is a binary variable taking a value of 1 if a worker�saverage output is above the median of all low wage workers over the periods 1-3 and AbilityB is that for the period 1. In Table 4, we present the coe¢ cients of correlation betweenthese two measures of ability in this task with the CRT and Numeracy measures. Ourability measures here are restricted to the �rst few periods as this should provide a measureof ability in this task without substantial impact from treatment e¤ects. What we see isthat a subject�s categorization into CRT and Numeracy groups is uncorrelated with eachother and is uncorrelated with these additional productivity measures as well. This �ndingis important as had either of the cognitive measures been correlated with productivity thenwere we to see a greater discouragement e¤ect for Low CRT/Numeracy subjects it wouldnot have been clear if the e¤ect was related to a lack of skill or facility with this task orto the CRT/Numeracy trait. Since productivity is in general not correlated with any ofour cognitive or demographic characteristics this means that this task is well suited to our

treatments.

16

Figure 4: Average production over time by numeracy.

purposes. Further, the lack of correlation between CRT and Numeracy indicates that thesetwo tasks are measuring di¤erent aspects of our subjects.

4.2 E¤ects of Inequality

Due to the nature of the hypothesized e¤ects it would seem reasonable to assume that anydiscouragement e¤ect in particular would take time to develop rather than existing from the�rst period of the experiment. The discouragement e¤ect is predicated on the notion thatsomeone who is faced with a situation in which they are treated unequally will eventuallybe frustrated by this unfair treatment and will respond to that frustration by exerting lessere¤ort. This hypothesized e¤ect may therefore require time to develop. Our experimentswere designed around exactly this possibility. This is why we had subjects produce formultiple periods and why we reminded the subjects of their wage rate as well as the wagerate of the others on every result screen. The experience of exerting e¤ort round afterround yet seeing that others are consistently better rewarded for their e¤ort is exactly thefeedback that one would suspect could lead to the development of a discouragement e¤ect.It is less obvious how this experiment structure would foster or inhibit an encouragemente¤ect, though. That is, any encouragement e¤ect might be more of a response to the initialstimulus and then decay over time as one has acquired substantial enough earnings. Onthe other hand, after seeing the large reward continue round after round this could lead toan increase in the encouragement e¤ect. The key point in either case is that the types of

17

Table 4: Correlation between CRT, Numeracy and the initial performance in theword-encoding task.

L-CRT L-Numeracy Ability A Ability BL-CRT 1L-Numeracy 0.0664 1Ability A 0 -0.107 1Ability B 0.1068 -0.0973 0.7507 1

This table is based on the sample of low wage workers only.

Ability A is a measure of performance based on the average over periods 1�3.

Ability B is a measure of performance based on period 1.

e¤ects that we are investigating here are ones in which time is almost certain to play animportant role. A visual inspection of Figures 1 - 4 will con�rm that in many cases thereappear to be systematic di¤erences in responses to the treatments over time and so ourstatistical analysis will need to take that into account.

We will present a series of regressions to investigate whether or not there are statisti-cally signi�cant treatment e¤ects and also whether they build up over time. To allow forcleaner inference we only want to compare low (high) wage subjects in the relevant commonwage treatment to low (high) wage subjects in the inequality treatments and conduct sep-arate regressions for low and high wage subjects. When we later investigate the treatmente¤ects according to CRT/Numeracy traits, we will conduct separate regressions for eachpopulation so that we compare Low CRT and Low Wage subjects between treatments andthen separately compare High CRT and Low wage subjects in a di¤erent regression. Thefundamental form of all of the regressions will be as follows:

yit = �0 + �1D1i + �2D2i + 0St

+ 1 (D1i � St) + 2 (D2i � St) + �3Periodt +Xi� + ci + "it (2)

where D1i and D2i represent dummy variables for the Disadvantaged Minority and Disad-vantaged Majority treatments, respectively, and St is a dummy variable which is set equalto 1 for the second half of the experiment (periods 7-12). The additional elements, Periodtand Xi; are standard controls where Periodt captures the learning e¤ect over time13 andXi is a vector of control variables while ci is an unobserved individual e¤ect and "it is astandard error term. We can conduct this regression with and without the St terms toexamine how the treatment e¤ects change over time. We also present results from identi-cally speci�ed regressions with DTTT as the dependent variable which is a binary variableindicating whether or not a subject played TTT at least once in a period.

The two base hypotheses underlying this study concern how low wage and high wageworkers alter their productivity in the presence of inequality. Tables 5 and 6 contain the re-gression results indicating how low and high wage earners respond to inequality. Examining

13We note that the learning e¤ect is not quite linear as shown in the �gures. We have conducted theseregressions with dummy variables for each period to allow for a more general detrending of the data but �ndno substantial di¤erences in the results and therefore choose to present the more parsimonious speci�cation.

18

Table 5: Treatment e¤ects from regressions examining response to inequality taking into account di¤erences over time for LowWage workers.

Dependent variable:Output DTTT

(1) (2) (3) (4) (5) (6) (7) (8)Disad Min -0.518 0.750 -0.518 0.751 0.003 -0.115 -0.011 -0.128

(1.741) (1.376) (1.716) (1.426) (0.079) (0.083) (0.073) (0.079)

Disad Maj -1.466 -0.538 -1.771 -0.843 -0.049 -0.073 -0.049 -0.072(1.370) (1.171) (1.302) (1.151) (0.055) (0.069) (0.053) (0.068)

Disad Min*S -2.536� -2.536� 0.234��� 0.234���

(1.373) (1.377) (0.077) (0.078)

Disad Maj*S -1.856� -1.856� 0.047 0.047(1.003) (1.006) (0.068) (0.068)

S -0.316 -0.316 0.049 0.049(0.671) (0.673) (0.064) (0.064)

Controls No No Yes Yes No No Yes YesLinear trend Yes Yes Yes Yes Yes Yes Yes YesObservations 1152 1152 1152 1152 1152 1152 1152 1152Clusters 96 96 96 96 96 96 96 96

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Demographic controls include L-CRT, L-Numeracy, female, age, age squared, NonWhite, and Upperclass.

The estimates in this table are robust to the inclusion of period dummies instead of a linear trend.

19

Table 6: Treatment e¤ects from regressions examining response to inequality taking into account di¤erences over time for HighWage workers.

Dependent variable:Output DTTT

(1) (2) (3) (4) (5) (6) (7) (8)Disad Min 1.193 1.226 0.177 0.210 -0.125 -0.181� -0.073 -0.129

(1.976) (1.637) (1.918) (1.662) (0.083) (0.096) (0.080) (0.099)

Disad Maj 1.880 2.990� 0.791 1.900 -0.198�� -0.281��� -0.147� -0.230��

(2.145) (1.736) (1.910) (1.575) (0.096) (0.107) (0.080) (0.098)

Disad Min*S -0.066 -0.066 0.111 0.111(1.330) (1.335) (0.080) (0.080)

Disad Maj*S -2.219 -2.219 0.167�� 0.167��

(1.485) (1.490) (0.081) (0.082)

S 0.753 0.753 -0.082 -0.082(1.041) (1.045) (0.079) (0.079)

Controls No No Yes Yes No No Yes YesLinear trend Yes Yes Yes Yes Yes Yes Yes YesObservations 960 960 960 960 960 960 960 960Clusters 80 80 80 80 80 80 80 80

Robust standard errors clustered by individual are in parentheses.

*** p<0.01, ** p<0.05, * p<0.1

Demographic controls include L-CRT, L-Numeracy, female, age, age squared, NonWhite, and Upperclass.

The estimates in this table are robust to the inclusion of period dummies instead of a linear trend.

20

these results leads to our �rst two results.

Result 1 (Discouragement Hypothesis) - Workers facing disadvantageousinequality exhibit a larger drop in output in the second half of the experimentthan workers receiving a low wage without the presence of high wage workers.

Result 2 (Encouragement Hypothesis) - Workers facing advantageous in-equality show no sensitivity in their output to the presence or absence of inequal-ity over the entire duration of the experiment.

The support for result 1 is based on the fact that the base treatment dummy variablesin Table 5 are not signi�cant indicating that low wage workers show no signi�cant ini-tial response to the existence of inequality. However the interaction variables between thetreatment e¤ects and the dummy for the second half of the experiment are negative andstatistically signi�cant at the 10% level. This is an indication that there is a signi�cant dis-couragement e¤ect in both treatments but it takes time to develop. For the DisadvantagedMinority treatment, the TTT regressions indicate one reason for the drop in productivityon the encoding task as there is a signi�cant increase in the propensity of the subjects toplay TTT in the second half of the experiment.

Result 2 is supported by the results in Table 6 which shows that both the base treatmentdummies and the interactions with the second half dummy are generally insigni�cant.14 Thebase treatment e¤ects are positive indicating there may be some initial encouragement e¤ectbut it is not strong enough to be robustly signi�cant and the negative values for the changein the second half indicate that any initial encouragement e¤ect may dissipate over timethough this too is insigni�cant.

Our next result relates to a test of the Income Inequality Aversion Hypothesis. Thesupport for this result is obvious since this hypothesis generated predictions exactly oppositeof the �rst two. Thus our third result is of a failure to �nd support for the Income InequalityAversion Hypothesis.

Result 3 (Income Inequality Aversion Hypothesis) - The productivity oflow wage earners declines in the presence of inequality while that of high wageearners increases or is unchanged in contrast to the predictions of the IncomeInequality Aversion hypothesis.

The next hypothesis that we will test is the group status hypothesis which states thatthe productivity response for the low wage workers should be larger in the DisadvantagedMinority treatment than in the Disadvantaged Majority treatment. Since there are nosigni�cant productivity e¤ects for the high wage workers, this hypothesis is not applicableto them but our fourth result is based on testing this hypothesis for the low wage earners.

Result 4 (Group Status Hypothesis) - While the decrease in production inthe second half of the experiment for workers facing disadvantageous inequalityis larger (in absolute value) in the Disadvantaged Minority treatment than the

14The base treatment e¤ect is posisitve and signi�cant for the Disadvantaged Majority treatment but onlyin the regression without demongraphic controls.

21

Disadvantaged Majority treatment, these di¤erences are not statistically signi�-cant.

We do �nd that the predicted ordinal ranking holds in that the decline in productivityin the second half of the experiment is greater in the Disadvantaged Minority than theDisadvantaged Majority treatment but a test to determine if the di¤erence is signi�cant failsto reject the null (p�value=0.604). Consequently we fail to �nd strong evidence in supportof this hypothesis. This indicates the possibility that individuals may judge the fairness ofrelative wages without substantial consideration for the relative sizes of the advantaged anddisadvantaged groups or that our sample size was not large enough to allow us to establishthe signi�cance of the e¤ect.

We now investigate whether we �nd a di¤erential response to inequality based on cog-nitive characteristics as measured by the CRT and Numeracy modules. Our hypothesisrelated to the CRT grouping concerned the response of the Low Wage workers as does ourreason for being interested in the Numeracy score. Given that the �gures above alreadydemonstrated little of interest for the high wage workers, we will omit the regressions datafor the high wage workers to conserve space. Table 7 provides the regression results toexamine if there is a di¤erential response to inequality between Low CRT and High CRTsubjects as well as Low Numeracy and High Numeracy subjects. An important point toremember is that as shown in Table 4, these two cognitive measures are uncorrelated witheach other and with overall performance on this task.

Result 5 (CRT Hypothesis) - Low CRT subjects exhibit a signi�cant dis-couragement e¤ect while High CRT subjects do not.

Result 6 (Numeracy Hypothesis) - Low Numeracy subjects exhibit a sig-ni�cant discouragement e¤ect while High Numeracy subjects do not.

We �nd strong support for the CRT and Numeracy hypotheses in that we �nd a strongdrop in productivity in the second half of the experiments involving inequality for the LowCRT and Low Numeracy subjects but not for the High CRT and High Numeracy subjects.The High CRT subjects exhibit an insigni�cant increase in productivity while the HighNumeracy subjects exhibit an insigni�cant decline in productivity. Consequently it is clearthat we see stronger discouragement among Low CRT and Low Numeracy subjects thanHigh CRT and High Numeracy subjects, at least for the second half of the experiment.

If one accepts the claim that the CRT does measure the degree to which our subjectsengage in re�ective thinking then the di¤erential e¤ect observed between low and highCRT subjects leads to an interesting potential explanation.15 Since it is the more re�ectivethinkers who are more likely to consider the fairness of the allocation procedure in judging

15We do note that since the CRT and Numeracy measures were taken after the main experiment it ispossible that poor performance on them is related to the degree of discouragement a subject experienced inthe experiment. Were that true, then the CRT and Numeracy measures would be correlated with each other.As we demonstrated in Table 4, the two measures are almost completely orthogonal to each other in theoverall sample and the same is true if we consider only the low wage earners in the sessions with inequality(coe¢ cient of correlation = 0.012). The lack of correlation between these two measures should indicate thatthey can not both be a product of the level of discouragement experienced in the main experiment.

22

Table 7: Treatment e¤ects from regressions examining response to inequality taking into account di¤erences over time for LowWage workers separated out by CRT and Numeracy.

Dependent variable:Output DTTT

CRT: Numeracy: CRT: Numeracy:Low High Low High Low High Low High(1) (2) (3) (4) (5) (6) (7) (8)

Disad Min -0.833 4.067 -0.586 2.920 -0.047 -0.372��� -0.092 -0.184(1.652) (2.665) (1.723) (2.192) (0.096) (0.078) (0.100) (0.121)

Disad Maj -1.675 -0.621 -1.239 -0.169 -0.022 -0.154� 0.048 -0.259���

(1.385) (2.519) (1.642) (1.833) (0.094) (0.080) (0.095) (0.085)

Disad Min*S -4.455��� 2.090 -2.811�� -2.333 0.218�� 0.285� 0.113 0.411���

(1.385) (2.663) (1.294) (2.890) (0.091) (0.165) (0.082) (0.144)

Disad Maj*S -3.248��� 0.987 -2.174�� -1.632 0.084 -0.051 -0.038 0.175�

(1.071) (1.908) (1.092) (1.799) (0.088) (0.104) (0.089) (0.102)

S 0.694 -1.995� -0.022 -0.564 0.014 0.125 0.065 0.045(0.795) (1.091) (0.824) (1.031) (0.083) (0.103) (0.077) (0.112)

L-Numeracy Yes Yes No No Yes Yes No NoL-CRT No No Yes Yes No No Yes YesObservations 792 360 708 444 792 360 708 444Clusters 66 30 59 37 66 30 59 37

Robust standard errors clustered by individual are in parentheses.

*** p<0.01, ** p<0.05, * p<0.1

All regressions include a linear trend, female, age, age squared, NonWhite, and Upperclass.

The estimates in this table are robust to the inclusion of period dummies instead of a linear trend.

23

the fairness of the allocation, as did some of the subjects in Bolton, Brandts, and Ockenfels(2005), it seems the explanation for this di¤erential e¤ect is due to the low CRT subjectsbeing more likely to view the di¤erential wage assignment as unfair. This result is quiteuseful in helping to understand how our results may generalize outside of this laboratoryenvironment.

4.3 Inequality and E¢ ciency

The previous section focused on testing the hypotheses regarding the behavioral responsesof individuals to the presence of inequality. One of the reasons that those responses areinteresting is in how those individual behavioral responses aggregate into overall productiv-ity. Due to the fact that we generally �nd support for the discouragement e¤ect and fail to�nd support for the encouragement e¤ect it should be clear that the overall e¤ect we �ndfrom inequality on productivity and e¢ ciency is negative.

To help interpret the magnitude of the e¤ect of inequality on e¢ ciency we can provide afew simple calculations of the e¢ ciency drop implied by the coe¢ cients from the regressions.In the overall sample we �nd that production in the second half of the experiment declinesby 1.9-2.5 encoded strings per round for the low wage subjects. Given that in the CommonWage - Low sessions average productivity over the second half of the experiment was 32.13strings per round per person, the decrease implied by the coe¢ cients represents a 5.9-7.8%drop in productivity. Were we to have found support for the encouragement e¤ect amongthe high wage workers then this drop might have been o¤set by increased productivityamong high wage earners but we found that inequality had a neutral impact on the outputof high wage workers. So the productivity of the high wage subjects does not counteractthe productivity drop by low wage subjects.

In the results from the low CRT subjects we have a reasonable argument that thesesubjects were more likely to see the wage inequality as unfair and since what we really wantto measure is the consequences on e¢ ciency from inequality viewed as unfair then it is inthe results from this sub-sample which might provide a more reliable benchmark for thee¢ ciency consequences of inequality. The coe¢ cients on the two interaction variables forthe low CRT subjects receiving a low wage range from -3.25 to -4.46. In the Common Wage- Low treatment, the subjects in the same low CRT classi�cation produced on average 33.95encodings per period and so those coe¢ cients suggest a 9.6-13.1% drop in productivity. Thelow CRT subjects earning a high wage exhibit no signi�cant response to the inequality sotheir response does not o¤set this productivity decline.

We do want to be clear that we are not proposing that the approximately 10% declinein productivity we �nd among low wage workers be interpreted as a reliable estimate of themagnitude of the discouragement e¤ect that might exist among, for example, members ofa low caste in India. The results from this experiment can certainly not provide an answerthat speci�c or that well calibrated to any speci�c situation. What we claim is that sincewe were able to generate a discouragement e¤ect of non-trivial size in this setting, then itprovides strong support for the claim that there should exist a discouragement e¤ect, forexample, among members of a low caste in India. This is therefore an important issue toconsider in the design of policies aimed at enhancing economic development in countrieswith a substantial amount of discrimination based inequality. Combining this e¤ect with the

24

theoretical work cited in the introduction the indication is that such inequality is likely tobecome persistent and will lead to negative consequences for economic growth and e¢ ciency.

5 Conclusion

The question that motivated this study concerns whether or not individuals who are facedwith unequal earnings opportunities will respond to any perceived unfairness by those re-ceiving lesser opportunities decreasing work e¤ort. We �nd evidence in our overall samplethat while there is no initial response to the inequality, after our subjects have experiencedthe inequality for several rounds those receiving a lower wage begin exerting less e¤ort thantheir counterparts in a control group with no inequality. For the subset of our sample whoare measured to be impulsive decision makers through their score on the CRT, we �nd amuch stronger discouragement e¤ect which is consistent with the claim that those who aremore likely to see the wage allocation as unfair exhibit a stronger discouragement e¤ect.

These results represent clear and compelling evidence that in external situations whenthere are individuals faced with unequal opportunities which they deem unfair that theywill also exhibit lower e¤ort and the consequences of this behavioral response could besubstantial. This discouragement e¤ect could show up not only in on the job work e¤ortbut also in human capital investment and other activities which help a person advanceinto higher earnings groups. If the inequality in opportunity is not transient, then thisdiscouragement e¤ect could grow and combined with the forces described in Mookherjeeand Ray (2003) and related studies can lead to persistent inequality and poverty. Thus thisshort term behavioral e¤ect could have long term consequences for the initial generation ofworkers exhibiting the response as well as their descendents.

At the aggregate level, if there are populations of workers exhibiting lower work e¤ort,investment in human capital and so on then there will certainly be negative impacts on eco-nomic growth and development. In our experiment we found output decreases around 10%and while we will certainly not claim that this number is an accurate estimate of the magni-tude of the discouragement e¤ect in any other situation, it does suggest that the e¤ects willbe of non-trivial magnitude. The reason is that given the setup in this experiment, there isevery reason to suspect that subjects should be immune to a discouragement e¤ect buildingup over such a short time horizon from purely idiosyncratic wage assignment for performinga trivial task. Given the strength of the response that we �nd, it seems reasonable that insituations in which opportunity inequality is permanent and tied to an individual�s race orcaste then a discouragement e¤ect should be even more likely to occur and could well bestronger than what we measure here. Given the long run consequences to the individualsand the aggregate economy, this issue should be of concern to those designing policies tofoster economic growth in countries in which such inequality exists.

An immediate follow-up question to the demonstration of this e¤ect is how robust it isto the inclusion of other elements which exist in labor markets such as the ability to improveone�s wages or general returns on e¤ort. The �rst point in response to that question is thatthe main environments to which our study is meant to apply are situations of ethnic, racial,gender or caste based discrimination in which such inequality is (or as at least is perceived tobe) permanent and outside the control of any single individual to a¤ect. For these situations,the lack of opportunity for the disadvantaged workers to be promoted to the advantaged

25

group is entirely appropriate. Still there will be other related situations in which there maybe some possibility of moving from the disadvantaged to the advantaged group and one mayconsider policies which speci�cally allow that as a means of overcoming the discouragemente¤ect. This leads to a question of how much of an advancement opportunity is necessaryto overcome any discouragement e¤ects. This is not an issue considered in this paper butit is an important question to be investigated in future work.

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Appendix A: Supplementary Tables

Table A: Demographic Characteristics by Treatment and Wage CategoryLow wage workers High wage workers

Common Disad Disad Common Disad DisadWage Min Maj Wage Min Maj

Female 0:41(0:50)

0:38(0:50)

0:52(0:50)

0:63(0:50)

0:38(0:49)

0:50(0:52)

Age 20:38(2:76)

20:25(1:57)

20:13(1:66)

20:06(1:48)

20:38(1:48)

20:13(1:26)

NonWhite 0:44(0:50)

0:31(0:48)

0:42(0:50)

0:38(0:50)

0:58(0:50)

0:25(0:45)

Upperclass 0:56(0:50)

0:50(0:52)

0:58(0:50)

0:56(0:51)

0:56(0:50)

0:56(0:51)

LCRT 0:59(0:50)

0:75(0:45)

0:73(0:45)

0:69(0:48)

0:73(0:45)

0:44(0:51)

LNUM 0:53(0:51)

0:63(0:50)

0:67(0:48)

0:63(0:50)

0:42(0:50)

0:44(0:51)

Obs. 32 16 48 16 48 16

Standard errors in parentheses.

Table B: CRT and Numeracy Characteristics by TreatmentCommon Disadvantaged DisadvantagedWage Minority Majority(1) (2) (3)

Low Wage Workers LCRT 0:59(0:09)

0:75(0:11)

0:73(0:06)

[pA= 0:30] [pB= 0:21]LNUM 0:53

(0:09)0:63(0:13)

0:67(0:07)

[pA= 0:55] [pB= 0:23]Obs. 32 16 48

High Wage Workers LCRT 0:69(0:12)

0:73(0:06)

0:44(0:13)

[pA= 0:75] [pB= 0:16]LNUM 0:63

(0:13)0:42(0:07)

0:44(0:13)

[pA= 0:15] [pB= 0:30]Obs. 16 48 16

Standard errors in parentheses.

pA is the p-value associated with the t-test of the di¤erence in means: H0: (1)-(2)=0, Ha:(1)-(2) 6=0pB is the p-value associated with the t-test of the di¤erence in means: H0: (1)-(3)=0, Ha:(1)-(3) 6=0

29