Statistical Discrimination and Moral Hazard

Transcription

1 Statistical Discrimination and Moral Hazard Saltuk Ozerturk Department of Economics Southern Methodist University March 2015 Abstract This paper studies an agency problem where an employer has to choose between a maority group candidate and a minority one to fill a ob vacancy. The ob performance depends both on the candidate s ability and unobservable effort. The precontracting evaluation generates a more precise information signal for the maority group candidate s ability. I show that the principal can always elicit more effort from the maority candidate. The minority candidate is hired only if he/she can generate a sufficiently superior ability signal than the maority candidate. The analysis relates the extent of bias against the minority candidate to the parameters of the underlying agency problem. The results predict that minorities face less bias in occupations with higher technological uncertainty. Keywords: statistical discrimination, moral hazard, incentive compensation, effort inducement, signal precision. JEL Codes: J71, D86 Associate Professor of Economics, Southern Methodist University, Department of Economics, 3300 Dyer Street, Suite: 301, Dallas, TX. Tel: , Fax: , ozerturk@smu.edu.

2 1 Introduction A common problem in the labor markets of developed countries with ethnically diverse populations is discrimination. According to a report by International Centre for Migration Policy Development in 2003, while high unemployment in the European Union (EU) can be attributed to labor market rigidities, minorities consistently suffer higher unemployment than do nonminority groups. 1 The lack of representation of minorities in the workforce is not unique to EU, but a widespread problem. Large disparities between age, skill and education levels do exist and work against minorities in labor markets. Furthermore, employers might also have an outright preference to hire and fraternize with workers from the same cultural and ethnic background. While comparative disadvantage in education/skill levels and outright preference for discrimination are clearly important factors, an alternative explanation for discrimination is offered by the statistical discrimination literature. Starting with Phelps (1972) and Arrow (1973), the common theme in this literature is that discrimination can emerge as an equilibrium even when groups are ex ante identical and employers have no pyschic preference for either group. 2 This body of work suggests that minorities may lack success in the labor market simply because they convey more noisy signals on their competence levels than maority candidates. The idea is one of statistical inference. Due to lack of a shared cultural background and discourse system, the interaction between the employers and ob candidates of the different groups generates a less accurate assessment of skill levels, and this disparity is sufficient for discrimination to emerge as an equilibrium. This paper contributes to the statistical discrimination literature by introducing moral hazard considerations into a recruitment problem. I describe a model in which an employer (principal) cares not only for the ability level of the worker (agent) but also for the amount of effort that can be elicited from that worker. The employer belongs to the maority group and seeks to choose between two candidates, one from the maority group, and the other from the minority group. As in the statistical discrimination literature, prior to the recruitment decision the interaction between parties generates noisy signals on the ability levels of the two candidates. The information signal for the minority candidate is assumed to be less precise. Different than the previous literature on statistical discrimination, however, the principal has to design a compensation contract to elicit unobservable effort from the candidate, as well as inferring the candidate s ability before making a ob offer. This simple exercise allows me to relate the extent of favoritism that a maority worker enoys to the parameters of the underlying agency problem. 1 See Morgan and Vardy (2009). 2 Section 2 provides a more detailed discussion of this literature. 2

3 The analysis illustrates that in this environment the principal can always elicit more effort from the maority candidate. I refer to this difference in effort levels that can be elicited as the "effort gap". This gap arises simply because the information signal on the maority candidate s ability is more precise. Since the uncertainty related to a candidate s ability adds to the riskiness of final performance and because the candidates are risk averse, the principal can offer more high powered performance based incentive compensation to the maority candidate. Hence, risk sharing with the maority candidate is easier and more effort can be elicited from the maority candidate. This key observation implies that the minority candidate is only recruited if he/she can make up for this effort gap by generating a sufficiently superior ability signal than the maority candidate in the pre-contracting stage. In other words, the maority candidate enoys a favoritism although the two candidates are ex ante identical. I show that the magnitude of this favoritism is decreasing in the degree of technological uncertainty common to both candidates and also decreasing in the candidates risk aversion. These results add to the existing literature on statistical discrimination as the favoritism displayed towards the maority candidate arises due to the effort inducement problem. The paper relates the extent of statistical discrimination in the recruitment process to the severity of the agency problem. For example, when the effort inducement problem becomes more severe due to higher technological uncertainty, the maority candidate enoys less favoritism. Accordingly, one novel testable implication that emerges from the analysis is that minority candidates face less discrimination in riskier and innovative occupations where output is a noisier signal of their effort. The plan of the paper is as follows. The next section discusses the related literature. Section 3 introduces the model. Section 4 presents the analysis and the results. Section 5 concludes. 2 Related Literature A large literature on the economics of discrimination attempts to explain why minorities are under-represented in the workforce and receive lower wages. 3 In particular, the literature on statistical discrimination proposes that discrimination can emerge in equilibrium even when groups are ex ante identical in terms of skill distribution and employers have no inherent preference for either group. In the seminal papers by Phelps (1972) and Arrow (1973), different racial and gender groups do not differ in average productivity, but minorities face discrimination because they have less precise produc- 3 See Arrow (1998) for an overview of the literature. 3

4 tivity signals. Coate and Loury (1993) expand upon this theory and show that employer beliefs may lead minorities being disproportionately assigned to low skill obs. They also analyze whether affirmative action policies will eliminate statistical discrimination. Moro and Norman (2004) allow for endogenous wages and analyze affirmative action in a competitive market. The most closely related papers to this one are work by Cornell and Welch (1996) and Morgan and Vardy (2009). These papers also argue that the ability signals for minorities might be less precise due to differences in culture and discourse systems, and provide search-theoretic explanations for discrimination in the workplace. Cornell and Welch (1996) employ a fixed sample search model and show that discrimination is more likely to occur in sectors in which underlying worker skill is important but difficult to observe. Morgan and Vardy (2009) show that when employers are selective, that is, if they only hire a candidate when the ex-post probability of competence is higher than the prior estimate, then the equilibrium always entails underrepresentation of minorities. the other hand, if employers are "unselective" and hire a candidate as long as he/she does not disappoint too much during the evaluation stage, then ninorities are overrepresented. They also link the selectiveness of the recruitment regime and the resulting workplace diversity to firing costs and the business cycle. Unlike my paper, these two papers do not address moral hazard considerations. On Their discrimination results are driven due to the way the employer updates his/her beliefs given the different precision in the candidates ability signals. In this paper, however, the mechanism through which discrimination emerges is the effect of pre-contracting ability signal on the subsequent effort inducement problem of the employer. In that respect, the novelty of this paper is the way it relates the extent of statistical discrimination in the recruitment process to the severity of the underlying agency problem. 4 In two other related papers, Fryer (2007) and Berk (2008) present dynamic models of statistical discrimination. Fryer (2007) suggests that employers might be pessimistic about a group in general, but optimistic about the succesful members of that group which he refers to as "belief flipping". He shows that even though minority members face discrimination initially, some may be ex post better off because of it after surviving the initial discrimination. Berk (2008) illustrates that equally skilled workers from different groups may have different chances of making it to the top obs in the economy even under a non-discriminatory promotion policy. These papers, however, do not focus on a moral hazard problem which is the focus of my paper. 4 I discuss this issue further at the end of Section 4. 4

5 3 The Model The model considers a principal who seeks to hire one worker/agent to fill a ob vacancy. There are two candidates that I refer to as A and B. The principal and Candidate A are both members of the maority culture, whereas Candidate B belongs to the minority culture. The cultural background of both candidates is fully observable. The model is detailed below The Agency Problem: The specification of the output technology and the informational assumptions follow from the additive-normal framework of Holmstrom (1999). If hired, candidate {A, B} expends costly effort e 0 to produce a stochastic output x according to a technology x = e + θ + ε (1) where θ is candidate s uncertain ability, and ε is a technology shock common to both candidates. Furthermore, ε and θ are independent. The output x is observable to all parties. Both candidates have the same cost of effort described by the functional form c(e ) = e 2 /2. I employ the standard normality assumptions and assume that ε N(0, σε 2 ) and θ N( θ, σθ 2 ). (2) Hence, the prior estimate of ability is the same for both candidates. A candidate s ability is unknown also by the candidate, and candidate has no superior information on θ. The agency problem arises because regardless of the candidate employed, the effort choice e is not observable by the principal. The principal can only provide effort incentives by tying the candidate s compensation to the observable output. This incentive contract is described next Compensation Contract: I follow the standard CARA-normal agency model and restrict attention to linear compensation schemes. In particular, if candidate {A, B} is employed, the principal offers that candidate a linear contract f + b x where f is a fixed payment and b is the candidate s share of output. Both candidates have the same CARA preferences described by U( w ) exp( a w ) over final wealth w with the common CARA coefficient a > 0. Both candidates also have the same certainty equivalent outside option that I normalize to zero. Given the normality assumptions and the CARA preferences, if employed, candidate 5

6 {A, B} chooses e to maximize the mean-variance obective function 5 E[ w ] a 2 Var[ w ] (3) where the final wealth distribution is given by w = f + b x c(e ). (4) Information Signal on Ability: Prior to the recruitment decision, the principal s interaction with the candidates generate a pair of publicly observable and noisy information signals s on the candidates ability levels where θ = s + δ for {A, B}. The particular signal realization s and its precision τ are also observable by candidate. In the above specification, the noise term δ is distributed with δ N(0, τ 1 ) for {A, B}. I refer to τ as the precision of the ability signal observed for candidate. Furthermore, as in Grossman and Stiglitz (1980), I impose the following restrictions: E[ s δ ] = 0 (A1) Var[ θ s ] = τ 1. (A2) Given (A1)-(A2), the principal and candidate update their beliefs on θ. The posterior distribution of candidate s ability conditional on s is given by ( θ s ) N(s, τ 1 ) for {A, B}. (5) The pre-contracting evaluation of the candidate s ability in this model can be thought as a short internship, a trial period or residency program during which all involved parties receive further information on the extent that the candidates skill set matches with the work environment in question. For example, most law firms have one-year "opportunity associate programs" during which recent law school graduates work for the firm as trainees. 6 Similarly, hospitals offer residency programs for new medical 5 This follows because when a random variable X is normally distributed with X N(µ, σ 2 ), the moment generating function (see Hogg and Craig (1978)) is given by M(t) = E[exp(t X)] = exp(tµ + t2 σ 2 2 ) 6 See the Forbes article "The Millennial Lawyer And BigLaw Hunger Games" by Parnell (2013). 6

7 school graduates at the end of which they decide whether or not to offer a permanent position. Alternatively, the model can be interpreted as a model of promotion. Crucially for my purposes in this paper, I follow Morgan and Vardy (2009) and Cornell and Welch (1996) and assume that the information signal for the maority candidate A is more precise and hence we have τ A > τ B. (6) This key assumption is based on the idea that the interaction with a candidate produces a less noisy signal when he or she is from a similar "cultural background". As in those two papers, cultural background here should be understood broadly to include discourse systems, ethnic background, schooling, etc. 7 To summarize, in the above framework the employer has no inherent taste for discrimination. The ability levels of the two candidates have the same prior distribution. In terms of the severity of the agency problem, both candidates face the same technology shock, have the same productivity of effort, risk preferences and effort cost. The only difference between the two candidates is the precision of the information signal that the pre-contracting stage interaction generates on their ability levels. Since the principal and candidate A have the same cultural background, the information signal on candidate A s ability level is assumed to be more precise. Sequence of Events: For convenience, the sequence of events in the model is summarized below. Date 0: The pre-contracting interaction between the principal and the candidates generate a pair of publicly observable information signals on the candidates ability levels. Date 1: The principal decides which candidate to recruit and sets a compensation contract. Date 2: The candidate employed chooses effort given the pre-contract ability signal and the compensation contract. Date 3: Output is realized and the compensation contract is executed. 7 Language based theories of discrimination also suggest that "cultural bias" in ob assigments can also arise when communication between workers has efficiency implications (see Lang (1986)). 7

8 4 Analysis Optimal Effort: The analysis first describes the principal s optimal contract problem and determines the effort levels that the principal can optimally elicit from each candidate. Given an ability signal s for candidate {A, B}, the principal sets a compensation contract ( f, b ) to maximize the expected output net of the employed candidate s compensation. Using the definition of the candidate s final wealth distribution w in (4), one can formally state the principal s problem as choosing ( f, b ) to maximize E[(1 b ) x (e ) s ] f subect to E[b x (e ) + f s ] a 2 Var[b x (e ) s ] c(e ) 0 (7) e arg max E[b x (e ) + f s ] a 2 Var[b x (e ) + f s ] c(e ) (8) In the above formulation, the inequality in (7) stands for the employed candidates s participation constraint and (8) describes the candidate s optimal effort decision. Using the output technology in (1) and conditioning on a signal realization s, the optimal effort problem in (8) becomes and yields e = b. e arg max b (e + s ) + f e2 2 a ( ) 2 b (τ σε 2 ) In equilibrium, the agent s participation constraint in (7) holds as an equality. After solving for f using the binding participation constraint and substituting for e = b, one can rewrite the principal s problem as choosing b to maximize E[(1 b ) x (e ) s ] f = b + s a 2 ( b ) 2 (τ 1 + σ 2 ε ) (b ) 2 2 (9) By maximizing (9), one finds the agent s optimal output share and effort as e = b = a(σ 2 ε + τ 1 ) (10) Since τ A < τ B, the following key observation follows from (10). Proposition 1 The principal can always elicit more effort from the maority candidate A, that is, e A > e B 8

9 The above result follows from the well known trade-off between risk and incentives in designing incentive compensation contracts. 8 The key channel is the manner that the precision of the information signal on a candidate s ability affects this trade-off. Increasing the agent s share b from final output improves effort incentives, but it also increases the risk averse agent s disutility from risk given by the term (a/2) ( b ) 2 (τ 1 + σ 2 ε ) in (9). Since the agent s uncertain ability is part of this risk, a more precise signal on ability reduces the riskiness of a given compensation contract and hence lowers the principal s cost of inducing effort. As a result, the principal can always provide steeper incentives (higher b ) to the candidate with a more precise ability signal (higher τ ) and elicit more effort. Recruitment Decision: One can now describe the principal s optimal recruitment decision. To do so, let us define the principal s net expected payoff V (s ) from contracting with candidate {A, B} upon observing an ability signal s. This net expected payoff is given by V (s ) E[ x (e ) s ] a 2 Var[b x (e ) s ] c(e ) (11) ( ) 2 b [ ] V (s ) = s + b a(σε 2 + τ 1 2 ) + 1 Using the optimal b in (10), one obtains [ ] V (s ) = s a(σε 2 + τ 1 ) (12) The principal recruits the minority candidate B if and only if V B (s B ) > V A (s A ). The following result, which follows from (12), characterizes the principal s optimal recruitment decision. Proposition 2 The principal recruits the minority candidate B if and only if s B s A > s 1 ( ) τ A τ B 2 [τ A + a(τ A σε 2 + 1)] [τ B + a(τ B σε 2 > 0 (13) + 1)] Hence, the minority candidate B is recruited only if B s ability signal s B beats the maority candidate s ability signal s A by at least s. 8 The trade-off between risk and incentives is well understood in the literature on executive compensation. Aggarwal and Samwick (1999) provides empirical support for the key predictions that emerge from this trade-off. 9

10 The above result follows because the principal can always elicit more effort from the maority candidate with an incentive contract. As a result, the minority candidate needs to make up for the effort gap by generating a strictly superior ability signal than the maority candidate. If one interprets the ability signals as the two candidates performances during the pre-contracting evaluation stage, the analysis implies that the minority candidate is always subect to a more strict ability standard than the maority candidate as long as τ A > τ B. Degree of Favoritism: One can refer to s as the favoritism that the principal displays towards the maority candidate. The key reason that favoritism emerges in this model is the difference τ τ A τ B in the precision of ability signals. The magnitude of s is driven by the extent that this precision difference affects the principal s problem of eliciting effort from the candidates. The determinants of s follow from (13) and are described below. Proposition 3 The favoritism s that the principal displays towards the maority candidate is (i) increasing in τ τ A τ B. (ii) decreasing in the degree of common technological uncertainty σε 2. (iii) decreasing in the candidates coefficient of risk aversion a. The intuition for the above comparative statics results is as follows. As the gap τ τ A τ B between the precision of ability signals on the candidates increases, the effort gap e A e B in favor of the maority candidate becomes larger. Hence, the minority candidate needs to overcome a larger favoritism s by genarating a superior ability signal to be hired. Similarly, as the degree of common technological uncertainty σε 2 and/or the candidates aversion to risk a increase, the effort gap e A e B shrinks. Therefore, a larger σε 2 and/or a larger risk aversion coefficient a reduce the favoritism s that the maority candidate enoys. Discussion: The main contribution of this analysis is the link that it provides between the extent of discrimination and the severity of the underlying agency problem. As the degree of technological uncertainty increases, output becomes a more noisy indicator of effort and it becomes harder for the principal to elicit effort from both candidates. In other words, the underlying agency problem becomes more severe. However, this also implies that the maority candidate enoys less of an advantage in the effort inducement problem, and hence receives less favoritism. Accordingly, an empirical prediction of the analysis is that minorities face less bias in occupations with greater technological uncertainty. The mechanism in this paper that gives rise to bias in favor of the maority candidate is entirely different from the existing models of statistical discrimination. The reason for 10

11 the bias is the way precision of the pre-contacting stage ability signal affect contracting efficiency. The difference τ τ A τ B between the precision of the signals implies that the insurance cost of providing effort incentives to the maority group candidate is lower. A given piece rate b introduces less wealth uncertainty and hence a lower disutility from bearing risk for the maority candidate. As a result, more effort is optimally elicited from the maority candidate. The minority candidate needs to make up for this effort gap by generating a strictly superior ability signal. In other words, bias arises due to the way a more precise ability signal for the maority candidate affects the effort inducement problem. In contrast, the mechanism in the previous papers on statistical discrimination works through the way the employer updates his/her beliefs on ability after receiving a less precise signal on the minority candidate. For example, in Vardy and Morgan (2009) the relative uninformativeness of a minority candidate s ability signal is a disadvantage when the employer is selective since it is much harder to change the employer s prior beliefs with a noisy signal. For the same reason, when the employer is unselective, a less precise ability signal is an advange for the minority worker since it is very unlikely to sufficiently disappoint the employer with a noisy signal. In Cornell and Welch (1996), the information signal is more precise for a maority candidate, and the conditional probability distribution has a greater variance the more accurate this information becomes. Therefore, when a single best candidate is chosen from a fixed sample of candidates, it is more likely that the top applicant comes from the set of apllicants with the widest distribution. In short, unlike this paper, the underlying mechanism is one of statistical inference. 5 Conclusion This paper analyzes an agency framework in which a principal (employer) has to choose between two ob candidates, one from the maority group and the other from a minority group. The two candidates differ only in the precision of the information signal that is generated on their uncertain ability levels during the pre-contracting stage. The signal for the maority candidate is assumed to be more precise. The analysis shows that the principal can always elicit more effort from the maority candidate. Furthermore, the minority candidate is hired only if he/she can generate a sufficiently superior ability signal than the maority candidate. The magnitude of the favoritism that the maority candidate enoys is increasing in the gap between the precision of the ability signals, and decreasing in the technological uncertainty common to both candidates. These re- 11

12 sults contribute to the existing literature on statistical discrimination by introducing an agency framework where the bias favoring the maority candidate is driven not only by inference of ability, but by the different effort levels that the principal can elicit from candidates from different cultural or etnic groups. Hence, the paper provides a novel framework which relates the extent of favoritism to the parameters of the underlying agency problem. A testable implication of the analysis is that minority candidates face less discrimination in riskier occupations. References [1] Aggarwal, R., and Samwick, A., 1999, The other side of the trade-off: The impact of risk on executive compensation, Journal of Political Economy 107, [2] Arrow, K., 1973, The theory of discrimination, In Discrimination in Labor Markets, ed. Orley Ashenfelter and Albert Rees, 3-33, Princeton University Press [3] Arrow, K., 1998, What has economics to say about racial discrimination, Journal of Economic Perspectives 12(22), [4] Berk, D., 2008, Glass ceilings or sticky floors? Statistical discrimination in a dynamic model of hiring an promotion, Economic Journal 118, [5] Coate, S., and Loury, S., 1993, Will affirmative-action policies eliminate negative stereotypes, American Economic Review, 83(5): [6] Cornell, B., and Welch, I., 1996, Culture, information, and screening discrimination, Journal of Political Economy 104(3), [7] Grossman, S., and Stiglitz, J., 1980, On the impossibility of informationally efficient markets, American Economic Review 70, [8] Fryer, R.G., 2007, Belief flipping in a dynamic model of statistical discrimination, Journal of Public Economics 91, [9] Hogg, R., and Craig, A., 1978, Introduction to Mathematical Statistics, Fourth Edition, Macmillan Publishing Co,. New York [10] Holmstrom, B., 1999, Managerial incentive problems: A dynamic perspective, Review of Economic Studies 66(1),

13 [11] International Centre for Migration Policy Development, 2003, Migrants, Minorities and Unemployment: Exclusion, Discrimination and Anti-Discrimination in the 15 Member States of the European Union. Vienna: European Monitoring Centre on Racism and Xenophobia. [12] Lang, K., 1986, A language theory of discrimination, Quarterly Journal of Economics 101(2), [13] Morgan, J., and Vardy, F., 2009, Diversity in the workplace, American Economic Review 99(1), [14] Moro, A., and Norman, P., 2004, A general equilibrium model of statistical discrimination, Journal of Economic Theory 114(1), [15] Parnell, D., The Millennial Lawyer And BigLaw Hunger Games, Forbes Magazine, October [16] Phelps, E.S., 1972, The statistical theory of racism and sexism, American Economic Review 62(4),