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Risk and Discrimination

Josh Ederington, Jenny Minier and C. Jill Stowe

Abstract

In the traditional Becker model of employer discrimination, discriminatory behavior arises from a utility-maximizing owner who balances firm profits against the disutility of hiring workers from the disadvantaged demographic group. However, in the modern firm, many human resource decisions are made by agents of the owner (managers) whose actions may not reflect the preferences of even profit-maximizing owners. We present a principal-agent model of discrimination with a profit-maximizing owner and a gender-discriminating manager and show that managerial discrimination is increasing with the degree of risk in the firm’s revenue stream. Empirical tests using a Colombian plant-level dataset support a prediction of our model that female workers should be under-represented in more revenue volatile firms and industries.

Acknowledgements

We are grateful to Ken Troske, two anonymous referees and seminar participants at the Unversité Libre de Bruxelles for many comments and suggestions, as well as to Mark Roberts for making the Colombian manufacturing data available to us.

Appendix

A

A.1 Hiring Model

As an application, consider the case where the principal (the owner) assigns the task of interviewing and hiring workers to the agent (upper management). Initially, the firm has no workers other than the agent. Each period, the agent is faced with an exogenous pool of applicants consisting of im male applicants and if female applicants. The profit πi=riwi earned for the principal by any worker, i, (male or female) is the result of an iid draw from a uniform distribution with support [πL,πH] where ri is the amount of revenue generated by the agent while wi is the agent’s wage demand.[25] The agent observes each applicant’s expected profitability draw before making the hiring decision.

The agent chooses whether or not to hire each applicant to maximize his expected utility. The agent has exponential utility u(x)=exp(rx), where x is the agent’s net wage and r > 0 is the agent’s coefficient of absolute risk aversion. The net wage is determined by x=wα(f). The variable w is the wage paid to the agent by the principal. The number of female applicants hired by the agent is denoted by f, and α(f) represents the agent’s taste for discrimination, or the disutility from having more female workers in the firm. Purely for tractability, we assume that α(f) = αf, where α > 0.

The principal wants to incentivise the agent to hire profitable workers, and so the wage paid to the agent, w=s+bR consists of both a salary, s, and a piece rate component, b. The principal will choose s and b to maximize expected profit.

Since the agent is discriminatory, he faces a tradeoff. Rather than hiring to maximize his expected wage, he prefers to hire fewer female workers, even if they exhibit higher expected profitability than male applicants, in order to decrease the number of female workers. However, he may be unwilling to pass up too many high-productivity females, since this would reduce his wage more significantly. Thus, we model the agents decision as choosing minimum productivity cut-offs for both male (πm) and female applicants (πf) such that he hires male applicants as long as ππm (which happens with probability πHπmπHπL), and female applicants as long as ππf (which happens with probability πHπfπHπL).

In this case, the expected (realized) profitability to the firm of a female-applicant is:

E[πf]=πHπfπHπLπH+πf2

with the expected profitability of a male applicant (E[πm]) being defined symmetrically (i.e. the product of the probability the applicant is at least the minimum type and the expected profitability of the applicant conditional on at least being the minimum type). While the variance of these profits is given by:[26]

Var[πf]=4(πH3πf3)12(πHπL)3(πH+πf)2(πHπf)212(πHπL)2

Thus, the central limit theorem suggests that firm revenue can be approximated by R=y(πm,πf))+ε, where y(πm,πf)=imE[πm]+ifE[πf] is the total expected profit from all the workers and ɛ is an idiosyncratic shock drawn from a normal distribution ϕ(ɛ)with zero mean and variance σ2=imVar[πm]++ifVar[πf]. The principal’s profit, then, can be represented by Rw, where w is the wage paid to the agent. A complication arises from the fact that variance of firm profits is also affected by the agent’s decisions (i.e. the choice of the profitability cut-offs for applicants). To solve the model, we impose the assumption that the affect of the agent’s decisions on the variance of firm profits is de minimus and thus is ignored by the agent in making his decisions.[27]

Since the expected number of females hired is f = if(πHπfπHπL), the agent’s expected utility is given by

(8)εexprs+b(y+εαifπHπfπHπLϕ(ε)dε.

We first maximize (8) wrt πm and πf.

(9)EUπm=byπm=0
(10)EUπf=byπfαfπf=0.

From (9), we find

(11)πm=0.

From (10), we have

(12)πf=αb.

Since b > 0, πf>πm. Furthermore, the second-order conditions are satisfied so that πf and πm are interior solutions. Thus, the agent hires a male as long as he is a non-negative profit type, whereas a hired female must earn a strictly positive profit for the principal. In addition, in (12), it is clear that the agent acts less discriminatory (πf decreases) as the principal offers a higher piece rate (b) and acts more discriminatory as the marginal disutility of hiring a female (α) increases.

The above model makes clear that we are only modeling a link between incentive contracts and employment discrimination in which discrimination results in potentially profitable hiring of some female workers (for both the worker and the firm) not occurring. This is due to the structure of the model in which the worker makes a take-it-or-leave-it wage offer and the only decision by the manager is the hiring decision. Alternatively, one could consider a model of wage discrimination in which the worker and manager engage in wage bargaining and the manager systemically makes lower offers (or bargains harder) with female potential workers. What is interesting is that, to the extent that the manager can successfully hire female workers for lower wages, such wage discrimination would not necessarily be deterred by incentive contracts as it would result in higher profits for the firm. Indeed, this behavior (lower offers to female workers) would only be discouraged to the extent that it resulted in potentially profitable female workers not accepting the position (i.e. to the extent that it resulted in lower than optimal female-shares of the labor force). Thus, we see our model being more about employment discrimination than wage discrimination.

The agent’s certainty equivalent (CE) is the wage received less the disutility from hiring females, and the cost of bearing risk:

(13)CE=s+byαifπHαbπHπL12rb2σ2.

The principal’s expected profit is (1b)ys. Since the principal has full bargaining power, maximizing profit is equivalent to maximizing efficiency, or total surplus, which is the firm’s expected profit less the agent’s CE:

TS=yαifπHαbπHπL12rb2σ2.

Substituting for y, total surplus is:

(14)TS=imπH2+if(πH2(αb)2)2αif(πHαb)2(πHπL)12rb2σ2.

The principal chooses b to maximize (14). The optimal piece rate is the value of b for which

(15)ifα2(πHπL)[1b]rσ2b4=0.

An interior solution is ensured because the necessary second order condition is satisfied:

(16)ifα2(πHπL)4b3rσ2<0.

The optimal salary component of the wage, s, is chosen to satisfy the agent’s participation constraint determined by setting his CE as defined in (13) equal to zero.

Total differentiation of (15) with respect to b and σ2 gives

(17)dbdσ2=rb4ifα2(πHπL)4b3rσ2<0.

The numerator of (17) is positive, and the denominator is negative by (16). Consequently, we find that an increase in risk (σ2) results in a smaller piece rate. From (12) this implies that:

(18)dπfdσ2>0.

Hence, an increase in risk (σ2) ultimately results in greater discrimination (an increase in πf. Intuitively, an environment with greater profit uncertainty provides discriminating managers less incentive to moderate their tendency to discriminate. In contrast, when the signal about a worker’s productivity has less noise, then a discriminating manager has more incentive to reduce discrimination (to increase his own wage).

A.2 Data

All data are taken from a plant-level dataset produced from the Colombian Manufacturing census by DANE (National Statistical Institute) for the years 1977 through 1991. Starting in 1983, the census covers industrial production for plants with more than 10 employees. Our empirics are a cross-section of plants operating in 1991, although earlier years are used to construct some of the variables, as noted below. For a thorough description of this dataset see Roberts (1996).

All variables are measured at the plant level unless otherwise noted.

Female share: female share of workers.

Productivity: value added for the plant divided by total employment.

Employment: total employment.

Salary: total payroll divided by total employment.

Wage: Average unskilled wage is calculated by total salary and benefits of unskilled workers divided by total number of unskilled workers.

Firm Age: years since the plant’s establishment until 1984.

Exports: plant exports scaled by total sales.

Skill Ratio: share of skilled employment in skilled and unskilled employment.

Capital/Labor Ratio: ratio of fixed capital to total employment. A small number of plants with fixed capital reported as zero are dropped.

Energy Use: one plus the ratio of energy consumed to total employment.

Office Equipment: office equipment’s share of total capital equipment.

Variability: Revenue: the variance of total revenue scaled by its mean for the plant over 1986–90, for all plants with at least two years of non-missing data.

Variability: Net income: the variance of net income scaled by its mean for the plant over 1986–90, for all plants with at least two years of non-missing data.

Variability: Profit: the variance of profit scaled by its mean for the plant over 1986–90, for all plants with at least two years of non-missing data.

Market Share Correlation: the correlation between plants’ market share in 1984 and market share in 1991, at the 4-digit industry level. Any plant present in only one year is treated as having a market share of zero in the missing year.

Absolute Value of Market Share Changes: the sum of the absolute value of changes in market share from 1984 to 1991, at the 4-digit industry level. Any plant present in one year is treated as having a market share of zero in the missing year.

Mean, Revenue Variability: the mean of the revenue variability measure for the 4-digit industry.

Type of Enterprise: The data set classifies plants by 10 different enterprise types. We omit firms classified as collectives, cooperatives, official entities, and religious communities (overall, these comprise less than 2 % of the sample). We construct dummy variables for Corporations (this includes plants classified as corporations, de facto corporations, and joint stock companies), Proprietorships, and Partnerships (including limited partnerships and joint partnerships).

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Published Online: 2018-12-11

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