New evidence on workers' willingness to pay for job attributes.

• Author: McCue, Kristin

1. Introduction

   This paper reports the results of an unorthodox approach to measuring workers' willingness to pay for job attributes. For a wide variety of reasons, researchers have long been interested in attaching monetary units to the values that workers associate with the nonwage portions of their work. With some exceptions, these studies have generally come to the conclusion that nonwage job attributes are of relatively minor importance to workers.(1)

   The bulk of this work has relied on the theory of compensating wage differentials. The attraction of this theory is that it holds the promise of inferring workers' willingness to pay by observing wage differences across jobs having different attributes.(2) Unfortunately, empirical application of this theory has been plagued by a number of anomalies. Surveying the literature over a decade ago, Brown wrote "The overall pattern that emerges . . . is one of mixed results: some clear support for the theory but an uncomfortable number of exceptions [3, 118]." Dickens [6] echoes this evaluation in a more recent survey.(3)

   There are no lack of explanations for this. Hypotheses range from unobserved heterogeneity [10; 16], omitted variables [23], measurement error [7], and misspecification [17]. Several recent studies have shown just how severe these problems can be in real labor market data. Hwang, Reed, and Hubbard [16] decompose the bias associated with unobserved worker productivity into three components. Using reasonable estimates for the sizes of these components, they show that estimates of workers' willingness to pay for job attributes based on compensating wage studies are likely to be downwardly biased by 50 percent or more, even resulting in wrong-signed estimates. In another paper, Hwang, Mortenson, and Reed [17] establish that unobserved firm productivity also generates a bias in the downward direction when estimates of workers' willingness to pay are based upon compensating wage models. Gronberg and Reed [11] demonstrate that this latter source of bias can also be quantitatively large in actual labor market data. These studies raise the possibility that workers attach greater value to nonwage job attributes than is measured by the compensating wages approach.

   The shortcomings of the conventional methodology underscore the importance of alternative approaches to valuing workers' willingness to pay for job attributes. Accordingly, this paper turns to a series of questions in the National Longitudinal Survey, Youth Cohort (NLSY) in which workers were asked to report the minimum wage they would have to receive to accept various types of work. Like others, we have our reservations about data based on what workers say, as opposed to the job choices workers make. Nevertheless, there are mitigating factors which recommend this particular data set.

   First, the NLSY surveyed all 12686 individuals about their willingness to accept a variety of jobs. This is a very large sample. It is rare for willingness to pay studies to have more than one or two thousand observations, most have only several hundred. Second, a number of other researchers have used these self-reported values from the NLSY and found them useful. These include Borus [2] and Holzer [15].(4) And third, each worker in the NLSY survey supplied reservation wage data for a number of different jobs. Thus, one can look at differences in reservations wages for different kinds of work for the same worker. This eliminates the unobserved heterogeneity problem which is so problematic in conventional compensating wage studies. In summary, given the unsettled state of the literature on workers' willingness to pay for job attributes, we believe that the data here provide a useful alternative approach to this subject.

   Two questions form the core of our analysis. First, how large are the monetary premia/penalties that workers attach to differences in alternative kinds of work? And second, how much taste heterogeneity exists across workers in their job evaluations? We proceed as follows. Section II uses the theory of job search to derive the relationship between reservation wages and the monetary value of nonwage job attributes. Section III presents our methodology for using the categorical data of the NLSY to make inferences about continuous reservation wage data. Section IV discusses the data. Section V investigates the reliability of the self-reported reservation wages. Section VI discusses our empirical findings and section VII concludes.

2. Theory

   Khandker [18] develops a model of job search where jobs differ in their nonwage characteristics. Suppose a worker follows an optimal sequential search strategy with the purpose of maximizing her expected lifetime utility. Suppose further that there are J different types of jobs, where each type is defined by its nonwage attributes. Let the instantaneous utility of the worker be given by

   u = {b, if searching {[w.sub.j] + [v.sub.j], if working in a Type j job; j = 1, 2, . . ., J;

   where b is the value of leisure net of search cost, [w.sub.j] is the wage paid in a Type j job, and [v.sub.j] is a parameter that imputes a dollar value to the utility associated with the nonwage attributes in a Type j job. If one defines [Rho] as the interest rate, [V.sup.u] as the (discounted present) value of unemployment, and [r.sub.j] as the jth reservation wage, then Khandker [18] shows that the equilibrium reservation wage for a Type j job is given by

   [Mathematical Expression Omitted];

   where [([Rho][V.sup.u]).sup.*] is uniquely determined by the parameters of the J wage distributions, the vector of separation rates for the J job types, the arrival rate of job offers, the probabilities of the different kinds of jobs, the interest rate ([Rho]), the value of leisure net of search costs (b), and the vector of nonwage parameters (the [v.sub.j]'s). It follows that

   [Mathematical Expression Omitted].

   The importance of equation (3) is that it states that the (negative of the) difference in reservation wages between jobs j and k provides a monetary value of the difference in utilities that the worker receives from the nonwage components of work at those jobs. For example, if a worker revealed that her reservation wage for working at a hamburger place was $3.85/hour, while her reservation wage for washing dishes was $4.45/hour, we would know that she viewed working at a hamburger place 60 cents/hour more attractive than washing dishes. The remainder of this paper is concerned with estimating differences in reservation wages across job categories for the workers in this data set.

3. Predicting Job- and Worker-Specific Reservation Wages

   The reservation wage data used in this study derives from a series of questions contained in the 1979 NLSY survey.(5) Each individual in that survey was asked whether they would accept a given type of work if it offered $2.50 an hour in pay. They responded either positively or negatively. If negatively, they were asked if they would accept it at $3.50 an hour. If they once again said no, they were asked one last time about accepting the job at $5.00 an hour. Thus, for any given job, each respondent in the NLSY identified their reservation wage as belonging to one of four categories: (1) less than $2.50/hour, (2) between $2.50 and $3.50/hour, (3) between $3.50 and $5.00/hour, and (4) greater than $5.00/hour.

   This procedure was used to acquire reservation wage information for six different jobs: (i) "working at a check-out counter in a supermarket" (SUPRMRKT), (ii) "working away from home in a national forest or park" (PARKS), (iii) "working at a hamburger place" (BURGERS), (iv) "washing dishes" (DISHES), (v) "working as a cleaning person" (CLEANING), and (vi) "working cleaning up neighborhoods" (NEIGH).(6) A desirable feature of the data set is that all six jobs are narrowly defined and would be reasonably well-known to the NLSY respondents.

   Given that the reservation wage data is categorical in nature, we are left with the task of using this information to estimate continuous differences in reservation wages across job types as in equation (3). Accordingly, we estimate categorical log wage equations in order to obtain predicted values of the reservation wage for each individual on each job. Let the distribution of reservation wages for individual i at job j be given by

   log [r.sub.ij] = [X[prime].sub.i][[Beta].sub.j] + [[Sigma].sub.j][[Epsilon].sub.ij], (4)

   where [X.sub.i] represents a vector of personal and labor market characteristics; [[Beta].sub.j] is the associated vector of coefficients; and [[Epsilon].sub.ij] is an error term having the logistic distribution with positive scale parameter [[Sigma].sub.j]. The observed categorical data take on the values:

   [C.sub.ij] = {1, if log [r.sub.ij] [less than] log (2.50) {2, if log (2.50) [less than] log [r.sub.ij] [less than] log (3.50) {3, if log (3.50) [less than] log [r.sub.ij] [less than] log (5.00) {4, if log (5.00) [less than] log [r.sub.ij].

   Maximum likelihood estimation of the parameters [[Beta].sub.j] and [[Sigma].sub.j] based on data ([C.sub.ij], [X.sub.i]) for a single job is straightforward.(7) However, if [[Epsilon].sub.ij] and [[Epsilon].sub.ik] are not independent for j [not equal to] k, estimating six independent, categorical log wage equations ignores potentially useful information. For example, if an individual with an above average reservation wage on job k (given [X.sub.i]) is also likely to have an above average reservation wage on job j, knowledge of [C.sub.ik] can improve our prediction of [r.sub.ij]. Efficient estimation of [[Beta].sub.j] and [[Sigma].sub.j] would require specifying the joint distribution of the variables [C.sub.i1], [C.sub.i2], . . ., [C.sub.i6]. Estimation involving anything of higher dimension than a bivariate distribution is computationally difficult and likely to be plagued by numerical problems. As a result, we take a simpler approach: we include dummy variables...