Estimating reservation wages of employed workers using a stochastic frontier.

• Author: Hofler, Richard A.

1. Introduction

   According to search theory, workers form "reservation" wages such that employment offers paying wages less than the reservation wage are rejected. The first job offer paying a wage higher than the reservation wage is accepted and search is terminated. Though the reservation wage is clearly a matter of individual taste and unobservable, a number of empirical articles have nevertheless appeared on the subject. The present paper adds to this literature. Its novel aspects are that it uses data on employed workers rather than unemployed workers (as is usually the case) and that it applies a comparatively new econometric technique, stochastic frontier estimation, to the problem of estimating reservation wages.

   Our interests in this paper are twofold. First, the paper provides estimates of worker reservation wages utilizing the stochastic frontier regression technique. Second, we use these estimates to test various hypotheses regarding the response of reservation wages to factors that search theory suggests are important in the determination of reservation wages.

   The remainder of the paper is organized as follows. Section II discusses the previous empirical literature on the reservation wage. Section III sketches the theory and estimation techniques we use. Section IV lays out a framework for assessing the validity of the approach used here. Finally, section V presents the empirical results.

2. Background

   Studies of reservation wages fall into one of two categories. One type of study utilizes survey responses to a question that directly asks the respondent what his or her reservation wage is. Studies in this category are: Crosslin and Stevens |4~, Lancaster and Chesher |20~, Feldstein and Poterba |5~, Lancaster |19~, Holzer |12~, Jones |14; 15~, and Heywood and White |8~. The second type of study of the reservation wage takes the reservation wage as an unobservable and attempts to infer it econometrically. Papers employing this approach are: Kiefer and Neumann |16; 17; 18~ and Fishe |6~. Both types of study, whether the reservation wage is a survey response or is inferred econometrically, use data on workers who are either experiencing a spell of unemployment or who have recently completed a spell of unemployment.

   We regard the studies in which reservation wages are inferred econometrically to be somewhat superior on methodological grounds. This is because the reservation wage, regardless of what answer a respondent might give on a questionnaire, is not likely to be measured with accuracy. There are a number of reasons why reservation wages culled from labor market surveys may be biased. First, survey respondents when confronted with the question, "What is the lowest amount of take-home pay that you would be prepared to accept from a new job?" may simply not have a good idea of what the true answer to this question is. They may, for example, engage in wishful thinking and respond with an amount higher than that which would actually be necessary to entice them to accept new employment if confronted with a realistic opportunity.

   A second source of response bias, interrelated with the first source, is that it is very difficult on a survey to control for other characteristics that a job might possess. Thus a worker confronted with an opportunity in his or her industry or occupation of choice might be willing to accept a lower wage than otherwise. The British studies |14; 15; 19; 20~ suffer from this problem in particular when compared to the American work |5; 8; 12~. The former utilize data in which a single question is asked regarding the reservation wage, worded to the effect, "What is the lowest amount in take-home pay you would be prepared to accept for a new job?" The American studies use data that rely on a two-tiered question regarding the reservation wage. The questions are generally worded in this fashion: (1) "What type of work have you been looking for?" and (2) "What would the wage or salary have to be for you to be willing to take employment in this type of work?" Thus the latter type of two-tiered approach at least confronts the respondent with a more clearly defined question.

   A third source of bias in reservation wages recorded in survey data is that in most of the instances the questions are posed by a government agency. Feldstein and Poterba |5~, for example, use data collected in a supplement of the Current Population Survey. Crosslin and Stevens |4~ and Heywood and White |8~ use data collected by state employment security agencies. Only Holzer |12~ and Jones |14; 15~ clearly use data not collected by a government agency. The old saw in the response bias literature is that people will answer a question about income differently depending on whether they think the answer will affect their taxes or their credit. This cliche is no doubt applicable in the case at hand, as it is the government that administers unemployment insurance benefits. Receipt of unemployment insurance benefits is conditioned by the recipient demonstrating availability and active search for work. Thus a UI recipient may feel it's in his or her best interest to provide a low figure in response to the reservation wage question to convince the government of the seriousness of the intent to find work. In actual fact, however, the recipient may be quite content to receive benefits for the full duration of the eligibility period unless a really good offer were to materialize.

   A fourth source of inaccuracy in data sets using worker reported reservation wages is non-response bias. Not all studies using this type of data discuss this problem, but two that do are |5~ and |8~. Feldstein and Poterba report a non-response rate of 31% in their data set which was collected as a supplement to the May 1976 CPS. Even more remarkably, Heywood and White report a non-response rate of 67% in their data set which was collected by the Wisconsin Job Service for Milwaukee County in November of 1984. Other authors using this type of data don't discuss the non-response problem, but, on the basis of those that do, the problem appears to be fairly serious. If respondents select out of the sample in a systematic way, then the repercussions for the validity of the reservation wage data may be very significant.

   In light of the various possible sources of inaccuracy in self-reported reservation wage data, it is our conviction that empirical studies relying on such data may be flawed by systematic error. If a suitable econometric technique existed to deduce reservation wages from observed labor market data, more reliable inferences regarding the determinants of reservation wages could be obtained. As noted above, |16; 17; 18~, and |6~ do employ an econometric technique to deduce reservation wages. Specifically, these papers use data on completed and incomplete spells of unemployment in conjunction with Heckman's |7~ censored regression model to estimate a reservation wage equation. Our paper will employ a similar philosophical approach, i.e., estimation of the reservation wage, though we shall employ a different econometric technique to obtain the estimates. A second distinguishing feature of our research is the data set we use. All reservation wage studies to date have utilized data on unemployed or recently unemployed workers and therefore may not be representative of the labor market experiences of the overall work force. Kiefer and Neumann, in particular, note that their data set (used in all three of their papers) is "not representative of the entire U.S. population or even of the unemployed population" |17, 196~. Our paper instead will estimate reservation wages of workers who are employed. Specifically, we use data from the Current Population Survey. This data set has the advantage that it is intentionally designed to be representative of the U.S. population.(1)

3. Search Theory, the Reservation Wage, and Stochastic Frontier Estimation

   The reservation wage enjoys a long and distinguished history in the search theory literature. It is that wage necessary to induce somebody to accept an offer of employment. The main problem with the concept is that it is unobservable as far as the economic analyst is concerned. What the economic analyst does observe is the actual wage paid to a given worker. This wage, by definition of the reservation wage, is...