Response Error and the Union Wage Differential.

• Author: Bollinger, Christopher R.

Christopher R. Bollinger [*]

Broad variation in estimates of the union wage gap has perplexed labor economists. One specification error that is consistent with the observed variation is measurement error in reported union status. This article applies results of Bollinger (1996) to estimate a range for the union wage gap. Both a cross-sectional model and a fixed-effects model are estimated. In order for the true coefficient in the fixed-effects model to be bounded below the true coefficient in the cross-sectional estimates, measurement error would have to be less than 0.8%. The difference between the fixed-effects estimates and the cross-sectional estimates is primarily due to measurement error rather than to unobserved heterogeneity. An examination of differences in returns to union membership by industry, occupation, and educational level shows that these differences are largely robust to measurement error. Many of these differences would be found even if error rates were as high as 10% or more.

1. Introduction

   An array of empirical estimates for the union wage differential has resulted from the variety of approaches to estimation. Lewis (1986) reviews the vast literature that attempts to estimate the union wage effect. Two extremes are represented by Mincer (1983), who estimates the wage differential to be 0.01, while Farber (1990) reports an estimate of 0.26. Clearly, specification error is the root cause of these differences. The literature has focused upon unobserved heterogeneity in worker status as the main specification error. Frequently, estimation approaches based on "within" estimators applied to fixed-effects models using panel data are used to account for the possibility of unobserved heterogeneity. As would be predicted by unobserved heterogeneity, Lewis (1986, p. 94) reports that "the panel wage gap estimates surveyed in the chapter on the average are roughly half as large as the corresponding cross-section estimates." This is often taken as evidence for bias in the cross-section estimates due to the presence of fixed effects. However, these results are also consistent with measurement error in the report of the union status. Indeed, chapter 5 in Lewis (1986) focuses upon this possibility: "the difference might be the result of union status measurement error" (p. 94).

   This article applies results of Bollinger (1996) to compare the effect of measurement error on cross-sectional estimates and panel estimates of the union wage differential. Bollinger (1996) establishes bounds for the slope coefficients of a linear regression when a binary regressor is thought to have measurement error. The results here do not identify a point estimate of the union wage differential; they relax many of the assumptions that are required to obtain the point estimates. These bounds serve the purpose of sensitivity analysis as called for by Leamer (1985).

   Bounds for parameter estimates answer the question, "How sensitive to measurement error are the results we typically observe?" The results below establish that, in the presence of no prior information on the extent of measurement error in the union status, a remarkably wide range of estimates for the union wage differential are allowed: in cross section, from 15% to over 600%, and in fixed-effects panel model, from 5% to over 4000%. In spite of the wide range demonstrated by the bound, the analysis here reveals a number of important results. First, the bounds for the cross section are much tighter than those for the fixed-effects estimates, clearly demonstrating the extraordinary impact of measurement error on "within" estimators: The cross-sectional estimates are much less biased by measurement error. The upper bounds represent a case of maximal measurement error; additional information will substantially tighten these bounds. This allows the hypothetical question "How low does measurement error have to be f or the panel estimates to be bounded below the cross sectional estimates?" to be answered. The results are striking: There must be less than 1% misclassification, a rate substantially lower than any estimates currently available. These two points suggest, as Lewis (1986) argues, that the cross-sectional estimates may be more reliable than the panel estimates. This implies that the differences between cross-sectional and fixed-effects estimates of the union wage differential are due to measurement error rather than unobserved heterogeneity.

   This article also examines how robust differences in returns to union status across occupation, industry, and educational groups are to measurement error. It has typically been found in cross section that the union wage differential varies across these groups. One possibility for this finding is that the error rates differ across these groups. Here, many of the differences typically found in the union literature appear to be quite robust to measurement error: Rates even as high as 10% would support differences in some categories. In particular, it is found that workers in the construction and retail industry earn the highest union premium, but differences between construction and retail may be due to measurement error. Manufacturing and service industry workers earn the lowest (and a negative return for the financial industry), but measurement error may be the reason for differences between them. It is also found that service occupations and operators, fabricators, and laborers have the highest union premium , but measurement error may account for differences between service and operators, fabricators and laborers. Also, measurement error may account for differences between precision production craft and repair occupations and technical sales and administrative support. The educational findings are somewhat stronger. The return to union membership for those with no high school is clearly higher than any other category. The return to union membership is next highest for high school graduates and is clearly larger than for those with college. This relationship appears robust to measurement error.

   This article differs from Bollinger (1996) in three important ways. Bollinger (1996) derives and proves the theorems upon which the analysis here is based. The theoretical results are the primary contribution of that paper. That paper uses a small subsample of the outgoing rotation groups of the May 1985 Current Population Survey (CPS) to illustrate the bounds and has a limited set of analysis examining the sensitivity of the bounds to additional information. This article extends the methodology in Bollinger (1996) to include "within" estimators applied to panel data. The methodology then allows a comparison between panel and cross-sectional bounds, which is a major focus of this article. This article also examines union differentials by six industry and six occupational categories and establishes that some of the differences in returns to union status may be due to differential response error across industry or occupational group, but some of the differences are robust. Finally, this article examines union differentials by educational level. Here, in contrast to the occupation and industry category, the differences in return to union status are found to be quite robust to measurement error. The article also differs in a number of other dimensions: The sample includes all outgoing rotation groups from 1989, resulting in a much larger sample than in Bollinger (1996). The sample here is composed only of prime aged men, removing questions concerning selection of women into the labor force.

   That measurement error exists is quite well documented. An excellent survey can be found in Bound, Brown, and Mathiowetz (2001). Freeman (1984), Peracchi and Welch (1995), Bound and Kreuger (1991), and Bollinger (1998) all explore measurement error in the CPS. Some papers that attempt to address measurement error in union status reports are Chowdhury and Nickell (1985), Mellow and Sider (1983), Freeman (1984), Jakubson (1991), Card (1996), Hirsch and Schumacher (1998), and Budd and Na (2000). In Mellow and Sider (1983), Freeman (1984), and Card (1996), auxiliary data from the 1977 CPS employer-employee match were used to estimate the misclassification rate in CPS reports of union status. This approach has considerable appeal. However, in order to use the matched data, one of two approaches is taken. Both Mellow and Sider (1983) and Freeman (1984) assume that the employer report of union status is without error. While certainly possible, Card (1996) argues convincingly that it is improbable. Card (1996) then assumes that the employer and employee can both make errors, but then must go on to assume that the error processes are independent yet have the same error rate. He further must assume that the rate of classifying union workers as nonunion is equal to the rate of classifying nonunion workers as union. Again, while possible, these are not trivial assumptions. Another concern when using the 1977 match data is the differences in the CPS questionnaire. Many of the reforms (both in 1988 and again in 1991) were designed to reduce measurement error. For a review of these reforms, see Polivka and Rothgeb (1993).

   Chowdhury and Nickell (1985) do not arrive at estimates that are free from measurement error, but argue that an instrumental variable approach, using multiple years of union status data, reduces the bias. Similarly, Hirsch and Schumacher (1998) examine the effect of removing observations with allocated union status or proxy interviews. The data used here remove allocated observations, but Bollinger and David (1997) find that proxy interviews are at least as accurate as actual interviews. Hirsch and Schumacher (1998) further explore using changes in occupation or industry coincident with changes in union status to reduce measurement error. Budd and Na (2000) argue that agreement in reports across years indicates more likelihood that the...