Response Error and the Union Wage Differential

Abstract

Broad variation in estimates of union wage gap has perplexed labor economists. One specification that is consistent with observed variation is measurement in reported union status. This article applies results of Bollinger (1996) to estimate a range for union wage gap. Both a cross-sectional model and a fixed-effects model are estimated. In order for true coefficient in fixed-effects model to be bounded below true coefficient in cross-sectional estimates, measurement would have to be less than 0.8%. The difference between fixed-effects estimates and cross-sectional estimates is primarily due to measurement 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 rates were as high as 10% or more. An array of empirical estimates for union wage differential has resulted from variety of approaches to estimation. Lewis (1986) reviews vast literature that attempts to estimate union wage effect. Two extremes are represented by Mincer (1983), who estimates wage differential to be 0.01, while Farber (1990) reports an estimate of 0.26. Clearly, specification is root cause of these differences. The literature has focused upon unobserved heterogeneity in worker status as main specification error. Frequently, estimation approaches based on within estimators applied to fixed-effects models using panel data are used to account for possibility of unobserved heterogeneity. As would be predicted by unobserved heterogeneity, Lewis (1986, p. 94) reports that the panel wage gap estimates surveyed in chapter on average are roughly half as large as corresponding cross-section This is often taken as evidence for bias in cross-section estimates due to presence of fixed effects. However, these results are also consistent with measurement in report of union status. Indeed, chapter 5 in Lewis (1986) focuses upon this possibility: the difference might be result of union status measurement error (p. 94). This article applies results of Bollinger (1996) to compare effect of measurement on cross-sectional estimates and panel estimates of union wage differential. Bollinger (1996) establishes bounds for 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 union wage differential; they relax many of assumptions that are required to obtain point estimates. These bounds serve purpose of sensitivity analysis as called for by Leamer (1985).