Self-selection Bias in Longitudinal Estimation of Wage Gaps

The empirical literature in labor economics abounds with studies of wage gaps between union and non-union workers, workers in safe and dangerous jobs, workers for small and large employers, and so forth. Most of these studies have used cross-sectional data on individual workers to estimate regressions of the wage (or, more commonly, its natural logarithm) on the variable of main interest while attempting the ‘hold other things equal’ by controlling for a vector of other worker and job characteristics. Despite these efforts to control for other factors, the possibility remains that cross-sectional estimation of wage gaps has been biased by failure to control for unobserved worker characteristics related to both the wage and included regressors. This possibility has motivated a legion of recent researchers to ‘difference out’ unobserved individual characteristics by estimating fixed-effects models with longitudinal data. This longitudinal literature has grown so rapidly that a full listing of references would be futile, but notable examples include he studies by Freeman (1984) and Mellow (1981) on union-non-union wage differences, Brown (1980) and Duncan and Holmlund (1983) on wage premiums for dangerous or unpleasant working conditions, Brown and Medoff (1985) on wage differences by employer size, Krueger and Summers (1988) on interindustry wage differences, and Madden (1985) on wage differences by length of commuting trip. The purpose of this paper is to question whether such longitudinal analyses produce consistent estimation of wage gaps. Section 2 motivates the discussion with a graphical exposition of an extreme but illustrative case. Section 3 provides a formal analysis of the general problem that self-selection of job changers can cause longitudinal estimation to confound the true wage gap with worker taste parameters related to the job changing decision. Section 4 summarizes and discusses the analysis.