Longitudinal Analyses of the Effects of Trade Unions

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Abstract
This paper examines how measurement error biases longitudinal estimates of union effects. It develops numerical examples, statistical models, and econometric estimates which indicate that measurement error is a major problem in longitudinal data sets, so that longitudinal analyses do not provide the research panacea for determining the effects of unionism (or other economic forces) some have suggested. There are three major findings: (1) The difference between the cross-section and longitudinal estimates is attributable in large part to random error in the measurement of who changes union status. Given modest errors of measurement, of the magnitudes observed, and a moderate proportion of workers changing union status, also of the magnitudes observed, measurement error biases estimated effects of unions downward by substantial amounts. (2) Longitudinal analysis of the effects of unionism on nonwage and wage outcomes tends to confirm the significant impact of unionism found in cross-section studies, with the longitudinal estimates of both nonwage and wage outcomes lower in the longitudinal analysis than in the cross-section analysis of the same data set. (3) The likely upward bias of cross-section estimates of the effect of unions and the likely downward bias of longitudinal estimates suggests that, under reasonable conditions, the two sets of estimates bound the "true" union impact posited in standard models of what unions do.

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