High Wage Workers and Low Wage Firms: Negative Assortative Matching or Limited Mobility Bias?

Abstract

In the empirical literature on assortative matching using linked employer-employee data, unobserved worker quality appears to be "negatively" correlated with unobserved firm quality. We show that this can be caused by standard estimation error. We develop formulae that show that the estimated correlation is biased downwards if there is true positive assortative matching and when any conditioning covariates are uncorrelated with the firm and worker fixed effects. We show that this bias is bigger the fewer movers there are in the data, which is 'limited mobility bias'. This result applies to any two-way (or higher) error components model that is estimated by fixed effects methods. We apply these bias corrections to a large German linked employer-employee data set. We find that, although the biases can be considerable, they are not sufficiently large to remove the negative correlation entirely. Copyright (c) 2008 Royal Statistical Society.

Firms and Labor Market Inequality: Evidence and Some Theory

“…For example, Abowd, Lengermann, and McKinney (2003) report a correlation of 0.08 for U.S. workers, while Card, Heining and Kline (2013) report a correlation of 0.23 for male German workers in the 2000s. As discussed by Abowd et al (2004) and Andrews et al (2008) these correlations are biased down in nite samples with the size of the bias depending inversely on the degree of worker mobility among rms. Maré and Hyslop (2006) and 12 Abowd, Lengermann and McKinney (2003) impose a normalization on the experience pro les in their estimation of an AKM model for the LEHD data that leads to large variances of the α i and X it β components, and a large negative covariance (ρ = −0.55), similar to the pattern in column 4.…”

“…In sampling experiments they nd that the correlation of the estimated e ects becomes more negative when the AKM model is estimated on smaller subsets of the available data. While Andrews et al (2008) and Gaure (2014) provide approaches to correcting for this downward bias in the correlation (and the upward biases in the estimated variances of person and rm e ects), their procedures require a complete speci cation of the covariance structure of the time-varying errors, which makes such corrections highly model dependent.…”

“…14 For example Andrews et al (2008) compute bias corrections in a linked sample of German workers and establishments under the assumption that the transitory errors in wages are homoscedastic and serially uncorrelated. They nd that the corrections have little e ect on the estimated correlation between worker and rm e ects.…”

Augmenting the Human Capital Earnings Equation with Measures of Where People Work

“…By contrast, the fixed effect of individuals is weakly positively correlated with the establishment observables, while the individual unobservables and unobserved establishment fixed effects are negatively correlated-a result consistent with Abowd et al (2014). As Andrews et al (2008) notes, a negative correlation between two unobserved components of earnings could result from sampling and measurement errors, 19 so the safest conclusion from these correlations is that sorting of workers occurs largely on observable characteristics.…”

Globalization and imperfect labor market sorting

“…The Swedish data set is ideal for this, since it is both extensive, including roughly 50% of the workforce and all firms in Sweden with more than 20 employees, and rich in detail concerning worker characteristics, firm characteristics and employment relationships. The data set is also characterized by considerable worker mobility, allowing us to avoid the issue of "limited mobility bias" that has been associated with previous empirical studies of assortative matching using linked employeeemployer data (see Andrews, Gill, Schank and Upward 2008). We construct the measure of the degree of matching in disaggregated industries using both observed attributes and unobserved fixed effects of workers and firms.…”