Robust Estimation of Wage Dispersion with Censored Data: An Application to Occupational Earnings Risk and Risk Attitudes
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Robust Estimation of Wage Dispersion with Censored Data: An Application to Occupational Earnings Risk and Risk Attitudes Daniel Pollmann1 · Thomas Dohmen2 · Franz Palm3 Published online: 17 September 2020 © The Author(s) 2020
Abstract We present a semiparametric method to estimate group-level dispersion, which is particularly effective in the presence of censored data. We apply this procedure to obtain measures of occupation-specific wage dispersion using top-coded administrative wage data from the German IAB Employment Sample. We then relate these robust measures of earnings risk to the risk attitudes of individuals working in these occupations. We find that willingness to take risk is positively correlated with the wage dispersion of an individual’s occupation. Keywords Dispersion estimation · Earnings risk · Censoring · Quantile regression · Occupational choice · Sorting · Risk preferences · SOEP · IABS JEL Classification C14 · C21 · C24 · J24 · J31 · D01 · D81
1 Introduction Important economic issues often center on the shape of distributions. Examples include questions relating to income inequality, the shape of wage offer distributions, or the riskiness of returns to financial assets. In various settings, empirical labor economists have been interested in measures of wage dispersion. More than often, such measures have to be estimated from censored data. For example, the March Current Population Survey (CPS), which contains survey responses on weekly earnings top-coded for anonymization purposes, has been used in several studies. Researchers have frequently dealt with this problem by multiplying top-coded * Thomas Dohmen t.dohmen@uni‑bonn.de 1
QuantCo, Inc., Boston, USA
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Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany
3
Maastricht University, Maastricht, The Netherlands
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earnings by a factor of 1.3 to 1.5 (e.g., Katz and Murphy 1992; Juhn et al. 1993). Other studies have relied on distributional assumptions to impute censored earnings in their data (e.g., Dustmann et al. 2009). Closely related, moments can typically be recovered if the shape of the distribution and the censoring rule are known. In many settings, however, the shape of the wage distribution is unknown and possibly itself of interest, and estimation methods that require parametric assumptions typically yield inconsistent estimates when these are violated.1 More advanced semiparametric methods have been used for social security earnings records matched to the CPS, which suffer from a much higher degree of censoring due to a legal contribution limit (e.g., Chay and Honoré 1998; Hu 2002). We present a measure of group-level dispersion that can be straightforwardly obtained from quantile regression (QR). Our method does not require parametric assumptions on the error terms and is as such consistent under heteroskedasticity and non-normality even for censored data. In addition, by using this simple-to-compute method, which is based on group coefficient estimates at different
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