Counterfactual distributions with sample selection adjustments: Econometric theory and an application to the Netherlands

Abstract

Several recent papers use the quantile regression decomposition method of Machado and Mata (2005) to analyze the gender gap in log wages across the distribution. Since employment rates often differ substantially by gender, sample selection is potentially a serious issue for such studies. To address this issue, we extend the Machado-Mata technique to account for selection. In addition, we prove that this procedure yields consistent and asymptotically normal estimates of the quantiles of the counterfactual distribution that it is designed to simulate.We illustrate our approach by analyzing the gender log wage gap between men and women who work full time in the Netherlands. Because the fraction of women working full time in the Netherlands is quite low, this is a case in which sample selection is clearly important. We find a positive selection of women into full-time work and find that about two thirds of this selection is due to observables such as education and experience with the remainder due to unobservables. Our decompositions show that the majority of the gender gap across the log wage distribution is due to differences between men and women in the distributions of returns to labor market characteristics rather than to differences in the distributions of the characteristics themselves.

Gender gaps across the earnings distribution for full-time employees in Britain: Allowing for sample selection

“…The possibility of a relationship between the probability of women working and their having characteristics associated with higher wages (such as higher education found in De la Rica et al, (2008)) has been long recognised in the literature (Heckman 1979;Buchinsky 1998;Melly, 2006;Blundell et al, 2007;Albrecht et al, 2009). Olivetti and Petrongolo (2008) recently explore the non random presentation of women into employment and gender wage gaps (measured at the median of the distribution) for the US and a range of European countries (including the UK).…”

“…The Machado-Mata (MM) decomposition across the wage distribution methodology is further developed to account for sample selection by Albrecht et al, (2009) who decompose the gender gap among full-time workers in the Netherlands.…”

“…In this paper, we use the quantile regression decomposition method (Machado and Mata, 2005) to study the gender wage gap in log average hourly earnings across the distribution for full-time workers in Britain including allowance for possible nonrandom selection of women into full-time employment (Albrecht et al, 2009). Our results can be seen as building on the quantile regression analysis (without sample 2 Spain, France, Greece, Italy and Portugal.…”

Alternative measures of homeownership gaps across segregated neighborhoods

“…The second term measures the "unexplained" portion of the homeownership gap. Albrecht et al (2006) have shown that the decomposition is consistent and asymptotically normal.…”

“…This study implements a new decomposition technique that identifies the unexplained portion of the gap not only at the mean, but at every percentile of the distribution of the dependent variable. This method was first proposed by Machado and Mata (2005), extended by Albrecht et al (2006), and has been used in several applications in labor economics. Similar to the labor market application, differences in homeownership gaps at the mean reflect a combination of nonsignificant differences at the upper end and much larger gaps at the lowest end of the distribution of homeowners.…”