# Tools of the Trade: Beyond mean decompositions (with an application to the gender wage gap in China)

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Suppose you were investigating the observed wage gap in urban China, where men are paid approximately 30% more than women. The first thing you would like to know is whether the higher wages paid to men are a result of the greater average years of schooling and years in the labor force that men have or whether, instead, men are paid more even after accounting for education and experience. If the latter situation is the case then the difference in wages may at least in part be due to labor market discrimination. One of the principle tools used in economics to decompose the wage gap into the portion of the gap explained by factors such as education and experience, and the portion explained by differences in returns to those factors, is the familiar Oaxaca-Blinder (OB) decomposition.

OB is the earliest and most well-known example of a decomposition method although today there are many. Fortin, Lemieux, and Firpo have put together a comprehensive review of decomposition methods that places these methods in the framework of program evaluation econometrics. This is helpful since decomposition methods implicitly consider a counterfactual state of the world that can’t be observed and the framework they adopt explicitly draws out the assumptions required by the various methods.

The OB method has two well-known limitations – it must assume that wages are a linear function of observables, and it can only be used to decompose the mean and not any other point in the wage distribution such as the median or the 95^{th} percentile (both of these points in the distribution are examples of what we call quantiles). Previous methods have been developed to decompose differences at quantiles of the distribution, but all of them are relatively complex and/or computationally intensive.

However a recent paper by Firpo, Fortin, and Lemieux introduces a decomposition method based on unconditional quantile regression that is a natural extension of the traditional OB method, and relatively easy to use (here is the Stata code courtesy of Nicole Fortin).

The unconditional quantile regression involves the use of what is termed a Recentered Influence Function (RIF) and I refer readers to both the review paper and to the original paper for estimation details rather than get too far into the math here. Suffice to say, the RIF captures a change in the statistic of interest (say the 25^{th} percentile of the wage distribution) in response to a change in the underlying distribution of explanatory variables and this allows for regression based quantile decomposition.

What is nice about the RIF (as opposed to all other quantile decomposition methods) is that regression coefficients can be used to perform a detailed decomposition in an analogous way to OB where the effect due to observables (i.e. the “composition effect”) and the effect due to differential returns to the observables (i.e. the “wage structure effect”) are further decomposed into the contribution of individual explanatory variables.

Chi and Li apply the RIF approach to decompose the gender wage gap observed in China during the transition to a market economy. The male-female wage gap has been rising in China, but it is not clear if this is due to the increasing returns to education and experience observed in the transition period (and men on average have more of both education and experience) or, perhaps, there has been a rise in discrimination against women in the labor market.

In 2004, men earned about 30% more on average in urban labor markets – and roughly one-third of this difference is explained by the composition effect (the observable differences between men and women). However this wage gap was much greater at the bottom of the distribution – at the 20^{th} percentile men earned 35% more while at the 80^{th} percentile they only earned 22% more. And, further, the gap unexplained by observable factors is greater at the bottom of the distribution.

In contrast to the glass ceiling observed in the US, it appears that in China there is a “sticky floor” – females towards the bottom of the wage distribution are at a comparatively greater disadvantage. This is especially true, as revealed by the decomposition into individual explanatory variables, for women with less education working in the loosely regulated private sector.

Chi and Li argue that the relative abundance of unskilled workers enable employers to express their discriminatory preferences much more readily. Among skilled workers, which are in relative undersupply, the market is tighter and employers have to pay women at a level closer to their male counterparts (although still lower). Whether this assertion is true would require further investigation, but the application of unconditional quantile regression has brought the fact of a greater unexplained wage gap at the bottom of the distribution into the light.

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The RIF approach is indeed useful for a number of applications that we may care about.

In this particular application, it is important to recognize that the authors are not using hourly earnings, but either monthly or annual (it isn't clear), and that by 2004, 10 percent of women in the sample were self-employed (Table 1). Before making too much out of the results, one must recognize that many low-skilled self-employed women are choosing their hours and thus also their earnings. So is a larger gender earnings gap at low wages driven by discrimination? Or labor supply decisions?

...I was fairly agnostic in this blog about Bao and Li's interpretation of their results since the post was meant to highlight the method, but you are absolutely correct to raise this issue - thanks for the contribution, and please contribute more!