Most of the literature on gender wage gaps, using decomposition methods such as the Blinder-Oaxaca decomposition, typically ignores selection bias. Some of the most recent studies on this topic have tried to control for self-selection of individuals in the labor market e.g. by using Heckman procedures. However, studies commonly consider that selection only occurs for one of the groups (e.g. women in gender wage gaps studies), i.e. selection correction is only included in the wage equation for one of the two groups. Is this correct? Should we instead correct for overall selection (of both groups) and then apply decomposition methods to the overall estimation? Actually, "oaxaca" command for Stata, when using "heckman twostep" option automatically corrects selection issues for one of the groups, assuming that the inverse Mills ratio is equal to zero for the other group. Why not correct selection bias for both groups in these cases?
I guess this is because it is assumed that women self-select into participating in the labor market because of the family related responsibilities, which is assumed not to be true for men. In consequence, women's selection that we correct for is of different nature than men's selection (that is because of what?) and it is like "additional" to standard men's selection. However, I think for some economies it makes sense to correct both women's and men's selection...
There is no point in a priori assuming the inverse Mills ratio to be zero for one group of the two. No matter if one uses the Oaxaca-Ransom (1994) (pooled regression as the non-discriminatory norm) or any of the other specific ones (Cotton, or Oaxaca 1973, where the nondiscriminatory norm is either that of males or females), regardless of all these, the wage equation assumes that one has a wage. In every group there are people who are NOT in the labor market and have no wage; a decision that might be due to self selection. In which case one is required to correct the equation of EACH group for selectivity correction. You ask "why not correct selection bias for both groups", but you are right, we have to correct for selection in both equations. Only after that can you decompose the differential into discrimination, human capital, and selectivity. You can find this exercise, with additional segregation component, in my paper (Asali, 2010. "Jewish-Arab Wage Gaps: What are the Causes," Defence and Peace Economics, 21(4): 367-380), also previous papers offering the selectivity correction into the Oaxaca by Oaxaca himself, and some coauthored with Shoshana Neuman and Michael Ransom).
I had a referee once commented on the self-selection issue of using the Oaxaca-Blinder decomposition. Her suggestion was to look at the Nopo decompostion, which is non-parametrical. Nopo only differs between explained and not-explained as one cannot assure that the unexplained component is all discrimination.
See http://ideas.repec.org/c/boc/bocode/s457157.html
Thank you for your opinions and suggestions!
My doubt arises from the paper of Jann (2008) - “The Blinder-Oaxaca decomposition for linear regression models” in STATA JOURNAL. In this paper, when correcting for selection bias through Heckman procedure, one of the groups (e.g., men) is not considered in selection (actually, when computing the mills ratio "by hand", it is recommended to replace it by zero for one of the groups). This sounds me strange and unusual, as both groups may suffer from selection bias (even if the reasons for selection are different). Even so, some of the very few papers on gender wage gaps taking into account selection issues also seem to only correct for selection of women...
Dear Pandelis, could you please provide me the reference of that study you refer? Thank you in advance!
I agree with Carlos Ospino. The no parametric approach provide you a more flexible framework because you do not need to set a explicit functional form to link with the DGP. Additionally, you can to set the common support on observables, a critical assumption when you are estimating the gender wage gap. Moreover, if you can explore the potential effects of selection bias , you can use sensitivity bounds to evaluate how much important the bias should be in order to reduce the estimated gender gap.
Dear Pandelis, I think, even though the functional form is different (OLS linear, versus nonlinear probit in the selection equation), the explanatory variables in the wage equation and the selection equation have to different, for identification purposes. I can imagine X, a vector of covariates in the wage equation, but Z as the vector of covariates in the selection equation: while Z can be =(X,W), so added some variables to X, or can be nesting X, or mutually exclusive. All these alternatives are better (and maybe essential) than having X in both the OLS wage equation and the Probit selection equation. In the paper I alluded to above, for example, I used different mix of variables in the selection equation: but this was based roughly on economic theory or intuition. It is that the main identification variable I added to the selection equation is, I claim, affecting the decision of participating in the labor market, but does not have an independent effect on the wage determination. This economic distinction allows using the variable as such--and actually made for the strength of the paper. Economic theory and intuition should be behind the choice of variables, and not just a technical exercise. Although, on the technical side, I think if X is the same in both equations there won't be identification, or would be at most a poor one.
Dear Pandelis, thank you very much for the reference.
About selection, as you mention in your last answer, the probit equation must be your selection equation, while the wage regression is the outcome equation.
You must include exclusion restrictions in your selection equation (probit) - at least one, as you mention. As Muhammad said, you should choose those/that exclusion restriction(s) based on intuition and theory whenever possible; you can also try to find other references on the topic you are studying and support your decision in other papers that you consider to be key references for your study.
Muhammad, Pandelis, on identification of the Heckman selection model see
http://onlinelibrary.wiley.com/doi/10.1111/1467-6419.00104/abstract
Vera, potentially, it would be interesting to correct for selection into labor force participation (LFP) of both men and women . It mainly depends on what is LFP for men in your sample. If it is 90%, then selection is not a big issue. If you are considering LFP of the elderly, though, selection will be a BIG issue also for men (health status, etc.). Correcting for gender differential selection by age could be even more important if, for instance, you are interested in gender wage gaps of elder workers and women tend to be on average healthier than men when they age (so as you will find in the labor force the `average' woman, and the` healthiest' man, since the sickest already retired).
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