Almost all of the studies on earning differential between immigrants and natives ignore selection bias. I am using a wage decomposition approach, namely Blinder-Oaxaca, to estimate wage differential between immigrants and natives. My supervisor suggested employing Heckman two-step method to correct selection bias. However, to me it is not clear whether there is any self-selection among immigrants to participate in the labor market, causing a selection bias in their wage equation. There are intuition and theory behind selectivity among females in the gender wage gap since women may have a self-selection decision to NOT participate in the labor market due to family issues. So, what would be the intuition behind selection bias in the case of migrant-native wage gap? and if it is the case, then how should I consider the exclusion restriction and the identification of wage equation and LFP equation?
Dear Taghi Ghadiri Abkenar ,
Self-selection might typically arise in any group if the selection into the sample is not random. Let's for a moment forget about native-immigrant differentials and focus on only a group (e.g., migrants). Basically, if only migrants with certain unobservable characteristics (for instance, language proficiency, quality of education, personality traits, etc.) are employed, then, if some of the covariates (e.g., educational level) are correlated with those unobserved characteristics, the estimated coefficient for those covariates will be biased. This is a problem in any regression framework, included obviously the Oaxaca-Blinder framework, where both models (for migrants and natives) will yield biased coefficients; the differences in biased coefficients is not very useful.
Having said that, the problem is many times to find a reasonable exclusion restriction. It is difficult to find anything affecting employment but not wages. Typically, people use marital status, number of children, housing tenure status, availability of child care facilities... They are far from perfect, as many of these factors can affect wages (e.g., people with children could not devote so much time to work, etc.).
Overall, there is indeed some self-selection in both equations, which makes things a little bit messy. A possible strategy can be to see perform the regression for each group testing the existence of selection. In men, it is usually smaller or non-existent. In other words, carry out the regressions employing the Heckman equation using one of the mentioned exclusion restrictions and check the significance of the MIlls ratio. If there is no selection, proceed normally with OLS. If there is selection, either try to consider it in the OA decomposition or proceed with OLS, but stating clearly that you do not consider it and it might be a problem.
I hope it helps.
Best,
José-Ignacio Antón
Dear José-Ignacio Antón
Thank you for your detailed reply. Regarding the first part of your discussion, I should say that my aim is NOT to capture differences in coefficient, rather I would like to capture the differences in output (dependent variable or wage) therefore, I think a biased coefficient may not damage the analysis dramatically, I might be wrong! Also, a minor thing is that I can observe the language proficiency of immigrants in the data (it is a longitudinal surveyed data, GSOEP). BUT, surely it will not solve the endogeneity problem. Therefore, if it is a major problem then, I would like to ask you an important question, how can I control those unobservable characteristics to the extent that I achieve some reliable results?
Well, when talking about the differences in coefficients, we mean "the part of the difference in wages explained by the differences in coefficients". Basically, this type of decomposition tries to split the total different into the "gap due to observable characteristics" and the "gap due to coefficients". The latter is the same as the gap due to unobservable characteristics. Depending on the context and with caution, one can talk about "discrimination".
In this respect, I would try to control for as many (reasonable) variables as possible and to try to implent the sample selection correction...
Many thanks, and I think in the case of migrant-native wage gap (assimilation process of immigrants) we mostly deal with unobservable part of decomposition.
Yes, the unexplained part is the unobservable part. You should be a bit cautious when discussing it, because in that component many things might fall (selection if not controlled for, discrimination, preferences, etc.).
José-Ignacio Antón
Hello Guys, I would like to ask you a question about the application of the selection bias correction. I understand that the selection problem stems from the fact that we only held workers. So the salary regression is done with people who are employed. Should the variable (number of children, marital status, etc.) that I am going to use as an instrument be for workers too? Thanks for your consideration.
Best regards!
The instrument should be only in the selection equation, not in the wage regression
Thank you for your replied,
So the selection equation will include workers and non workers?
Best!
Hello, guys! I've been looking for material about the Oaxaca-Blinder decomposition because I would like to apply it in my thesis. I have a data base with only formal workers that work in Brazil, and I would like to estimate the wage differential between immigrants and natives. What are the selection bias that I should consider, once it does not have unemployed people in the data?
Thank you!
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