A Sample Selection Quantile Regression Model And Its Application To The Income Gap Of Migrant Workers

Sample Selection bias is a major issue that cannot be neglected in the empirical work of wage inequality,dealing with this problem in a wrong way will lead to significant bias in the estimation,and then draw a misleading conclusion.Generally speaking,most approaches that correcting for sample selection focus on estimating conditional mean models.However,with the development of quantile regression models,lots of researchers pay attention to analyze changes in the overall distribution of random variables,and obtain complete information through the change of quantile.Arellano and Bonhomme(2017)propose an estimator subject to sample selection in quantile regression models.They model the sample selection bias via the joint distribution function or Copula of the error term in the selection equation and the error term in the outcome equation,and use the correlation coefficient to measure the degree of sample selection.Correlation coefficient is estimated by minimizing a method of moments criterion to correct for sample selection bias in the quantile regression models.Then,the quantile parameters are estimated by a rotated check function.In the theoretical part of this paper,based on the model of Arellano and Bonhomme(2017),we apply Box Cox transformation to their model and propose a new estimator to make it satisfy the linear assumption.We discuss the identification and estimation of our estimator.Monte Carlo simulations indicate that our estimator performs well in finite samples.In addition,an empirical application also demonstrates the usefulness of our estimator in empirical work and the coefficient of Box Cox transformation tends to be larger when the quantile is at lower level.Moreover,we extend our estimator to the framework of quantile treatment effect directly,and discuss the identification and estimation of this quantile treatment effect as well.With the theoretical preparation,we apply the above method to correct for the sample selection bias in the wage differentials between urban migrants and rural migrants in China,based on the China Household Income Survey(CHIPS)in 2013.First of all,we investigate the wage equation of rural migrants,but OLS will result in biased estimation.Because there is a sample self-section problem in this issue,that is,only the wages of rural migrants who are still working in the cities can be observed,while some rural migrants might choose to return to their hometown,we cannot observe their wages,and their decision are the results of self-selection,which might be related to the unobservable individual characteristics such as abilities.Thus,the sample is nonrandom.To deal with this problem,we pick up rural migrants who once worked in the cities but return to the hometown at present from rural household sample.In turn,we compare the Heckman's two steps model with our estimator to correct the selection bias.In the first step,we estimate the selection equation.The results show that the return choice is a negative decision,since the rural migrants with higher abilities are more likely to return to their hometown after they earned enough money and reputations in cities.In the second step,we find that gender discrimination is still an important factor that influencing the wage equations,the hourly wage of women rural migrants is about 34.2% lower than that of men.Fortunately,the women rural migrants with higher abilities tend to be less affected by the gender discrimination.In addition,college degree including college specialty plays a significant positive role in increasing the wages of rural migrants,therefore,improving the education level of rural migrants is an important way to improve their income and situation.But the results show that work experiences have no influence on rural migrants' wages.On the other hand,if we ignore the sample of rural migrants is non-random,the estimation of wage differentials between return migrants and rural migrants in China will suffer from endogenous selection problems,which are related to the unobservable individual characteristics such as abilities.Based on this judgment,we employ the treatment effect to correct for the selection bias.After doing that,we find that the hourly wage differentials between migrants is not significant.However,the results of conditional quantile treatment effects show that,the wage differentials between migrants is not significant in the low and middle quantile,but with the improvement of quantile,the wage differential shows a growing trend.Among the most capable migrant workers,the hourly wage of return migrant is higher than that of staying in cities 47.5%of rural migrant.This may be caused by a series of factors,such as the narrowing of the income gap between urban and rural areas and the adjustment of the industrial structure in rural areas.