Estimating returns to schooling in urban China using conventional and heteroskedasticity-based instruments

A common problem when estimating the returns to schooling is the lack of conventional instrumental variables (IV) for education altogether or, if conventional IVs exist, there is often doubt as to whether they satisfy the exclusion restriction. We illustrate how a novel identification strategy, proposed by Lewbel (2012), which utilizes a heteroscedastic covariance restriction to construct an internal IV, can be used to obtain IV estimates for returns to education when alternatively there are no conventional IVs available or the conventional IVs that are available are potentially weak. To do so, we estimate the returns to schooling in urban China using two datasets. One dataset, which is for Shanghai, does not have any conventional IVs for education. The other dataset, which is for urban residents from across China, contains information on conventional IVs (parents' education). We find that, in the case of returns to schooling, the Lewbel method provides plausible estimates in datasets in which conventional IVs are not available and can be used to provide a robustness check on the findings from conventional IVs in datasets in which conventional IVs are available, but are weak. Our findings suggest that the method could prove useful in other contexts in which endogeneity is a problem and either conventional IVs are not available or those which are available may not satisfy the exclusion restriction.