Testing exogeneity in cross-section regression by sorting data

We introduce a framework to test for exogeneity of a variable in a regression based on cross-sectional data. By sorting data with respect to a function (sorting score) of known exogeneous variables it is possible to utilize a battery of tools originally develped to detecting model misspecification in at time series context. Thus, we are able to propose graphical tools for the identification of endogeneity, as well as formal tests, including a simple-to-use Chow test, needing a minimum of assumptions on the alternative endogeneity hypothesis. Models of endogenous treatment and selectivity are utilized to illustrate the methods. With Monte Carlo experiments, including continous and discrete response cases, we compare small sample performances with existing tests for exogeneity.