Graphical diagnostics of endogeneity

We show that in sorting cross-sectional data, the endogeneity of a variable may be successfully detected by graphically examining the cumulative sum of the recursive residuals. An interesting case arises with a continuous or ordered (e.g., years of schooling) endogenous variable. Then, a graphical test for misspecification due to endogeneity (e.g., self selection) can be obtained without instrumental variables. Moreover, the sign of the bias implied by this endogeneity becomes deducible through such graphs.