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. Moreover, the sign of the bias implied by the endogeneity may be deducible through such graphs. In general, instrumental variables are needed to implement the graphical test. However, when a continuous or ordered (e.g. years of schooling) variable is suspected to be endogenous, a graphical test for misspecification due to endogeneity (e.g. self-selection) can be obtained without instrumental variables.