A test for endogeneity in regressions

Textbook theory predicts that t-ratios decline towards zero in regressions when there is increasing collinearity between two independent variables. This article shows that this rarely happens if the two variables are endogenous, and coefficients increase greatly with more collinearity. The purposes of this article are 1) to illustrate this bias and explain why it occurs, and 2) to use the phenomenon to develop a test for endogeneity. For the test, one creates a variable that is highly collinear with the independent variable of interest, and endogeneity is indicated if t-ratios do not decline with increasing collinearity. False negatives are possible, but not likely. The test is confirmed with algebraic examples and simulations. I give many empirical examples of the bias and the test, including testing exogeneity assumptions behind instrumental variables and Granger causality.