Testing for Reverse Causation and Omitted Variable Bias in Regressions

This paper shows through regression simulations that, when there are two highly collinear regressors, at least one of which has a simultaneous relationship with the dependent variable, t-ratios typically do not decline to non-significance as text book theory predicts. Coefficients and/or t-ratios expand to extremely unrealistic levels as collinearity increases. I use this phenomenon to develop a test for the presence of contemporaneous simultaneity (here defined as reverse causation or missing variable bias), an important and intractable problem in many disciplines. The test is simple: one selects a regressor and, in addition, includes a second regressor that is highly correlated with the first, creating collinearity. Simultaneity is indicated if the t-ratios do not decline to non-significance as collinearity increases and if coefficient size increases. It can be used in most regression analyses. Unlike other tests it does not rely on lagged variables. I show the effect with simulations, and I give numerous empirical examples, including a test of causal assumptions in a Granger regression, a test of whether subjects are actually randomly assigned in a randomized controled experiment, and a test of whether instrumental variables in a two stage least square regression are endogenous