Testing for Reverse Causation and Omitted Variable Bias in Regressions

Abstract

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,

Keywords: simultaneity, collinearity, mulicollinearity, omitted variable bias, exogeneity, simulations, Granger test, two stage least squares, random experiments, quadratic variables, Kuznets curve

JEL Classification: C10, C15, C18, C29, K49