Testing for Reverse Causation and Omitted Variable Bias in Regressions
32 Pages Posted: 25 Jul 2019 Last revised: 21 Oct 2021
Date Written: September 18, 2020
Textbook theory predicts that t-ratios decline towards zero when there is near collinearity. This paper shows that this often does not occur if a regression model suffers from simultaneity or omitted variable bias. With more collinearity t-ratios can continue to rise or reach a plateau at a high level. Coefficients on the two regressors have opposite signs, and they increase indefinitely or reach a plateau. I use this phenomenon to develop a test for the presence of simultaneity or omitted variable bias, important and intractable problems in many disciplines. The test is simple: one selects a regressor and creates a second regressor that is highly correlated with the first. Simultaneity or omitted variable bias is indicated if t-ratios and coefficients undergo these trends with more collinearity. The test does not rely on lagged variables or instruments, and it can be used in most regression models. The test produces false negatives in some situations. I could find no evidence of false positives. 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 not randomly assigned in a randomized controlled experiment, and a test of whether instrumental variables in a two stage least square regression are endogenous.
Keywords: simultaneity, collinearity, multicollinearity, omitted variable bias, endogeneity, simulations, Granger test, two stage least squares, random experiments, quadratic variables,
JEL Classification: C10, C15, C18, C29, K49
Suggested Citation: Suggested Citation