How much should we trust R2 and adjusted R2: Evidence from regressions in top economics journals and Monte Carlo simulations - Qiang Chen; Ji Qi (Journal of Applied Economics, 2023)
R2 and adjusted R2 may exaggerate a model's true ability to predict the dependent variable in the presence of overfitting, whereas leave-one-out R2 (LOOR2) is robust to overfitting. We demonstrate this by replicating 279 regressions from 100 papers in top economics journals, where the median increases of R2 and adjusted R2 over LOOR2 reach 40.2% and 21.4% respectively. The inflation of test errors over training errors increases with the severity of overfitting as measured by the number of regressors and nonlinear terms, and the presence of outliers, but decreases with the sample size. These results are further validated by Monte Carlo simulations.
Keywords: R2; 330; adjusted R2; goodness of fit; leave-one-outR2