Detecting Neglected Nonlinearity in Dynamic Panel Data with Time-Varying Conditional Heteroskedasticity

A new class of specification tests is proposed to detect for neglected nonlinearity and dynamic misspecification in panel models. The tests can detect a wide range of model misspecifications while being robust to conditional heteroskedasticity and higher order time-varying moments of unknown form. They check a large number of lags so that they can capture dynamic misspecification at any lag order. The large number of lag orders does not cause loss of degrees of freedom because our tests naturally discount higher order lags, which is consistent with the stylized fact that economic behaviors are more affected by recent past events than by remote past events. No specific estimation method is required, and the tests have the appealing "nuisance parameter free" property that parameter estimation uncertainty has no impact on the limit distribution of the test. Simulations show the proposed tests have good finite sample properties. It is important to take into account conditional heteroskedasticity; failure to do so will cause overrejection of a correct linear panel model. Our tests have omnibus and robust power against a variety of alternatives relative to some existing tests for linearity in panel models