Testing for Slope Homogeneity in a Linear Panel Model with Fixed Effects and Conditional Heteroskedasticity

This paper proposes a test for slope homogeneity across units in a linear panel data model, in which additive fixed effects and conditional intra-unit heteroskedasticity are incorporated. There are various tests of parameter homogeneity in the existing literature. However, none of them is valid when time dimension is short and fixed effects and conditional heteroskedasticicty are both present. The new test is robust regardless whether or not a linear model has fixed effects or conditional heteroskedasticity even when there are many units/individuals but each only has a small number of observations. Moreover, the test can be extended to autoregressive panels. Its asymptotic properties are established and Monte Carlo simulation indicates that the test delivers satisfactory finite-sample properties for static and autoregressive panels. As an illustration, our test is used to detect the slope heterogeneity in the autoregressive models using the PSID earnings data.