Abstract
Chamberlain (1982) showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of dependent variables on all leads and lags of independent variables. Angrist and Newey (1991) suggested computing this test statistic as the degrees of freedom times the R2 from a regression of within residuals on all leads and lags of the exogenous variables. Despite the simplicity of these tests, they are not commonly used in practice. Instead, a Hausman (1978) test is used based on a contrast of the fixed and random effects specifications. We advocate the use of Chamberlain (1982) test if the researcher wants to settle on the FE specification and we check this test’s performance using Monte Carlo experiments and we apply it to the crime example of Cornwell and Trumbull (1994).
Highlights
Chamberlain (1982) showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of the dependent variable on all leads and lags of the independent variables
The random effects (RE) model in panel data is usually criticized for imposing restrictive conditions requiring the independence of the individual effects and the regressors
One caveat, is that like the Sargan overidentification test for dynamic panels, the minimum chi-squared (MCS) test tends to understate the true variance of the test statistic as T gets large
Summary
Chamberlain (1982) showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of the dependent variable on all leads and lags of the independent variables. Angrist and Newey (1991) demonstrated that this MCS method has 3SLS equivalents and that the resulting over-identification test statistic is equivalent to the MCS test statistic suggested by Chamberlain (1982) They showed that in the standard fixed effects model with remainder disturbances having a scalar identity covariance matrix, this MCS test statistic can be obtained as the sum of T terms. Each term of this sum is the degrees of freedom times the R2 from a regression of within residuals for a particular period on all leads and lags of the independent variables.
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