922—Chapter 29. Panel Estimation

The standard errors that we report here are the standard Arellano-Bond 2-step estimator standard errors. Note that there is evidence in the literature that the standard errors for the two-step estimator may not be reliable.

The bottom portion of the output displays additional information about the specification and summary statistics:

Effects Specification

Cross-section fixed (first differences)

Period fixed (dummy variables)

Note in particular the results labeled “J-statistic” and “Instrument rank”. Since the reported J-statistic is simply the Sargan statistic (value of the GMM objective function at estimated parameters), and the instrument rank of 38 is greater than the number of estimated coefficients (13), we may use it to construct the Sargan test of over-identifying restrictions. It is worth noting here that the J-statistic reported by a panel equation differs from that reported by an ordinary equation by a factor equal to the number of observations. Under the null hypothesis that the over-identifying restrictions are valid, the Sargan statistic is distributed as a χ( k − p ) , where k is the number of estimated coefficients and p is the instrument rank. The p-value of 0.22 in this example may be computed using “scalar pval = @chisq(30.11247, 25)”.

Panel Equation Testing

Omitted Variables Test

You may perform an F-est of the joint significance of variables that are presently omitted from a panel or pool equation estimated by list. Select View/Coefficient Tests/Omitted Variables - Likelihood Ratio... and in the resulting dialog, enter the names of the variables you wish to add to the default specification. If estimating in a pool setting, you should enter the desired pool or ordinary series in the appropriate edit box (common, cross-section specific, period specific).

When you click on OK, EViews will first estimate the unrestricted specification, then form the usual F-est, and will display both the test results as well as the results from the unrestricted specification in the equation or pool window.

924—Chapter 29. Panel Estimation

Test Equation:

Dependent Variable: D(LSCRAP)

Method: Panel Least Squares

Date: 11/24/04 Time: 09:52

Sample: 1988 1989

Cross-sections included: 54

Total panel (balanced) observations: 108

Note that if appropriate, the alternative specification will be estimated using the cross-sec- tion or period GLS weights obtained from the restricted specification. If these weights were not saved with the restricted specification and are not available, you may first be asked to reestimate the original specification.

Redundant Variables Test

You may perform an F-est of the joint significance of variables that are presently included in a panel or pool equation estimated by list. Select View/Coefficient Tests/Redundant Variables - Likelihood Ratio... and in the resulting dialog, enter the names of the variables in the current specification that you wish to remove in the restricted model.

When you click on OK, EViews will estimate the restricted specification, form the usual F- est, and will display the test results and restricted estimates. Note that if appropriate, the alternative specification will be estimated using the cross-section or period GLS weights obtained from the unrestricted specification. If these weights were not saved with the specification and are not available, you may first be asked to reestimate the original specification.

To illustrate the redundant variables test, consider Example 10.4 from Wooldridge (2002, p. 262), where we test for the redundancy of GRANT and GRANT_1 in a specification estimated with cross-section random effects. The top portion of the unrestricted specification is given by:

926—Chapter 29. Panel Estimation

Test Equation:

Dependent Variable: LSCRAP

Method: Panel EGLS (Cross-section random effects)

Date: 11/24/04 Time: 11:31

Sample: 1987 1989

Cross-sections included: 54

Total panel (balanced) observations: 162

Use pre-specified random component estimates

Swamy and Arora estimator of component variances

The first thing to note is that the restricted specification removes the test variables GRANT and GRANT_1. Note further that the output indicates that we are using existing estimates of the random component variances (“Use pre-specified random component estimates”), and that the displayed results for the effects match those for the unrestricted specification.

Fixed Effects Testing

EViews 5.1 provides built-in tools for testing the joint significance of the fixed effects estimates in least squares specifications. To test the significance of your effects you must first estimate the unrestricted specification that includes the effects of interest. Next, select

View/Fixed/Random Effects Testing/Redundant Fixed Effects – Likelihood Ratio. EViews will estimate the appropriate restricted specifications, and will display the test output as well as the results for the restricted specifications.

Note that where the unrestricted specification is a two-way fixed effects estimator, EViews will test the joint significance of all of the effects as well as the joint significance of the cross-section effects and the period effects separately.

Let us consider Example 3.6.2 in Baltagi (2001), in which we estimate a two-way fixed effects model. The results for the unrestricted estimated gasoline demand equation are given by:

928—Chapter 29. Panel Estimation

Notice that there are three sets of tests. The first set consists of two tests that evaluate the joint significance of the cross-section effects using sums-of-squares (F-est) and the likelihod function (Chi-square test). The corresponding restricted specification is one in which there are period effects only. The two statistic values (113.35 and 682.64) and the associated p-values strongly reject the null that the effects are redundant.

The remaining results evaluate the joint significance of the period effects, and of all of the effects, respectively. All of the results suggest that the corresponding effects are statistically significant.

Below the test statistic results, EViews displays the results for the test equations. In this example, there are three distinct restricted equations so EViews shows three sets of estimates.

Lastly, note that this test statistic is not currently available for instrumental variables and GMM specifications.

Hausman Test for Correlated Random Effects

A central assumption in random effects estimation is the assumption that the random effects are uncorrelated with the explanatory variables. One common method for testing this assumption is to employ a Hausman (1978) test to compare the fixed and random effects estimates of coefficients (for discussion see, for example Wooldridge (2002, p. 288), and Baltagi (2001, p. 65)).

To perform the Hausman test, you must first estimate a model with your random effects specification. Next, select View/Fixed/Random Effects Testing/Correlated Random Effects - Hausman Test. EViews will automatically estimate the corresponding fixed effects specifications, compute the test statistics, and display the results and auxiliary equations.

For example, Baltagi (2001) considers an example of Hausman testing (Example 1, p. 69), in which the results for a Swamy-Arora random effects estimator for the Grunfeld data are compared with those obtained from the corresponding fixed effects estimator. To perform this test in EViews 5.1, we first estimate the random effects estimator, obtaining the results: