668—Chapter 37. Panel Estimation

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 x(p – k), 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-test of the joint significance of variables that are presently omitted from a panel or pool equation estimated by list. Select View/Coefficient Diagnostics/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-test, and will display both the test results as well as the results from the unrestricted specification in the equation or pool window.

Adapting Example 10.6 from Wooldridge (2002, p. 282) slightly, we may first estimate a pooled sample equation for a model of the effect of job training grants on LSCRAP using first differencing. The restricted set of explanatory variables includes a constant and D89. The results from the restricted estimator are given by:

670—Chapter 37. Panel Estimation

F-test summary:

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-test of the joint significance of variables that are presently included in a panel or pool equation estimated by list. Select View/Coefficient Diagnostics/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- test, 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:

672—Chapter 37. Panel Estimation

Here we see that the statistic value of 1.832 does not, at conventional significance levels, lead us to reject the null hypothesis that GRANT and GRANT_1 are redundant in the unrestricted specification.

The restricted test equation results are depicted in the bottom portion of the window. Here we see the top portion of the results for the restricted equation:

Restricted Test Equation:

Dependent Variable: LSCRAP

Method: Panel EGLS (Cross-section random effects)

Date: 08/18/09 Time: 12:39

Sample: 1987 1989

Periods included: 3

Cross-sections included: 54

Total panel (balanced) observations: 162

Use pre-specified random component estimates

Swamy and Arora estimator of component variances

The important 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 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.

674—Chapter 37. Panel Estimation

Redundant Fixed Effects Tests

Equation: Untitled

Test cross-section and period fixed effects

Notice that there are three sets of tests. The first set consists of two tests (“Cross-section F” and “Cross-section Chi-square”) that evaluate the joint significance of the cross-section effects using sums-of-squares (F-test) and the likelihood 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 cross-section effects are redundant.

The next two tests evaluate the significance of the period dummies in the unrestricted model against a restricted specification in which there are cross-section effects only. Both forms of the statistic strongly reject the null of no period effects.

The remaining results evaluate the joint significance of all of the effects, respectively. Both of the test statistics reject the restricted model in which there is only a single intercept.

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 (2005, p. 66)).

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.

Panel Equation Testing—675

For example, Baltagi (2005) considers an example of Hausman testing (Example 1, p. 70), in which the results for a Swamy-Arora random effects estimator for the Grunfeld data (“Grunfeld_baltagi_panel.WF1”) are compared with those obtained from the corresponding fixed effects estimator. To perform this test we must first estimate a random effects estimator, obtaining the results:

Dependent Variable: I

Method: Panel EGLS (Cross-section random effects)

Date: 08/18/09 Time: 12:50

Sample: 1935 1954

Periods included: 20

Cross-sections included: 10

Total panel (balanced) observations: 200

Swamy and Arora estimator of component variances

Next we select the Hausman test from the equation menu by clicking on View/Fixed/Random Effects Testing/Correlated Random Effects - Hausman Test. EViews estimates the corresponding fixed effects estimator, evaluates the test, and displays the results in the equation window. If the original specification is a two-way random effects model, EViews will test the two sets of effects separately as well as jointly.

There are three parts to the output. The top portion describes the test statistic and provides a summary of the results. Here we have:

Correlated Random Effects - Hausman Test

Equation: Untitled

Test cross-section random effects

The statistic provides little evidence against the null hypothesis that there is no misspecification.