Chapter 3. EViews 5.1 Panel and Pool Testing
EViews 5.1 updates panel and pool equations to provide built-in support for testing the statistical significance of omitted and redundant variables, testing the significance of estimated fixed effects in least squares estimation, and performing Hausman specification tests for correlated effects in a random effects setting.
The following discussion documents the new features.
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 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-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:
50—Chapter 3. EViews 5.1 Panel and Pool Testing
Dependent Variable: D(LSCRAP)
Method: Panel Least Squares
Date: 11/24/04 Time: 09:15
Sample (adjusted): 1988 1989
Cross-sections included: 54
Total panel (balanced) observations: 108
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
|
|
|
|
|
|
|
|
C |
-0.168993 |
0.078872 |
-2.142622 |
0.0344 |
D89 |
-0.104279 |
0.111542 |
-0.934881 |
0.3520 |
|
|
|
|
|
|
|
|
|
|
R-squared |
0.008178 |
Mean dependent var |
-0.221132 |
|
Adjusted R-squared |
-0.001179 |
S.D. dependent var |
0.579248 |
|
S.E. of regression |
0.579589 |
Akaike info criterion |
1.765351 |
|
Sum squared resid |
35.60793 |
Schwarz criterion |
1.815020 |
|
Log likelihood |
-93.32896 |
F-statistic |
|
0.874003 |
Durbin-Watson stat |
1.445487 |
Prob(F-statistic) |
0.351974 |
|
|
|
|
|
|
|
|
|
|
|
We wish to test the significance of the first differences of the omitted job training grant variables GRANT and GRANT_1. Click on View/Coefficient Tests/Omitted Variables - Likelihood Ratio... and type “D(GRANT)” and “D(GRANT_1)” to enter the two variables in differences. Click on OK to display the omitted variables test results.
The top portion of the results contains a brief description of the test, the test statistic values, and the associated significance levels:
Omitted Variables: D(GRANT) D(GRANT_1)
F-statistic |
1.529525 |
Prob. F(2,104) |
0.221471 |
Log likelihood ratio |
3.130883 |
Prob. Chi-Square(2) |
0.208996 |
Here, the test statistics do not reject, at conventional significance levels, the null hypothesis that D(GRANT) and D(GRANT_1) are jointly irrelevant.
The bottom portion of the results shows the test equation which estimates under the unrestricted alternative:
Redundant Variables Test—51
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
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
|
|
|
|
|
|
|
|
C |
-0.090607 |
0.090970 |
-0.996017 |
0.3216 |
D89 |
-0.096208 |
0.125447 |
-0.766923 |
0.4449 |
D(GRANT) |
-0.222781 |
0.130742 |
-1.703970 |
0.0914 |
D(GRANT_1) |
-0.351246 |
0.235085 |
-1.494124 |
0.1382 |
|
|
|
|
|
|
|
|
|
|
R-squared |
0.036518 |
Mean dependent var |
-0.221132 |
Adjusted R-squared |
0.008725 |
S.D. dependent var |
0.579248 |
S.E. of regression |
0.576716 |
Akaike info criterion |
1.773399 |
Sum squared resid |
34.59049 |
Schwarz criterion |
1.872737 |
Log likelihood |
-91.76352 |
F-statistic |
1.313929 |
Durbin-Watson stat |
1.498132 |
Prob(F-statistic) |
0.273884 |
|
|
|
|
|
|
|
|
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 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- 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:
52—Chapter 3. EViews 5.1 Panel and Pool Testing
.
Dependent Variable: LSCRAP
Method: Panel EGLS (Cross-section random effects)
Date: 11/24/04 Time: 11:25
Sample: 1987 1989
Cross-sections included: 54
Total panel (balanced) observations: 162
Swamy and Arora estimator of component variances
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
|
|
|
|
|
|
|
|
C |
0.414833 |
0.242965 |
1.707379 |
0.0897 |
D88 |
-0.093452 |
0.108946 |
-0.857779 |
0.3923 |
D89 |
-0.269834 |
0.131397 |
-2.053577 |
0.0417 |
UNION |
0.547802 |
0.409837 |
1.336635 |
0.1833 |
GRANT |
-0.214696 |
0.147500 |
-1.455565 |
0.1475 |
GRANT_1 |
-0.377070 |
0.204957 |
-1.839747 |
0.0677 |
|
|
|
|
|
|
|
|
|
|
|
Effects Specification |
|
|
|
|
|
|
S.D. |
Rho |
|
|
|
|
|
|
|
|
|
|
Cross-section random |
|
|
1.390029 |
0.8863 |
Idiosyncratic random |
|
|
0.497744 |
0.1137 |
|
|
|
|
|
|
|
|
|
|
Note in particular that our unrestricted model is a random effects specification using Swamy and Arora estimators for the component variances, and that the estimates of the cross-section and idiosyncratic random effects standard deviations are 1.390 and 0.4978, respectively.
If we select the redundant variables test, and perform a joint test on GRANT and GRANT_1, EViews displays the test results in the top of the results window:
Redundant Variables: GRANT GRANT_1
F-statistic |
1.832264 |
Prob. F(2,156) |
0.163478 |
|
|
|
|
|
|
|
|
Here we see that the statistic value of 1.832 does not lead us to reject, at conventional significant levels, 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: