908—Chapter 29. Panel Estimation

“@LEV” is not provided, EViews will transform the instrument to match the equation transformation.

If, for example, you estimate an equation that uses orthogonal deviations to remove a cross-section fixed effect, EViews will, by default, compute orthogonal deviations of the instruments provided prior to their use. Thus, the instrument list:

z1 z2 @lev(z3)

will use the transformed Z1 and Z2, and the original Z3 as the instruments for the specification.

Note that in specifications where “@DYN” and “@LEV” keywords are not relevant, they will be ignored. If, for example, you first estimate a GMM specification using first differences with both dynamic and level instruments, and then re-estimate the equation using LS, EViews will ignore the keywords, and use the instruments in their original forms.

GMM Options

Lastly, clicking on the Options tab in the dialog brings up a page displaying computational options for GMM estimation. These options are virtually identical to those for both LS and IV estimation (see “LS Options” on page 904). The one difference is in the option for saving estimation weights with the object. In the GMM context, this option applies to both the saving of GLS as well as GMM weights.

Panel Estimation Examples

Least Squares Examples

To illustrate the estimation of panel equations in EViews, we first consider an example involving unbalanced panel data from Harrison and Rubinfeld (1978) for the study of hedonic pricing. The data are well known and used as an example dataset in many sources (e.g., Baltagi (2001), p. 166).

The data consist of 506 census tract observations on 92 towns in the Boston area with group sizes ranging from 1 to 30. The dependent variable of interest is the median value of owner occupied towns (MV), and the regressors include various measures of housing desirability.

We begin our example by structuring our workfile as an undated panel. Click on the “Range:” description in the workfile window,

910—Chapter 29. Panel Estimation

Dependent Variable: MV

Method: Panel Least Squares

Date: 02/16/04 Time: 12:07

Sample: 1 506

Cross-sections included: 92

Total panel (unbalanced) observations: 506

Effects Specification

Cross-section fixed (dummy variables)

The results for the fixed effects estimation are depicted here. Note that as in pooled estimation, the reported R-squared and F-statistics are based on the difference between the residuals sums of squares from the estimated model, and the sums of squares from a single constant-only specification, not from a fixed-effect-only specification. Similarly, the reported information criteria report likelihoods adjusted for the number of estimated coefficients, including fixed effects. Lastly, the reported Durbin-Watson stat is formed simply by computing the first-order residual correlation on the stacked set of residuals.

We may click on the Estimate button to modify the specification to match the WallaceHussain random effects specification considered by Baltagi and Chang. We modify the specification to include the additional regressors used in estimation, change the cross-sec- tion effects to be estimated as a random effect, and use the Options page to set the random effects computation method to Wallace-Hussain.

The top portion of the resulting output is given by:

912—Chapter 29. Panel Estimation

EViews will structure the workfile so that it is a panel workfile with 157 cross-sections, and three annual observations. Note that even though there are 471 observations in the workfile, a

large number of them contain missing values for variables of interest.

To estimate the fixed effect specification with robust standard errors (Wooldridge example 10.5, p. 276), click on specification Quick/Estimate Equation from the main EViews menu. Enter the list specification:

lscrap c d88 d89 grant grant_1

in the Equation specification edit box on the main page and select Fixed in the Cross-sec- tion effects specification combo box on the Panel Options page. Lastly, since we wish to compute standard errors that are robust to serial correlation (Arellano (1987), White (1984)), we choose White period as the Coef covariance method. To match the reported Wooldridge example, we must select No d.f. correction in the covariance calculation.

Click on OK to accept the options. EViews displays the results from estimation:

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Dependent Variable: D(LSCRAP)

Method: Panel Least Squares

Date: 02/16/04 Time: 14:51

Sample (adjusted): 1988 1988

Cross-sections included: 54

Total panel (balanced) observations: 108

White period standard errors & covariance (d.f. corrected)

While current versions of EViews do not provide a full set of specification tests for panel equations, it is a straightforward task to construct some tests using residuals obtained from the panel estimation.

To continue with the Wooldridge example, we may test for AR(1) serial correlation in the first-differenced equation by regressing the residuals from this specification on the lagged residuals using data for the year 1989. First, we save the residual series in the workfile.

Click on Proc/Make Residual Series... on the estimated equation toolbar, and save the residuals to the series RESID01.

Next, regress RESID01 on RESID01(-1), yielding:

Panel Estimation Examples—915

Dependent Variable: RESID01

Method: Panel Least Squares

Date: 02/16/04 Time: 14:57

Sample (adjusted):

Cross-sections included: 54

Total panel (balanced) observations: 54

Under the null hypothesis that the original idiosyncratic errors are uncorrelated, the residuals from this equation should have an autocorrelation coefficient of -0.5. Here, we obtain an estimate of ρˆ 1 = 0.237 which appears to be far from the null value. A formal Wald hypothesis test rejects the null that the original idiosyncratic errors are serially uncorrelated:

Wald Test:

Equation: Untitled

Restrictions are linear in coefficients.

Instrumental Variables Example

To illustrate the estimation of instrumental variables panel estimators, we consider an example taken from Papke (1994) for enterprise zone data for 22 communities in Indiana that is outlined in Wooldridge (2002, p. 306).

916—Chapter 29. Panel Estimation

The panel workfile for this example is structured using YEAR as the period identifier, and CITY as the cross-section identifier. The result is a balanced annual panel for dates from 1980 to 1988 for 22 cross-sections.

To estimate the example specification, create a new equation by typing “TSLS” in the command line, or by clicking on

Quick/Estimate Equation... in the

main menu. Selecting TSLS - Two-Stage Least Squares (and AR) in the Method combo box to display the instrumental variables estimator dialog, if necessary, and enter:

d(luclms) c d(luclms(-1)) d(ez)

to regress the difference of log unemployment claims (LUCLMS) on the lag difference, and the difference of enterprise zone designation (EZ). Since the model is estimated with time intercepts, you should click on the Panel Options page, and select Fixed for the Period effects.

Next, click on the Instruments tab, and add the names:

c d(luclms(-2)) d(ez)

to the Instrument list edit box. Note that adding the constant C to the regressor and instrument boxes is not required since the fixed effects estimator will add it for you. Click on OK to accept the dialog settings. EViews displays the output for the IV regression:

918—Chapter 29. Panel Estimation

The workfile is structured as a dated annual panel using ID as the cross-sec- tion identifier series and YEAR as the date classification series.

Since the model is assumed to be dynamic, we employ EViews tools for estimating dynamic panel data models. To bring up the GMM dialog, enter “GMM” in the command line, or select

Quick/Estimate Equation... from the main menu, and choose GMM/DPD -

Generalized Method of Moments /Dynamic Panel Data in the Method combo box to display the IV estimator dialog.

Click on the button labeled Dynamic Panel Wizard... to bring up the DPD wizard. The DPD wizard is a tool that will aid you in filling out the general GMM dialog. The first page is an introductory screen describing the basic purpose of the wizard. Click Next to continue.

The second page of the wizard prompts you for the dependent variable and the number of its lags to include as explanatory variables. In this example, we wish to estimate an equation with N as the dependent variable and N(-1) and N(-2) as explanatory variables so we enter “N” and select “2” lags in the combo box. Click on Next to continue to the next page, where you will specify the

remaining explanatory variables.

In the third page, you will complete the specification of your explanatory variables. First, enter the list:

920—Chapter 29. Panel Estimation

You should now specify the remaining instruments. There are two lists that should be provided. The first list, which is entered in the edit field labeled Transform, should contain a list of the strictly exogenous instruments that you wish to transform prior to use in estimating the transformed equation. The second list, which should be entered in the No transform edit box should contain a list of instruments that should be used directly without transformation. Enter the remaining instruments:

w w(-1) k ys ys(-1)

in the first edit box and click on Next to proceed to the final page.

The final page allows you to specify your GMM weighting and coefficient covariance calculation choices. In the first combo box, you will choose a GMM Iteration option. You may select 1-step (for i.i.d. innovations) to compute the ArellanoBond 1-step estimator, 2- step (update weights once), to compute the Arellano-Bond 2-step estimator, or n-step (iterate