654—Chapter 37. Panel Estimation

If, for example, you estimate an equation that uses orthogonal deviations to remove a crosssection 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 650). 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 (“Harrison_panel.WF1”). The data are well known and used as an example dataset in many sources (e.g., Baltagi (2005), p. 171).

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 logarithm of the median value of owner occupied houses (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, select Undated Panel, and enter “TOWNID” as the Identifier series. EViews will prompt you twice to create a CELLID series to uniquely identify observations. Click on OK to both questions to accept your settings.

656—Chapter 37. Panel Estimation

Dependent Variable: MV

Method: Panel Least Squares

Date: 08/23/06 Time: 14:29

Sample: 1 506

Periods included: 30

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 Wallace-Hus- sain random effects specification considered by Baltagi and Chang. We modify the specification to include the additional regressors (ZN, INDUS, RAD, TAX, PTRATIO) used in estimation, change the cross-section 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:

658—Chapter 37. Panel Estimation

on Range: to bring up the dialog, and enter “YEAR” as the date identifier and “FCODE” as the cross-section ID.

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-section 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 (1980)), we choose White period as the Coef covari-

ance 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:

Panel Estimation Examples—659

Dependent Variable: LSCRAP

Method: Panel Least Squares

Date: 08/18/09 Time: 12:03

Sample: 1987 1989

Periods included: 3

Cross-sections included: 54

Total panel (balanced) observations: 162

White period standard errors & covariance (no d.f. correction)

WARNING: estimated coefficient covariance matrix is of reduced rank

Effects Specification

Cross-section fixed (dummy variables)

Note that EViews automatically adjusts for the missing values in the data. There are only 162 observations on 54 cross-sections used in estimation. The top portion of the output indicates that the results use robust White period standard errors with no d.f. correction. Notice that EViews warns you that the estimated coefficient covariances is not of full rank.

Alternately, we may estimate a first difference estimator for these data with robust standard errors (Wooldridge example 10.6, p. 282). Open a new equation dialog by clicking on Quick/Estimate Equation..., or modify the existing equation by clicking on the Estimate button on the equation toolbar. Enter the specification:

d(lscrap) c d89 d(grant) d(grant_1)

in the Equation specification edit box on the main page, select None in the Cross-section effects specification combo box, White period and No d.f. correction for the coefficient covariance method on the Panel Options page. The results are given by:

660—Chapter 37. Panel Estimation

Dependent Variable: D(LSCRAP)

Method: Panel Least Squares

Date: 08/18/09 Time: 12:05

Sample (adjusted): 1988 1989

Periods included: 2

Cross-sections included: 54

Total panel (balanced) observations: 108

White period standard errors & covariance (no d.f. correction)

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—661

Dependent Variable: RESID01

Method: Panel Least Squares

Date: 08/18/09 Time: 12:11

Sample (adjusted): 1989 1989

Periods included: 1

Cross-sections included: 54

Total panel (balanced) observations: 54

Under the null hypothesis that the original idiosyncratic errors are uncorrelated, the residu-

als from this equation should have an autocorrelation coefficient of -0.5. Here, we obtain an estimate of rˆ 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. Perform a Wald test on the test equation by clicking on View/Coefficient Diagnostics/ Wald-Coefficient Restrictions... and entering the restriction “C(1)=-0.5” in the edit box:

Wald Test:

Equation: Untitled

Null Hypothesis: C(1)=-0.5

Restrictions are linear in coefficients.

The formal test confirms our casual observation, strongly rejecting the null hypothesis.

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).

662—Chapter 37. 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 entering the keyword 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:

664—Chapter 37. Panel Estimation

The workfile is structured as a dated annual panel using ID as the cross-section 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 the keyword 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 next page, you will complete the specification of your explanatory variables. First, enter the list:

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

in the regressor edit box to include these variables. Since the desired specification will include time dummies, make certain that the checkbox for Include period dummy variables is selected, then click on Next to proceed.

666—Chapter 37. 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 Arellano-Bond 1- step estimator, 2-step (update weights once), to compute the ArellanoBond 2-step estimator, or n-step (iterate to convergence), to iterate the

weight calculations. In the first case, EViews will provide you with choices for computing the standard errors, but here only White period robust standard errors are allowed. Clicking on Next takes you to the final page. Click on Finish to return to the Equation Estimation dialog.