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both the coefficients and weighting matrix converge. This is the iteration method employed in EViews prior to version 4.

•Iterate Weights and Coefs—Sequential updating repeats the default method of updating weights and then iterating coefficients to convergence until both the coefficients and the weighting matrix converge.

Note that all four of the estimation techniques yield results that are asymptotically efficient. For linear models, the two Iterate Weights and Coefs options are equivalent, and the two One-Step Weighting Matrix options are equivalent, since obtaining coefficient estimates does not require iteration.

In addition, the Iteration Options tab allows you to set a number of options for estimation, including convergence criterion, maximum number of iterations, and derivative calculation settings. See “Setting Estimation Options” on page 951 for related discussion.

Estimation Output

The system estimation output contains parameter estimates, standard errors, and t-statis- tics for each of the coefficients in the system. Additionally, EViews reports the determinant of the residual covariance matrix, and, for FIML estimates, the maximized likelihood value.

In addition, EViews reports a set of summary statistics for each equation. The R2 statistic, Durbin-Watson statistic, standard error of the regression, sum-of-squared residuals, etc., are computed for each equation using the standard definitions, based on the residuals from the system estimation procedure.

You may access most of these results using regression statistics functions. See Chapter 15, page 454 for a discussion of the use of these functions, and Appendix A, “Object, View and Procedure Reference”, on page 153 of the Command and Programming Reference for a full listing of the available functions for systems.

Working With Systems

After obtaining estimates, the system object provides a number of tools for examining the equation results, and performing inference and specification testing.

System Views

Some of the system views are familiar from the discussion in previous chapters:

•You can examine the estimated covariance matrix by selecting the Coefficient Covariance Matrix view.

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•Make Residuals creates a number of series containing the residuals for each equation in the system. The residuals will be given the next unused name of the form RESID01, RESID02, etc., in the order that the equations are specified in the system.

•Make Endogenous Group creates an untitled group object containing the endogenous variables.

Example

As an illustration of the process of estimating a system of equations in EViews, we estimate a translog cost function using data from Berndt and Wood (1975) as tabulated in Greene (1997). The translog cost function has four factors with three equations of the form:

where ci and pi are the cost share and price of factor i , respectively. β and δ are the parameters to be estimated. Note that there are cross equation coefficient restrictions that ensure symmetry of the cross partial derivatives.

We first estimate this system without imposing the cross equation restrictions and test whether the symmetry restrictions hold. Create a system by clicking Object/New Object.../System in the main toolbar or type system in the command window. Press the Name button and type in the name “SYS_UR” to name the system.

Next, type in the system window and specify the system as:

We estimate this model by full information maximum likelihood (FIML). FIML is invariant to the equation that is dropped. Press the Estimate button and choose Full Information Maximum Likelihood. EViews presents the estimated coefficients and regression statistics for each equation. The top portion of the output describes the coefficient estimates:

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Wald Test:

System: SYS_UR

Restrictions are linear in coefficients.

fails to reject the symmetry restrictions. To estimate the system imposing the symmetry restrictions, copy the object using Object/Copy Object, click View/System Specification and modify the system.

We have named the system SYS_TLOG. Note that to impose symmetry in the translog specification, we have restricted the coefficients on the cross-price terms to be the same (we have also renumbered the 9 remaining coefficients so that they are consecutive). The restrictions are imposed by using the same coefficients in each equation. For example, the coefficient

on the log(P_L/P_M) term in the C_K equation, C(3), is the same as the coefficient on the log(P_K/P_M) term in the C_L equation.

To estimate this model using FIML, click Estimate and choose Full Information Maximum Likelihood. The top part of the equation describes the estimation specification, and provides coefficient and standard error estimates, t-statistics, p-values, and summary statistics: