Estimation—679

Estimation

Once you have specified the logl object, you can ask EViews to find the parameter values which maximize the likelihood parameters. Simply click the Estimate button in the likelihood window toolbar to open the Estimation Options dialog.

There are a number of options which allow you to control various aspects of the estimation procedure. See “Setting Estimation Options” on page 951 for a discussion of these options. The default settings, however, should provide a good start for most problems. When you click on OK, EViews will begin estimation using the current settings.

Starting Values

Since EViews uses an iterative algorithm to

find the maximum likelihood estimates, the choice of starting values is important. For problems in which the likelihood function is globally concave, it will influence how many iterations are taken for estimation to converge. For problems where the likelihood function is not concave, it may determine which of several local maxima is found. In some cases, estimation will fail unless reasonable starting values are provided.

By default, EViews uses the values stored in the coefficient vector or vectors prior to estimation. If a @param statement is included in the specification, the values specified in the statement will be used instead.

In our conditional heteroskedasticity regression example, one choice for starting values for the coefficients of the mean equation coefficients are the simple OLS estimates, since OLS provides consistent point estimates even in the presence of (bounded) heteroskedasticity. To use the OLS estimates as starting values, first estimate the OLS equation by the command:

equation eq1.ls y c x z

After estimating this equation, the elements C(1), C(2), C(3) of the C coefficient vector will contain the OLS estimates. To set the variance scale parameter C(4) to the estimated OLS residual variance, you can type the assignment statement in the command window:

c(4) = eq1.@se^2

For the final heteroskedasticity parameter C(5), you can use the residuals from the original OLS regression to carry out a second OLS regression, and set the value of C(5) to the appropriate coefficient. Alternatively, you can arbitrarily set the parameter value using a simple assignment statement:

LogL Procs—681

•Gradients: displays view of the gradients (first derivatives) of the log likelihood at the current parameter values (if the model has not yet been estimated), or at the converged parameter values (if the model has been estimated). These views may prove to be useful diagnostic tools if you are experiencing problems with convergence.

•Check Derivatives: displays the values of the numeric derivatives and analytic derivatives (if available) at the starting values (if a @param statement is included), or at current parameter values (if there is no @param statement).

LogL Procs

•Estimate…: brings up a dialog to set estimation options, and to estimate the parameters of the log likelihood.

•Make Model: creates an untitled model object out of the estimated likelihood specification.

•Make Gradient Group: creates an untitled group of the gradients (first derivatives) of the log likelihood at the estimated parameter values. These gradients are often used in constructing Lagrange multiplier tests.

•Update Coefs from LogL: updates the coefficient vector(s) with the estimates from the likelihood object. This procedure allows you to export the maximum likelihood estimates for use as starting values in other estimation problems.

Most of these procedures should be familiar to you from other EViews estimation objects. We describe below the features that are specific to the logl object.

Estimation Output

In addition to the coefficient and standard error estimates, the standard output for the logl object describes the method of estimation, sample used in estimation, date and time that the logl was estimated, evaluation order, and information about the convergence of the estimation procedure.

LogL Procs—683

You may find this view to be a useful diagnostic tool when experiencing problems with convergence or singularity. One common problem leading to singular matrices is a zero derivative for a parameter due to an incorrectly specified likelihood, poor starting values, or a lack of model identification. See the discussion below for further details.

Check Derivatives

You can use the Check Derivatives view to examine your numeric derivatives or to check the validity of your expressions for the analytic derivatives. If the logl specification contains a @param statement, the derivatives will be evaluated at the specified values, otherwise, the derivatives will be computed at the current coefficient values.

The first part of this view displays the names of the user supplied derivatives, step size parameters, and the coefficient values at which the derivatives are evaluated. The relative and minimum step sizes shown in this example are the default settings.

The second part of the view computes the sum (over all individuals in the sample) of the numeric and, if applicable, the analytic derivatives for each coefficient. If appropriate, EViews will also compute the

largest individual difference between the analytic and the numeric derivatives in both absolute, and percentage terms.