* Variance Estimators for an MLE Electricity Costs Model * * Keywords: * regression, mle, variance estimation * * Description: * We illustrate how to estimate a model for Average Costs in Electricity * Supply industry nonparametrically * and plot it * * Author(s): * Noel Roy * Skif Pankov * * Source: * William H. Greene, Econometric Analysis - 7th Edition * Pearson International Edition, Chapter 14, Example 14.4 (page 562) * * Reading the data and naming variables, specifying to ignore the first * line read (TableFC-1.shd) i y x / list skiplines=1 * Doing the Maximum Likelihood Estimation of the model with non-normal errors mle y x * Testing the hypothesis that the coefficient on x is unity test x=1 * Using nl command as a more general approach to maximum likelihood * estimation, specifying to save standard errors in a variable sigma and * (through logden option) that the equation given on the eq command * is the log-density for a single observation nl 1 /ncoef=1 logden genrvar stderr=sigma eq -log(beta+x)-y/(beta+x) end * The default asymptotic variance as calculated is gen1 sigma**2 * Calculating the three forms of the asymptotic variance of beta * First, that based on the expectation of the hessian genr ey=beta+x genr v1=-1/(beta+x)**2+2*ey/(beta+x)**3 * Second, that based on the actual value of the hessian genr v2=-1/(beta+x)**2+2*y/(beta+x)**3 * third, that based the outer product of the gradient genr v3=(-1/(beta+x)+y/(beta+x)**2)**2 * Summing these values, and inverting ?stat v1-v3 /sums=varinv matrix var=1/varinv * print the three estimates. print var stop