On the Asymptotic Normality of Fourier Flexible Form Estimates
نویسنده
چکیده
Rates of increase in the number of parameters of a Fourier factor demand system that imply asymptotically normal elasticity estimates are characterized. The main technical problem in achieving this characterization is caused by the fact that the eigenvalues of the sample sum of squares and cross products matrix of the generalized least squares estimator are not bounded from below. This problem is addressed by establishing a uniform strong law with rate for the eigenvalues of this matrix so as to relate them to the eigenvalues of the expected sum of squares and cross products matrix. Because the minimum eigenvalue of the latter matrix considered as a function of the number of parameters decreases faster than any polynomial, the rate at which parameters may increase is slower than any fractional power of the sample size.
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