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On the asymptotic normality of Fourier flexible form estimates. (English) Zbl 0792.62102
The paper deals with the determination of a class of rules for increasing the number of parameters of the Fourier factor demand system that imply asymptotically normal elasticity estimates. After assuming a deterministic version of factor demand theory satisfying that observed factor cost shares follow some distribution with certain location parameter, a theorem is proved related to the asymptotic normality of the relative error.
It is interesting to stress the originality of the proof strategy followed by the authors, consisting in relating the minimum eigenvalue of the sample sum of squares and cross-product matrix to the minimum eigenvalue of the population matrix via a uniform strong law.
If the rate at which parameters may increase is slower than any fractional power of the sample size, the rate is coincident with the one given by D. W. K. Andrews [see ibid. 47, No. 2/3, 359-377 (1991; Zbl 0734.62069); Econometrika 59, No. 3, 817-858 (1991; Zbl 0732.62052) and ibid., No. 2, 307-345 (1991; Zbl 0727.62047)]. This is the case when the results are applied to a multivariate regression with minimum eigenvalue that is bounded or declines at a polynomial rate. In the referred conditions, the method proposed in this paper gives faster rates than Andrews’, and it seems therefore to be “preferable” although it does not cover the heteroscedastic case.
Reviewer: R.Pérez (Oviedo)

MSC:
62P20 Applications of statistics to economics
62F12 Asymptotic properties of parametric estimators
62E20 Asymptotic distribution theory in statistics
91B42 Consumer behavior, demand theory
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