Knowledge that Transforms

This paper is part of a Ph.D. dissertation submitted by the author to the Graduate College, University of Iowa, and was partially supported by the National Science Foundation Grant GS-1491. The author acknowledges the guidance and encouragement received from Professor S. Y. Wu.

T HE geometric distributed lag model developed by Koyck [8] and Nerlove [11] has been widely used in many empirical studies. The appropriate estimation method for parameters of these models is determined by the true probability distribution of random errors. If the random errors follow a first-order Markov process, Klein [7] has shown that the method of weighted regressions yields maximum likelihood estimators.' However, Klein's method requires prior knowledge of the true serial correlation of random errors. In the absence of such prior knowledge, one can resort to several alternative estimation methods.2 In this paper, I establish a bracketing rule applicable to a subset of the admissible probability distributions of random errors. Consider two special cases of Klein's method in which the true serial correlation p is (i) equal to zero and (ii) equal to the coefficient of the lagged dependent variable (1 X). The former case implies an orthogonal regression while the latter is equivalent to ordinary least squares (OLS). The orthogonal and OLS regressions yield two sets of parameter estimates lying on either side of the maximum likelihood parameter estimates provided that the true serial correlation lies in the interval 0 < p < 1 L, the OLS estimate of the population parameter 1 X. This basic bracketing theorem can be shown to hold even for fixed sample size. Moreover, the width of the interval bracketing the maximum likelihood parameter estimates is narrower, the larger is the partial correlation with the lagged dependent variable. This last result leads to an important implication. If a geometric distributed lag constitutes the correct specification of economic behavior, the dependent variable should be highly correlated with the lagged dependent variable. In this event, the discrepancy between OLS and orthogonal parameter estimates (which bracket the maximum likelihood estimates) will be small. Thus, the bias due to least squares is negligibly small provided that the true serial correlation lies in the interval 0 < p < 1 X. A simple geometric distributed lag model is described by a system of two structural equations. Yt a + 8Zt* + Ut + (1)

John F. Helliwell, Lawrence H. Officer, Harold T. Shapiro, Ian A. Stewart, Econometric Analysis of Policy Choices for an Open Economy, The Review of Economics and Statistics, Vol. 51, No. 4 (Nov., 1969), pp. 383-398

that the size coefficient (i8jl) was statistically significant at the 0.05 level in thirty-five of the 118 industries examined.6 The results for these industries are reported in table 1. The range of variation in the magnitude of i,/3 is considerable; the high, in Perfume and Cosmetics, is 0.114, and the low, 0.014, is found in Men's Clothing. The mean coefficient for the thirty-five industries is 0.0405 suggesting that on the basis of this group one would expect the rate of return to rise by 1.2 per cent if size doubles, and by 4.05 per cent for a ten-fold increase in size. VI Conclusions

T HIS paper has the dual purpose of presenting spectral analysis in a different, perhaps more appropriate application than that of past work and of analyzing differences among industries in the relation of gross changes in employment and changes in output. Spectral analysis has been applied to a problem in labor economics only once.' The cause of the dearth of studies using the technique is possibly the limited number of observations available on most variables relating to labor. Even if we had such information, there are relatively few problems for which spectral analysis might be expected to give interesting results. The technique does not seem to have produced much new evidence about the cyclical relationships to which it has been applied, perhaps because we have so few observations on complete cycles in economic activity, or perhaps because these low-frequency movements are of such irregular length as to be undetectable by spectral analysis.2 Because of these problems the major use of this technique in labor economics must lie in the analysis of behavior reflected at higher frequencies, particularly to those we call seasonal. It is only at those frequencies that we have enough information on behavior to make any inferences about it.

Joel Bergsman, Samuel A. Morley, Import Constraints and Development: Causes of the Recent Decline of Brazilian Economic Growth: A Comment, The Review of Economics and Statistics, Vol. 51, No. 1 (Feb., 1969), pp. 101-102