On the Estimation of an Exponential Function
In estimating a function, certain assumptions are made about the random term. This paper deals with the influence of such assumptions on estimators for the function y = x0. The case of a normally distributed random term, both in its multiplicative and additive forms, is considered here. The major part of the article is devoted to a hypothesis concerning a lognormally distributed random term, for which consistent estimators are derived. THE EXPONENTIAL function is very familiar in economic research. For instance, the relationship between consumption and income is often expressed as y=x', where y denotes consumption and x is income. Usually it is assumed that the actual observations on y are determined by the function x' and by an additional random term s. In estimating this function, the statistical properties of the estimators of a and E(y) will depend on the assumptions made about the random term.2 In this paper some alternative specifications of this random term will be given and their influence on the estimates considered.
- DOI
- 10.2307/1910362
- Volume
- 33 (4)
- Pages
- 863
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