Estimation of the Liquidity Trap Using Spline Functions
LMOST all discussions concerning the imA portance of money in affecting economic activity make reference to the liquidity-trap hypothesis. This important hypothesis states that the elasticity of the demand for money with respect to the rate of becomes infinite at low rates. As J. M. Keynes himself expresses it, after the rate of has fallen to a certain level, liquidity preference may become virtually absolute in the sense that almost anyone prefers cash to holding a debt which yields so low a rate of interest (1936, p. 207). Studies by Bronfenbrenner and Mayer (1960), Konstas and Khouja (1969), Laidler (1966), Meltzer (1963) and White (1972), among others, have attempted to confirm or disconfirm this hypothesis by testing whether the elasticity of the demand for money increases as the rate of falls, on the basis that this is the only way it can pass from a finite to an infinite value. Thus far, the evidence mainly disconfirms the liquidity-trap hypothesis. This evidence, however, has generally been obtained by employing ordinary least squares regression methods. Yet, as David Laidler points out, it is not possible to fit directly by regression analysis a function which has a negative slope over part of its range and no slope at all over another part . (1969, p. 97). Past studies, therefore, have not been directly able to determine whether the elasticity becomes infinite at low rates. The purpose of this paper is to test the liquidity-trap hypothesis by employing spline functions. Briefly, these functions represent a special class of approximating functions which allow the dependent variable in a regression to take on different functional relationships with respect to the independent variable in various subintervals of the domain of the independent variable in a continuous fashion. In this way, the problem inherent in previous studies using ordinary least squares techniques can be avoided, permitting a more direct test of the liquidity-trap hypothesis. In short, this paper will provide new and more direct evidence bearing on the issue of an infinitely elastic demand for money function as well as the way in which the important but relatively unknown spline functions may be used to capture various empirical economic relationships. The plan of the remainder of the paper is as follows. The next section contains a discussion of spline theory, followed by a section containing the empirical results obtained by using spline functions. The summary and conclusions are then reported in the last section.
- DOI
- 10.2307/1924028
- Volume
- 58 (2)
- Pages
- 218
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