The Interest Elasticity of Saving and the Functional Form of the Utility Function

Abstract

The interest elasticity of aggregate saving rate is a key parameter for a number of important questions concerning government's influence on capital formation. Recently, significant attempts have been made to examine and estimate effects of interest rate changes on aggregate saving. Hamburger [9] and Wright [17] attempted to estimate interest elasticity of saving. Subsequent studies have reported divergent results, and with publication of Boskin's [5] controversial study, profession has moved away from a consensus on this issue.' In a challenge to widely held view that elasticity is low, Summers [ 16] claimed to have formulated a realistic life-cycle model yielding a large and positive interest elasticity of saving. In fact he made strong claim that the theory when formulated realistically implies interest elasticities well in excess of unity [16, 534]. The claim has been questioned by Evans [7], who showed that with negative time preferences interest elasticities are far lower. Furthermore, he incorporated intergenerational transfers into model and demonstrated that negative elasticities are not implausible. Seidman [13] introduced bequests into model and obtained results that are qualitatively similar to those of Summers. The studies by Summers [16], Evans [7] and Seidman [13] share a common feature in that each employed a standard homothetic CES utility function (SHCES) to represent preferences of individual. None of these authors addressed issue of interest elasticity of saving in relation to alternative functional forms of utility function. A natural and fruitful way of generalizing utility function considered by these authors is to introduce minimum or subsistence consumption levels as its argument. According to literature on consumer theory, utility functions that make allowance for subsistence consumption levels are desirable for various reasons. First, to capture notion that consumers require some minimal consumption levels for physiological and psychological needs in order to survive. Second, to account for habit forming nature of some goods and to make allowance for future habit forming effect of current consumption. Third, to reflect fact that some consumption expenditures are contractually fixed and therefore prevent consumers from adjusting some portion