The Stock Demand Elasticities of Non-Farm Housing: Comment

Abstract

Several years ago I inferred that the stock demand elasticity of non-farm housing with respect to income is about unity from a time-series regression analysis of the rate of new construction on income, other determinants of desired stock demand, and the actual housing stock.1 In a recent paper, Tong Hun Lee argues that I used an improper measure of the rate of interest and, because credit terms which I omitted were positively correlated with income, my estimate of the income elasticity of housing demand was upward biased.2 Lee concludes that this elasticity is substantially less than unity. In this comment I shall argue that Lee's results are inconsistent with other recent evidence on the income elasticity of housing demand and that his interpretation of the relation between interest rates and contract lengths is unsatisfactory on both a priori and empirical grounds. Even if Lee's criticism could be accepted at face value, his modification of my flow demand equation for non-farm housing yields an estimated income elasticity which is inconsistent with other recent evidence. In my study, I estimated the income elasticity of housing demand in several ways, one of which was a comparison of the rental value of housing with the housing stock and income. This comparison yielded an estimated income elasticity of 0.94,3 which is quite close to the value I inferred from my flow demand regression equation. Now, this latter estimate in no way depends upon the rate of interest or other aspects of the cost of capital to home buyers. While the profitability of adding to the housing stock, and hence the stock in existence at any time, is influenced by the cost of capital, the rental value of the existing housing stock depends only upon the size of this stock and the position of the demand curve for the services of housing. I am the first to admit that this estimate of mine could be in error for several reasons, but the omission of credit terms is not one of them. More recently, Margaret G. Reid's exhaustive analysis of the effect of income on housing demand suggested that the income elasticity is substantially larger than unity, perhaps as large as two.4 Lee mentions her results in a footnote but claims they are upward biased because she, too, omits credit terms.5 In my opinion, however, Lee brushes Reid's results aside much too lightly. Her comparisons of the expenditures of tenants with their incomes are completely free of any bias due to the omission of credit terms for the reasons already discussed in the paragraph above. These estimates are all substantially larger than those shown by Lee in his equations (6) and (11), the latter being about 0.34. In addition, while the value of housing an owner inhabits is influenced by the cost of borrowing for him, there is no reason to expect the cost of borrowing to differ among different borrowers in the same city at a given time apart from differences associated with different administrative costs and risk premiums for different kinds of mortgage loans. (Of course, owners may have originally acquired their homes at differing times, but there is likewise little reason to suppose that differences in the cost of borrowing associated with different time of acquisition is systematically associated with income differences among owners.) income elasticities Margaret Reid found for owners in different parts of the same metropolitan area at a given time exceed Lee's estimates even more than do her estimates for renters.6 I conclude, therefore, that Lee's findings are highly questionable because his income elasticity estimate is so much less than those referred to above. Many economists believe that, in addition to contract interest rates, measures of contract maturities and loan-to-value ratios are needed to describe the cost of borrowing on mortgages. When interest rates fall, so the argument goes, mortgage lenders reduce contract interest rates but also will make longrer maturity and higher loan-to-value ratio loans than previously. If some borrowers prefer longer maturities and lower down payments, the more generous terms which lenders allow reduce the cost of borrowing in addition to the cost reduction resulting from the fall in contract interest rates. 1 Richard F. Muth, The Demand for Non-Farm Housing, in Arnold C. Harberger, ed., Demand for Durable Goods (Chicago: University of Chicago Press, 1960), 29-96. 'Tong Hun Lee, The Stock Demand Elasticities of Non-Farm Housing, this REVIEW, XLVI (Feb., 1964), 82-89. 3 Richard F. Muth, op. cit., 64. 'Margaret G. Reid, Housing and Income (Chicago: University of Chicago Press, 1962). 'Tong Hun Lee, op. cit., footnote 31, p. 88. 'Margaret Reid, op. cit., especially Chaps. 7 and 8, pp. 162-207.