Knowledge that Transforms

IN recent years several attempts have beeni made to set up macro-econometric models for the United States and to derive statistical estimates of relevant parameters for the prewar period.1 To the knowledge of the present author few, if any, attempts have been made to deal statistically with econometric models using postwar data. There are good reasons for this. In the first place if annual data are used, too few observations will be available for an adequate statistical analysis. If monthly or quarterly data are utilized, then difficult problems arise, for example the treatment of seasonal variation and the possibility of substantial correlation of disturbances. In spite of these latter difficulties an attempt is made in the present paper to analyze statistically a very simple econometric model for the United States using quarterly national income data for the period I947-50. The statistical analysis is admittedly weak at certain points and must therefore be regarded as preliminary and tentative. In addition to the difficulties mentioned above the problem of multicollinearity 2 is present, as is usually the case in multiple correlation studies involving economnic data. All of this means, of course. that the regression coefficients tend to be rather uncertain and that therefore the estimates of the structural parameters must be interpreted with caution.

The paper shall be concerned with short run (cyclical) functional relationships as well as long run (secular) relationships between the variables. In fact, the fundamental difference between the cyclical and secular character of these relationships will be stressed. In general, though with some exceptions, which will be explained presently, these variables are related in constant proportions secularly, i.e., a graphic representation of the secular functional relationship would go through the origin. On the other hand, the cyclical relationship is not one of constant proportions, so that the cyclical function does not go through the origin; it would have a positive intercept. The main conclusions of this paper are as follows: i) Personal consumption expenditures are primarily a function of disposable personal income. Consumption is roughly the same proportion of deflated per capita disposable personal income in peak years.4 This is the secular relationship of consumption and income. Thus in Chart i, which presents the actual deflated per capita data, the line joining the origin with I929 comes much closer to the actual observations of I948-50 than the regression line calculated for the cyclical period I929-40. Presumably, if a serious depression were to develop from the secular peaks of 1948-50, the line of relationship would be the indicated broken line in Chart i, parallel to the interwar cyclical line relating consumption to income, but at a higher level. In other words, while the secular relationship is primarily characterized by constant proportions between consumption and disposable income, in the short run the ratio of consumption expenditures to income varies with the cycle, falling as income rises and rising with declining incomes. Thus, the fact that actual postwar personal consumption expenditures are in excess of those expected from prewar cyclical relationships with disposable income is primarily due to the upward secular drift of the consumption function. 2) This functional relationship between personal consumption expenditures and disposable personal income does not hold for periods of unprecedented disturbances in the economy associated with total war and the postwar transition to a peacetime market. Thus in Chart i, the years I946 and I947 are still considerably off the secular line of relationship. However, by 1948, the function appears to have resumed a mnore normal shape. The relative speed with which the functional relationship of consumption to income reasserted itself after the great shocks assoCiated with World WVar II is indeed ' This article represents part of a larger project on the consumption function which will examine in greater detail its short run aspects as well as the component parts of the aggregates. Appreciation is expressed for the aid of Professors Alvin H1. Hansen, G. H. Orcutt, and J. S. Duesenberry, of Harvard, none of whom, of course, is responsible for any errors that remain. The author is currently on leave from the U. S. Department of Commerce; the views expressed are his own. 2 The sources of the data used in this article are explained in a note at the end of the article. This article was written before the i95T National Income Supplement to the Survey of Current BEusiness was available. 8 J. R. Hicks, A Contribution to the Theory of the Trade Cycle (London, 1950), p. 33. 'For an early statement of the relative constancy of the ratio of consumption to income in peak years see A. H Hansen, Fiscal Policy and Business Cycles (New York, I941), p. 237.