T HE I953-54 contraction in United States economic activity was brief and mild. According to the business cycle chronology of the National Bureau of Economic Research it lasted I3 months, extending from a peak in July I953 to a trough in August of the following year. Measured in constant dollars, gross national product declined I.5 per cent from I953 to I954. This decline in aggregate production reflected principally a 20 per cent reduction in the real volume of federal expenditures for final goods and services. The annual flow of consumer expenditures in I947 prices increased nearly two per cent. Residential construction was up I4 per cent, while other private construction rose 3 per cent and expenditures of state and local governments 9 per cent. In fact, the only major component of final expenditure which declined along with federal spending was private purchases of producers' durable equipment, which dropped 8 per cent. These figures suggest a somewhat cut-anddried picture of a strongly buoyant economy depressed briefly by an autonomous reduction in government expenditures. There is a great deal of truth in this impression, for the cutback in federal spending was the major deflationary force acting throughout the contraction, and the private economy quickly absorbed the impact of this and other depressing influences and began an early and vigorous recovery, though not without the assistance of contra-cyclical actions in the tax and monetary fields. The experience merits closer examination, however, for a number of reasons. To begin with, the processes by which the economy responds to external disturbances are an important part of the subject matter of cyclical analysis. The part played in the decline and recovery by induced changes in consumption and inventory investment will accordingly receive a good deal of attention below. But as soon as the subject is approached in this manner, it becomes apparent that the contraction was more than a passive response to the decline in government demand. For example, the rate of growth of consumer spending diminished

FIRMS determine their demands for factors of production by finding the combination of factor inputs that will maximize profits or minimize costs, subject to a technological constraint the production function. Because the production function is common to decisions for all factors, the factor demands must be interrelated; each factor demand function contains parameters from the underlying production function which also appear in other demand functions. Yet factor demand equations are commonly estimated independently, with the consequence that production function parameters implied by the different equation estimates may well be inconsistent. If the demand functions are to be included in a complete model of an economy, it is certainly desirable, if not essential, that they be consistent, i.e., that they imply a single set of parameters for the underlying production function. The authors are currently engaged in constructing a medium-term macro-model of the United States economy, an important subsector of which consists of aggregative labor and investment demand functions. This paper summarizes our efforts at estimating these two demand functions with data extending back to the early 1920's, treating relative prices and financial variables as exogenous. To illuminate the methodological issue just raised, we present results for three estimation procedures: (1) independent estimation of both relations, (2) a two-step approach in which production function parameters implied by independent estimates of one function are imposed in estimating the other relation, (3) joint estimation of both functions. By the nature of our approach, we obtain estimates of the production function from estimates of the factor demand relations. Indirect estimation of the production function in this way has also been suggested, though not carried out, by Dhrymes [7] and Nerlove [15]. It seems to us to be preferable to several alternatives. The production function is a constraint relating desired or expected (long-run equilibrium) output to desired (long-run equilibrium) factor inputs, and these are generally not observable variables. Expected output may be related to current and past levels of output, and observed factor inputs are likely to be disequilibrium values associated with lagged adjustment to desired levels. Use of actual current output and actual current inputs to estimate the production function directly is objectionable for these reasons. The frequent practice of correcting measured capital stock for its utilization (usually by assuming that capital is unemployed to the same extent as labor) recognizes that the observed capital stock is not the equilibrium quantity to which the production function refers, but it seems an inadequate way of accounting for expectations and adjustment lags in capital stock decisions. Also, if lagged adjustment characterizes the labor input so that labor, like capital, is a partially fixed factor, then labor input (employment) should also be corrected for utilization. The procyclical behavior of labor productivity suggests that this is the case. A second shortcoming of many direct estimates of the production function is that they ignore information contained in marginal productivity conditions. This information can usually be summarized in a so-called expansion path equation, i.e., an equation relating the ratio of desired factor inputs to the ratio of their prices. If the production function is estimated independently of the expansion path equation, the estimates will be statistically inconsistent. For this reason, among others, the expansion path is sometimes estimated first, and the information so obtained is then used in *This research was supported by National Science Foundation Grant No. GS1686. The authors wish to acknowledge the assistance of Richard Freeman, Margaret Simms, and Robert Willig on much of the computational work. A preliminary version of the paper was read at the Winter Meetings of the Econometric Society, December 28, 1968. We are indebted to Sherwin Rosen for his constructive suggestions, especially as concerns the clarification of our hypotheses on the adjustment process.