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David Backus Publications

Publish Date
Journal of Money

This paper extends the multivariate stock-adjustment model commonly used in empirical studies of portfolio behavior in order to analyze the complete set of flow allocation decisions made by households (including consumption, expenditures on durables and houses, and various financial aggregates). The model is then confronted with quarterly household sector data from the United States Flow of Funds Accounts for the period 1954 to 1975. Besides presenting OLS estimates, we test parameter restrictions suggested by our theoretical structure; the data supports the view that the explanatory power of the model is enhanced by allowing non-zero cross-effects on interest rates and lagged stocks, and by the integration of real and financial decisions.

While these results are encouraging, the specification requires a large number of independent variables. This leads, in many cases, to rather poor determination of a number of coefficients. We therefore combine with the data some inexact subjective information about the coefficients, using the Theil-Goldberger mixed estimation technique. The OLS estimates and the mixed estimates are then compared by examining the forecasting accuracy of the model in- and out-of-sample. Overall the model performs very well, and the simulation results confirm that inclusion of prior information is of considerable value for forecasting purposes.

Since the publication of William Brainard and James Tobin’s pioneering paper, “Pitfalls in Financial Model Building,” the multivariate stock-adjustment model has been widely used to study dynamic portfolio adjustment. The framework which they developed is especially useful for analyzing a given sector’s allocation of a predetermined aggregate among competing alternatives; when dealing with the household sector most applications (including their own) have specified wealth as a predetermined aggregate which, in turn, was allocated to various assets and liabilities. The purpose of the present paper is to use an extended version of the Pitfalls model to examine in an integrated manner the household sector’s allocation of income to financial and real expenditures for the United States from 1954 to the present.

The plan of the paper is as follows. In Section I we outline our basic theoretical framework, explain its motivation, and relate our approach to other recent flow-of-funds models. Then in Section II we describe the data and present ordinary least squares estimates of the model; in addition, we test for the “asset composition effect” which is central to our particular extension of the Pitfalls model. In Section III we use Brainard and Gary Smith’s adaptation of the Theil-Goldberger mixed estimation technique to combine subjective prior information about the coefficients with that embodied in the data. We further examine in Section IV both the model and the value of our a priori beliefs by performing in-sample and out-of-sample dynamic simulations. Finally, conclusions are drawn in Section V.