Dynamic Factor Demand with Final and Intermediate Inventories

This paper analyses an empirical, dynamic optimization-based model of factor demand for n quasi-fixed factors in US industries, under the assumption that firms produce output to stock subject to polynomial adjustment costs. Each factor and the stock of inventories adjust to discrepancies in all inputs and the stock. Although it is theoretically plausible to consider input and storage decisions separately, such a decomposition does not accord with empirically observed cross correlations in the data. In general, a model of factor choice is also a model of inventories, and vice versa. An implication of dynamic multiple-factor demand theory is that the derived static factor demand equations are interdependent. Firms are assumed to store intermediate goods along with finished goods. If final and intermediate goods cannot be observed separately, the model imposes certain restrictions on the vector Euler conditions obtained from optimization, estimated as autoregressive moving average forms of matrix error corrections to an expected moving forward-looking target vector, itself derived from optimization involving the reciprocal unstable roots of the system. The number of independent co-integrating vectors are shown to correspond to the number of quasi-fixed inputs, barring the influence of unit-root technologies that could eliminate or weaken the stationarity of factor demand. For a variety of specifications, estimates of the vector error-correction models indicate that inventories adjust significantly to their own disequilibrium gaps as well as to those for hours. Fixed investment responds mainly to it sown disequilibrium, as does hours