Robert J. Rossana, Interrelated Demands for Buffer Stocks and Productive Inputs: Estimates for Two-Digit Manufacturing Industries, The Review of Economics and Statistics, Vol. 72, No. 1 (Feb., 1990), pp. 19-29

This paper presents estimates of a multivariate flexible accelerator model of labor demand (hours and the number of production workers) which shows that stocks of finished goods, unfilled orders and materials inventories have significant impacts upon labor demand. Univariate time series models are used to capture expectations of the determinants of desired stocks (new orders, real wages and real raw materials prices) and these magnitudes are found to follow a random walk without drift. Expected new orders and errors in forecasting new orders are found to have an important impact upon labor inputs. Real wage forecasting errors are found to be important for hours demand.

THIS paper presents estimates of hours equations based upon optimizing behavior of firms in a dynamic context. The order-stock distinction is the point of departure for this paper. Firms will be presumed here to produce to stock or to order. Hours equations will be derived which link hours worked to levels of inventories of finished goods or unfilled orders. Early work on the demand for labor ignored the effects of inventones and unfilled orders on the choice of labor input levels. However, some evidence on this subject was provided by the important and well-known work of Nadiri and Rosen (1973).1 Using a theoretical framework first studied by Lucas (1967), they estimate dynamic factor demand schedules for six quasi-fixed factors of production, i.e., factor inputs which are subject to adjustment costs. Among these six inputs are employment, hours per man and total inventories. It is well known that the accumulation of any input will then depend upon the gaps between desired and actual levels of all quasi-fixed factors. Thus the demand for hours per man is taken to depend, among other things, upon lagged hours, employment and total inventories. The cyclical interaction between inventories and the demand for labor arises through adjustment parameters attached to these lagged stocks. Completing the specification of the model by including the determinants of desired stocks (sales, the wage relative to capital costs and a time trend), they apply the model to industrial aggregate data. Their results provide little evidence that inventories are an important determinant of the demand for hours. Of the eighteen industries examined, only six produce negative and significant inventory coefficients. Further, relative factor prices are found to be significant in only six industries. Apart from aggregation bias issues, there are several misspecifications which could account for these results. There is no reason why the impact of each inventory stock should have an identical impact upon hours. For example, it is reasonable to suppose that if the firm holds excess finished goods relative to desired levels, it will reduce hours per worker. But if the firm holds stocks of materials which exceed desired levels, the firm may wish to increase hours so as to offset the output effects (through the production function) of declining stocks of materials. Similar comments can be offered about work in process inventories. Thus, disaggregating by stage of fabrication would appear to be appropriate to sort out inventory effects on hours demand. Second, Nadiri and Rosen ignore the impact of order backlogs upon hours. Following Belsley (1969), it is well known that many of the firms in these industries produce not to stock but to order. For firms producing goods requiring special attention, order backlogs replace finished goods as a buffer against fluctuations in demand. Thus order backlogs should appear directly in the hours equation. Finally, the dynamics of labor demand and factor prices may require a distributed lag representation to capture the response of labor demand to shifts in expected real wages. As suggested by Neftci (1978) in a different context, the effects of real wages on hours may be captured if allowance is made for a distributed lag relationship between hours and real wages. This paper presents two models which are designed to address some of these issues. Extending Received for publication June 30, 1982. Revision accepted for publication January 7, 1983. * Pennsylvania State University. The research reported in this paper was partially supported by the Employment and Training Administration, U.S. Department of Labor under Research and Development Grant No. 91-24-77-34 and by the Federal Reserve Bank of Philadelphia. The views expressed herein are those of the author and do not necessarily reflect those of the sponsoring institutions or the Federal Reserve System in any way. I wish to thank Professors C. F. Christ, L. J. Maccini, H. Rose and M. Ali Khan for their constructive criticisms of this research. Two anonymous referees also provided excellent comments. John Hinrichs of the Bureau of Economic Analysis kindly provided the deflated inventory data used here. Diane Mayer and Donna Robinson provided expert research assistance. Any remaining errors are the responsibility of the author. l See Nadiri and Rosen (1973) for a survey of the employment demand literature.

It is well known that fluctuations in inventory investment are a major source of fluctuations in gross national product. This has stimulated numerous empirical studies designed to understand the causes of changes in inventory investment. These studies include those (for example, Michael Lovell) that utilize a flexible accelerator model of inventory behavior as well as those (for example, David Belsley) that utilize the linear decision rule approach to optimal inventory holding. The latter approach, however, can be interpreted in terms of a flexible accelerator model. See J. C. R. Rowley and P. K. Trivedi for a survey of the literature. Recently, several authors (for example, Martin Feldstein and Alan Auerbach) observed that these studies yield very implausible empirical results. The basic difficulty is that the estimates of the speed with which firms close gaps between desired and actual inventory stocks are very low. Often, the estimated speed of adjustment is less than 10 percent per quarter. As Feldstein and Auerbach stress, this is extremely implausible when even the largest swings in inventories in a given quarter amount to less than one day's production. The purpose of this paper is to undertake an analysis of adjustment speeds for finished goods inventory investment. In our empirical work, we utilize a modified flexible accelerator model of inventory investment.1 Like the conventional flexible accelerator, the model permits firms to close a fraction of the gap between desired and actual inventories in any period. The relevant fraction is of course the adjustment coefficient, and it may vary in principle between zero and unity. Our model differs from the conventional model in assuming that the desired stock of finished goods inventories depends on the normal levels of exogenous variables that firms must forecast to make decisions on inventory holdings. These include not only the normal level or orders, or demand, which is a standard explanatory variable in the empirical literature, but also the normal levels of real factor-input prices and real interest rates. In addition, we permit the normal levels to change relatively slowly in response to changes in past levels of orders, real factor-input prices, and real interest rates. Our objective is to investigate whether the slow adjustment speeds that have been estimated in the literature are due to the use of models which contain an incomplete menu of exogenous variables to determine desired inventories and pay inadequate attention to lags in the adjustment of normal levels of exogenous variables.