Robert J. Rossana

Temporal Aggregation and Economic Time Series

The authors examine the effects of temporal aggregation on the estimated time-series properties of economic data. Theory predicts temporal aggregation loses information about the underlying data processes. The authors find those losses to be substantial. Monthly and quarterly data are governed by complex time-series processes with much low-frequency cyclical variation, whereas annual data are governed by extremely simple processes with virtually no cyclical variation. Cycles of much more than a years duration in the monthly data disappear when the data are aggregated to annual observations. Also, the aggregated data show more long-run persistence than the underlying disaggregated data.

Two-stage optimal control problems with an explicit switch point dependence : Optimality criteria and an example of delivery lags and investment

Abstract This paper provides necessary conditions for the solution of two-stage optimal control problems where the switch point is a choice variable and where the switch point appears as an argument of the integrands in each integral which comprise the criterion index to be maximized. Problems of this variety have arisen in the exhaustible resource and neoclassical investment literature. Using the conditions necessary for the solution of these problems, we analyze an example of optimal investment in the presence of delivery lags and show how the optimal switch point (delivery lag) responds to shifts in exogenous parameters.

Aggregation, Unit Roots and the Time Series Structure on Manufacturing Real Wages

The effects of both temporal and cross-sectional aggregation on the estimated time-series characteristics of manufacturing real wage data are examined. The effects, especially of temporal aggregation, are found to be quite large and in accord with statistical theory. The well-known results of J. Altonji and O. Ashenfelter (1980), that real wages are a random walk, and of C. R. Nelson and C. I. Plosser (1982), that real wages are an IMA(1, 1) process, both seem to be entirely artifacts of temporal aggregation, with the true models following processes that are much more complex and that display substantial cyclical behavior. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Interrelated Demands for Buffer Stocks and Productive Inputs: Estimates for Two-Digit Manufacturing Industries

Empirical estimates of interrelated factor demand equations for inventories, labor inputs, capital stocks, and unfilled orders in selected two-digit industries are provided. This framework is more comprehensive than previous research as it disaggregates inventories by stage of fabrication, accounts for production-to-stock and production-to-order, and disaggregates capital and labor inputs. All estimated decision rules display stock-adjustment effects, but there are asymmetries in the parameter estimates that are puzzling. There is evidence that factor input prices have a role in explaining stock levels, but own-factor price effects are largely absent. Evidence is uncovered that stocks are sensitive to expectations errors attached to output demand. Copyright 1990 by MIT Press.

Estimating the Speed of Adjustment in Partial Adjustment Models

We reexamine a recent controversy in the inventory literature regarding the impact of estimator choice on estimated speeds of adjustment in partial adjustment models. We compare the properties of two asymptotically equivalent estimators, the residual-adjusted Aitken (RAA) and nonlinear least squares (NLS) estimators. Our results indicate that (a) the RAA estimator is very sensitive to the quality of the instrument used in first-round estimation, and (b) model mis-specification may cause substantial differences in the finite-sample distributions of the two estimators. An empirical analysis of inventory equations suggests that adjustment speeds are more sensitive to model specification than to choice of estimator.

Structural instability and the production-smoothing model of inventories

The production-smoothing model of inventories implies that inventories, labor inputs, sales, and factor input prices are cointegrated if sales and factor prices are I(1) with one cointegrating vector for each state variable held. These propositions are tested in six nondurable-goods industries. All industries provide evidence of cointegration. Fewer quasi-fixed factors are found than previous research often assumed. Estimates of cointegrating vectors provide implausible parameter estimates. Rank stability tests, with fixed or seqentially chosen breakpoints, indicate that the cointegrating matrix has unstable rank. Parameter estimates of cointegrating vectors do not provide much support for the production-smoothing model of inventories.

Technology Shocks and Cointegration in Quadratic Models of the Firm

In two quadratic models of a firm, it is shown that, if the firms production function is not separable in its arguments, then the presence of any unit root technology shock will prevent factor inputs from being cointegrated with input prices. Absent integrated technology shocks, there will be one cointegrating vector for every quasi-fixed factor held by the firm, thereby providing one possible rationale for multiple cointegrating vectors in multivariate time series systems. The parameters of these cointegrating vectors may be used to recover the parameters of the static factor demand functions obeyed by the firm. Copyright 1995 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Delivery lags and buffer stocks in the theory of investment by the firm

Abstract This paper contains a dynamic model of a firm holding a stock of unfilled orders for output while facing a fixed delivery lag attached to acquiring new capital goods. The model leads to a two-stage optimal control problem where the initial time interval corresponds to the Marshallian short-run and the second interval is the period during which deliveries of capital goods may arrive. Optimality criteria are provided for both time intervals and the behavior of the firm is characterized along both adjustment paths. The short-run decisions of the firm are shown to be tied to long-run decisions planned by the firm.

On the adjustment matrix in error correction models

Abstract This paper explores the determinants of the adjustment matrix in error correction models within two intertemporal models of the firm. In a production smoothing model of inventories, it is shown that the adjustment matrix contains the speed of adjustment of inventories as conjectured in previous work but this parameter matrix also contains the parameters from the autoregressive polynomials associated with the stochastic, unobservable shocks in the model. Two empirical examples are provided suggesting that these unobservable shocks cannot be assumed to be serially uncorrelated. In a flexible wage model of a labor market, the impact upon the adjustment matrix of normalizing the cointegrating matrix is studied. In contrast to one-state variable problems, normalization of the cointegrating matrix is arbitrary on economic and statistical grounds in this model and it is shown that, even with serially uncorrelated shocks, estimating the elements of the adjustment matrix may not provide an estimate of the speed of adjustment under some normalizations of the cointegrating matrix. The implication of the analysis is that without guidance from an economic model about the interpretation of elements of the adjustment matrix under alternative normalizations of the cointegrating matrix, or when unobservable shocks are serially correlated, economic interpretation of estimates of the adjustment matrix will be hazardous.

Some Empirical Estimates of the Demand for Hours in U.S. Manufacturing Industries

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.