An Empirical Investigation of Fluctuations in Manufacturing Sales and Inventory within a Sticky-Price Framework.(Statistical Data Included)

The macroeconomics literature has recently witnessed a resurgence of interest in issues related to nominal price rigidities. In particular, advances in computational methods have allowed for the analysis of fully articulated quantitative general equilibrium models with inflexible prices. [1] Because nominal price rigidities create predictable variations in sales, these models provide a natural setting for the study of inventory behavior. Specifically, firms that face increasing marginal costs wish to smooth production and, given predictable variations in sales, can naturally use inventories to accommodate any difference between a smooth production volume and sales.

Hornstein and Sarte (1998) study the implications of sticky prices for inventory behavior under different assumptions about the nature of the driving process. Regardless of whether the economy is driven by nominal demand or real supply shocks, the authors find that an equilibrium model with inflexible prices can replicate the main stylized facts of inventory behavior. Namely, production is more volatile than sales while inventory investment is positively correlated with sales at business cycle frequencies. More importantly, their study also makes specific predictions about the dynamic adjustment of inventories and sales to these shocks. In response to a permanent positive money growth innovation, both sales and inventories contemporaneously rise before gradually returning to the steady state. In contrast, a permanent positive technology shock leads to a rise in sales and a fall in inventories on impact. As time passes by, sales increase monotonically and eventually reach a new higher steady-state level.

In this article, we estimate a structural vector autoregression (SVAR), where money is constrained to be neutral in the long run, in order to gauge the degree to which these theoretical dynamic adjustment paths hold in the data. Using manufacturing data, we find that the impulse response of sales and inventories to nominal shocks is generally consistent with the predictions of a sticky-price model. Furthermore, both sales and inventories also behave as predicted in the long run in response to a technology shock. Contrary to theory, however, we find that inventories contemporaneously rise in response to a positive innovation in technology. In all cases, the data indicate significantly more sluggishness in the dynamic adjustment of sales and inventories to shocks than implied by current models with sticky prices. The latter finding is consistent with earlier work by Feldstein and Auerbach (1976), as well as Blinder and Maccini (1991), using stock-adjustment equations. More recently, Ramey and West (1997) also find that the inventory:sales relationship is unusually sluggish. They are able to explain this result by appealing either to persistent shocks to the cost of production or to a strong accelerator motive within a linear quadratic framework.

Although the earlier analysis in Hornstein and Sarte (1998) makes specific predictions regarding the dynamic response of sales and inventories to various shocks, it does not assess the relative importance of these shocks as sources of fluctuations. Here we use our estimated VAR to acquire some insight into the significance of both real and nominal shocks in generating fluctuations in sales and the inventory:sales ratio. We find that nominal shocks generally contribute little to the forecast error variance in the latter variables at both short and long horizons. Instead, consistent with earlier work such as King, Plosser, Stock, and Watson (1991), fluctuations in real variables tend to be dominated by real disturbances. Moreover, these empirical findings tend to hold consistently throughout different historical episodes at the business cycle frequency. One exception concerns monetary disturbances that play a noticeably more important role in generating inventory:sales ratio fluctuations in the early 1990s.

This article is organized as follows. We first set up and motivate an empirical model that is consistent with generic restrictions implied by an equilibrium model of inventory behavior. In particular, we assume that money is neutral in the long run and that the inventory: sales ratio is a stationary process without trend. Note that we do not impose any a priori restrictions that are directly tied to the assumption of sticky prices. The next section examines various integration and cointegration properties of the data under consideration. We then analyze the impulse responses of sales and the inventory: sakle ratio to various shocks. We also try to gauge the relative importance of these shocks as sources of fluctuations in the latter variables. After that, we offer some cautionary remarks regarding the specific empirical implementation in this article. The final section concludes the analysis.

1. INVENTORY FLUCTUATIONS: THEORETICAL MOTIVATION

To set the stage and notation for the econometric specification, we will provide some theoretical background on the behavior of inventories. The basic framework we have in mind is one in which firms use inventories to smooth production in a setting with staggered nominal prices. [2] The assumption of inflexible price adjustment provides a natural role for production smoothing as the underlying factor driving inventory behavior. In particular, nominal price rigidity creates predictable variations in sales. Suppose, for instance, that the nominal price set by a given firm is fixed over some time interval. If the general price level increases over that time interval, then the firm's relative price correspondingly falls and its sales rise, all else being equal. Given this rising sales path, the firm also attempts to minimize total production costs by keeping production relatively smooth. Inventories can then be used to make up for the differences between production and sales. In addition to identifying this stick y-price motive, we, like Khan (1987), assume that firms may also hold inventories to avoid costly stock-outs.

Within the context of this framework, the dynamic adjustment of inventories and sales to various shocks will generally depend on how preferences and technology are specified. In the long run, however, the model exhibits basic neoclassical properties that can be used for the purposes of identification. One of these properties suggests that money is neutral and, moreover, that changes in the steady-state level of sales ultimately arise from innovations in technology. With this in mind, we let the long-run component of the sales process evolve according to

[[s.sup.*].sub.t] = [[delta].sub.s] + [[s.sup.*].sub.t-1] + [[phi].sub.s](L)[a.sub.t], (1)

where [[s.sup.*].sub.t] denotes the log level of sales and [a.sub.t] captures shocks to technology. The lag polynomial [[phi].sub.s](L), as well as all other polynomials described below, is assumed to have absolutely summable coefficients with roots lying outside the unit circle. Observe that equation (1) implicitly assumes that the sales process possesses a unit root. We formally test this assumption later in this article.

In principle, the steady-state level of inventories can be thought of as being determined by the two forces we described previously. Note that in a model with rigid prices, firms naturally wish to hold inventories to accommodate any difference between predictable variations in sales and a smooth production volume. Moreover, by using inventories to avoid costly stock-outs, firms generally target some appropriate inventory:sales ratio in the long run. …

To read the full text of this article and others like it, subscribe today!