The role of inventories and capacity utilization as shock absorbers

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Abstract

We examine the role of inventories and capacity utilization (of both capital and labor) for the propagation of business cycle fluctuations. We document a new set of facts regarding the U.S. cyclical regularities of inventories and capacity utilization. First, we find that capital utilization and the flows of services from both capital and labor are procyclical, and comove with the holdings of inventories. Second, we find that labor utilization is procyclical as well, but is weakly negatively correlated with inventories. We build a model that accounts for these facts, and also accounts for the stylized inventory facts, i.e., inventory holdings are procyclical, while the inventory-to-sales ratio is countercyclical. The analysis is centered on the effects of two possible shocks: preference (demand) shocks and technology shocks. Our model shows that inventories and the rate of capital utilization are mostly complements, while inventories and the rate of labor utilization are mostly substitutes. It further shows that temporary demand shocks emphasize the role of inventories as being a “shock absorber,” whereas high-persistence demand shocks, as well as technology shocks of any persistence, emphasize the role of inventories as being a complement to consumption.

Introduction

The primary goal of this paper is to analyze the role of inventories and capacity utilization – the intensity of use of both capital and labor – in the transmission of business cycle fluctuations. We study the relationship between these variables and whether they respond symmetrically to supply and demand shocks of different rates of persistence.

Stylized facts on inventory cycles show that, at the aggregate level, output is more variable than sales, and thus inventory investment is procyclical, while the inventory-to-sales ratio turns out to be countercyclical. We show that capital utilization and the flows of services from both capital and labor are procyclical and comove with the holdings of inventories. Further, we find that labor utilization is procyclical as well, but is weakly negatively associated with inventory holdings. We finally observe that the cyclical components of both the stock of inventories and inventory investment are positively correlated with consumption expenditures. Our model is able to replicate these facts and further provide novel explanations, as it examines both roles of inventories in the business cycle: as shock absorbers and as complements to consumption.

We find that temporary demand shocks result in a negative correlation between inventories and both rates of capacity utilization, so that they behave as substitutes. Temporary shocks to technology, in contrast, make inventories complement the utilization of both factors of production. Finally, high-persistence shocks either to preferences or technology make inventories complement capital utilization but substitute labor utilization.

Our contributions are important for the following reasons. Empirically, it has long been recognized that inventory fluctuations play an important role in the business cycle. Although inventory investment has averaged roughly one-half of 1 percent of U.S.ʼ GDP over the post-World War II period, changes in inventory investment have averaged more than one-third the changes in quarterly GDP, while the drop in inventory investment accounted for more than 80% of the drop in total output during the average postwar recession period in the U.S.2 Blinder suggests that “business cycles are, to a surprisingly large degree, inventory cycles.” (Blinder, 1990, p. 8). Moreover, the literature is still debating the role of inventories for the propagation of business cycle fluctuations.3 Hence, understanding the dynamics of inventories is key to understanding business cycles.

Capacity utilization, being a central component of the economyʼs supply side, is also recognized as having an important role in the business cycle. For instance, variable factor utilization is thought to account for much of the variation in the Solow residual (40–60 percent according to Basu and Kimball, 1997), and thus provides an important insight in characterizing the state of real activity.

At a theoretical level, an analysis of the association between inventories and capacity utilization seems natural, since physical capital can be seen as a stock ultimately destined to be transformed into an inventory of finished goods. Likewise, inventories could be seen as a stock of physical capital already transformed into finished goods. Moreover, once we introduce the possibility of variable rates of utilization of both capital and labor, then such rates of utilization and inventories can be seen as providing a short-run adjustment “buffer stock” mechanism.

Our paper, therefore, contributes to the existing literature by providing a theoretical intuition of how these components relate to each other and, as a result, affect the transmission of business cycles. Most of the previous related research has either examined partial-equilibrium settings; for example, Galeotti et al. (2005) integrate inventories and labor decisions, distinguishing between employment, hours and effort in a partial-equilibrium model; or have focused on the effects of inventory shocks as drivers of business cycles; for instance, Iacoviello et al. (2011) introduce inventories into a general-equilibrium model with variable capital utilization, to examine the propagation mechanisms of each one of input and output inventories.

The new set of business cycle facts that we document show, essentially, that inventories are highly (and positively) associated to the flows of services of both factors of production, but less related to their rates of utilization – indeed, inventories appear to be negatively related to the rate of labor utilization. What we learn from our theory is that the association between inventory holdings and factor services emphasizes their complementarity mechanism, while the association between inventory holdings and the rates of capacity utilization emphasizes their short-run adjustment buffer-stock mechanism. Our findings provide additional insights to the understanding of the business cycle transmission mechanism.

Finally, our paper also contributes to the discussion on how aggregate labor supply responds over the business cycle (see, e.g., Ljungqvist and Sargent, 2011). Aggregate shocks, in particular demand shocks, are not only ‘buffered’ by fluctuations in average hours (and changes in the intensity of use of capital) but also by fluctuations in inventory stocks. Introducing inventory investment and variable capacity utilization together into a standard macroeconomic model allows us to identify the short-run substitutability that exists between inventories and hours worked. This provides an additional explanation to reconcile the relative lack of variability of average hours worked seen in the data.

We develop a dynamic, stochastic general equilibrium (DSGE) model that distinguishes from earlier models in that it introduces (i) endogenous capital depreciation, (ii) variable use of the labor force, (iii) adjustment costs in physical capital, and (iv) inventory holdings. Endogenous capital depreciation captures the idea that the depreciation rate is a variable subject to choice by the user of the capital good. As such, this rate enters into the model as a function of the intensity of use of capital – see, e.g., the works of Greenwood et al. (1988), and of Rumbos and Auernheimer (2001). Variable labor utilization, which can also be interpreted as variable effort, is introduced into the model by allowing the agent to modify the working time during the production process. Investment adjustment costs are introduced as in Christiano et al. (2005).

The demand for inventories, which are zero-return assets, is motivated by the idea that a larger stock allows consumers either to match their tastes more effectively or to economize on shopping costs. As in Kahn et al. (2002) and Iacoviello et al. (2011), we assume that inventories enter the consumersʼ utility function. This specification is equivalent to one in which inventories enter instead in the budget constraint reducing shopping time costs.4 Other approaches for generating a demand for inventory holdings introduce inventories as inputs in the production function (e.g., Kydland and Prescott, 1982) or emphasize the timing of deliveries rather than the timing of production, such as the (S,s) specifications of Caballero and Engel (1999), Fisher and Hornstein (2000) and Khan and Thomas (2007b).5

We are aware that the shortcut of introducing inventories in the utility function makes the model lack of a deeper, microfounded demand for inventories. However, by doing so we obtain, as a first step in the literature, a general-equilibrium model that allows us to find an easily interpretable relationship between inventories and capacity utilization, both in the long run and during the business cycle.

The only sources of uncertainty in the model are preference (demand) and technology shocks, that make inventories useful beyond their role in the utility function. This motivation is related to Kahn (1987)ʼs “stock-out avoidance” idea, for our agent will also shield herself from the uncertainty associated to the disentanglement between production decisions and shocks realizations.6 The nature of the shocks will emphasize either the crowding-out attribute of the shock-absorbing mechanism of inventories (especially demand shocks) or the consumption-complementarity mechanism of inventories (especially supply shocks).

The paper proceeds as follows. The next section introduces our model. We describe the environment and discuss the assumptions. In Section 3, we proceed with the solution to the model, show the main results, and examine in detail the source of uncertainty and persistence behind these results. Finally, Section 4 presents the conclusion to this work.

Section snippets

Environment

The model economy is populated by a continuum of identical agents with unit mass who perform all activities (production, investment, and consumption). By assuming that markets are competitive, we can abstract from the presence of firms for they would not affect the economyʼs optimal allocation.7 There is one

Solving the model: Main results

We proceed here with the model solution and show the main results. First, we discuss the specific functional forms and the calibration of the model economy. Then, we analyze the model equilibrium dynamics by studying the impulse–response functions. Later on, we evaluate the performance of our model with respect to the evidence, analyze the source and persistence of the shocks behind the results, and study the implications of incorporating both inventories and capacity utilization in a standard

Concluding remarks

The primary goal of this work is to gain a better understanding of the role of inventories and capacity utilization (of both capital and labor) in the propagation of business cycles and, in particular, the relationship among them. These are variables which have long been recognized as playing an important role, and having rather well defined associations both among each other and with other indicators in the business cycle. Understanding these relationships is important also theoretically

Acknowledgments

We are thankful to the editor Gianluca Violante, Juan Dubra, Kishore Gawande, Zvi Hercowitz, Manuel Hernandez, Paula Hernandez, Matteo Iacoviello, Dennis Jansen, Omar Licandro, Michael McMahon, John Moore, and seminar participants at Texas A&M University, Universidad de Montevideo, Universidad Torcuato Di Tella, Universidad de Buenos Aires, the Dallas Fed, the ISIR Session at the 2013 ASSA Meeting, and the Central Banks of Uruguay and Argentina for helpful comments. A set of perceptive and

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