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# Studies in Nonlinear Dynamics & Econometrics

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Volume 18, Issue 3

# Inventories, business cycles, and variable capital utilization

Lucas M. Engelhardt
• Corresponding author
• Assistant Professor, Department of Economics, Kent State University, Stark Campus, 6000 Frank Ave NW, North Canton, Ohio 44720, USA
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• Other articles by this author:
Published Online: 2013-10-11 | DOI: https://doi.org/10.1515/snde-2012-0078

## Abstract

Bils and Kahn [Bils, M., and J. A. Kahn. 2000. “What Inventory Behavior Tells us about Business Cycles.” American Economic Review 90, 458–481.] conjectured that a competitive technology-driven business cycle model could not generate countercyclical inventory-sales ratios. Khan and Thomas [Khan, A., and J. Thomas. 2007a. “Explaining Inventories: A Business Cycle Assessment of the Stockout Avoidance and (s,s) Motives.” Macroeconomic Dynamics 11(5): 638–664. Khan, A., and J. K. Thomas. 2007b. “Inventories and the Business Cycle: An Equilibrium Analysis of (s,s) Policies.” American Economic Review 94(4): 1165–1188.] developed a model that disproved this conjecture. However, as this paper shows, that model underperforms a baseline model without inventories for many important moments. However, when variable utilization is added to the model, many of these moments perform better in the full model than in the baseline. The results suggest important interactions between variable utilization and inventory dynamics.

This article offers supplementary material which is provided at the end of the article.

## References

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Corresponding author: Lucas M. Engelhardt, Assistant Professor, Department of Economics, Kent State University, Stark Campus, 6000 Frank Ave NW, North Canton, Ohio 44720, USA, Phone: +330-244-3307, e-mail:

Published Online: 2013-10-11

Published in Print: 2014-05-01

Correlation between detrended inventories and GDP are 0.65 for manufacturing inventories, which is roughly twice the correlation for retail and wholesale inventories.

This is the most significant difference between the model presented in this paper and that in Trupkin (2008). In Trupkin (2008), inventories are of final goods. In this paper, as in Khan and Thomas (2007b), inventories are held because of a fixed cost of delivery of intermediate goods to final goods producers. In Trupkin (2008), inventories provide direct utility to households, as a proxy for decreased shopping time and increased variety.

The approximation is formed using the technique described in Tauchen (1987).

a is the quantity of those Arrow securities that paid off in the current period.

It is theoretically possible for firms to want to sell off some of their inventories. For example, if they adjust their inventory level in one period, and then the optimal level of inventories falls faster than the amount of intermediate goods used in production. In that case, s is above s* – and the further above, the more likely the firm will adjust its holding of inventories. The main text here describes the typical case where actual inventory levels fall faster than the optimum level does.

These restrictions are present in Christiano, Eichenbaum, and Evans (2005) which finds δ(κ) to be nearly linear, and also in Altig et al. (2011) which finds δ to be approximately cubic. The estimate of Justiniano and Primiceri (2008) suggests a much more convex function, with this coefficient in the neighborhood of 7 or 8.

The more general form $δ(κ)=a+δ0κδ1,$ as used in Trupkin (2008), which includes both wear-and-tear and rust-and-dust depreciation was considered, but calibrating such a form resulted in a degree of convexity that was not plausible, as it was far beyond the levels found in Christiano, Eichenbaum, and Evans (2005) or Altig et al. (2011). The chosen form has a precedent in Smith (1970).

I used 2501 nodes spread evenly between 0 and 2.5, which span the range that inventories take in simulations.

The term s′–s can be broken down into the components of intermediate good purchases and use of intermediate goods in production. s1s gives the purchase of new intermediate goods. s1s′ gives the goods that get used in production. The change in inventories then would subtract those used in production from those purchased: (s1s)–(s1s′), which simplifies to (s′–s) , which is then weighted by the price of intermediate goods to get the change in value of those goods.

Because Table 3 reports standard deviations in relative terms, it appears that the relative price of intermediate goods q has gotten less volatile. However, this is not entirely accurate. The relative price of intermediate goods has gotten less volatile compared to the volatility of output.

As δ1 goes to infinity, this ratio goes toward the ratio for a fixed cost. That is because δ1=∞ is equivalent to the marginal cost of changing utilization being infinite – so that utilization is no longer variable.

This point was noted by Khan and Thomas (2007b).

Wang, Wen, and Xu (2011) suggests that when variable utilization is added to a model in the style of Khan and Thomas (2007b) that inventories play a significant destabilizing role during business cycles. Khan and Thomas (2007b) also make this point about the version of their model where the capital share is decreased.

Thank you to an anonymous referee for recommending this possibility.

Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 18, Issue 3, Pages 291–308, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826,

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