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1、Inventory Investment and the Cost of CapitalChristopher S. Jones Selale TuzelMarshall School of Business Marshall School of Business University of Southern California University of Southern California Los Angeles, CA 90089Los Angeles, CA christopher.jonesmarshall.usc.edu tuzelusc.edu213-740-948 13-7
2、40-9486First draft: November 2008This revision: January 2010Inventory Investment and the Cost of CapitalAbstractWe examine the relation between inventory investment and the cost of capital in a theoretical model and empirically using data from 1958 to 2006. We construct an equilibrium model of inves
3、tment with two types of capital, xed capital and inventory, and a pricing kernel that generates a countercyclical price of risk. In our calibrated economy, we nd that inventory investment is negatively related to the equity risk premium, whose uctuations account for approximately 80% of the variatio
4、n in inventory investment. In support of this result, our empirical work documents that risk premia, rather than real interest rates, are strongly negatively related to future inventory growth. This relation is highly signicant and robust to a number of variations in estimation method, inventory typ
5、e, and risk premium proxy. Furthermore, the eect is stronger for durable goods, whose sales are highly procyclical, than for nondurables, and for industries whose sales are more procyclical.1IntroductionAs a form of investment, a rms optimal inventory stock should naturally be expected to vary with
6、its cost of capital. At a macro level, we would expect aggregate inventory investment to vary with measures of the average cost of capital. One of the puzzling results from the empirical macroeconomic literature on inventories is the apparent lack of relation between the accumulation of inventories
7、and the cost of capital, at least as proxied by short-term real interest rates. Maccini, Moore, and Schaller (2004) note that although there is a “perception of an inverse relationship between inventory investment and interest rates, . almost no evidence exists for such an eect.”The inability to rel
8、ate inventory investment to the cost of capital is disconcerting given the importance of inventory investment over the business cycle. Table 1 shows that inventory investment, as a fraction of GDP, is more volatile than xed investment or consumption, and it is strongly procyclical. As many other aut
9、hors have noted, the typical decline in GDP during a recession is almost exactly accounted for by the contemporaneous decline in inventories. Understanding the cycles in inventories is therefore central to understanding the cycles in output. While many types of inventories, like food or tobacco, wou
10、ld appear to carry little systematic risk, other types may be risky for a number of reasons. The value of commodity-like inventories, for instance, might uctuate substantially with macroeconomic growth. Other goods, like automobiles, which are held in nished goods inventory for longer amounts of tim
11、e, may face considerable demand risk over the period from when they are produced until when they are sold. This demand risk may be even more substantial for work progress inventories of goods that require a substantial amount of time to produce. In contrast to risk premia, volatility in real rates w
12、as quite low over much of the post-war sample period. With a dataset covering 1953-1971, for instance, Fama (1975) fails to reject the hypothesis of constant ex ante real rates. While subsequent rates have proved signicantly more volatile, it is possible that they may still represent the least volat
13、ile component of the average rms cost of capital. If inventories are suciently risky, then the variation in the real interest rate might be only weakly related to the appropriate cost of capital。If inventories are risky, then the real interest rate used in prior work may be a poor proxy for the rele
14、vant cost of capital. Over the last several decades, the asset pricing literature has documented substantial variation in risk premia, both in stock and bond returns, and this variation may dwarf that found in the real short- term interest rate. In bond markets, work starting with Fama and Bliss (19
15、87) and Campbell and Shiller (1991) documented extensive levels of predictability in excess bond returns, much of it correlated with the term spread. In particular, Cochrane and Piazzesi (2005) nd that up to 44% of the variation in one-year excess returns is predictable, suggesting that bond risk pr
16、emia may change substantially from one month to the next. The literature on stock market predictability is no less convincing, having documenting signicant variation in expected returns that is correlated with variables including the short-term interest rate, the dividend yield, and several interest
17、 rate spreads (e.g. Fama and Schwert (1977), Keim and Stambaugh (1986) and Fama and French (1989). Recently, Jones and Tuzel (2010) nd predictability in stocks and bonds using the ratio of new orders of durable goods to shipments of durable goods.In contrast to risk premia, volatility in real rates
18、was quite low over much of the post-war sample period. With a dataset covering 1953-1971, for instance, Fama (1975) fails to reject the hypothesis of constant ex ante real rates. While subsequent rates have proved signicantly more volatile, it is possible that they may still represent the least vola
19、tile component of the average rms cost of capital. If inventories are suciently risky, then the variation in the real interest rate might be only weakly related to the appropriate cost of capital.An alternative explanation for the lack of any response to real interest rates is the presence of nancin
20、g constraints. Kashyap, Stein, and Wilcox (1993) investigated this possibility at the aggregate level and found that a proxy for bank loan supply helps predict inventory growth. Studies examining inventory patterns and nancial constraints in the cross section of rms include Gertler and Gilchrist (19
21、94), Kashyap, Lamont, and Stein (1994), and Carpenter, Fazzari, and Petersen (1994). All three of these papers document some relationship between a rms balance sheet and its future inventory investment. Together, these results suggest that there is variation in the eective cost of capital that is no
22、t captured by observed short-term interest rates.Whether or not inventories are in fact risky and how they respond to changes in the cost of capital are issues we investigate directly in a theoretical model and indirectly in our empirical work. Our model builds o the classic dynamic production econo
23、my of Kydland and Prescott (1982) and Christiano (1988). In their model, production requires investment in both capital goods and inventories. Like Kydland and Prescott, we introduce a friction into the adjustment of the capital stock, but we replace Kydland and Prescott time-to-build constraint wit
24、h a simple adjustment cost that has the eect of smoothing aggregate capital. Somewhat dierently from their model, we allow for inventories to depreciate, and in our calibrations we assume this depreciation is at a rate that exceeds that of capital. As in these seminal papers, we model inventories as
25、 a factor of production, a framework that has beenadopted more recently by Belo and Lin (2009), Gomes, Kogan, and Yogo (2009), and (in a model with working capital rather than inventories) by Wu, Zhang, and Zhang (2010). Using inventories as a factor of production can be motivated in several ways. B
26、y investing more in inventories, rms can reduce the number of costly factory changeovers in which the capital stock is recongured to produce a dierent output good. Alternatively, if the rm faces uctuating demand or supply, then holding inventories can ensure high capacity utilization, and thus high
27、production output for a given level of capital. Finally, inventory investment can be considered as a substitute to investing in and maintaining a just-in-time production environment.Because of this riskiness, inventory investment responds strongly to uctuations in the equity risk pre-mium. Even afte
28、r controlling for other variables in the model that would be expected to drive inventories, a one percentage point increase in the one-quarter equity risk premium lowers inventory growth by about one third of a percent. Furthermore, if we “turn o ” time varying risk premia by imposing constant volat
29、ility in our pricing kernel, the volatility of inventory growth drops by over 80%. Both of these results suggest an important role for equity risk premia in explaining inventory behavior.Most signicantly, we diverge from the approach of Kydland and Prescott (1982) and Christiano (1988) by assuming a
30、n exogenous pricing kernel, along the lines of Berk, Green, and Naik (1999) and Zhang (2005), that has the potential to generate realistic asset pricing implications, such as the level, volatility, predictability of excess stock market returns. As stressed by Cochrane (2007), in the context of a pro
31、duction economy the nature of risk premia will likely eect investment decisions of rms and other business cycle dynamics. While general equilibrium production models such as Jermann (1998) and Boldrin, Christiano, and Fisher (2001) have been successful in replicating the average equity risk premium,
32、 they do not produce the countercyclical variation in risk premia observed in the data. Since our emphasis is on relating variation in risk premia to inventory growth rather than on explaining the source of that variation, the exogenous pricing kernel is a natural choice.The riskiness of inventory i
33、nvestment may be measured using the beta of the returns to inventory invest- ment with respect to the pricing kernel, or equivalently with the expected excess return. After calibrating our model to match both macro moments, namely the volatilities of growth rates in output, xed capital in- vestment,
34、 and inventories, and return moments, namely the average riskless rate and the mean and standard deviation of excess equity returns, we nd that the the expected excess return to inventory investment is roughly half as large as that of xed capital investment or the rm as a whole. This suggests that t
35、he cost of capital appropriate for discounting the returns from inventory investment is of the same order of magnitude as the cost of capital for the rm as a whole. Investment is risky due to the presence of productivity shocks, and this risk is amplied by capital adjustment costs, which hamper the
36、rms ability to adjust its capital holdings in response to changing business conditions. Thus, adjustment costs increase the riskiness of investment. Convex adjustment costs also induce the rm to make smaller changes in its capital stock, thereby reducing the volatility of its investment. Inventory i
37、nvestment, which is much more volatile than xed investment, necessitates a much lower level of adjustment costs.3 It is a priori unclear whether such low adjustment costs are consistent with a signicant level of risk in inventory investment. Our calibration implies that the steady-state elasticity o
38、f inventory investment to Tobins q is 2.44, as compared to an elasticity of 0.34 for xed investment. This seven-fold dierence reects much lower adjustment costs in inventory investment. Nevertheless, we nd the riskiness of inventory investment to be substantial.Because of this riskiness, inventory i
39、nvestment responds strongly to uctuations in the equity risk pre-mium. Even after controlling for other variables in the model that would be expected to drive inventories, a one percentage point increase in the one-quarter equity risk premium lowers inventory growth by about one third of a percent.
40、Furthermore, if we “turn o ” time varying risk premia by imposing constant volatility in our pricing kernel, the volatility of inventory growth drops by over 80%. Both of these results suggest an important role for equity risk premia in explaining inventory behavior.Building o some loose predictions
41、 from the model, but also based on prior empirical work, our empirical analysis investigates the relationship between the cost of equity and debt capital and the growth rate of inventories. We nd strong evidence documenting that forecasts of aggregate inventory growth can be improved by adding varia
42、bles that have been found by the nance literature to forecast future stock and bond returns. Yet, this evidence is dicult to interpret because these same variables also forecast future output growth. Hence, inventory growth may rise when costs of capital are low only because those costs of capital f
43、orecast future demand for goods.We separate these channels with a simple instrumental variables approach. We nd that while variables related to the cost of capital clearly aect growth in future sales, they have an additional eect on inventory investment that we interpret as a pure discount rate eect
44、. Specically, we nd that when expected excess bond or stock returns are low, the growth rate of inventories tends to be high. This eect is highly signicant and holds for several alternative measures of the cost of capital. In contrast, but in line with most In this paper, our goal is to investigate
45、the time series relationship between risk premia and inventory investment. A related line of research, originating from within the accounting literature, examines cross sectional relationships between rm returns, inventory investment, and accruals. Sloan (1996) documents that rms with high levels of
46、 accruals, of which the change in inventories is one component, signicantly underperform those with low accruals. Thomas and Zhang (2002) rene this result by demonstrating that the component of accruals that seems to drive the anomaly discovered by Sloan is in fact the change in inventories. Wu, Zha
47、ng, and Zhang (2010) document that the accruals phenomenon is consistent with the optimal investment behavior of rms in a q-theoretical framework; hence is not necessarily an anomaly. They model accruals as an input to the production of the rm (i.e., an investment good) and nd, within the model, tha
48、t they respond to changes in discount rates. They argue that this channel can explain the literature, we nd no relation between ex ante real interest rates and aggregate inventory behavior.Our empirical work examines both input inventories (raw materials and work in progress) and output inventories (nished goods). It is well known that these two types are qualitatively dierent. Input inventories are larger and, at least in the case of durable goods, exhibit greater volatility and are more procycli
