Inventory Behavior and Financial Constraints: Theory and Evidence

Inventory Behavior and Financial Constraints: Theory and Evidence Sudipto Dasgupta, Erica X.N. Li and Dong Yan August 11, 2014 Abstract Financially more constrained firms hold substantially more inventory than do financially less constrained firms and also show much more volatility in inventory holdings. To understand why, we model the interaction of financial constraints, capacity constraints, and the response of production and inventory to cost shocks. We develop several implications as to how financial constraints affect the inventory response to cost shocks of constrained firms relative to unconstrained firms, which cannot be derived from any of a host of other ways in which two groups of firms are differentiated in our model. We find very consistent results when we take these implications to the real data. JEL Classification: G30, G31 Keywords: Inventory, Financial Constraints, Capital Investments Dasgupta gratefully acknowledges financial support from Hong Kong s Research Grant Council under grant number 641211. Li acknowledges the support from Cheung Kong Graduate School of Business. All errors are our own. Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; Tel: (852) 23587685; E-mail: dasgupta@ust.hk. Department of Finance, Cheung Kong Graduate School of Business, Beijing, China, 100738; Tel: (86)10 85378102; E-mail: xnli@ckgsb.edu.cn. Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; Tel: (852) 62340862; E-mail: dyan@ust.hk. 1

1 Introduction Inventory investment is widely regarded as an important contributor to business cycle fluctuations. Even though it constitutes less than 1 percent of GDP in advanced countries, aggregate inventory investment is 20 times more volatile than GDP and can account for up to 87% of the drop in GNP during the average postwar recession in the United States (Blinder and Maccini (1991)). A less well-known fact is that among publicly traded firms in the U.S. between 1971-2010, the inventory investments of financially more constrained firms are 73% more volatile than those of financially less constrained firms. Financially constrained firms also hold 50% more inventory than the less constrained ones. Given that private firms are generally more financially constrained than public firms, financial constraint could potentially play an important role in generating the large volatility of aggregate inventory investments. However, financial constraint has not received much attention in the literature on understanding what drives inventory movements. Two of the earliest studies of the financial determinants of inventory holdings (Kashyap, Stein and Wilcox (1993) and Kashyap, Lamont and Stein (1994)) attempted to resolve the puzzling lack of evidence that the cost of finance (or the cost of carry for inventory) affects inventory behavior. Both papers found evidence that in recent U.S. recessions, a so-called bank-lending channel seemed to have affected the ability of bank-dependent and liquidity constrained firms to invest in inventory. Subsequently, Carpenter, Fazzari and Petersen (1994) (hereinafter CFP), using quarterly data from Compustat, demonstrated that during three sub-periods from 1981-1992 when monetary policy had a different stance in the U.S. and an inventory cycle was generated, corporate cash flows affected inventory behavior, and more so for financially constrained firms (smaller firms) than for unconstrained firms (larger firms). CFP interpreted this evidence as consistent with the idea that, when faced with a liquidity shortage, financially constrained firms are more likely to cut inventory investment than other types of investment (for example, investment in fixed assets or in R&D) which are associated with larger adjustment costs (that is, are less flexible). 1

In this paper, we present a model of inventory behavior in which production capacity, sales, and inventory holding decisions are simultaneously made by financially unconstrained as well as constrained firms. We calibrate the model to replicate observed differences in first and second moments of sales and inventory holdings (scaled by lagged capital) as well as changes in inventory, sales and capital (also scaled by lagged capital) between financially unconstrained and financially constrained firms. In particular, our model calibrations generate similar differences in the ratio of inventory holdings to lagged capital for constrained and unconstrained firms as in the actual data (median values of 16 and 24 percent, respectively, for financially unconstrained and constrained firms for the model generated data versus 22 and 30 percent in the Compustat data at quarterly frequency), and also similar differences in the variability of inventory over lagged capital as well as inventory growth between the two groups as in the actual data. Based on our model, we then derive two key empirical implications of financially constrained behavior, test these implications on model-generated data, and then take the same test to the real data. We find very consistent results. An important feature of our tests is that, unlike most other tests of financially constrained behavior, we do not need to rely on cash flow sensitivities to interpret our results. Our model builds on the notion that capital investment is not only associated with higher adjustment costs relative to inventory, but for financially constrained firms, capital is also difficult to rebuild. The main building blocks of our inventory model are traditional. We use a variant of the standard linear-quadratic model 1, and allow a role for both cost and demand shocks, although the former play a more important role in our calibrated model. This latter feature is consistent with the widely documented fact that inventory movements are procyclical. In these linearquadratic models, persistent shocks to both cost and demand are the main drivers of inventory behavior. However, in reality, investment in capital and capacity constraints are also likely to play an important role, especially for financially constrained firms. When shocks to marginal 1 See, for example, Ramey and West (1999), section 3. CFP (1994) provide an excellent overview of the literature, including prior work on the effect of monetary policy on inventory holdings. 2

cost of production are present, given negatively sloped demand and marginal revenue, firms have an incentive to produce more than the quantity that equates marginal revenue and marginal cost when the marginal cost curve is lower, and carry inventory to periods when the marginal cost curve is higher, in order to equalize marginal cost of production across periods. In other words, firms will attempt to produce more than they would sell in good cost states, and sell from inventory in bad cost states 2. The optimal level of inventory holdings will trade off the benefits of production cost smoothing with the cost of holding inventory. Such smoothing of production costs (or, equivalently, of sales) is likely to be more important for financially constrained firms for two reasons. First, financially constrained firms may have to cut investment or divest assets in bad cost states (when profits are low) to cover operating costs because they are unable to access external finance, and capital is difficult to rebuild for such firms even under better times. Second, investment adjustment costs not only limit the ability to cut investment when profits are low, they also make it more costly to rebuild capital. For both these reasons, selling from inventory is more attractive in bad cost states, which implies that it is more important to accumulate inventory when costs are more favorable. In effect, financially constrained firms are willing to engage in more complete production cost smoothing behavior and pay the cost of holding inventory when they can afford to do so, in return for more sales revenue in bad cost states, which allows them to avoid costly capital adjustment. 3 2 For manufacturing firms, cost shocks can originate in shocks to input prices, e.g. prices of energy inputs, productivity shocks to input suppliers, or exchange rate fluctuations. An extensive literature documents the importance of input price shocks for aggregate economic fluctuations (see, for example, Bruno and Sachs (1982)). Eichenbaum (1989) finds evidence consistent with production-cost smoothing and the importance of cost shocks for inventory behavior. Blanchard (1983), Durlauf and Maccini (1995), Ramey (1989) and West (1986) all emphasize the importance of cost shocks for inventory behavior. A recent paper by Wang and Wen (2011) develops a General Equilibrium model based on production-cost smoothing behavior that is consistent with many stylized facts regarding aggregate inventory fluctuations. 3 We do not model cash holdings, primarily because it is difficult to argue why financially unconstrained firms should hold cash. However, as our model shows, pure smoothing incentives can lead to inventory holdings by unconstrained firms even when they have no motive for holding cash. For constrained firms, the smoothing incentives are exacerbated by the presence of financial constraints. In Appendix B, we show that as long as there is some cost to cash holdings, constrained firms hold more (less) inventory than unconstrained firms in relatively good (bad) cost states. Holding cash in the form of interest-bearing assets such as treasury bills is costly because interest on cash holdings is taxed (Riddick and Whited (2009)), and shareholders get less than the appropriate risk-adjusted 3

As noted above, unconstrained firms also have incentives to smooth sales by building inventory in favorable cost states and depleting inventory in unfavorable cost states. However, a key implications of the model is that relative sensitivity of the inventory response by unconstrained firms vis-a-vis the constrained firms to favorable and unfavorable shocks will be asymmetric. Capacity constraints play a more important role for the difference in the response on the upside, that is, when the cost shock is favorable. Not only do unconstrained firms have more (physical) capital than constrained firms, because they have better access to external finance, they are also able to adjust capital immediately in response to shocks. Thus, inventory and capital start to build up immediately after favorable cost shocks. In contrast, financially constrained firms are able to build up capital and inventory less rapidly, as profitability improves in response to a persistent favorable shock. Eventually, however, as the good state persists, they accumulate significant inventory. On the other hand, when the cost shock is adverse, as discussed above, constrained firms have a stronger incentive to liquidate inventory than do unconstrained firms immediately, and this effect also persists for a few periods. Thus, our model predicts that the difference in sensitivity of inventory growth to cost shocks between financially constrained firms and unconstrained firms in the short-term will be asymmetric, with constrained firms responding more sluggishly to favorable shocks but more aggressively to unfavorable shocks; however, this asymmetry no longer exists over a longer period, and constrained firms eventually accumulate (deplete) more inventory than do unconstrained firms in response to favorable (unfavorable) shocks. These implications provide the main identification strategy for our empirical tests on the real data. This identification issue needs to be addressed because potentially, financially constrained firms, which are typically smaller firms in most measures of financial return. Shareholders are better off if the firm uses the cash to repurchase shares rather than hold it in the form of an interest-bearing asset the income from which is taxed twice. If the cash is held in the form of currency or non-interest-bearing deposits, the value of this cash erodes in an inflationary environment, and inventory offers a better hedge against inflation (this would be the case in our model if the cost shocks are correlated across firms). Finally, we could assume that shareholders prefer managers to pay out cash and hold an inventory buffer instead since managers can deviate from the pursuit of shareholder value maximizing policies when private benefit-laden projects are present. 4

constraints, could differ from the larger unconstrained firms in many dimensions. Thus, for us to identify the effect of financial constraints, our model would have to generate implications for financial constrained behavior that are unlikely to be generated by differences in any other parameters between these two types of firms. This is precisely what we demonstrate. We first demonstrate the asymmetric response for our calibrated model generated data via regressions of inventory and capital growth on the cost shocks, as well as the lagged cost realization (to capture the effects of unexpected shocks). 4 Next, because we do not try to measure the shocks in the real data, and use sales growth to proxy for these shocks, we show that in the model, the shocks to cost translate to change in sales or sales shocks, again by way of regressing sales growth on the shocks. Finally, we show that keeping the degree of financial constraint unchanged, allowing firms to differ along a host of other dimensions that generate similar differences in the average level of inventory holdings between unconstrained and constrained firms does not generate the asymmetric response, either in the short or the longer term. When we take the model to the real data, we run similar regressions of change in inventory and capital on sales growth as on the model-generated data, and find consistent evidence in favor of asymmetric response. In particular, when sales growth is positive, in both the model data and the actual data, while both types of firms increase inventory growth in response to higher sales growth, the effect is more muted for constrained firms. When sales growth is negative, for the model data, we find financially constrained firms deplete inventory more rapidly when the sales shock is more negative than to the unconstrained firms. However, for the real data, the sensitivity of inventory depletion to sales changes when the latter is negative is essentially zero for both types of firms, with an important exception. If the quarter in question follows an NBER recession quarter, or one that follows a quarter characterized by a sales growth that is in the bottom 20th percentile of the firm-specific distribution of sales growth, financially constrained firms deplete inventory 4 We focus mainly on cost realizations and cost shocks since, as shown later, idiosyncratic cost shocks play a much more important role in our model than the aggregate demand shock. Here, a shock represents a change in the level of the random component of cost. 5

significantly more rapidly than do unconstrained firms. We find similar results for capital growth. We also run the same tests using lagged sales growth instead of contemporaneous sales growth to address potential endogeneity arising out of the fact that inventory and sales decisions are jointly made conditional on the state, and find very similar results. In the regressions where sales growth (or lagged sales growth) proxies for shocks to cost, we control of cash flows at one period lag to sales growth. Cash flow in our simulated data is highly correlated with the cost states and hence, lagged cash flow proxies for lagged values of the cost states. Therefore, given the AR(1) structure of the cost realizations, controlling for lagged values of the cost states is equivalent to controlling for anticipated changes to cost realizations, or anticipated sales growth. On average, constrained firms carry more inventory (both in reality as well as in our modelgenerated data) than do unconstrained firms. They also exhibit significantly more variability in inventory growth and the ratio of inventory to lagged capital than do unconstrained firms for both the actual and model-generated data. Our model provides insights as to which factors are important in affecting the inventory holding behavior for these two types of firms. Consistent with the intuition that constrained firms carry more inventory to avoid selling capital when they run into operating losses, but unconstrained firms do not have the same concern because they can raise external finance to cover operating losses, we find that higher fixed operating costs lower invested capital and raise inventory holdings of constrained firms (so that the ratio of inventory holding to capital increases and is highly sensitive to this parameter), but there is no effect on either invested capital or inventory holdings of unconstrained firms. Higher investment adjustment costs decrease the average level of invested capital by both types of firms 5, and the level of inventory holdings also decreases (because production is lower with more capital). However, constrained firms want to carry even more inventory because depleting capital is more costly when they run into operating losses, and thus there is a much smaller decrease in inventory for these firms (and 5 Since capital has to be committed in advance of production, even unconstrained firms can be capacity constrained and lose profits. If capital is less flexible, given volatility of cost and demand shocks, firms are less willing to invest. 6

the ratio of inventory to capital increases substantially, unlike unconstrained firms). We also explore the consequences for steeper slopes of marginal cost and demand curves and volatility of cost and demand shocks for both types of firms. The variability of inventory over lagged capital and inventory growth is also sensitive to all the above parameter changes. Generally, the variability for financially constrained firms is more than that for unconstrained firms. This is because relaxation or tightening of capacity constraints has a major effect on the variability of inventory in the presence of cost shocks. When capacity constraints tighten, inventory volatility increases. Our model is perhaps most directly relevant for finished goods inventories of manufacturing firms. A limitation of quarterly data from Compustat is that we do not get sufficient coverage of disaggregated inventory data at that frequency earlier than the year 2004. However, in the inventory literature, several authors have argued that intermediate goods inventories are similar to factors of production like capital 6. In particular, if raw material inventory is held in fixed proportion to capital, it is possible to interpret firms capital investment response to shocks as representative of the response of intermediate goods inventory. For our model-generated data, capital investment responds to shocks in a similar way to inventory. Moreover, the invisible hand argument (Blanchard (1983)) suggests that if costs shocks are common across producers and users of intermediate goods, then intermediate goods will be accumulated precisely when costs are low and their producers have excess inventories, and they will be depleted when costs go up and producers produce less. Thus, investment in intermediate goods should also be procyclical, and constrained firms may have a stronger incentive to cut investment in intermediate goods inventory 6 See Ramey (1989), and also section 3.4 in Ramey and West (1999). Two recent papers model inventory as a factor of production together with capital. Jones and Tuzel (2013) study the effects of cost of capital on inventory investment and find that risk premium is negatively related to future inventory growth. They use risk premium to proxy for financial conditions and find results that are consistent with previous literature. Belo and Lin (2012) model inventory the same way as Jones and Tuzel (2013), but study the relation between stock returns and inventory growth rate. They find that firms with lower inventory growth rate outperform firms with higher inventory growth rate. Inventory adjustment costs are important in these models in explaining the return spreads between high and low inventory growth firms, following standard q-theory logic. 7

in bad times (and therefore buffer up in good times). In summary, we make four major contributions in this paper. The first is to explicitly model capital accumulation, and the interaction between production capacity and inventory accumulation, previously unmodelled in the literature. The second is to model and examine the effect of financial constraints on this interaction. Similar to the informal arguments in CFP, our model captures the idea that when faced with poor profitability, financially constrained firms without access to external financial markets may prefer to liquidate inventory rather than capital. While CFP test their hypothesis in terms of cash flow coefficients, we derive and test a different implication which does not require us to rely on the interpretation of cash flow coefficients, an issue that has been the subject of much debate in recent literature. Herein lies our third contribution. Finally, we attempt to isolate several factors that affect inventory holding behavior both in the presence and absence of financial constraints, and in the process, suggest possible reasons for the much higher inventory holdings of constrained firms. This is an issue that, unlike cash holdings, has been completely untouched in recent literature, and could potentially be tested with suitable firm-level constructs. The paper is organized as follows. Section 2 introduces the model and explores the implications. Sections 3 and 4 explain the data sample and the calibration of the model, respectively. Section 5 shows our empirical findings. Section 6 discusses alternative hypothesis and robustness checks. Section 7 concludes. 2 The Model Production function. Assume Cobb-Douglas production function: ( Y t = e Xt 1 hs ) t S t (1) A t Q t A 0 A 1 α t K α t 1 (2) 8

where Y t is the sales measured in dollars, X t is the aggregate demand shock, h is a constant referring to the slope of the demand curve, S t is the sales measured in quantity, Q t is the output level, K t 1 is the capacity/capital at the beginning of period t, and α is the capital-to-output ratio, and A 0 A t is the aggregate productivity level with A 0 being a constant scaling factor. Assume that the demand shock follows an AR(1) process X t+1 = X + ρ X ( Xt X ) + ε X t+1, where ε X t+1 is an i.i.d. process with standard deviation of σ X. X is the long-run average of the demand shock and is a scaling factor in the model. To isolate the effects of demand shocks and for simplicity, we assume that productivity level A t grows at a constant rate g, i.e., A t = g t. The appearance of A t in the demand curve is to ensure balanced growth. Production costs. Production costs include time-varying linear costs and quadratic costs: [ C Qt = e Zt d 1 Q t + d ] 2 Q 2 t, (3) 2A t where Z t is the cost shock, d 1 and d 2 are constants, and Q t is the output level at time t. The productivity level A t appears in front of the quadratic term to ensure balanced growth. Past literature (see, for example, Eichenbaum (1989) and West (1986)) show that production cost shock plays more important role than demand shock in determining the time-series properties of inventory investment. To study the cross-sectional inventory behavior, we assume that the cost shock Z t is firm-specific and is uncorrelated across firm and time. The cost shocks have a common stationary and monotone Markov transition function, Q Z (Z t+1 Z t ), given by: 9

Z t+1 = ρ Z Z t + σ Z ε Z t+1, (4) where ρ Z is the autocorrelation coefficient and ε Z t+1 is an i.i.d. standard normal variable. Inventory stockout avoidance costs. Following Blanchard (1983), we assume quadratic stockout avoidance costs for inventory holdings, i.e., C Nt = b 2 ( St A t ) γ ( 1 c N ) 2 t, (5) S t where γ measures the elasticity of the stockout avoidance costs to sales and N t is the inventory level whose change follows the identity Q t = S t + N t N t 1. (6) Constant b measures the magnitude of the stockout costs and c refers to the sales-to-inventory ratio that results in zero stockout costs. Again, we include A t in the cost function to ensure balanced growth. The underlying justification for the stockout avoidance costs is that this cost function is itself the sum of two cost functions: the first is the physical cost of carrying inventories, which is an increasing function of the level of inventories; the second is the expected cost of stocking out, which is a decreasing function of the level of inventories given sales, as a higher inventory- to-sales ratio decreases the probability of stocking out. The sum of these two costs reaches a minimum for some level of inventories. Capital accumulation. The law of capital accumulation follows K t = (1 δ)k t 1 + I t, where δ is the depreciation rate and I t is the investment made at time t. 10

Investment adjustment costs. We assume quadratic adjustment costs: ( It ) 2 K t 1, C It = a 2 K t 1 where a is a positive constant. Operating costs. Assume that the operating costs include both fixed and variable costs, where the latter depends on the production capacity. By introducing the variable costs of capacity, firms will also have the incentive to decrease capacity during bad times. [ ( )] Kt 1 C Ot = A t f 0 + f 1, A t 1 where f 0 and f 1 are constants and the appearance of A t 1 is to ensure balanced growth. Dividend payout. The dividend of the firm at time t is then given by D t = Y t C Ot C Qt C Nt C It I t. Value maximization. For simplicity, we assume that the firm is an all-equity firm and there is no agency problems. The optimal firm value is given by the following optimization problem: V t (K t 1, N t 1, X t, Z t ) = max {D t + βe t [V t+1 ]}. (7) {Q t,n t,i t} where the discount rate β is assumed to be constant for simplicity and the maximization is subject to constraint equation (6). We solve the model for two types of firms: (1) financially unconstrained firms who can seek external financing with no costs; (2) financially constrained firms whose dividend has to be nonnegative. Both constrained and unconstrained firms face the same optimization problem described by equation (7), except that the optimization problem of constrained firm is solved subject to an 11

additional constraint D t 0. It can be easily shown that firm value V t, capital level K t, sales S t, inventory N t, all the costs C Qt, C Ot, and C It, and dividend D t all grow at the same rate as A t. Define the scaled variables as K t = K t A t Ĩ t = I t A t Dt = D t A t CQ,t = C Q,t A t CN,t = C N,t A t CI,t = C I,t A t CO,t = C O,t A t Ṽ t = V t A t Qt = Q t A t St = S t A t Ñ t = N t A t. All scaled variables have a stationary distribution. The optimal production, inventory holding, and investment policies for financially unconstrained and constrained firms are solved numerically using the perturbation method. The details of the solution method are included in Appendix A. 3 Data Our data sample consists of firms listed in the Compustat Industrial Quarterly Files at any point between 1971 and 2010. Following standard practice, we exclude financial, insurance, and real estate firms (SIC code 6000-6900), and utilities (SIC code 4900-4999). We exclude from the sample any firm-quarter observation that has missing book value of asset, sales or inventory. We also restrict the sample to firms with at least five consecutive years of data. All dollar values are converted into 2000 constant dollars. Firm characteristics, such as sales (scaled by lagged capital) and inventory (scaled by lagged capital) are winsorized at 1% level at both tails of the distribution to alleviate the impact of outliers. In addition, following CFP, we drop firms with total asset less than 15.5 million (in 2000 constant dollars). The final dataset is an unbalanced panel consisting of 285,075 firm-quarter observations. 12

3.1 Variables Inventory (N t ) in our study is given by Compustat data item INVTQ, which includes raw materials, finished goods, work-in-progress and other inventory. Ideally, we would like to use each of these components separately for our empirical study. Unfortunately,we do not get sufficient coverage of disaggregated inventory data at quarterly frequency earlier than the year 2004. Even in year 2010, 30% of the firms do not have inventory components data on quarterly frequency. In addition, to correct the bias that inventory stock value is understated under LIFO and overstated under FIFO, following CFP, we apply an algorithm developed by Michael Salinger and Lawrence Summers to adjust for LIFO (last in, first out) and FIFO (first in, first out) accounting. 7 Capital (K t ) is defined as total asset minus inventory. This is because capital stock in the model does not include inventory. 8 Sales (S t ) in actual data is the level of net sales (SALEQ). Cash Flow (CF t ) is calculated as the sum of earnings before extraordinary items (IBQ) and depreciation (DPQ) scaled by lag capital. Investment (I t ) is the quarterly capital expenditure calculated by converting the Compustat Year-To-Date item CAPXY to quarterly frequency. Ratios including N t /K t 1, S t /K t 1, I t /K t 1 and CF t /K t 1 are all scaled by lagged capital. N Growth, S Growth and P P E Growth are defined as change in the levels of inventory, sales and property plant and equipment (PPENTQ) (in 2000 constant dollars) from year t to year t 1, scaled by capital in year t 1. We use the reported fiscal quarter end to assign fiscal quarters with calendar quarters. Following CFP(1994) and Carpenter, Fazzari and Petersen (1998), in cases where the end of a fiscal quarter does not coincide with the end of a calendar quarter, we adjust the data so that the majority of the fiscal quarter is assigned to the appropriate calendar quarter. 7 For more detailed description of the adjustment method, please refer to Salinger and Summers (1983) and the appendix of Carpenter, Fazzari and Petersen (1994). Our results are robust if we do not adjust for FIFO and LIFO. 8 All our results are robust if we use total asset as capital. 13

3.2 Financially Constrained Firms Following CFP, we use firm size as the basis for classification schemes for the financial constraint status. In each quarter, we rank firms according to the book value of asset at the beginning of the period and assign the top 30% to the financially unconstrained group (UFC), while the bottom 30% to the financially constrained group (FC). Thus, we allow the status to vary over time. 4 Calibration and Simulation We calibrate the model at quarterly frequency. Table 1 presents the parameter values used in the calibration. Our calibration strategy is as follows. The capital-to-output ratio α is set to 0.7 to be consistent with the estimate in Hennessy and Whited (2007). The growth rate of productivity g is 1.009, chosen to match the average growth rate of sales in our sample. Since we assume riskneutrality in the model, the discount rate is the risk-free rate, given by 1. The discount factor βg β is hence set to 0.982 to generate a quarterly interest rate of 0.91%. In equilibrium, the average investment-to-capital ratio is given by 1 (1 δ)/g in the model. Capital depreciation rate δ is then chosen to match the quarterly investment-to-capital ratio of 0.024 in our sample period. Investment adjustment cost parameter a is chosen to match the volatility of investment-to-capital ratio. The slope of the demand curve h is chosen to generate an average markup of 20%, consistent with the calibration in Altig et al. (2011). The scaling factor A 0 in the capacity constraint is chosen to match the average capacity utilization rate of 80% for the sample period 1971-2010. 9 The stockout avoidance cost ratio c is set to 1.3 to match the mean of inventory-to-capital ratio. The persistence and volatility of aggregate demand shock ρ X and σ X are taken from King and Rebelo (1999). The remaining 9 parameters, long-run mean of demand X, the stockout avoidance cost parameter b, elasticity of stockout-avoidance cost to sales γ, production cost parameters d 1 and d 2, the persistences and volatilities of costs shocks ρ Z and σ Z, and the operating cost parameters 9 The capacity utilization data is from the IHS Global Insight dataset. 14

f 0 and f 1, are chosen to match the means and volatilities of sales-to-capital ratio, sales change-tocapital ratio, inventory change-to-capital ratio, and cash flow-to-capital ratio and the volatility of inventory-to-capital ratio. In total, we have 19 parameters to match 19 moments in the data. We simulate 100 panels, each with 1440 quarters and 600 firms, half of which are financially constrained and the other half are financially unconstrained. For each panel, the simulation starts from the steady state values of the state variables. We drop the first 720 quarters to ensure that the simulated economy has reached the equilibrium. The regressions are conducted for each simulated panel separately. The reported regression coefficients and the associated t-statistics are computed using the Fama-MacBeth method, i.e., β = 1 N N β i σ(β) = N (β i β) 2 N i=1 i=1 t = β σ(β)/ N, where i refers to the i th simulated panel. 5 Empirical Results from Both Actual and Simulated Samples 5.1 Comparing Actual and Simulation Samples Table 2 reports summary statistics for the actual and simulation samples for the variables which are either targeted for our calibration exercise, or are key regression variables. For the simulation sample, we throughout consider two measures of the change in inventory. The first, denoted by N, measures inventory change as the change in the number of units times the market price. The second, denoted by Nc, measures inventory at cost of production. In an attempt to mimic LIFO method, when the change is positive (current production exceeds sales), consistent with LIFO, we value the change at current period per unit production cost. If the change is negative (sales 15

exceeds current production), we value the change at the previous period s per unit production cost. For all variables, the simulation preserves the order of the first moment, i.e., in every case, if the mean is higher (lower) for unconstrained firms in comparison to constrained firms in the actual data, this is also the case in the simulated data. With two exceptions, this is also the case for the second moments. 10 The table shows that we are able to obtain a reasonable match between the first and second moments of the target variables in the real data and the simulated data. It is important to emphasize that financially constrained and unconstrained firms differ in our model only in one dimension, namely, the degree of financial constraint. It is possible to argue, however, that these firms would differ in many other dimensions, which potentially could improve our calibration exercise. Hennessy and Whited (2007), for example, estimate parameters for small firms and large firms separately, and find that these firms differ in many dimensions. However, we choose not to go in that direction because we want to identify, as clearly as possible, the difference that financial constraints make to the inventory decisions of firms. Table 3 presents correlations between variables in the simulated data. The main issue of interest here is to see how well the state variables (the random realizations of demand and cost) correlate with other firm variables that commonly feature in inventory studies. There are several noteworthy features. First, with one exception, the correlations of all other variables with the demand and cost states are all positive (note that for cost, the correlations are with the negative of the cost realization, indicating a more favorable state). However, the correlations are much higher for cost realizations than for demand realizations. This reflects the fact that the variability of idiosyncratic cost shocks dominates that of the aggregate demand shock. Particularly noticeable is the very low correlation 10 The exceptions occur for sales over capital and sales growth, and even here, the difference between constrained and unconstrained firms is minor. 16

of (3 percent) between the demand state and capacity utilization. This suggests that even when the demand realization is high, firms need not be capacity constrained, since capacity utilization is much more responsive to the cost realizations. Thus, the interactions of capacity constraints and shocks, crucial for our model, are likely to be driven primarily by the cost shocks. 11 The correlations reveal that a better state of cost (and demand) is associated with higher sales over lagged capital, inventory growth and sales growth, higher investment scaled by lagged capital, cash flow scaled by lagged capital, and capacity utilization. Firms mainly accumulate inventory when the cost shock is favorable, consistent with sales smoothing, and stock up for bad times. The correlations among the remaining variables are consistent with expectations. One interesting set of comparisons between unconstrained and constrained firms involves capacity utilization. First, consistent with financially constrained behavior, constrained firms need to build capital much more rapidly when existing production capacity is being fully utilized than do unconstrained firms the correlation between capacity utilization and capital growth is 0.65 for constrained firms but only 0.28 for unconstrained firms. In other words, unconstrained firms generally appear to be closer to optimal capacity when they reach fuller utilization of capacity, but constrained firms need to expand capacity much more quickly. Second, when capacity is more fully utilized, unconstrained firms carry more inventory in relation to capital than do constrained firms: the correlation between capacity utilization and inventory-to-capital ratio is 0.97 for unconstrained firms compared to 0.68 for constrained firms. This suggests a need for the constrained firms of building up inventory when capacity is more fully utilized (in response to favorable cost shocks). Consistent with this, we find that the correlation of capacity utilization and inventory growth for unconstrained firms is 0.44, compared to 0.61 for constrained firms. 12 11 In unreported experiments, we simulated data with the variability of cost shocks set to zero. Not surprisingly, the correlations with the demand shock amplify greatly (but the signs are preserved). 12 The correlations of sales growth with inventory growth, especially for unconstrained firms, are very high. While in the real data unconstrained firms also exhibit higher correlation of sales and inventory growth than do constrained firms, the magnitudes are much smaller. Two factors account for this difference. First,unconstrained firms are identical in our simulation panels, unlike real data where there is significant cross-sectional heterogeneity. 17

5.2 Results on Model-generated Data The Determinants of Inventory Holdings Little is known about the cross-sectional determinants of inventory holdings, and even less as to why financially constrained firms hold 50 percent more inventory as a proportion of lagged capital than do unconstrained firms. To gain some intuition about the model and this question, in this section, we essentially do a series of comparative static exercises on the model-generated inventory holding levels by changing various parameters of the model. The results are summarized in Table 4. Given a negatively sloped demand curve and stochastic and upward sloping marginal cost curve, firms have a natural incentive to produce more when the marginal cost curve is lower, and carry inventory for sale to periods when it is higher. This incentive for inventory accumulation exists for both unconstrained and constrained firms. What makes such sales-smoothing behavior especially important for the latter is the possibility that in the bad cost states, when profits are low, they face the risk of having to sell capital or adjust capital investment too drastically, which is costly because of capital adjustment costs. If they manage to carry inventory produced in good cost states to such bad cost-low profit states, they can avoid costly capital adjustment by generating sales via depletion of inventory instead. Thus, any parameter that affects profitability in the high production cost state will affect inventory and investment behavior of constrained firms. Our comparative static results are reported in Table 4. We report the effects of parameter changes one at a time on both the mean level of inventory holding (inventory over lagged capital) for each type of firm, as well as the standard deviation of the same variable (within Second, our assumption that unconstrained firms face no financing frictions is admittedly extreme and made for simplicity allowing some degree of friction would make these firms more similar to constrained firms and would reduce the correlations. In regression results reported below, it will be seen that the higher correlations translate to regression coefficients when inventory growth is regressed on sales growth that are three times larger than those we get for the actual data. However, the focus of our analysis is to understand the asymmetric response of financially constrained firms vis-a-vis the unconstrained firms, which is preserved in the real data. 18

square brackets). 13 We focus on fixed operating costs, f 0. 14 All values in this table for inventory (N) and capital (K) are expressed as percentages of the corresponding values for financially unconstrained firms at the baseline parameter values. In column (1) of Table 4, we find that if we raise f 0 from its baseline value of 0.0665 to 0.076, there is no effect on the capital investment or inventory holdings of the financially unconstrained firms. This is because the unconstrained firms do not accumulate inventory with the objective of avoiding capital depletion in bad cost states. However, the constrained firms do. So when this parameter becomes higher, the constrained firms reduce capital and increase inventory. Therefore, the inventory-to-capital ratio increases for the financially constrained firms from 0.229 to 0.272. Raising f 1, the cost of operations per unit of capital, has the following effects. As shown in Column (2), the primary effect is to discourage investment in capital. Inventory holdings go down for unconstrained firms as production decreases with capital; however, constrained firms keep inventory holdings unchanged since they also have a greater need for inventory buffer as the variable part of their operating costs increases. Consequently, the ratio of inventory-to-capital goes up for the constrained firms increases, though there is not much effect on unconstrained firms. Next, consider the parameter of the accelerator term, b (Column (3)). A higher value increases the penalty of being out of stock (i.e., too little inventory), and also the penalty for holding too much inventory in relation to sales. Unconstrained firms normally do not need to hold large amounts of inventory, since they have no concern of having to deplete capital in bad cost states as they can raise external financing to cover temporary losses. A higher penalty for stockout forces them to hold more inventory. In contrast, financially constrained firms already have a need to more inventory, so when the cost of holding insufficient inventory is even higher, they also increase inventory holdings, but to a lesser extent. There is very little effect on capital investment; thus, 13 Results for the variability of inventory growth are similar. 14 The baseline value of f 0 implies that fixed operating costs are 21 percent of production costs. 19

both types increase inventory-to-capital and unconstrained firms increase it more. Investment is less flexible than inventory because it is associated with adjustment cost. When these adjustment costs increase, firms are discouraged from investing in capital. This is seen in Column (4). Inventory holdings also decrease, again possibly because capital and production decrease. The inventory-to-capital ratio, however, is higher for both types. However, it increases much more for constrained firms, consistent with the idea that when investment adjustment costs are higher, cutting capital in bad states is even more costly, so that it is more important to carry inventory to bad cost states. A reduction in the linear production cost (intercept of the marginal cost curve) leads to higher production and sales, and therefore encourages firms to invest in capital, as seen in Column (5). More important, constrained firms increase capital by a larger amount since the higher profitability makes them less financially constrained. Thus, they have less need to carry inventory to the bad cost states. Moreover, they are also less capacity constrained with lower linear production cost, and add substantially to capital stock and production, as a result of which the overall level of inventory holding does go up. The net result is that they have a lower inventory-to-capital ratio. On the contrary, financially unconstrained firms increase the inventory-to-capital ratio with lower linear production cost. One contributing factor is that the stockout cost increases with sales in exponential of γ > 1 and higher sales increase the stockout costs, motivating unconstrained firms to hold more inventory per unit of capital. (This effect also applies to financially constrained firms, but is less important as they already hold substantial inventory.) Two key parameters for smoothing behavior are the slopes of the marginal cost curve d 2 and the demand curve h. Consider the former first. As seen in Column (6), a flatter marginal cost curve (with intercept unchanged) encourages both types of firms to invest in capital. This is because production is likely to be higher when the marginal cost becomes flatter with an unchanged intercept. The incentives to carry inventory for production cost smoothing also increase. 20

However, unlike the unconstrained firms, the constrained firms have less incentive to increase inventory holding: the return from sales smoothing is likely to decrease for these firms as profits will not be squeezed as much in the bad cost states. Thus, while the inventory-to-capital ratio for unconstrained increases, that for constrained firms decreases. For the same reason, a steeper marginal revenue curve with unchanged intercept reduces incentives for inventory holding, but also reduces capital and output. As Column (7) shows, both types of firms reduce capital; however, while unconstrained firms reduce inventory, constrained firms increase it, since their profits in bad states will be lower, so that the ratio of inventory-to-capital increases. Without uncertainty, there is no reason for inventory smoothing. In columns (8) and (9), we examine the effects of higher cost and demand volatility, respectively. Consider cost volatility first. In column (8), we see that higher cost volatility causes unconstrained firms to invest more in capital 15. There is almost no effect on the level of inventory holding for unconstrained firms. However, constrained firms increase inventory and the inventory-to-capital ratio increases. This is because with greater volatility, the risk of more severe bad cost states increases, requiring more inventory to be carried over into these states. A similar effect occurs when demand volatility increases. While both types of firms increase capital and inventory, the net effect on the inventory-to-capital ratio is small. To summarize, the following factors widen the ratio of inventory holdings to capital between financially constrained and unconstrained firms: (a) higher operating costs, (b) higher capital adjustment costs, (c) lower penalty for stockout (d) higher linear production cost, (e) steeper marginal cost and marginal revenue (with unchanged intercept), and (f) higher volatility of idiosyncratic cost and aggregate demand realizations. These predictions of our model are in principle testable using suitable proxies for the above mentioned model parameters. Turning to the volatility (measured by the mean time-series standard deviation) of inventory, 15 Since capital is costly to adjust, and firms gain more from increasing output when cost is low than they lose from cutting output when cost is high, they increase investment on average when cost volatility increases. 21

there are two key observations. First, the volatility of inventory of financially constrained firms is much more sensitive in general to the parameter changes than that for the unconstrained firms. The second observation is that parameter changes that increase investment reduce the volatility of inventory. This second observation also explains the first one: when capacity constraints tighten, financially constrained firms take longer to build an inventory buffer, which leads to greater volatility in inventory holdings. Regression Results Our purpose in this section is to first test whether the hypothesis of asymmetric response is valid in the model-simulated data. To do so, we regress model-generated inventory growth (change in inventory scaled by lagged capital) on the change in the level of the cost realization scaled by its standard deviation (this is what we call a cost shock ). We focus on cost shocks only as demand shocks contribute very little to the overall variability of variables of interest in our model, as seen from Table 3. In our regression specification, in addition to the cost shock, we include an interaction of the shock with an indicator variable that takes a value of 1 if the firm is financially constrained in the model, and 0 if it is unconstrained. We consider favorable (positive, denoted with a plus sign) and unfavorable (negative, denoted with a minus sign) shocks separately 16. We also run exactly the same regression with growth of capital in place of inventory growth. To control for expected shocks, in these regressions we also control for the lagged state, that is, the lagged value of the cost realization. The result reported in column (1) of Table 5 is very supportive of the asymmetric response of inventory to cost shocks. Both the positive and negative cost shock variables have significant positive coefficients, indicating that unconstrained firms add (deplete) inventory in response to a larger magnitude of a positive (negative) cost shock. The interaction of the positive cost shock with the financial constraint dummy is negative, indicating that financially constrained firms respond more sluggishly to positive shocks; in contrast, the interaction of the negative cost shock 16 Recall that a cost shock is the negative of a change in the level of the cost realization. 22

with the dummy is positive, suggesting more aggressive inventory depletion. We get very similar results in column (2), where the dependent variable is valued at cost. Note that we control for the lagged cost state (higher values represent more favorable state), which also has a positive coefficient. Since the lagged state predicts the expected magnitude of the shock, our results can be interpreted as firms response to the unexpected component of the shock. Finally, in column (3), we present results for the regression of capital growth on the positive and negative shocks and their interactions with the financial constraint dummy. Here also, the results are very consistent with our hypothesis, and exactly mirror those for the inventory regression. Next, we examine the extent to which sales growth (or sales shocks) are a good proxy for the dominant underlying cost shock. In the actual data, we do not observe the shocks to cost (or demand), but we do observe shocks to sales, which are likely to be highly correlated with at least the dominant cost shock. In Table 6, we verify that this is indeed the case by regressing sales growth (change in sales scaled by lagged capital) on standardized cost shocks. Consistent with our expectation, in column (1), the cost shock is significantly and positively related to sales growth. The regression R 2 is high about 30 percent. In column (2), when an interaction term with the financial constraint dummy is included, it is insignificant, and the economic magnitude is very small relative to that of the uninteracted term, suggesting that in regressions in which sales growth is proxy for shocks to cost, it is unlikely that differences in the coefficients of sales growth for constrained and unconstrained firms are driven by different degrees of measurement error. Moreover, since the sales response to shocks is approximately the same for constrained and unconstrained firms, these results also suggest that any difference in the response of inventory to shocks is likely driven by differences in the response of production to these shocks, which could reflect the presence of more binding capacity constraints for constrained firms. We next turn to regressions on the simulated data where sales growth proxy for shocks to cost and demand. We first discuss the results of regressing inventory growth on sales growth, reported in the first two columns of Table 7. 23

The baseline regressions of inventory growth on sales growth are reported in columns (1) and (2) of Table 7. In column (1) (column (2)), the dependent variable is inventory growth (change in inventory scaled by lagged capital) when the change is valued at market price (respectively, at marginal cost). Sales growth is again split into positive and negative growth, and each is interacted with a financial constraint dummy. We control for the financial constraint dummy, and the lagged value of inventory over lagged capital. In both columns, we also include a dummy variable, Below, and its interaction with the financial constraint dummy. Below takes a value of 1 if the firm s lagged sales growth is below the 20th percentile, and zero otherwise. The motivation is to see whether firms in our model, especially financially constrained ones, deplete more inventory when the shock is extremely adverse. Moreover, we control for lagged cash flow, which has the highest correlation with the demand and cost realizations among all other financial variables in Table 3, to control for expected shocks to sales. In column (1), the regression of inventory growth on sales growth and its interactions with the financial constraint dummy is very consistent with those we observed when the cost shock was directly included. In fact, the coefficients on sales growth can be approximately derived directly from the regressions reported in the above tables because Nt SG = Nt Shock Shock, where SG denotes sales SG growth.17 In Column (2), results are mostly consistent, with one exception: the interaction between sales growth when it is negative and the financial constraint dummy is negative, though small in magnitude. We also find very consistent results for the Below dummy. In both columns, both the dummy and its interaction are significantly negative, and the coefficient estimate on the interaction term is quite large. Firms deplete inventory more rapidly when the sales shock is very adverse, and constrained firms do so more aggressively. Since contemporaneous sales and inventory growth are jointly determined, there may be con- 17 For the financially unconstrained firms, this approximation almost exactly replicates the coefficients in Table 7. For financially constrained firms, the upside coefficient is smaller and the downside coefficient larger than implied by the conversion. It is likely that the presence of other control variables in the regression affects the coefficient estimates more in Table 7 for the constrained firms. 24

cern about endogeneity. To address this issue, we repeat the regressions of Table 7 by lagging sales growth one period, and the Below dummy and cash flows one more period. The results in the first two columns of Table 8 are very consistent with the corresponding ones in Table 7. In column (1), the signs of the coefficients of positive and negative lagged sales growth and their interaction with the financial constraint dummy are exactly as those for contemporaneous sales growth. With the exception of the interaction of negative sales growth with the financial constraint dummy, the coefficients are smaller in magnitude. The exception implies that the constrained firms respond to lagged negative sales shocks by selling inventory even more aggressively, suggesting deeper financial stress when hit with an adverse cost shock. The two-period lagged Below dummy becomes positive, indicating that unconstrained firms start rebuilding inventory quickly. However, the Below dummy interacted with the financial constraint dummy remains negative and significant, and the economic magnitude of the coefficient remains as important. In column (2), we also have results similar to those in Table 7, with the exception now that the downside interaction of sales growth and the financial constraint dummy is positive, suggesting that the financially constrained firms start depleting inventory (measured at cost) with a one period lag. 18 Next, we turn to the regression of capital growth on sales growth, reported in columns (3) of Table 7. We use an almost identical specification as for inventory growth. While capital growth responds positively to positive sales shocks, consistent with financially constrained behavior, constrained firms respond somewhat more sluggishly. On the other hand, while both types of firms reduce capital growth in response to negative sales shocks, constrained firms do so more aggressively. Results based on lagged sales growth, reported in the last column of Table 8, are almost identical. 18 It may be noted that in the regressions in columns (1)-(2), the coefficient on negative sales growth is somewhat larger than for positive sales growth even for unconstrained firms. One possible reason for this is that while in the model firms face no constraints in depleting inventory, even unconstrained firms in the model face capacity constraints (since capital is committed one period early for production) and adjustment costs of increasing production capacity when they want to increase inventory. The asymmetry disappears and even to some extent reverses when we consider lagged sales growth, since one period after the initial favorable shock, firms are able to add to capacity and accumulate inventory more aggressively. 25

5.3 Results on Actual Data When we estimate the baseline model on real data, we incorporate firm fixed effects and to account for seasonality, we run regressions for each quarter. Regression results with inventory growth as the dependent variable for all four quarters are reported in Table 9. The results for positive sales growth are similar to what we observe in Table 7. Unconstrained firms respond to positive sales shocks by increasing inventory; constrained firms follow suit, but less aggressively. This is consistent with our hypothesis and the model. For negative sales growth, however, we do not see any consistent pattern. Firms appear not to adjust inventory when sales growth drops. However, when sales growth drops sharply i.e., below the firm-level 20th percentile cutoff both unconstrained and constrained firms deplete inventory, and the latter deplete more. 19 These results are consistent with the model and the results in Table 7. In Table 10, where we repeat the same regressions on lagged sales growth instead of the contemporaneous one, we do see constrained firms reduce inventory in response to negative sales shocks with a lag. The responses to positive sales shocks, however, get weaker at one period lag, and in two of the quarters, the interaction of positive sales growth with the financial constraint dummy become insignificant. Overall, this pattern that the upside responses become weaker and the downside response for the financially constrained firms becomes stronger at one period lag is very consistent with the results in tables 7 and 8. Moreover, also consistent with the results in these tables, in Table 10, the Below dummy lagged two periods interacted with the financial constraint dummy continues to be significantly negative; however, we do not find a consistent pattern for unconstrained firms. The lack of sensitivity of inventory to contemporaneous moderately negative sales declines 19 We get very similar results for all our regressions if, instead of the Below dummy as defined, we include a dummy variable that takes a value of 1 if the previous quarter is an NBER recession quarter. To save space, these results are not reported. 26

is puzzling. One possibility is that firms face costs of cutting production immediately (that is, within the quarter) due to pre-existing contracts with labor or suppliers. Since these are essentially committed fixed costs, the firm cannot save these costs by cutting production, so it might as well produce and maintain its inventory. This interpretation is consistent with the evidence documented above that, at least for constrained firms (who may have the most need to cut production costs), inventory declines with a lag for negative sales shocks. Another possibility is that firms may have converted inventory accumulated when production costs were low to cash by gradually depleting inventory and holding cash as a buffer against bad cost shocks. Converting inventory to cash to avoid inventory holding costs would make sense as long as stockout costs are not very high. Constrained firms may run out of cash faster when faced with negative shocks, and may deplete inventory with a lag. In Table 11, we report results on PPE growth and Capex. Results are mostly consistent with our hypothesis and those in Table 7, especially for positive sales shocks. For positive sales shocks, while both unconstrained and constrained firms increase both PPE growth and Capex, the latter do so less aggressively. There are some differences, however, when the sales shock is negative. Somewhat surprisingly, unconstrained firms increase Capex when (negative) sales growth is more negative; however, constrained firms reduce Capex when the sales shock is more negative, and more so when sales growth drop below the bottom 20 percent cutoff for sales growth, consistent with our hypothesis. With respect to PPE, unconstrained firms do cut PPE growth when a negative sales shock is more negative; however, there is no evidence that the constrained firms do so more aggressively. Results in Table 12 where we regress Capex and PPE growth on lagged sales are similar, but the magnitudes are smaller, as expected. Overall, the results on capital growth, especially the response to positive sales growth, line up well with the model results. This is the direction of response to unanticipated sales shocks that is more important for our hypothesis that binding capacity constraints affect the relative 27

sensitivity of the response of inventory growth (or production, holding sales shock constant) of financially unconstrained and constrained firms. The sensitivity of Capex to negative sales shocks of constrained firms vis-a-vis unconstrained firms is very consistent with the model; but less so for PPE growth. However, it is conceivable that the ability to deplete inventory carried over from good times to bad times allows the financially constrained firms to avoid depleting capital relative to the unconstrained firms, as indicated by the PPE growth results. The capital growth results are important for another reason as well. As noted in the introduction, our model is primarily one for finished goods inventory. However, intermediate goods inventory can be modeled as a factor of production similar to capital, and is held in relative fixed proportion to capital, would generate results very similar to those for capital growth in our model namely, that financially constrained firms increase intermediate goods inventory more sluggishly in response to positive sales shocks, and reduce such inventory more aggressively in response to negative sales shocks, than do unconstrained firms. As noted, these implications are very consistent with our inventory regressions on the actual data. 5.4 The Cumulative Effect of Past Sales Shocks In the results presented so far, we have mainly focused on the immediate response of inventory to shocks to sales. We have paid particular attention to a key asymmetry implied by the model, i.e., due to capacity constraints, the inventory accumulation by constrained firms in response to favorable shocks is more sluggish than that of unconstrained firms, but more aggressive in response to unfavorable shocks. What remains to be shown is that once capacity constraints become less binding as profitability improves in favorable cost states, the response of the constrained firms to positive and negative sales shocks becomes more symmetric vis-a-vis unconstrained firms, that is, the former respond more aggressively in response to both types of shocks. This is what is implied by the 28

model. The key insight from the model is that financially constrained firms engage in more aggressive production-cost smoothing because they benefit more from accumulating inventory in low production-cost states, and selling from inventory in high production cost states (when financial constraints are more likely to be binding). We now provide evidence consistent with this behavior 20. To do so, we examine the cumulative lagged effects of shocks on the inventory behavior of both types of firms. We focus on extreme shocks and use a specification very similar to that in Table 9. Specifically, we create an Above dummy that takes a value of 1 in a given quarter if a firm s sales growth exceeds the 80th percentile of the distribution for that firm, and zero otherwise. This is analogous to the Below dummy in Table 9 which corresponds to sales growth lower than the 20th percentile of the distribution. We then include up to six lags of the Above and Below dummies, and their interactions with the financial constraint dummy, in specifications similar to that in Table 9. We also control for the financial constraint dummy, contemporaneous positive and negative sales growth, cash flow and the interaction of cash flow with the financial constraint dummy, the lagged ratio of inventory to lagged capital and its interaction with the financial constraint dummy. Column (1) are (2) in Table 13 report results for the simulated data. Consistent with a symmetric and more aggressive response to both positive and negative extreme sales shocks, the cumulative coefficients of the lagged Above and Below dummies interacted with the financial constraint dummy are, respectively, positive and negative. This suggests that over six periods after an extreme shocks, the financially constrained firms not only accumulate more inventory in response to a positive extreme sales shock, they also deplete more inventory in response to a negative extreme sales shock, than their unconstrained counterparts. Column (3) reports the results for the real data. The regressions are run for each quarter, and 20 While we do not model cash holding behavior, constrained firms would generally find it optimal to hold cash if that possibility were introduced. However, the result that constrained firms accumulate (deplete) inventory more aggressively in good (bad) cost states than unconstrained firms do, continues to hold if the former are allowed to hold cash, as long as there is a carry cost of cash holdings. This is shown in the Appendix. Unconstrained firms in our model do not have any incentive to hold cash. 29

the average coefficients over all quarters in a year are reported. For the lags of the Above and Below dummies, the reported coefficients are further cumulated over the six lags. The results are very consistent with those in column (1). In particular, the cumulative coefficients of the Above dummy interacted with the financial constraint dummy is positive and significant, while that of the Below dummy is negative and significant. 6 Discussion 6.1 Are We Capturing the Effects of Financial Constraints? Previously, to isolate the effect of financial constraints on a firm s inventory behavior, financially constrained and unconstrained firms in the model were assumed to have only one difference, namely, the cost of external financing. In reality, these two groups of firms could be different in many other respects. For example, Gaur and Kesavan (2007) document that the stockout cost per unit of inventory is larger for smaller firms, which also have higher costs of external financing. One may argue that it is the difference in stockout cost, instead of financing cost, that truly drives the differences in inventory and capital investment behaviors between those two groups of firms. In this subsection, we use the model as a laboratory to examine whether the observed empirical patterns in previous sections could be possibly driven by differences in other aspects except financing costs. Our strategy is as follows. Our model identifies two key differences in the inventory response of financially unconstrained and constrained firms to cost shocks, which translate to sales shocks. First, the short-term response of these two groups of firms to favorable and unfavorable shocks is asymmetric: constrained firms respond more sluggishly to positive sales shocks but more aggressively to negative sales shocks than do unconstrained firms. However, this asymmetry disappears with time, and the financially constrained firms accumulate more inventory in response to a posi- 30

tive sales shock, and also deplete more inventory in response to a negative sales shock. We use our model to see whether similar asymmetry can be reproduced by varying other parameters, keeping the degree of financial constraints the same. We study two groups of firms: one group comprises of financially unconstrained firms as in the main results, while the other group comprises of firms that differ from the first group now on dimensions other than external financing cost. Specifically, we model two groups of firms with only one difference at a time: financially unconstrained firms in our baseline calibration, referred as benchmark firms, and firms with the same calibration but higher operating cost, higher investment adjustment cost, higher inventory stockout cost, or lower production cost, respectively. The latter group of firms, referred as comparison firms, have higher inventory-to-capital ratios on average as shown in Table 4 so that they mimic financially constrained firms. 21 The same regression in Table 7 is then conducted using the simulated data with the FC indicator replaced by an indicator, D, that equals one if a firm is in the latter group and zero otherwise. The results are reported in Table 14. For considerations of space, here we report the short-term responses only. 22 Fixed operating cost Fixed cost has little impact on a firm s choices of inventory and capital investment in the absence of financing frictions because fixed cost does not impact either cost or profit at the margin. Thus, the sensitivities of inventory and capital investment to sales growth react little to differences in fixed cost. Consistently, rows (1) and (2) show that only one out of four interaction terms with the high-cost indicator D is statistically significant at 5% level. Moreover, the relative sensitivity of inventory to positive and negative sales growth between firms with different levels of fixed cost is symmetric, opposite of what we observed in Table 7. Therefore, 21 The capital-to-output ratio α in the production function can be different between financially constrained and unconstrained firms. For example, Hennessy and Whited (2007) show that small firms are estimated to have larger α and higher financing costs. The simulated data shows that firms with larger α on average hold less inventory per capital than firms with smaller α, opposite to what observed for financially constrained and unconstrained firms. Therefore, the difference in α cannot generate the different inventory behaviors between those two groups of firms. 22 Since the response patters for the comparison groups relative to the benchmark groups cannot mimic those for financially constrained firms vis-a-vis the unconstrained firms, the long-term responses do not add much for our conclusions here. However, for the record, we fail to replicate similar patterns here as well. 31

the large and asymmetric differences in sensitivity of inventory to sales growth between financially unconstrained and constrained firms are not likely due to difference in fixed operating cost. Linear operating cost The relative sensitivities of inventory and capital investments to positive and negative sales growth of comparison firms with higher f 1 and the benchmark firms are symmetric, as shown in rows (3) and (4). Therefore, difference in linear operating cost can not lead to the aforementioned differences between financially constrained and unconstrained firms. Investment adjustment cost Firms with higher adjustment cost invest in inventory more aggressively in good states and deplete inventory less aggressively in bad states, as shown in row (5). Therefore, difference in adjustment cost can not generate the empirically observed difference in inventory behavior between financially constrained and unconstrained firms. Inventory stockout cost The sensitivity of inventory growth and capital growth to sales growth is larger for firms with greater b, indicated by a positive interaction between positive sales growth with high-stockout cost indicator D in rows (7) and (8). Therefore, the smaller sensitivity of inventory and capital investment to positive sales growth observed in the data cannot be driven by higher inventory stockout cost. Moreover, the effect of inventory stockout cost on inventory is much larger than that on capital investment. The difference in sensitivity of capital investment to sales growth is an order-of-magnitude smaller than that of inventory investment, different from what we observed in the data. Production cost Rows (9) and (11) show that the interaction of positive sales growth with low-production cost indicator D is positive. The same patterns are observed in rows (10) and (12) for capital investment. Therefore, the observed difference in inventory and capital investment behaviors between financially constrained and unconstrained firms cannot be driven by differences in production costs. In summary, the different inventory and capital investment behaviors between financially constrained and unconstrained firms observed in the data are not likely to be driven by differences 32

other than financial constraints within our model framework. 6.2 Alternative Measures of Financial Constraints The literature on financial constraints offers many different measures to identify financially constrained firms. Firm size the one that we follow in this paper is one of the most commonly used and relatively non-controversial. Following Almeida, Campello and Weisbach (2004), we also repeat our results on for financial constraint classifications based on the availability of bond ratings, dividend payouts, and availability of commercial paper ratings. Our results are very similar. These results are not reported, but are available on request. 6.3 Demand Shocks vs. Cost Shocks Our model implies that cost shocks are the main driver for the asymmetric differences in the sensitivity of inventory and capital growth to positive and negative sales growth between financially constrained and unconstrained firms. Empirically, it is hard to peel out the effects of demand shocks on sales growth from those of cost shocks because both shocks are likely to affect sales growth. To demonstrate that in reality, inventory behavior as modeled here can be driven by cost shocks, in this subsection, we identify a sample period, namely, the post year 2000 period, when demand shocks were arguably a lesser concern for inventory management than cost shocks, and show that our results hold during this period. Before the early 1980s, demand management appears to have been an important consideration under the so-called Just-in-Case (JIC) system. Stimulated by the success of Japanese car makers, a new inventory management system, the Just-in-Time (JIT), has been gradually adopted by U.S. manufacture firms and has become the dominate practice nowadays. According to the report Physical Risks to the Supply Chain provided by CFO Research Services, nearly two-third of U.S. firms had implemented the JIT inventory practice by 2008. Moreover, larger firms are more likely 33

to have adopted JIT (White, Pearson and Wilson, 1999). We expect that the fraction of firms that adopt JIT is even larger in our sample because our sample only includes public firms. Under such a system, firms produce goods to meet current needs rather than anticipate future demand. Studies (Chen, Frank and Wu, 2005) have shown that the adoption of JIT has contributed to a steady decline of inventory holdings since the early 1980s, and the trend in inventory holdings becomes flat only around year 2000. Figure 1 plots the trends of total inventory holdings and its three components, raw materials, work-in-process, and finished goods, separately. Consistent with the findings in the previous literature, the same decline exist in our sample. For our purposes, the important consequence of the JIT adoption is that demand shocks become a lesser concern in determining inventory holdings. In the extreme case, when firms react to current demand quickly enough, they only hold inventory to smooth production and hedge cost shocks. We expect that during the period of 2000-2010 when most of firms have adopted the JIT practice, changes in inventory should be mainly driven by cost shocks. We repeat the baseline regression of inventory and capital growth on sales growth for that period. Consistent with our conjecture, Table 15 and Table 16 show that the same asymmetric differences in the sensitivity of inventory to positive and negative sales growth between financially constrained and unconstrained firms are found for the sample of 2000-2010. 6.4 Disaggregated Inventory Series Our model applies most directly to finished goods inventory. However, as argued in the introductory section, to the extent that raw materials are factors of production and may have to be used in fixed proportion to capital, our results should extend to raw material inventory as well. The invisible hand argument of Blanchard (1983) also suggests that raw materials inventory should behave in the same way as finished goods inventory as long as cost shocks in the economy are correlated. Unfortunately, disaggregated inventory series are only available in Compustat with sufficient coverage from the year 2004. When we repeat our baseline results on the disaggregated 34

series, we get qualitatively very similar results for both finished goods inventory and raw materials and work-in-progress inventory as our results on aggregated inventory over our entire sample period. In particular, both types of inventory adjust more sluggishly in response to positive sale shocks for constrained firms than for unconstrained firms in all four quarters. In NBER recession years, financially constrained firms deplete inventory more aggressively; however, the coefficient for the NBER recession quarter dummy is negative and significant in only two of the four quarters, for both types of inventory. These results are not reported in a table but are available on request. 7 Conclusion Changes to firms inventory holdings have long been regarded as an important component of business fluctuations, as has the propagation of monetary policy shocks to the real economy via firms access to finance. While earlier empirical attempts either found little relationship between the cost of finance and inventory holding behavior, more recent evidence suggests that monetary policy may have important effects on the inventory holding behavior of firms that have difficulty in accessing external finance. There has been little attempt, however, to link the effect of financial constraints to inventory policy theoretically. In this paper, we develop a theoretical model that studies the interaction of financial constraints and inventory behavior. The main intuition we try to model is that firms incentives to build inventory when costs are low and deplete inventory when costs are high are exacerbated when they face financial constraints and have difficulty in rebuilding capital. The model provides a number of insights on the determinants of inventory holdings in the presence of financial constraints. Using model-generated data, we develop several empirical tests of the theory. These tests have the advantage that we do not need to interpret coefficients of cash flows in our regressions, which has been controversial due to measurement error issues. When we take these tests to the actual data, we find very consistent results. 35

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King, Robert and Sergio Rebelo. 1999. Resuscitating Real Business Cycles. Elsevier pp. 927 1007. Ramey, Valerie Ann. 1989. Inventories as Factors of Production and Economic Fluctuations. American Economic Review 79(3):338 354. Ramey, Valerie Ann and Kenney D. West. 1999. Inventories. In Handbook of Macroeconomics, ed. J. B. Taylor and M. Woodford. 1 ed. Vol. 1 Elsevier chapter 13, pp. 863 923. Riddick, Leigh and Toni Whited. 2009. The Corporate Propensity to Save. Journal of Finance 64:1729 1766. Salinger, Michael and Lawrence H. Summers. 1983. Tax Reform and Corporate Investment: A Microeconometric Simulation Study. National Bureau of Economic Research, Inc. pp. 247 288. Wang, Pengfei and Yi Wen. 2011. Inventory Accelerator in General Equilibrium. Manuscript, Hong Kong University of Science and Technology and Federal Reserve Bank of St. Louis. West, Kenneth. 1986. A Variance Bounds Test of the Linear Quadratic Inventory Model. Journal of Political Economy 94(2):374 401. White, Richard E, John N Pearson and Jeffrey R Wilson. 1999. JIT Manufacturing: A Survey of Implementations in Small and Large U.S. Manufacturers. Management Science 45(1):1 15. 37

A Solution Method The model is solved using second-order perturbation method, which requires that the objective function is differentiable and unconstrained. 23 For constrained firm, the optimization problem can be approximated by the following ] ( ) ( )} At Dt ˆV t (K t 1, N t 1, X t, Z t ) = max {D t + E t [M t+1 ˆVt+1 + log, {Q t,n t,i t} ϖ 1 A t where the last term drops to negative infinity rapidly as D t is close to zero and is called logarithmic barrier. As ϖ increases to, the above optimization problem converges to our original optimization problem. To add the constraints that output cannot exceed the capacity, we follow the same strategy, i.e., ] ˆV t (K t 1, N t 1, X t, Z t ) = max {D t + E t [M t+1 ˆVt+1 {Q t,n t,i t} ( ) ( ) ( ) [ ( ) α ( )]} At Dt At Kt 1 Qt + log + log A 0. ϖ 1 A t ϖ 2 A t A t For financially constrained firms, the first order conditions w.r.t. Ñ t, Qt and Ĩt using scaled variables are given by ( Ñ t : 1 + 1 ) [ e Xt (1 2h S ] {( ) 1 [ } t ) H t = βe t 1 + e X t+1 (1 2h S t+1) G t+1] ϖ 1 Dt ϖ 1 Dt+1 ( Q t : 1 + 1 ) [ e Xt (1 2h S ) ] 1 t ) e (d Zt 1 + d 2 Qt G t = ϖ 1 Dt [ϖ 2 (A 0 Kαt 1 g α Q )] t Ĩ t : ( Ĩt )] { ( = E t M t+1 g 1 + ( 1 + 1 ) [ 1 + ag ϖ 1 Dt K t 1 ) a 2 ( (Ĩt+1 2 g f 1 + (1 δ) g K 1 1 + ag t α 1 +M t+1 g α K t g ( α ϖ 2 A 0 Kα t g α Q ), t+1 (Ĩt+1 K t )) 1 ϖ 1 Dt+1 ) 23 The value function iteration method is not subjected to this constraint however it suffers from the curse of dimensionality. Given that our model has four state variable ({K t 1, N t 1, X t, Z t } and three independent endogenous variables {Q t, N t, I t }, the value function iteration method is not applicable. 38

where H t = bγ 2 G t = bγ 2 S γ 1 t S γ 1 t ( 1 cñt S t ( ) 2 1 cñt + bc S t ) 2 γ 2 + bc S t (Ñt + S t ) ( 1 cñt S t ( ) γ 2 S t Ñ t 1 cñt. S t ) For financially unconstrained firms, let ϖ 1 and we get Ñ t : Q t : Ĩ t : [e Xt (1 2h S t ) H t ] = βe t {[e X t+1 (1 2h S t+1 ) G t+1 ]} [e Xt (1 2h S ) ] t ) e (d Zt 1 + d 2 Qt G t = 1 [ϖ 2 (A 0 Kαt 1 g α Q t )] [ ( )] ) Ĩt 1 + ag = βe t { g a 2 (Ĩt+1 K t 2 g f 1 K t ))] α 1 (Ĩt+1 + (1 δ) g (1 1 + ag +g α K t g α ( K t ϖ 2 A 0 Kα t g α Q ). t+1 The above two sets of system equations are solved using second-order perturbation method. 39

B Model with Cash Holdings In this appendix, we explore the effect of cash holdings on firms inventory investment behavior by analyzing a special case under which an analytical analysis is available. Cash holdings are assumed to have no additional benefits except to hedge for liquidity risks, i.e., the one-period return of cash holdings, R H, is lower than or equal to the risk free rate 1/β. Therefore, financially unconstrained firms hold zero cash but financially constrained firms generally hold nonzero cash under this assumption. We argue that even in the presence of cash holdings, financially contained firms hold more inventory in good times and less inventory in bad times, compared to financially unconstrained firms. as Define λ t = 1 + 1 ϖ 1 Dt+1 and rewrite the FOC of inventory in equations (8) for constrained firms {( ) λt+1 [e e Xt X H t = βe t+1 ] } t G t+1 (8) λ t and the FOC of inventory for unconstrained firms in (8) as e Xt H t = βe t {[ e X t+1 G t+1 ]}. (9) Here, λ t measures the tightness of the financial constraints. In good times, the current dividend is high and future dividend is expected to be lower due to the mean-reverting demand and cost shocks and vice versa for bad times. Therefore, we have λ t+1 λ t > 1 for good times; λ t+1 λ t < 1 for bad times. It can be easily shown that H t N t < 0 and G t+1 N t < 0. Therefore, all else equal, constrained firms will hold more inventory in good times and hold less inventory in bad times than unconstrained firms. Now assume that we allow cash holdings, denoted as CH t. Dividend is then given by D t = Y t C Ot C Qt C Nt C It I t + R H CH t 1 CH t. Since cash holding has to be positive, we introduce an additional term log(ch t ) ϖ 3 to approximate this nonnegative-cash-holding constraint, where ϖ 3 so that the above term is close to zero when CH t > 0. As we argue before, unconstrained firms will hold zero cash. The 40

optimal cash holdings of constrained firms is given by the following FOC: λ t = βr H E t [λ t+1 ] + 1 ϖ 3 CH t. (10) The model generally has no analytical solution. To illustrate the mechanism, let s consider a special case where there is no uncertainty and agents know the time series of demand and cost shocks at time 0. Then we can substitute equation (10) into equation (8) and get {( ) 1 [e ] } e Xt Xt+1 H t = βe t βr H 1 G t+1. (11) + ϖ 3 CH t λ t+1 In this case, whether constrained firms will hold more or less inventory than unconstrained firms depends on whether 1 βr H 1 > 1 or < 1, (12) + ϖ 3 CH t λ t+1 respectively. In good times, CH t > 0 and ϖ 3 CH t λ t+1. Therefore, as long as R H < 1/β, i.e., there are costs associated with cash holdings, condition (12) is larger than one and constrained firms will hold more inventory. On the contrary, in bad times, constrained firms have cash holdings close to zero and the term ϖ 3 CH t λ t+1 could be a finite number (this term is always positive by definition). When cash holdings are low enough, we could have 1 βr H + 1 ϖ 3 CH t λ t+1 < 1, that is, constrained firms hold less inventory than unconstrained firms in an extremely bad situation even in the presence of cash holdings. A more general case has to be solved numerically and our argument can be shown through numerical exercises. 41

Table 1: Baseline Calibration This table lists the parameter values used to solve and simulate the baseline model. The capital-to-output ratio α is from Hennessy and Whited (2007). The growth rate of productivity g is chosen to match the average growth rate of sales in our sample. The discount factor β is set to match the quarterly interest rate. Capital depreciation rate δ and investment adjustment cost parameter a are chosen to match the mean and volatility of investmentto-capital ratio, respectively. The slope of the demand curve h is chosen to generate an average markup in Altig et al. (2011). The scaling factor A 0 in the capacity constraint is chosen to match the average capacity utilization rate from the IHS Global Insight dataset for the sample period 1971-2010. The stockout avoidance cost ratio c is set to match the mean of inventory-to-capital ratio. The persistence and volatility of aggregate demand shock ρ X and σ X are from King and Rebelo (1999). The remaining 9 parameters, long-run mean of demand X, the stockout avoidance cost parameter b, elasticity of stockout-avoidance cost to sales γ, production cost parameters d 1 and d 2, the persistences and volatilities of costs shocks, ρ Z, and σ Z, and the operating cost parameters f 0 and f 1, are chosen to match the means and volatilities of sales-to-capital ratio, sales change-to-capital ratio, inventory change-to-capital ratio, and cash flow-to-capital ratio and the volatility of inventory-to-capital ratio. Details of how the model is calibrated can be found in Section 4. Parameters are reported at quarterly frequency. Parameter Value Description Source α 0.7 Capital-to-output ratio Hennessy and Whited (2007) g 1.009 Growth rate of productivity β 0.982 Time-preference coefficient δ 0.015 Capital depreciation rate a 60 Quadratic investment adjustment cost h 0.01 Slope of demand curve Altig et al. (2011) A 0 3 Scaling factor in capacity constraint c 2.08 Stockout-avoidance ratio b 0.0032 Stockout-avoidance cost γ 1.5 Elasticity of stockout-avoidance cost to sales d 1 0.132 Linear production cost d 2 0.022 Quadratic production cost f 0 0.0665 Fixed operating cost f 1 0.0069 Linear operating cost ρ Z 0.92 Persistence coefficient of cost shock σ Z 0.147 Conditional volatility of cost shock X -1.45 Long-run average of demand shock ρ X 0.98 Persistence coefficient of demand shock King and Rebelo (1999) σ X 0.007 Conditional volatility of demand shock King and Rebelo (1999) 42

Table 2: Summary Statistics This table presents the summary statistics of real data and the unconditional sample moments from simulated data. In both panels, statistics are calculated as the time-series averages and reported separately for the Financial Unconstrained firms (UFC) and Financially Constrained firms (FC). Real data used in Panel A are collected from Compustat Industrial Quarterly Files for the period 1971 to 2010. Financial firms (SIC Code 6000-6900) and regulated utilities (SIC Code 4900-4999) are excluded. UFC and FC in real data are classified based on size. In a given quarter, UFC are the top 30% in beginning-of-period total asset and FC are the bottom 30%. The scaling variable Kt 1 is the level of beginning-of-period capital defined as total asset (ATQ) minus inventory (INVTQ). S Growth is the change in net sales (SALEQ) scaled by beginning-of-period capital. N Growth is the change in inventory scaled by the beginning-of-period capital, where the level of inventory is adjusted for the LIFO and FIFO accounting following Salinger and Summers (1983) and Carpenter, Fazzari and Petersen (1994). P P E Growth is the change in property plant and equipment (PPENTQ) scaled by lagged capital. It/Kt 1 is the quarterly investment-to-lagged capital ratio, where investment is calculated by converting the Compustat Year-to-Date item CAPXY to quarterly frequency. CFt/Kt 1 is the cash flow-to-lagged capital ratio, where cash flow is defined as earnings before extraordinary items (IBQ) plus depreciation (DPQ). Nt/Kt 1 and St/Kt 1 are the inventory-to-lagged capital ratio and sales-to-lagged capital ratio, respectively. Levels are converted to 2000 constant dollars. Ratios and changes are winsorized at 1% levels at both tails to mitigate the effect of outliers. Data in Panel B are generate from 100 simulated panels, each contains 720 quarters for 300 UFC and 300 FC firms. UFC are firms that can seek external financing with no cost, while FC are firms whose dividend have to be nonnegative. In the simulated data, S Growth is the change in the level of sales scaled by lagged capital stock. N Growth and Nc Growth are the change in inventory (which is the stock of goods firms carry in dollar value) scaled by lagged capital, where the former prices inventory at market value of the goods, and the latter prices inventory at production cost following LIFO accounting. It/Kt 1 is the investment-to-lagged capital ratio, where investment is defined as the change of capital net of depreciation. CFt/Kt 1 is the cash flow-to-lagged capital ratio where cash flow is calculated by subtracting production cost, operating cost, and investment adjustment cost from sales. Nt/Kt 1, N ct/kt 1, St/Kt 1 and Qt/Kt 1 are the level of inventory priced at market value, inventory priced at cost, sales and production, respectively, divided by beginning-of-period capital. U tilization is the proportion of capital that firms actually used to generate output over the total beginning-of-period stock of capital. Reported statistics including number of observations, mean, median and standard deviation (SD) are the calculated as cross-simulation average of the statistics from each simulation. 43

Panel A. Real Data UFC FC N Mean Median SD N Mean Median SD S Growth 140,777 0.0056 0.0065 0.0626 140,689 0.0206 0.0177 0.1031 N Growth 140,777 0.0003-0.0000 0.0269 140,689 0.0104 0.0098 0.0465 P P E Growth 139,623 0.0043 0.0016 0.0304 140,253 0.0147 0.0090 0.0371 It/Kt 1 115,201 0.0205 0.0181 0.0120 114,936 0.0263 0.0215 0.0200 CFt/Kt 1 122,893 0.0230 0.0253 0.0245 120,244 0.0135 0.0164 0.0417 Nt/Kt 1 140,777 0.2251 0.2195 0.0605 140,689 0.3168 0.3058 0.0993 St/Kt 1 140,777 0.3652 0.3565 0.0934 140,689 0.4967 0.4807 0.1474 Panel B. Simulated Data UFC FC N Mean Median SD N Mean Median SD S Growth 215,700 0.0051 0.0081 0.0569 215,700 0.0066 0.0088 0.0565 N Growth 215,700 0.0015 0.0033 0.0200 215,700 0.0032 0.0069 0.0347 N c Growth 215,700 0.0007 0.0012 0.0131 215,700 0.0011 0.0004 0.0203 It/Kt 1 215,700 0.0241 0.0235 0.0132 215,700 0.0242 0.0260 0.0187 CFt/Kt 1 215,700 0.0581 0.0732 0.0941 215,700 0.0539 0.0575 0.1168 Nt/Kt 1 215,700 0.1515 0.1674 0.0462 215,700 0.2295 0.2436 0.1343 N ct/kt 1 215,700 0.0652 0.0734 0.0330 215,700 0.0976 0.0794 0.0882 St/Kt 1 215,700 0.5081 0.5434 0.1214 215,700 0.5640 0.5850 0.1143 Qt/Kt 1 215,700 0.5096 0.5479 0.1292 215,700 0.5672 0.5956 0.1324 U tilization 215,700 0.6912 0.7680 0.2235 215,700 0.7357 0.8107 0.2112 44

Table 3: Correlation Matrix of Simulated Data This table reports the cross-simulation average of the pairwise correlation coefficients. Data are generated from 100 simulations. Each simulation has 720 quarters of 300 UFCs and 300 FCs. Correlations for the UFC group are reported in Panel A and for the FC group are in Panel B. S Growth is the change in the level of sales scaled by lagged capital stock. N Growth and Nc Growth are the change in inventory scaled by lagged capital, where the former prices inventory at market value of the goods, and the latter assumes a different price using production cost and following LIFO accounting. It/Kt 1 is the investment-to-lagged capital ratio. CFt/Kt 1 is the cash flow-to-lagged capital ratio. Nt/Kt 1, N ct/kt 1, St/Kt 1 and Qt/Kt 1 are the level of inventory priced at market value, inventory priced at cost, sales and production divided by beginning-of-period capital, respectively. U tilization is the proportion of capital that firms actually used to generate output over the total beginning-period stock of capital. Cost is the negative of the cost realization, indicating a more favorable state. Demand is the realization of aggregate demand. 95% confidence intervals for all the correlations do not span zero. Panel A. Correlation matrix of UFC in simulated data S Growth N Growth N c Growth It/Kt 1 CFt/Kt 1 Nt/Kt 1 N ct/kt 1 St/Kt 1 U tilization Cost Demand S Growth 1.000 N Growth 0.964 1.000 N c Growth 0.847 0.924 1.000 It/Kt 1 0.142 0.134 0.166 1.000 CFt/Kt 1 0.051 0.073 0.102 0.609 1.000 Nt/Kt 1 0.202 0.249 0.247 0.265 0.642 1.000 N ct/kt 1 0.137 0.181 0.215 0.275 0.755 0.871 1.000 St/Kt 1 0.281 0.312 0.290 0.345 0.551 0.959 0.751 1.000 U tilization 0.396 0.445 0.426 0.286 0.658 0.972 0.862 0.941 1.000 Cost 0.177 0.182 0.189 0.781 0.862 0.517 0.621 0.466 0.556 1.000 Demand 0.017 0.007 0.003 0.096 0.109 0.003-0.017 0.112 0.036 0.000 1.000 Panel B. Correlation matrix of FC in simulated data S Growth N Growth N c Growth It/Kt 1 CFt/Kt 1 Nt/Kt 1 N ct/kt 1 St/Kt 1 U tilization Cost Demand S Growth 1.000 N Growth 0.463 1.000 N c Growth 0.313 0.840 1.000 It/Kt 1 0.239 0.317 0.213 1.000 CFt/Kt 1 0.059-0.015 0.003 0.570 1.000 Nt/Kt 1 0.011 0.197 0.171 0.444 0.382 1.000 N ct/kt 1-0.014 0.094 0.156 0.135 0.409 0.667 1.000 St/Kt 1 0.365 0.395 0.227 0.736 0.240 0.510 0.170 1.000 U tilization 0.385 0.611 0.476 0.655 0.494 0.680 0.468 0.828 1.000 Cost 0.190 0.205 0.184 0.788 0.882 0.353 0.333 0.388 0.573 1.000 Demand 0.018 0.004 0.004 0.071 0.127-0.012-0.005 0.122 0.037-0.001 1.000 45

Table 4: Comparative Statics This table presents the comparative statics for our baseline model. Parameters of interest include fixed operating cost f0, linear operating cost f1, stockout-avoidance cost b, quadratic investment adjustment cost a, linear production cost d1, quadratic production cost d2, slope of the demand curve h2, conditional volatility of cost shock σz, and conditional volatility of demand shock σx. More detailed descriptions of the baseline calibration are included in Table 1 and Section 4. The top row shows the parameter value in the baseline calibration. The row beneath shows the corresponding new value. In column (1) to (9), one parameter value is changed each time while others are fixed at the baseline value. Moments include mean and standard deviation (in bracket) of the capital level (Kt), inventory level (Nt) and inventory-to-capital ratio (Nt/Kt). Moments under baseline parameters are reported first, followed by the ones generated from the new value. For each of these moments, we listed the value for UFC, FC and the difference between the two groups. The level variables K and N are divided by the corresponding level of UFC in the baseline and multiplied by 100. All results obtained use the same realization of shocks. (1) (2) (3) (4) (5) (6) (7) (8) (9) Variable Baseline high f0 high f1 high b high a0 low d1 low d2 high h high σz high σx Baseline Value f0=0.0665 f1=0.0069 b=0.0032 a0=60 d1=0.132 d2=0.022 h=0.01 σz=0.147 σx =0.007 New Value f0=0.0760 f1=0.0100 b=0.0048 a0=90 d1=0.099 d2=0.011 h=0.03 σz=0.182 σx =0.022 Kt (UFC s capital in the baseline = 100) UFC 100 100 95 100 79 140 155 86 108 114 [100] [100] [95] [100] [78] [137] [154] [86] [110] [117] FC 84 81 80 84 65 136 147 68 84 95 [85] [82] [80] [85] [65] [134] [146] [68] [86] [96] Diff(UFC-FC) 16 19 16 16 13 3 8 18 24 19 [15] [18] [15] [15] [12] [3] [7] [17] [24] [20] Nt (UFC s inventory in the baseline = 100) UFC 100 100 97 120 85 156 174 85 97 112 [100] [100] [97] [118] [83] [148] [165] [87] [102] [114] FC 131 153 131 132 124 157 176 148 163 146 [150] [183] [152] [142] [145] [150] [172] [185] [206] [169] Diff(UFC-FC) -31-53 -34-13 -39 0-1 -63-66 -35 [-50] [-83] [-55] [-24] [-62] [-2] [-6] [-98] [-103] [-55] Nt/Kt UFC 0.151 0.151 0.154 0.181 0.164 0.170 0.171 0.149 0.137 0.149 [0.047] [0.047] [0.046] [0.051] [0.043] [0.028] [0.025] [0.054] [0.055] [0.047] FC 0.229 0.272 0.242 0.233 0.278 0.174 0.181 0.312 0.281 0.231 [0.136] [0.181] [0.148] [0.107] [0.176] [0.037] [0.047] [0.229] [0.208] [0.140] Diff(UFC-FC) -0.077-0.121-0.088-0.052-0.114-0.004-0.009-0.162-0.145-0.082 [-0.089] [-0.135] [-0.102] [-0.056] [-0.134] [-0.009] [-0.021] [-0.175] [-0.153] [-0.093] 46

Table 5: Regression on Shocks with Simulated Data This table reports the regression results on the simulated data. The dependent variable in column (1) and (2) are N Growth and N c Growth, respectively. Both variables are the change in inventory scaled by lagged capital, where the former prices inventory at market value of the goods, and the latter prices inventory at production cost following LIFO accounting. The dependent variable I t /K t 1 in column (3) is the investment-to-lagged capital ratio, where investment is defined as the change of capital net of depreciation. F C is a dummy that equals to 1 if the firm is FC, and 0 otherwise. CostShock t is defined as the change in level of (adverse) cost realization scaled by its standard deviation. CostShock t + is the interaction of CostShock t with an indicator that equals to 1 if CostShock t is positive (favorable), and 0 otherwise. CostShockt is the interaction of CostShock t with an indicator that equals to 1 if CostShock t is negative (unfavorable), and 0 otherwise. CostShock t + F C and CostShockt F C are the interactions of CostShock t + and CostShockt with the F C dummy. The lagged state variable Cost t 1 which is the negative of the cost realization and the lagged inventory-to-capital ratio N t 1 /K t 2 are also included. The simulated data are generate from 100 simulations. Cross-simulation average of regression coefficients are reported. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. (1) (2) (3) N Growth t Nc Growth t I t /K t 1 F C 0.0074*** 0.0030*** 0.0024*** [0.0074, 0.0075] [0.0030, 0.0030] [0.0023, 0.0025] CostShock t + 0.0087*** 0.0043*** 0.0081*** [0.0086, 0.0088] [0.0043, 00044] [0.0081, 0.0081] CostShock t + F C -0.0041*** -0.0035*** -0.002*** [-0.0041, -0.0040] [-0.0036, -0.0035] [-0.0021, -0.0020] CostShockt 0.0107*** 0.0074*** 0.0045*** [0.0106, 0.0108] [0.0074, 0.0075] [0.0045, 0.0045] CostShockt F C 0.0056*** 0.0011*** 0.0041*** [0.0055, 0.0057] [0.0010, 0.0011] [0.0040, 0.0042] Cost t 1 0.0035*** 0.0021*** 0.0124*** [0.0035, 0.0036] [0.0021, 0.0021] [0.0123, 0.0125] N t 1 /K t 2-0.0279*** -0.0271*** [-0.0280. -0.0277] [-0.0272, -0.0269] Constant 0.0156*** 0.0053*** 0.0547*** [0.0154, 0.0157] [0.0051, 0.0055] [0.0546, 0.0548] Observations 430,800 430,800 431,400 Adj.R 2 0.148 0.123 0.612 47

Table 6: Sales Growth and Shocks This table reports the regression results on the simulated data. The dependent variable S Growth is the change in the level of sales scaled by lagged capital stock. CostShock t is defined as the change in level of (adverse) cost realization scaled by its standard deviation. CostShock t F C is the interaction of CostShock t with the dummy F C that equals to 1 if the firm is FC, and 0 otherwise. The reported estimates are the cross-simulation average of the coefficients from 100 simulations. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. (1) (2) S Growth t S Growth t CostShock t 0.0315*** 0.0315*** [0.0313, 0.0316] [0.0313, 0.0316] CostShock t F C -0.00008 [-0.0003, 0.0001] Constant 0.0058*** 0.0058*** [0.0058, 0.0059] [0.0058, 0.0059] Observations 431,400 431,400 Adj.R 2 0.305 0.305 48

Table 7: Regression on Sales Growth with Simulated Data This table reports the regression results on the simulated data. The dependent variable in column (1) and (2) are N Growth and N c Growth, respectively. Both variables are the change in inventory scaled by lagged capital, where the former prices inventory at market value of the goods, and the latter prices inventory at production cost following LIFO accounting. The dependent variable I t /K t 1 in column (3) is the investment-to-lagged capital ratio, where investment is defined as the change of capital net of depreciation. F C is a dummy that equals to 1 if the firm is FC, and 0 otherwise. S Growth is the change in the level of sales scaled by lagged capital stock. Therefore, S Growth + t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is positive, and 0 otherwise. S Growth t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is negative, and 0 otherwise. S Growth + t F C and S Growth t F C are the interactions of F C with S Growth + t and S Growth t, respectively. Below t is a dummy that equals to 1 if the lagged sales growth is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t F C is Below t interacted with F C. CF t 1 /K t 2 is the lagged cash flow-to-capital ratio. CF t 1 /K t 2 F C is CF t 1 /K t 2 interacted with F C. N t 1 /K t 2 is the lagged inventory-to-capital ratio. The reported estimates are the cross-simulation average of the coefficients from 100 simulations. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. (1) (2) (3) N Growth t Nc Growth t I t /K t 1 F C 0.017*** 0.005*** 0.005*** [0.017, 0.017] [0.005, 0.005] [0.005, 0.005] S Growth + t 0.277*** 0.143*** 0.078*** [0.277, 0.278] [0.142, 0.143] [0.077, 0.078] S Growth + t F C -0.215*** -0.116*** -0.020*** [-0.216, -0.124] [-0.117, -0.116] [-0.021, -0.019] S Growth t 0.388*** 0.244*** 0.016*** [0.387, 0.388] [0.244, 0.245] [0.015, 0.016] S Growth t F C 0.138*** -0.031*** 0.125*** [0.137, 0.140] [-0.033, -0.030] [0.124, 0.126] Below t -0.004*** -0.001*** -0.001*** [-0.004, -0.004] [-0.001, -0.001] [-0.001, -0.001] Below t F C -0.017*** -0.006*** -0.009*** [-0.018, -0.017] [-0.006, -0.006] [-0.009, -0.008] CF t 1 /K t 2 0.008*** 0.005*** 0.077*** [0.008, 0.008] [0.005, 0.005] [0.077, 0.077] CF t 1 /K t 2 F C -0.031*** -0.005*** -0.010*** [-0.031, -0.031] [-0.006, -0.005] [-0.011, -0.010] N t 1 /K t 2-0.046*** -0.029*** [-0.046, -0.046] [-0.029, -0.029] Constant 0.009*** 0.004*** 0.018*** [0.009, 0.009] [0.004, 0.004] [0.018, 0.018] Observations 430,800 430,800 430,800 Adj.R 2 0.491 0.333 0.344 49

Table 8: Regressions on Lagged Sales Growth with Simulated Data This table reports the regression results on the simulated data. The dependent variable in column (1) and (2) are N Growth and N c Growth, respectively. Both variables are the change in inventory scaled by lagged capital, where the former prices inventory at market value of the goods, and the latter prices inventory at production cost following LIFO accounting. The dependent variable I t /K t 1 in column (3) is the investment-to-lagged capital ratio, where investment is defined as the change of capital net of depreciation. F C is a dummy that equals to 1 if the firm is FC, and 0 otherwise. S Growth t 1 is the lagged sales growth. S Growth + t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is positive, and 0 otherwise. S Growth t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is negative, and 0 otherwise. S Growth + t 1 F C and S Growth t 1 F C are the interactions of F C with S Growth+ t 1 and S Growth t 1, respectively. Below t 1 is a dummy that equals to 1 if the sales growth in t 2 is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t 1 F C is Below t 1 interacted with F C. CF t 2 /K t 3 is the twoperiod-lagged cash flow-to-capital ratio. CF t 2 /K t 3 F C is CF t 2 /K t 3 interacted with F C. N t 1 /K t 2 is the lagged inventory-to-capital ratio. The reported estimates are the cross-simulation average of the coefficients from 100 simulations. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. (1) (2) (3) N Growth t Nc Growth t I t /K t 1 F C 0.012*** 0.004*** 0.005*** [0.012, 0.012] [0.004, 0.004] [0.005, 0.005] S Growth + t 1 0.129*** 0.080*** 0.069*** [0.128, 0.129] [0.080, 0.080] [0.068, 0.069] S Growth + t 1 F C -0.042*** -0.045*** -0.008*** [-0.043, -0.042] [-0.045, -0.044] [-0.009, -0.008] S Growth t 1 0.042*** 0.015*** 0.016*** [0.042, 0.043] [0.015, 0.015] [0.016, 0.017] S Growth t 1 F C 0.200*** 0.065*** 0.118*** [0.199, 0.200] [0.064, 0.065] [0.117, 0.119] Below t 1 0.001*** 0.001*** -0.001*** [0.001, 0.001] [0.001, 0.001] [-0.001, -0.001] Below t 1 F C -0.012*** -0.004*** -0.008*** [-0.012, -0.012] [-0.004, -0.004] [-0.008, -0.008] CF t 2 /K t 3-0.003*** 0.0008*** 0.064*** [-0.003, -0.003] [0.0008, 0.0009] [0.063, 0.064] CF t 2 /K t 3 F C -0.008*** 0.008*** -0.010*** [-0.008, -0.007] [0.008, 0.008] [-0.011, -0.010] N t 1 /K t 2-0.039*** -0.026*** [-0.039, -0.039] [-0.026, -0.026] Constant 0.005*** 0.0005*** 0.019*** [0.005, 0.005] [0.0005, 0.0005] [0.019, 0.019] Observations 430,200 430,200 430,200 Adj.R 2 0.090 0.045 0.256 50

Table 9: Inventory Regressions with Real Data This table presents the results on the actual data. The dependent variable N Growth is the change in inventory scaled by the beginning-of-period capital. In a given quarter, UFC are firms whose beginning-of-period total asset is among the top 30% of all firms and FC are those among the bottom 30%. F C t is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth t is the change in the level of sales scaled by lagged capital stock. Therefore, S Growth + t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is positive, and 0 otherwise. S Growth t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is negative, and 0 otherwise. S Growth + t F C t and S Growth t F C t are the interactions of F C t with S Growth + t and S Growth t, respectively. Below t is a dummy that equals to 1 if the lagged sales growth is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t F C t is Below t interacted with F C t. CF t 1 /K t 2 is the lagged cash flow-to-capital ratio. CF t 1 /K t 2 F C t is CF t 1 /K t 2 interacted with F C t. N t 1 /K t 2 is the lagged inventory-to-capital ratio. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters to avoid potential heteroskedasticity and serial correlation. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) Q1 Q2 Q3 Q4 N Growth t N Growth t N Growth t N Growth t F C t 0.0131*** 0.0147*** 0.00914*** 0.0223*** (4.88) (5.04) (3.76) (8.43) S Growth + t 0.118*** 0.170*** 0.212*** 0.0761*** (6.46) (7.43) (10.31) (5.90) S Growth + t F C t -0.0371** -0.0824*** -0.132*** -0.00525 (-2.34) (-3.11) (-5.54) (-0.40) S Growth t -0.0598*** 0.0406** -0.00593-0.00303 (-3.17) (2.21) (-0.38) (-0.12) S Growth t F C t 0.0531** -0.0324 0.0185-0.00695 (2.39) (-1.52) (0.98) (-0.25) Below t -0.00152** -0.00150*** -0.00357*** -0.000286 (-2.23) (-2.72) (-3.97) (-0.44) Below t F C t -0.00472*** -0.00194* -0.00272** -0.00296*** (-4.74) (-1.92) (-2.35) (-2.80) CF t 1 /K t 2 0.189*** 0.271*** 0.264*** 0.228*** (8.22) (10.58) (7.70) (8.63) CF t 1 /K t 2 F C t -0.0508* -0.0790** -0.109*** -0.0585* (-1.73) (-2.65) (-3.03) (-1.71) N t 1 /K t 2-0.0251*** -0.0299*** -0.0189*** -0.0550*** (-6.05) (-7.89) (-4.60) (-20.30) Constant -0.000201-0.00459** -0.00103-0.00623*** (-0.13) (-2.60) (-0.62) (-3.62) Observations 58,327 59,270 59,670 59,149 Adj.R 2 0.332 0.282 0.396 0.439 51

Table 10: Inventory Regressions on Lagged Sales Growth with Real Data This table presents the results on the actual data. The dependent variable N Growth is the change in inventory scaled by the beginning-of-period capital. In a given quarter, UFC are firms whose beginning-of-period total asset is among the top 30% of all firms and FC are those among the bottom 30%. F C t is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth t 1 is the lagged sales growth. S Growth + t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is positive, and 0 otherwise. S Growth t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is negative, and 0 otherwise. S Growth + t 1 F C t and S Growth t 1 F C t are the interactions of F C t with S Growth + t 1 and S Growth t 1, respectively. Below t 1 is a dummy that equals to 1 if the sales growth in t 2 is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t 1 F C t is Below t 1 interacted with F C t. CF t 2 /K t 3 is the two-period-lagged cash flow-to-capital ratio. CF t 2 /K t 3 F C t is CF t 2 /K t 3 interacted with F C t. N t 1 /K t 2 is the lagged inventory-to-capital ratio. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters to avoid potential heteroskedasticity and serial correlation. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) Q1 Q2 Q3 Q4 N Growth t N Growth t N Growth t N Growth t F C t 0.0140*** 0.0120*** 0.00960*** 0.0236*** (4.64) (5.01) (4.01) (7.98) S Growth + t 1 0.110*** 0.0462*** 0.153*** 0.0913*** (7.61) (3.26) (9.70) (5.53) S Growth + t 1 F C t -0.0446** 0.0224-0.0858*** -0.0298 (-2.09) (1.12) (-5.35) (-1.49) S Growth t 1-0.0124 0.00848 0.00629-0.0280 (-0.63) (0.57) (0.26) (-1.67) S Growth t 1 F C t 0.0760*** 0.0303* 0.0569** 0.0626*** (3.41) (1.94) (2.21) (3.19) Below t 1-0.00124* -0.000361 0.000222-0.000568 (-1.90) (-0.55) (0.38) (-0.65) Below t 1 F C t -0.00214* -0.00503*** -0.00275*** -0.00334*** (-1.73) (-4.29) (-2.82) (-3.35) CF t 2 /K t 3 0.224*** 0.166*** 0.219*** 0.216*** (5.81) (7.95) (7.13) (7.05) CF t 2 /K t 3 F C t -0.0803* -0.0375-0.0833** -0.0883*** (-1.89) (-1.45) (-2.58) (-2.75) N t 1 /K t 2-0.0272*** -0.0227*** -0.0179*** -0.0529*** (-6.55) (-6.05) (-4.04) (-18.14) Constant -0.000692 0.0000651-0.000504-0.00594*** (-0.35) (0.04) (-0.31) (-3.36) Observations 56,658 57,244 57,784 58,132 Adj.R 2 0.335 0.264 0.388 0.439 52

Table 11: Investment Regressions with Real Data This table reports the results on the actual data. The dependent variable in column (1) to (4) is the investment-to-lagged capital ratio It/Kt 1, where investment is calculated by converting the Compustat Year-to-Date capital expenditure (CAPXY) to quarterly frequency. The dependent variable P P E Growth in column (5) to (8) is the change in property plant and equipment scaled by lagged capital. F Ct is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth + t (S Growth t ) is the interaction of S Growtht and an indicator which equals to 1 if S Growtht is positive (negative), and 0 otherwise. S Growth + t F Ct and S Growth t F Ct are the interactions of F Ct with S Growth + t and S Growth t, respectively. Belowt is a dummy that equals to 1 if the lagged sales growth is below the 20th percentile of the firm s distribution, and zero otherwise. Belowt F Ct is Belowt interacted with F Ct. CFt 1/Kt 2 is the lagged cash flow-to-capital ratio. CFt 1/Kt 2 F Ct is CFt 1/Kt 2 interacted with F Ct. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) (5) (6) (7) (8) Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 It/Kt 1 It/Kt 1 It/Kt 1 It/Kt 1 P P E Growtht P P E Growtht P P E Growtht P P E Growtht F Ct 0.0120*** 0.0143*** 0.0153*** 0.0124*** 0.0139*** 0.0174*** 0.0216*** 0.0217*** (6.53) (8.13) (10.99) (8.74) (5.41) (7.37) (8.87) (9.81) S Growth + t 0.0336*** 0.0433*** 0.0522*** 0.0533*** 0.158*** 0.147*** 0.191*** 0.144*** (6.81) (9.80) (12.95) (12.96) (11.29) (11.54) (16.23) (13.34) S Growth + t F Ct -0.00127-0.0108* -0.0212*** -0.0266*** -0.0709*** -0.0776*** -0.108*** -0.0661*** (-0.20) (-1.96) (-4.17) (-5.59) (-5.37) (-6.45) (-9.57) (-5.01) S Growth t -0.00760** -0.0132** -0.0115* -0.0153** 0.0216*** 0.0134 0.0299** 0.0249** (-2.64) (-2.24) (-1.96) (-2.34) (2.97) (1.18) (2.68) (2.30) S Growth t F Ct 0.0125** 0.0219*** 0.0204*** 0.0276*** -0.00634 0.00247-0.0140-0.00206 (2.58) (3.68) (3.19) (3.60) (-0.73) (0.20) (-1.32) (-0.18) Belowt -0.000353-0.0000990 0.000317 0.00106** -0.00230** -0.00283*** -0.00142 0.000126 (-0.69) (-0.24) (0.80) (2.46) (-2.51) (-5.56) (-1.43) (0.16) Belowt F Ct -0.000654-0.000622-0.000735-0.00218*** 0.000495 0.00124-0.00110-0.00223* (-1.31) (-1.18) (-1.34) (-4.26) (0.51) (1.57) (-0.85) (-1.98) CFt 1/Kt 2 0.0654*** 0.125*** 0.119*** 0.106*** 0.103*** 0.170*** 0.159*** 0.173*** (12.63) (12.40) (12.37) (9.10) (15.33) (7.91) (12.65) (8.61) CFt 1/Kt 2 F Ct -0.0244*** -0.0730*** -0.0688*** -0.0544*** -0.0291*** -0.0680*** -0.0672*** -0.0648*** (-8.33) (-7.86) (-8.09) (-5.74) (-3.86) (-3.29) (-6.51) (-3.74) Constant 0.0112*** 0.0105*** 0.0100*** 0.0132*** -0.00706*** -0.00962*** -0.0109*** -0.0108*** (11.17) (10.08) (12.01) (13.95) (-5.34) (-6.89) (-7.57) (-7.56) Observations 50,606 50,713 51,071 50,462 58,083 59,012 59,406 58,890 Adj.R 2 0.382 0.381 0.399 0.386 0.132 0.134 0.148 0.137 53

Table 12: Investment Regressions on Lagged Sales Growth with Real Data This table reports the results on the actual data. The dependent variable in column (1) to (4) is the investment-to-lagged capital ratio It/Kt 1, where investment is measured as quarterly capital expenditure. The dependent variable P P E Growth in column (5) to (8) is the change in property plant and equipment scaled by lagged capital. F Ct is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth + t 1 (S Growth t 1 ) is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growtht 1 is positive (negative), and 0 otherwise. S Growth + t 1 F C t and S Growth t 1 F C t are the interactions of F Ct with S Growth + t 1 and S Growth t 1, respectively. Belowt 1 is a dummy that equals to 1 if the lagged sales growth is below the 20th percentile of the firm s distribution, and zero otherwise. Belowt 1 F Ct is Belowt 1 interacted with F Ct. CFt 2/Kt 3 is the lagged cash flow-to-capital ratio. CFt 2/Kt 3 F Ct is CFt 2/Kt 3 interacted with F Ct. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) (5) (6) (7) (8) Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 It/Kt 1 It/Kt 1 It/Kt 1 It/Kt 1 P P E Growtht P P E Growtht P P E Growtht P P E Growtht F Ct 0.0126*** 0.0123*** 0.0149*** 0.0116*** 0.0136*** 0.0156*** 0.0210*** 0.0209*** (7.08) (6.84) (9.88) (6.08) (4.76) (6.25) (8.41) (7.61) S Growth + t 1 0.0188*** 0.0224*** 0.0312*** 0.0341*** 0.0129** 0.0290*** 0.0444*** 0.0381*** (7.54) (4.75) (6.84) (7.55) (2.71) (3.55) (6.19) (5.04) S Growth + t 1 F C t -0.00320-0.00208-0.00684-0.0166*** 0.00386-0.00240-0.00759-0.0133* (-0.91) (-0.36) (-1.27) (-3.65) (0.58) (-0.28) (-1.07) (-1.92) S Growth t 1 0.000257-0.0129*** -0.0106*** -0.0174*** 0.0150 0.0194*** 0.000421-0.00683 (0.05) (-3.83) (-2.90) (-3.73) (1.14) (2.95) (0.04) (-0.58) S Growth t 1 F C t 0.00398 0.0182*** 0.0161*** 0.0246*** 0.000270 0.00294 0.00845 0.0148 (0.70) (4.63) (3.37) (4.31) (0.02) (0.35) (0.66) (1.08) Belowt 1 0.000222-0.000409-0.000139-0.00000495-0.000153 0.000285-0.00169*** -0.000857 (0.61) (-0.69) (-0.31) (-0.01) (-0.19) (0.36) (-3.08) (-0.67) Belowt 1 F Ct -0.000848-0.000368-0.000807-0.00105-0.00154-0.00186* 0.000715-0.000221 (-1.63) (-0.79) (-1.62) (-1.41) (-1.55) (-1.74) (0.83) (-0.13) CFt 2/Kt 3 0.0988*** 0.0823*** 0.136*** 0.136*** 0.131*** 0.126*** 0.176*** 0.224*** (10.00) (14.07) (12.25) (12.69) (9.87) (10.52) (10.30) (11.75) CFt 2/Kt 3 F Ct -0.0443*** -0.0367*** -0.0807*** -0.0819*** -0.0359*** -0.0457*** -0.0727*** -0.117*** (-6.24) (-8.70) (-8.10) (-8.47) (-3.19) (-4.15) (-4.26) (-7.57) Constant 0.0103*** 0.0126*** 0.0102*** 0.0137*** -0.00640*** -0.00537*** -0.00911*** -0.00870*** (10.47) (11.87) (12.52) (12.93) (-3.84) (-3.84) (-6.20) (-5.72) Observations 49437 49433 49717 49696 56418 57001 57538 57873 Adj.R 2 0.383 0.378 0.396 0.389 0.109 0.108 0.123 0.118 54

Table 13: Sales Shocks and Cumulative Inventory Growth This table presents the effects of sales shocks on cumulative inventory growth. Column (1) and (2) use simulated data and Column (3) uses the actual data. The dependent variable is the change in inventory scaled by lagged capital. In Column (1), inventory is priced at market value of the goods, while in column (2) it is priced at production cost following LIFO accounting. Inventory in Column (3) is from Compustat. S Growth t is the change in sales from period t 1 to t, scaled by capital in time t 1. Above t k is a dummy that equals to 1 if S Growth t k is above the 80th percentile of the firms distribution, and zero otherwise. Below t k is a dummy that equals to 1 if S Growth t k is below the 20th percentile, and zero otherwise. Above t k F C t and Below t k F C t are the interactions of F C with Above t k and Below t k, respectively. We include up to 6 lags in the regression. The reported coefficients 6 k=1 Above t k, 6 k=1 Above t k F C, 6 k=1 Below t k, and 6 k=1 Below t k F C are the sum of corresponding coefficients of Above t k, Above t k F C t, Below t k and Below t k F C t up to 6 lags. All the other independent variables are defined in Table 7 and 9. With Simulated data, we run the regression on 100 simulated panels. The reported estimates are the cross-simulation averages. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. With real data, we run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. The reported coefficients are the average over the four quarters. t-statistics in parentheses are calculated using the Fama-MacBeth method. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. 55

Simulated Data Simulated Data Real Data (1) (2) (3) N Growth t Nc Growth t N Growth t F C t 0.010*** -0.001*** 0.0174*** [0.010, 0.010] [-0.001, -0.001] (8.57) S Growth + t 0.283*** 0.132*** 0.1364** [0.282, 0.283] [0.132, 0.132] (5.25) S Growth + t F C t -0.213*** -0.111*** -0.0682* [-0.214, -0.212] [-0.112, -0.111] (-3.02) S Growth t 0.383*** 0.246*** 0.0052 [0.382, 0.384] [0.245, 0.246] (0.26) S Growth t F C t 0.132*** -0.030*** 0.0035 [0.130, 0.133] [-0.032, -0.028] (0.19) 6 k=1 Above t k 0.007*** 0.005*** 0.0049** [0.007, 0.008] [0.005, 0.005] (4.26) 6 k=1 Above t k F C t 0.036*** 0.011*** 0.0072** [0.036, 0.036] [0.011, 0.011] (4.20) 6 k=1 Below t k 0.0007*** 0.0004*** -0.0053*** [0.0007, 0.0007] [0.0004, 0.0004] (-6.19) 6 k=1 Below t k F C t -0.020*** -0.003*** -0.0081* [-0.020, -0.020] [-0.003, -0.003] (-2.93) CF t 1 /K t 2 0.004*** 0.015*** 0.224*** [0.004, 0.004] [0.015, 0.015] (10.50) CF t 1 /K t 2 F C t -0.023*** -0.013*** -0.076*** [-0.024, -0.022] [-0.013-0.013] (-5.8) N t 1 /K t 2-0.007*** -0.056*** -0.0190 [-0.007, -0.007] [-0.056, -0.055] (-1.43) N t 1 /K t 2 F C t -0.015*** 0.043*** -0.0245* [-0.015, -0.015] [0.042, 0.043] (-2.74) Constant 0.001*** 0.004*** -0.0044** [0.001, 0.001] [0.004, 0.004] (-4.59) Observations 428,400 428,400 51,689 Adj.R 2 0.536 0.354 0.374 56

Table 14: Tests on Alternative hypothesis This table reports the regression results on the simulated data when the difference in the two groups arises from difference in other parameters than financial constraints. Data are generate from 100 simulated panels, each contains 720 quarters for 300 benchmark firms and 300 comparison firms. Benchmark firms refer to the unconstrained firms with all parameter values set in the baseline calibration. Comparison firms refer to the unconstrained firms with all parameters fixed at the baseline calibration except for one parameter at a time. Specifically, comparison firms are the ones with the same calibration but higher fixed operating cost(f 0 ), higher linear operating cost(f 1 ), higher investment adjustment cost(a), higher inventory stockout cost(b), lower linear production cost(d 1 ), or lower quadratic production cost(d 2 ), respectively. The regressions are the same as model (1), in which the dependent variable is N Growth (the change in inventory scaled by lagged capital), and model (3), in which the dependent variable is I t /K t 1 (investment-to-lagged capital ratio where investment is defined as the change of capital net of depreciation), in Table 7. D is a dummy that equals to 1 if the firm is a comparison firm, and 0 if it is a benchmark firm. S Growth is the change in the level of sales scaled by lagged capital stock. Therefore, S Growth + t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is positive, and 0 otherwise. S Growth t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is negative, and 0 otherwise. S Growth + t D and S Growth t D are the interactions of D with S Growth + t and S Growth t, respectively. We also include the other independent variables as in Table 7, but only report the coefficients on four variables: S Growth + t, S Growth + t D, S Growth t, and S Growth t D. The reported estimates are the cross-simulation average of the coefficients from 100 simulations. 95% confidence intervals are included in brackets and coefficients are marked with *** if 95% confidence intervals do not span zero. 57

Dependent Coefficients on Sales Shocks D=0 D=1 Variable S Growth + t S Growth + t D S Growth t S Growth t D (1) f 0 = 0.0665 f 0 = 0.0760 N Growth t 0.288*** -0.000 0.385*** 0.000 [0.287,0.288] [-0.001,0.001] [0.384,0.385] [-0.001, 0.001] (2) f 0 = 0.0665 f 0 = 0.0760 I t /K t 1 0.078*** -0.001*** 0.016*** 0.001 [0.077,0.078] [-0.002,-0.001] [0.015,0.016] [0.000,0.002] (3) f 1 = 0.0069 f 1 = 0.0100 N Growth t 0.288*** -0.000 0.385*** -0.005*** [0.287,0.288] [-0.001,0.001] [0.384,0.385] [-0.006, -0.004] (4) f 1 = 0.0069 f 1 = 0.0100 I t /K t 1 0.078*** 0.005*** 0.016*** 0.004*** [0.077,0.078] [0.004,0.005] [0.015,0.016] [0.003,0.005] (5) a = 60 a = 90 N Growth t 0.288*** 0.002*** 0.385*** -0.020*** [0.287,0.288] [0.001,0.003] [0.384,0.385] [-0.022, -0.019] (6) a = 60 a = 90 I t /K t 1 0.078*** -0.008*** 0.016*** 0.005*** [0.077,0.078] [-0.008,-0.007] [0.015,0.016] [0.004,0.005] (7) b = 0.0032 b = 0.0048 N Growth t 0.289*** 0.048*** 0.384*** 0.049*** [0.289,0.290] [0.047,0.048] [0.383,0.385] [0.048, 0.050] (8) b = 0.0032 b = 0.0048 I t /K t 1 0.078*** 0.002*** 0.016*** 0.002*** [0.077,0.078] [0.002,0.002] [0.015,0.016] [0.001,0.003] (9) d 1 =0.132 d 1 =0.099 N Growth t 0.288*** 0.046*** 0.385*** 0.009*** [0.287,0.288] [0.046,0.047] [0.384,0.385] [0.008, 0.010] (10) d 1 =0.132 d 1 =0.099 I t /K t 1 0.078*** 0.057*** 0.016*** 0.033*** [0.077,0.078] [0.057,0.058] [0.015,0.016] [0.032,0.034] (11) d 2 =0.022 d 2 =0.011 N Growth t 0.288*** 0.045*** 0.385*** 0.002*** [0.288,0.289] [0.045,0.046] [0.384,0.385] [0.001, 0.003] (12) d 2 =0.022 d 2 =0.011 I t /K t 1 0.078*** 0.091*** 0.016*** 0.061*** [0.077,0.078] [0.090,0.092] [0.015,0.016] [0.060,0.062] 58

Table 15: Inventory Regressions on Sales Growth with Real Data: 2000 to 2010 This table presents the results on the actual data in sub-period 2000 to 2010. The dependent variable N Growth is the change in inventory scaled by the beginning-of-period capital. In a given quarter, UFC are firms whose beginning-of-period total asset is among the top 30% of all firms and FC are those among the bottom 30%. F C t is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth t is the change in the level of sales scaled by lagged capital stock. Therefore, S Growth + t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is positive, and 0 otherwise. S Growth t is the interaction of S Growth t and an indicator which equals to 1 if S Growth t is negative, and 0 otherwise. S Growth + t F C t and S Growth t F C t are the interactions of F C t with S Growth + t and S Growth t, respectively. Below t is a dummy that equals to 1 if the lagged sales growth is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t F C t is Below t interacted with F C t. CF t 1 /K t 2 is the lagged cash flow-to-capital ratio. CF t 1 /K t 2 F C t is CF t 1 /K t 2 interacted with F C t. N t 1 /K t 2 is the lagged inventory-to-capital ratio. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) Q1 Q2 Q3 Q4 N Growth t N Growth t N Growth t N Growth t F C t -0.00718 0.00233 0.0153 0.0212** (-1.09) (0.51) (1.62) (2.41) S Growth + t 0.184*** 0.320*** 0.276*** 0.122*** (5.21) (5.63) (5.52) (4.31) S Growth + t F C t -0.112*** -0.248*** -0.200** -0.0466 (-3.42) (-4.20) (-3.11) (-1.58) S Growth t 0.0193 0.0613*** 0.0503* -0.0212 (0.80) (4.18) (2.09) (-0.34) S Growth t F C t 0.0161-0.00210-0.0238 0.0216 (0.43) (-0.09) (-0.56) (0.40) Below t -0.00197** -0.00219** -0.00174-0.00239** (-2.29) (-2.79) (-1.49) (-2.60) Below t F C t -0.00380*** -0.00371*** -0.00181-0.00169 (-3.58) (-4.05) (-1.43) (-1.35) CF t 1 /K t 2 0.218*** 0.296*** 0.311*** 0.257*** (4.60) (6.50) (3.88) (5.23) CF t 1 /K t 2 F C t -0.136** -0.179*** -0.205** -0.180** (-2.56) (-3.80) (-2.58) (-3.06) N t 1 /K t 2-0.0386*** -0.0363** -0.0338** -0.0701*** (-3.14) (-3.07) (-2.46) (-9.01) Constant 0.0110** 0.000785-0.00280-0.00595 (2.72) (0.26) (-0.60) (-1.18) Observations 24043 23935 23665 23211 Adj.R 2 0.334 0.312 0.419 0.479 59

Table 16: Inventory Regressions on Lagged Sales Growth with Real Data: 2000 to 2010 This table presents the results on the actual data in sub-period 2000 to 2010. The dependent variable N Growth is the change in inventory scaled by the beginning-of-period capital. In a given quarter, UFC are firms whose beginning-of-period total asset is among the top 30% of all firms and FC are those among the bottom 30%. F C t is a dummy that equals to 1 if the firm is FC in year t, and 0 otherwise. S Growth t 1 is the lagged sales growth. S Growth + t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is positive, and 0 otherwise. S Growth t 1 is the interaction of S Growth t 1 and an indicator which equals to 1 if S Growth t 1 is negative, and 0 otherwise. S Growth + t 1 F C t and S Growth t 1 F C t are the interactions of F C t with S Growth + t 1 and S Growth t 1, respectively. Below t 1 is a dummy that equals to 1 if the sales growth in t 2 is below the 20th percentile of the firm s sales growth distribution, and zero otherwise. Below t 1 F C t is Below t 1 interacted with F C t. CF t 2 /K t 3 is the two-period-lagged cash flow-to-capital ratio. CF t 2 /K t 3 F C t is CF t 2 /K t 3 interacted with F C t. N t 1 /K t 2 is the lagged inventory-to-capital ratio. We run the regression for each quarter to account for seasonality. The regression model is estimated with firm-fixed effect. t-statistics in parentheses are adjusted using the Huber-White estimator allowing within firm clusters. Coefficients significant at the 10%, 5%, and 1% levels are marked with *, **, and ***, respectively. (1) (2) (3) (4) Q1 Q2 Q3 Q4 N Growth t N Growth t N Growth t N Growth t F C t -0.00347 0.00309 0.0168 0.0227** (-0.48) (0.45) (1.65) (2.26) S Growth + t 1 0.0831*** 0.106*** 0.210*** 0.154*** (3.25) (6.21) (4.22) (7.39) S Growth + t 1 F C t -0.0456-0.0398-0.138*** -0.0966** (-1.25) (-1.50) (-3.29) (-2.52) S Growth t 1 0.0401* 0.0396 0.0394 0.0488* (1.92) (1.61) (1.41) (2.19) S Growth t 1 F C t 0.0174 0.0294-0.0283-0.00989 (0.95) (0.88) (-1.44) (-0.30) Below t 1-0.00186 0.0000929 0.000661 0.000533 (-1.79) (0.10) (0.87) (0.46) Below t 1 F C t 0.00213* -0.00671*** -0.00289* -0.00508*** (1.84) (-4.56) (-2.17) (-3.30) CF t 2 /K t 3 0.295*** 0.191*** 0.249*** 0.252*** (3.74) (4.39) (4.23) (4.23) CF t 2 /K t 3 F C t -0.205** -0.119** -0.166** -0.202*** (-2.59) (-2.53) (-2.99) (-3.51) N t 1 /K t 2-0.0426*** -0.0232* -0.0325* -0.0676*** (-3.79) (-1.99) (-2.09) (-10.45) Constant 0.00787* 0.00331-0.00338-0.00552 (2.00) (0.77) (-0.68) (-1.09) Observations 23537 23450 23332 23235 Adj.R 2 0.328 0.280 0.396 0.474 60

Figure 1: Trends of the Inventory-to-Capital Ratio This figure plots the average of total inventory holding scaled by lagged capital, as well as each sub-category of inventory scaled by lagged capital: raw materials, work-in-progress, and finished goods for each year. are collected from Compustat Industrial Annual Files for the period 1971 to 2010. Financial firms (SIC Code 6000-6900) and regulated utilities (SIC Code 4900-4999) are excluded. The scaling variable is the level of beginning-of-period capital (K t 1 ) is defined as total asset (AT) minus total inventory (INVT). The final sample starts from 1973. The components of total inventory are the Compustat items INVRM, INVWIP and INVFG, respectively. 61