Heterogeneous Investment Dynamics of Manufacturing Firms

Transcription

1 Heterogeneous Investment Dynamics of Manufacturing Firms Alexandros Fakos a and Tiago Tavares b a ITAM - Business School b ITAM - Department of Economics February 15, 2017 Abstract In this paper we study firm-level investment dynamics by incorporating an idiosyncratic investment cost shock in a dynamic investment model of heterogeneous firms with adjustment costs. We interpret this idiosyncratic shock as an investment wedge summarizing firm deviations from model implied efficient behavior. We estimate our dynamic model using data micro-level data of Greek manufacturing firms, allowing for firms to be heterogenous in both profitability and investment cost. Our estimation results show that the level of dispersion of the idiosyncratic investment shock is of the same order of magnitude as the profitability shock which tends to be substantial in most micro-studies. We also find evidence that the investment wedge is correlated with variables not explicitly taken into account by our model such as measures of firmlevel leverage and export intensity. This suggests that a financial channel in models of capital accumulation may be crucial in explaining data patterns. 1 Introduction This paper attempts to measure the importance of firm level investment frictions and to inevestigate their sources. Understanding the relevant factors that determine capital Alexandros Fakos: alexandros.fakos@itam.mx; Tiago Tavares: tiago.gomes@itam.mx 1

2 accumulation is important to provide guidance in the design of policies aimed at influencing macroeconomic activity and welfare. It has been extensively documented in the literature (Olley and Pakes 1996; Hsieh and Klenow 2009, 2014; Bartelsman, Haltiwanger and Scarpetta 2013; and Gopinath, Kalemli-Ozcan, Karabarbounis and Villegas-Sanchez, 2015) that factors preventing an efficient adjustment of capital to productivity, implying misallocation of resources, can substantially reduce aggregate output. To the extent that capital allocation is influenced by the presence of multiple frictions associated with investment at the firm level, we develop a methodology to measure that additional source of heterogeneity. Following the accounting methodology proposed in Chari, Kehoe and McGrattan (2007) of inferring distortions from residuals of first-order conditions, Hsieh and Klenow (2009) propose a static model allowing them to measure distortions at the firm level and come up with a measurement of the aggregate implications of misallocation. In particular, these authors provide an analytical negative relationship between aggregate productivity (TFP) and the volatility of revenue total factor productivity (TFPR) which is directly related to distortions in inputs at the firm level reflected on the volatility of the marginal revenue product of capital (MPKR) and labor (MPLR). Misallocation of resources at the firm level can be traced to frictions in inputs or outputs and, in this paper, we focus mostly on the misallocation of capital at the firm level. The literature on misallocation acknowledges that dispersion of marginal revenue products alone is not evidence of the extent of misallocation and that the dynamic nature of capital can play an important role in explaining that dispersion. Asker, Collard-Wexler and De Loecker (2014), motivated by the literature on the importance of capital adjustment costs (Caballero and Engel, 1999; Cooper and Haltiwanger 2006; Bloom, 2009), present a model in which investment is subject to time-to-build, convex and non-convex adjustment 2

3 costs, establishing an empirical link between the volatility of firm-level TFPR and the volatility of the marginal product of capital. They show that if adjusting capital is costly, efficiency does not imply that the static marginal product of capital should be equalized across firms. In this paper, we aim at measuring firm-level heterogeneity in capital accumulation accounting for the dynamic nature of investment. In particular, we measure this heterogeneity directly from the micro data as a residual of the first order condition of an Euler equation associated with the investment decision. Our goal is to study the quantitative importance of these residuals, also known as investment wedges, for firm investment behavior. Furthermore, we can relate these firm level wedges with variables outside our model, such as financial variables or export status, in order to explore relevant extensions of investment models that may account for this unobserved heterogeneity. To that end, we develop a dynamic model of investment where firms face capital adjustment costs and time-to-build. Differently from the aforementioned papers, we also include an idiosyncratic shock that shifts the cost of investing, implying that firms explicitly take into account expectations about its evolution. To estimate our model we use firm-level data from the Greek manufacturing sector spanning the years of Production level data allow us to estimate a maximum-profit function and a profitability shock which are the drivers of the return to investment in the dynamic model. Dynamic parameters of the model, i.e. adjustment costs and the variance of the idiosyncratic shock, are estimated at a later stage using a simulated method of moments. With these parameters we finally extract firm-specific investment wedges and study their properties. Our estimates of the adjustment cost parameters are consistent with the literature and in particular we find that convex adjustment costs are economically significant. Regarding profitability shocks, our estimates exhibit heterogeneity that is consistent with results in 3

4 the literature concerned with the estimation of production functions (see Olley and Pakes (1996), De Loecker, Goldberg, Khandelwal and Pavcnik (2016)). As for the remaining source of firm level heterogeneity, our estimates of the investment wedge roughly imply that a firm with a realized shock at the 95th percentile of the distribution faces 60% higher cost of investing than the average firm. We also find that firms with high capital stock have, on average, lower estimated investment wedge and firms firms with high debt to capital ratio have a larger estimated investment wedge, implying that a model which explicitly takes into account the financial side of the firm might be appropriate to rationalize the data. This paper is related with the literature focusing on the estimation of production functions and capital adjustment costs, that includes papers such as Olley and Pakes (1996), Caballero and Engel (1999), Cooper and Haltiwanger (2006), Fuentes et al. (2006), Bloom (2009), Asker et al. (2014), and De Loecker, Goldberg, Khandelwal and Pavcnik (2016). All these papers conclude that investment dynamics are constrained by convex or nonconvex adjustment costs, but neither takes explicitly into account firm-level heterogeneity in these costs. Also related is the literature on firm-level misallocation, where Hsieh and Klenow (2009) and Restuccia and Rogerson (2008) are some of the most influential papers. Following these papers, other authors explored potential sources of misallocation of capital by adding financial frictions (Midrigan and Xu, 2014, Gopinath et al., 2015, or Meza et al., 2016) or by adding entry and exit margins of adjustment as in Bartelsman et al., Our paper summarizes some of the key implications, in terms of misallocation, generated by the main modeling assumptions in these papers in a convenient firm-level investment wedge, while maintaining some discipline in terms of investment dynamics captured by adjustment costs. 4

5 2 Model A very general specification of a dynamic investment model, following loosely from Cooper and Haltiwanger (2006), assumes that a representative firm is statically maximizing variable profits each period, while the investment problem takes into account a time-to-build lag before newly acquired capital becomes available for production. The solution of the former problem generates a maximum-profit function π (ω, K) depending on capital K and a profit shock ω following an AR(1) process. The details of the model are described below. 2.1 Firm Production Function We begin by describing the production function of a representative firm j and the demand for its output, which jointly determine variable profits. The demand and production function specifications are as in Asker, Collard-Wexler and De Loecker (2014). In what follows t = 1,..., T is an indicator of time and the j subscript is sometimes omitted to simplify notation. Firm s production function takes the Cobb-Douglas form with constant returns to scale and is specified as: Q jt = A jt K a K it L a L jt M a M jt, a K + a L + a M = 1 (1) where A is physical total factor productivity, K is the physical capital stock, L is labor, and M is materials input. Capital is quasi-fixed in the sense that a firm arrives at period t with capital stock K t which is used to produce period s t output Q t. This assumption is referred to as time-to-build in the sense that any investment in physical capital at period t becomes only productive at period t + 1. The firm buys labor and materials in competitive markets at prices w L and w M, respectively, and its total variable cost is TVC = Mw M + Lw L. 5

6 Demand for firm s output Q t takes an iso-elastic form and is given by: Q jt = B jt P η jt, η > 1 (2) where B depends on consumer income and the prices of other firms in the industry, P is the firm s price of output, and η is the elasticity of demand. Combining equations (1) and (2), we obtain the sales-generating production function: S jt = Ω sales jt K β K it L β L jt M β M jt (3) where the above coefficients correspond to β K = a K (1 1/η), β L = a L (1 1/η), β M = a M (1 1/η), Ω jt = A 1 1/η jt B 1/η jt and Ω sales jt is the revenue total factor productivity or TFPR. At the beginning of each period t firms observe their physical productivity A jt and idiosyncratic demand B jt, their predetermined capital stock K jt, variable-input prices w L, w M and choose the level of their variables inputs L, M to maximize variable profits P tj Q jt L jt w L + LM jt w M. Profit maximization implies that the revenue production function coefficient is equal to the input expenditure share in sales β L = w LL jt, β M = w MM jt (4) S jt S jt which is useful for the estimation of the model from the micro data. Substituting for the optimal variable input levels we get the maximum-variable-profit function conditional on 6

7 capital K and Ω sales (which corresponds to TFPR): π(ω sales, K) = λ[ω sales ] 1/(β k+η 1) K β K/(β K +η 1) Ω π K βπ K (5) with ( ) ( ) λ = (β K + η 1 βl ) β L /(β K + η 1 βm ) β M /(β K + η 1 ) w L w M The residual Ω π in the profit function is a log-linear transformation of the TFPR i.e. ln Ω π = ln λ + [1/(β k + η 1 )] ln Ω sales. 2.2 Productivity Evolution As in Asker, Collard-Wexler and De Loecker (2014) we assume that the logarithm of TFPR (ln Ω sales ω sales ) follows a first order autoregressive, AR(1), stochastic process that is independent of firm s choices, i.e. it evolves exogenously: ω sales t+1 = µ sales + ρω sales t + ξ sales, ξ sales iid (6) The process of the logarithm of TFPR implies that the logarithm of the profit function residual (ln Ω π ω) follows also an AR(1) process with the same persistence parameter ρ but with a different mean and a different distribution of the innovation. We assume that the distribution of the innovation of productivity is a normal distribution with mean zero and standard deviation σ ξ, that is: ω t+1 = µ + ρω t + ξ, ξ N(0, σ 2 ξ ) (7) 7

8 2.3 Dynamic Decision to Invest Here, we describe the firm s decision to invest in physical capital which is related to the models developed in Asker, Collard-Wexler and De Loecker (2014), Cooper and Haltiwanger (2006), and in Fuentes, Gilchrist and Rysman (2006). The key assumption is that investment is irreversible and newly purchased capital becomes operational one period after it is acquired, rendering capital as a dynamic input. Each firm arrives at the beginning of period t with a capital stock K t, observes the realization of productivity ω t, and an iid shock to the investment cost ɛ t and, given that this information is reflected in the state vector s t = (ω t, K t, ɛ t ), chooses the level of investment I t. Physical capital K is a quasi-fixed input, depreciates at rate δ and evolves in a deterministic fashion. More specifically, a firm investing I t at time t arrives at t + 1 with capital K t+1 = I t + (1 δ)k t (8) thus, choosing the quantity of investment today I t is equivalent to choosing next period capital stock K t+1 and the terms choice of investment and choice of next period s capital are used interchangeably. This time-to-build characteristic of capital accumulation along with the iid property of the shock to the investment cost ɛ imply that today s investment has no effect on current variable profits π(ω t, K t ), therefore variable inputs are decided independently of investment. The payoff of the firm at time t consists of two components: variable profits π(ω t, K t ) and the cost of investing [I t 1{i t > 0 + C(K t, K t+1 )] ɛ t, ln ɛ t N(0, σɛ 2 ). The cost of investment is equal to the investment expenditure I t plus a capital adjustment cost C(K t, K t+1 ), both multiplied by a factor ɛ t. The shock ɛ is independent across firms and 8

9 time and also independent of the other state variables. It represents idiosyncratic shocks to the cost of investment and it affects the optimal level of investment. The shock ɛ can be also viewed as an investment wedge or a distortion in the terminology of Restuccia and Rogerson (2008) which rationalize the deviation of a firm s actual investment from the efficient level of investment. Note that if gross investment I is negative, the investment cost for the firm is C(K, K ), which implies that selling existing capital stock not only generates zero revenue, but also requires the firm to incur an adjustment cost to dispose of it. In other words, any investment expenditure is a sunk cost. The firm s current payoff function is U(s t, K t+1 ) = π(ω t, K t ) [(K t+1 (1 δ)k t ) 1{I t > 0} C(K t, K t+1 )] ɛ t (9) In each period t, given the realization of the state s t, each firm chooses an optimal investment policy K t+1 (s t ) to maximize the expected discounted stream of payoffs E β v U(s t+v, K t+v+1 ) v=0 where β < 1 is the discount factor and the expectation E is consistent with the Markov transition function F ω (ω t+1 ω t )F ɛ (ɛ t+1 ). If U is bounded, this dynamic programming problem has a recursive representation through a Bellman equation. Recall that investment is irreversible or, equivalently, investment is a sunk cost. The one year time-to-build, durability, and sunk cost features of the capital accumulation process make investment a dynamic input, thus expectations about future states become pivotal in the investment decision. Notice that, since investment is irreversible, firms never find it optimal to undertake negative investment and the firm s dynamic programming problem can be represented by the 9

10 Bellman equation V (ω, K, ɛ) = st max π(ω, K) [ I + C(K, K ) ] ɛ + β V (ω, K, ɛ )df (ω ω)df ɛ (ɛ ) I 0 ω,ɛ K = I + (1 δ)k (10) Because ɛ is serially independent, the current value of ɛ affects firm s decision to invest only through current cost of investment and has no effect on the firm s expectations about the future values of ɛ. This formulation of the dynamic problem implicitly assumes that there is no firm exit. This assumption is mainly due to data limitations because when a firm drops out of the sample it could simply be because it has less than 10 employees 1 and thus, it is not possible to know whether the firm exited the market or just downsized. 2.4 Baseline Investment Adjustment Cost Specification We specify a convex adjustment cost function which includes a linear and a quadratic part C(K t, K t+1 ) = c 1 I c 2(I/K) 2 K. The quadratic adjustment cost is the same as in Cooper and Haltiwanger (2006) while the linear adjustment cost scales the investment cost relative to profits given our assumption that the distribution of log ɛ is mean zero. The Euler equation of the dynamic problem is ( ) I ɛ 1 + c 1 + c 2 β V K (K, ω, ɛ ( )df ω ω ω ) df ( ɛ ) K ω,ɛ (Euler equation) and under investment irreversibility the it holds with equality for positive investment values. 1 Firms with less than 10 employees are not surveyed. 10

11 3 Data The micro-level data used in the estimation of our model come from two sources: the Hellenic Statistical Authority and ICAP, a private consulting firm which collects balance sheet data from limited liability firms. Data on input and output flows come from the Annual Survey of Manufactures conducted by the Hellenic Statistical Authority at the plant level covering all manufacturing firms with at least 10 employees over the years Unlike census data the because of this truncation of firms contained in the sample, entry and exit is not a margin we can use in our analysis. Variables include gross investment, total labor cost, the wage bill, revenue, materials expenditures. Data on the book value of physical capital and the accumulated depreciation from firm s financial statements collected by ICAP are used in combination with investment flows from the Annual Survey of Manufactures to create the stock of physical capital at the firm level using the perpetual inventory method. Table 1 provides basic summary statistics of the data for the largest 2 sectors in terms of observations. Notice that firms exhibit substantial heterogeneity in inputs and gross output. Table 2 provides information on the heterogeneity in input mix which is substantial. However the coefficient of variation of capital as a share of sales is twice as large as the coefficient of variation of the labor and materials share which is consistent with our assumption that labor and materials are variable inputs while capital is quasi-fixed. For the purpose of the empirical analysis I assume that any decision is taken at the firm level and the unit of observation is the firm. 4 Estimation Strategy Our estimation approach is to use the firm s optimality conditions to estimate the parameters of interest: the capital coefficient in the maximum-profit function β π, the mean µ, 11

12 Table 1: Summary statistics of input and output variables Stats Sales Capital Wage bill Materials Var. Profit Gross inv. Inv. rate S K LC M π I I/K Food and Beverages Manufacturing mean p sd p p p p min max N #Firms 428 years Nonmetallic Minerals Manufacturing mean p sd p p p p min max N #Firms 216 years Monetary variables are expressed in 2005 million Euros. The median of the yearly share of total investment in the sample with respect to the sectoral aggregate investment is.59 The median of the yearly share of total investment in the sample with respect to the sectoral aggregate investment is.68 persistence ρ and the standard deviation of the innovation σ ξ of the productivity process, the adjustment cost parameters c 1, c 2 and the standard deviation of the adjustment cost shock σ ɛ. The time-to-build assumption, that newly acquired capital becomes productive next period, in combination with the exogeneity of the productivity process imply that the firm s investment decision is independent of the variable input choices of labor and materials. For our estimation, this means that we can estimate the production function coefficients at a first stage before estimating the dynamic parameters c 1, c 2, σ ɛ. We estimate 12

13 Table 2: Summary statistics of various ratios of inputs and gross output Stats K/LC M N /LC N M N /S N LC N /S N K/S Food and Beverages Manufacturing mean p sd p p N Nonmetallic Minerals Manufacturing mean p sd p p N subscript N indicates values at current prices. the variable input sales function coefficients using as the median of their shares in sales. The first order conditions for profit maximization of imply that the expenditure of each variable input in sales is equal to the coefficients of the sales function (see equation (4)). They also imply that these shares are constant across firms which, as table 2 shows, is not the case. This might be either because the production function is misspecified or because of input market frictions. Maintaining the Cobb-Douglass production function specification we can either use the mean or the median to estimate the variable inputs coefficients. We follow Asker, Collard-Wexler and De Loecker (2014) and use the median, although as you can see in table 2 the mean and the median are similar in magnitude. We cannot use the capital share in sales to estimate the capital coefficient because we have assumed that capital is not a variable input. We follow Asker, Collard-Wexler and De Loecker (2014) and estimate the capital coefficient using the constant returns to scale assumption and assuming that the demand elasticity is 4. The capital coefficient in the sales-generating production 13

14 function and the capital coefficient in the maximum-profit function are estimated as follows { } { } wl L jt wm M jt ˆβ L = Median, ˆβM = Median S jt S jt (11) ˆβ K = (η 1)/η ˆβ M ˆβ L, ˆβπ = ˆβ K /( ˆβ K + η 1 ), η = 4 (12) Using the profit function coefficient we can calculate productivity ω for each firm in our sample using data on variable profits as follows ˆω jt = ln π jt ˆβ π ln K jt (13) Since there are observations with negative profits in the data, these observations will be discarded. We also trim the empirical distribution of ω by discarding the top and bottom 1% in order to get rid of outliers. The trimmed distribution of ω is presented in table 4 and figure 1. In the food manufacturing sector the profitability of a firm in the 90th percentile is 33 times as high 2 as the profitability of a firm in the 10th percentile with the same amount of capital. In the minerals sector the a firm in the 90th percentile is 12 times as profitable as a firm in the 10th percentile of the productivity distribution which is evidence of substantial unobserved heterogeneity. Table 4 and figure 2 show the pairwise correlation between productivity and log capital which is positive and large implying that large firms are more productive. This feature of the data is consistent with our dynamic model where the persistence of the productivity shock induces productive firms to accumulate capital. The estimation of the parameters of the AR(1) process of the evolution of ω needs to take into account the truncated nature of the sample at the 10 employee threshold. Firms that are slightly above the threshold if they receive a negative productivity shock ξ will 2 Calculated as exp(2)/ exp( 1.5). 14

15 Figure 1: Distributions of profitability shocks 0.3 kdensity distribution of profitability shocks in Food and Beverages kdensity distribution of profitability shocks in Nonmetallic Minerals probably disappear from the sample. Table 4 shows that productivity is positively correlated with the log of the number of employees which implies that if we don t correct for selection our persistent coefficient will be estimated with the bias. Firms also disappear from the sample upon exiting the market but we cannot distinguish between exit and disappearance due to reduction in employment in our data. We use the selection-correction procedure developed by Olley and Pakes (1996) in which we first estimate a probit regression on some year dummies and a complete polynomial of the logarithm of capital and the logarithm of the number of employees and use the fitted probabilities of remaining in the 15

16 Figure 2: Scatter plot of log K and ω log of capital log of capital profitability shocks and log capital in Food and Beverages productivity shock profitability shocks and log capital in Nonmetallic Minerals productivity shock sample ˆP jt as an extra regression in the productivity autoregression. ˆω jt = µ + ρˆω jt 1 + β select ˆPjt + ξ jt (14) The estimated coefficients of the AR(1) process are presented in table 3. Productivity is persistent in both sectors and if you compare the standard deviation of ω t ω t 1 in table 4 with the standard deviation of the innovation of the productivity process they are almost equal. This is not surprising with such a high persistence in productivity which implies that most of the variation in ω t ω t 1 is coming from unanticipated shocks rather than reversion to the mean. 16

17 Table 3: Model Parameters Food Minerals Parameter Estimate Estimate Sales and Profit Function ˆβ L ˆβ M ˆβ K ˆβ π Productivity Process µ ρ σ ξ Dynamic Parameters c c σ ɛ Calibrated parameters η 4 4 δ Estimation of the adjustment cost parameters We estimate the adjustment cost parameters c 1, c 2 together with the standard deviation σ ɛ of the investment wedge using simulated method of moments. Since we want to estimate the nature of these wedges we need to make them consistent with the model in the sense that firms have correct expectations about the volatility of the wedge. In particular we follow an estimation method consisting of the following steps. First, the dynamic investment model is solved for an initial guess of the parameters Θ = (c 1, c 2, σ ɛ ). From this model, we extract policy functions used to generate a panel of simulated data, {{ω it, K it, I it } t=1,t } i=1,n, for some arbitrary initial conditions3. Then a set of simulated moments is calculated using simulated data: Ψ s (Θ). Finally, these simulated moments are compared with the equivalent moments in the our sample of observations Ψ. In order to 3 The dynamic model is solved using standard value function iteration, where value functions are approximated using cubic splines. Once the model is computed we run simulations for 3000 firms and 200 periods and we drop the first 190 periods. 17

18 Table 4: Summary statistics of the estimated productivity distribution Stats ω ω t ω t 1 ξ Food and Beverages Manufacturing mean e-10 p sd p p p p p p N Pairwise correlation between ω, K ln K t ln L t ω t Nonmetallic Minerals Manufacturing mean e-11 p sd p p p p p p N Pairwise correlation between ω, K, L ln K t ln L t ω t Truncated ω distribution at the top and bottom 1% to get rid of outliers. L is the number of employees. estimate the parameters, the following criterion is minimized: D (Θ) = min [Ψ Θ Ψs (Θ)] W 1 [Ψ Ψ s (Θ)] Here, W is the identity matrix. This procedure generates consistent estimates for (c 1, c 2, σ ɛ ). The particular moments we target are presented in table 5 and were chosen to reflect investment related variation in our data. The key determinant of investment in our model 18

19 is productivity and two moments are productivity related correlations. The other two moments are directly taken from the marginal distribution of the investment rate. Table 5: Target moments for the SMM estimation Moment Food Minerals Data Model Data Model corr( i t K t, i t 1 K t 1 ) corr(ω t, K t) spike: P rob( i t K t >.2) corr(ω t ω t 1, i t K t ) Distance: D(Θ) Dynamic Estimation Results The estimated dynamic parameters are shown in table 3. The quadratic adjustment cost parameter c 2 is 1.5 for the Food and Beverages manufacturing sector and 1.75 for the Nonmetallic Minerals manufacturing sector. The numbers are larger than the estimate of Cooper and Haltiwanger (2006) which is.455 and in line with the estimates of Asker, Collard-Wexler and De Loecker (2014) which range from.21 to 8.8. The linear adjustment cost parameter c 1 is 1.25 for the Food and Beverages manufacturing sector and.5 for the Nonmetallic Minerals manufacturing sector. The parameter c 1 can be interpreted as a scale parameter of the price of capital that rationalizes the observed investment given the estimated profit function. The standard deviation σ ɛ of the iid shock is.25 for the Food and Beverages manufacturing sector which implies that a firm with a realized shock ɛ at the 95th percentile of the distribution faces 50% higher cost of investing than the average firm. The standard deviation σ ɛ of the iid shock is.35 for the Nonmetallic Minerals manufacturing sector which implies that a firm with a realized shock ɛ at the 95th percentile of the distribution faces 70% higher cost of investing than the average firm. For both sectors 19

20 this implies that the investment wedge ɛ is quite high and provide evidence of substantial heterogeneity in investment cost. Table 6 presents the distribution of the residuals in the sample. Notice that the empirical standard deviation of ɛ is higher than the estimated one which is due to the fact that there are observations in the data that the model cannot rationalize. Table 6 also shows that estimated wedge ɛ is negatively correlated with capital implying that large firms face smaller investment costs (see figure 4). This correlation may indicate either that the functional form of the adjustment cost function is misspecified or that there are features of the economic environment not explicitly accounted for by our model. The correlation between productivity ω and the wedge is also negative which is consistent with the negative correlation between capital and the wage since large firms are more productive (see correlations in table 4). Our assumption that ɛ is iid is not supported by the estimates since the serial correlation of ɛ is high. This can either be a mechanical result coming from the correlation between capital and ɛ and the fact that capital is a persistent state variable or simply because wedges are persistent. Table 6: Summary statistics of the estimated investment cost residual ˆɛ Sector mean med sd p10 p25 p75 p90 N Food Minerals Pairwise correlation between ɛ t and ω, K, ɛ t 1 Food Minerals ln K t ω t ɛ t 1 ln K t ω t ɛ t 1 ɛ t Indicates significance at 5% 6 Correlation between the wedge ɛ and extra variables To further investigate the source of variation of the wedge we correlate the estimated wedge {ˆɛ jt } with other firm-level variables outside of our model i.e. leverage, and the share of export share of sales. Table 7 shows descriptive statistics of debt over capital (leverage), 20

21 Figure 3: Distributions of investment wedges kdensity distribution of investment wedges in Food and Beverages kdensity distribution of investment wedges in Nonmetallic Minerals short-term debt over capital (short-term leverage), debt over the sum of all inputs, and the share of exports in sales. Note that the data patterns are similar in both sectors with the median leverage equal to roughly 1.5 and a quartile of the firms not exporting at all. The table also reports correlations between the estimated investment wedge and the extra variables. The correlation between the investment wedge and both leverage and short-term leverage is negative, which could suggest that high-leverage firms face higher cost of investing. Also, our estimates of the investment wedge seem to suggest that large firms have, in general, lower adjustment costs. 21

22 Figure 4: Scatter plot of log K and log ɛ investment wedge investment wedge profitability shocks and log capital in Food and Beverages log of capital profitability shocks and log capital in Nonmetallic Minerals log of capital Such type of interpretations should be taken with caution. From the investment wedges analysis, we can only infer that these vary substantially across dimensions such capital size and leverage. This should indicate that other non-modeled features may affect what is estimated as an investment wedge. For example, a model where firms finance investment through debt and face a collateral a constraint (for example Jermann and Quadrini, 2012, and Buera and Moll, 2015) may be an appropriate to describing the data. Typically, in this type of models, highly leverage firms, have a lower net worth, which implies a higher cost of financing and therefore, investment less conditional on profitability shock realization. In absence of such channel, the leverage effect is reflected as a large positive adjustment cost 22

23 wedge. Also from the table, we see that the correlation between the investment wedge and export share is negative, albeit small. This can be an indication that exporting firms may face lower financial cost related which should imply an higher investment. In any case, our results also suggest that extending a baseline model to include a foreign market dimension can improve on the measurement of allocation of capital across firms. Table 7: Summary statistics of extra variables Stats Leverage Short-Term Leverage Debt over all inputs Export share of sales Debt/K SDebt/K Debt/(K + LC + M) Exp/S Food and Beverages Manufacturing mean p sd p p p p p min max N Pairwise correlation between ɛ and leverage, export share Debt/K SDebt/K Debt/(K + LC + M) Exp/S ɛ t Nonmetallic Minerals Manufacturing mean p sd p p p p p min max N Pairwise correlation between ɛ and leverage, export share Debt/K SDebt/K Debt/(K + LC + M) Exp/S ɛ t Leverage is calculated using variables expressed in 2005 million Euros. The export share variable has less observations than the whole sample because we excluded observations where sales are smaller than export value. Indicates significance at 5% 23

24 7 Conclusions This paper extends the current literature on firm level capital adjustment. We estimate a fully-structural model of investment for two manufacturing sectors of the Greek economy. The model is flexible enough to allow us to describe firm-level heterogeneity in profitability and also in the investment cost. Our results show that in our sample firms face high variability in investment wedges, even after appropriately controlling for traditional frictions in investment dynamics such as investment irreversibility, time-to-build, and convex adjustment costs. We find that our estimated measure of the investment wedge is correlated with non-modeled economic variables such as leverage. This positive correlation may indicate that traditional investment models not accounting for financial constraints may be misspecified. Furthermore, we find that for the study of firm capital allocation may be important to include financial frictions. An additional advantage of our proposed methodology relies on its simplicity of calculating investment wedges. For that reason, we conjecture that the above model/estimators can be applied, or extended to other frameworks. A non-exhaustive list may include: an extension to include non-convex adjustment costs in both capital and labor; an extension adding relevant market frictions, such as credit constraints or firm entry/exit; extensions taking into account investment constraints by firms that operate in multiple international markets or produce multiple products; and ex ante policy evaluation studies aiming to quantify the effect of different policy scenarios on aggregate investmentl. 24

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