Effects of Financial Market Imperfections and Non-convex Adjustment Costs in the Capital Adjustment Process

Transcription

1 Effects of Financial Market Imperfections and Non-convex Adjustment Costs in the Capital Adjustment Process Nihal Bayraktar, September 24, 2002 Abstract In this paper, a model with both convex and non-convex capital adjustment costs is improved by incorporating financial characteristics of firms into their investment decision process. The structural parameters of this model are solved by the indirect inference method reproducing the coefficients of a reduced form investment equation where profitability shocks and the cash-flow-to-capital ratio are independent variables. The findings show that the mixed model is more successful in reproducing the coefficients of the investment equation compared to the alternative models in the investment literature. While financially unconstrained firms follow fundamentals more closely in their investment decisions, investment of financially constrained firms is highly affected by changes in their internal funds. Correspondence: Department of Economics, University of Maryland, College Park, MD bayrakta@econ.umd.edu. I am grateful to John Haltiwanger for his generous support and advice, and Plutarchos Sakellaris and to John Shea for numerous comments and suggestions. I also would like to thank Prof. Haltiwanger for sharing his simulation programs used in Cooper and Haltiwanger (2002) with me. Any errors are my own. 1

2 1 Introduction The aim of this paper is to investigate the combined effects of convex and non-convex capital adjustment costs and financial market imperfections on investment. This study is essential to the better understanding of the complex dynamics of investment, which is an important part of aggregate output. Studying of these frictions together is also crucial to the evaluation of different fiscal and monetary policies. The introduction of non-convex capital adjustment costs and financial market imperfections constitutes two of the important developments in the investment literature. Traditional investment models, specifically neoclassical investment models with convex adjustment costs, are not successful in reproducing some features of investment. The basic weakness of these models is that even though they produce a linear relationship between the investment rate and fundamentals such as Tobin s q, micro-level data analyses reveal that the investment process is lumpy, infrequent, and asymmetric and these features are effective in shaping of the aggregate investment pattern. 1 In order to capture these non-linear features of investment, new models are developed in a way to relax strict assumptions of neoclassical models. In neoclassical models, it is assumed that agents face only convex adjustment costs. This assumption leads these models to produce a smooth investment pattern, which is not observed empirically. The inclusion of non-convex capital adjustment costs relaxes this assumption. 2 Since non-convex adjustment costs exhibit increasing returns to investment, it will not be profitable for agents to invest at each period even if fundamentals are in favor of investment. In this way, it is possible to model the lumpy, infrequent, and asymmetric nature of investment. Cooper and Haltiwanger (1993), Caballero and Engel (1994 and 1998), Caballero, Engel, and Haltiwanger (1995), Cooper, Haltiwanger, and Power (1999), and Cooper and Haltiwanger (2002) use non-convex adjustment costs in their models or in the empirical applications of their models. The incorporation of financial market imperfections into the investment decision process relaxes the perfect capital markets assumption of neoclassical investment models. This new literature shows that financial characteristics of agents also determine their investment behavior besides fundamentals. These models reveal that while financially unconstrained firms adjust their capital stock following a smoother investment path as suggested by neoclassical models, firms in a weak financial position follow a non-linear investment pattern. These in- 1 Doms and Dunne (1993 and 1998) and Caballero, Engel, and Haltiwanger (1995) reveal this nature of investment using plant-level data. Nilsen and Schiantarelli (1996) show similar results using Norwegian microlevel data. 2 Two examples of this new type of capital adjustment costs are fixed costs of capital adjustment and the opportunity cost of capital adjustment where the latter might be represented by foregone profit during the capital adjustment process. 2

3 vestment patterns are reasoned as follows. In the financial market imperfections literature, it is assumed that firms net worth (sum of liquid assets and collateral illiquid assets) determines their financial position. When firms have a low level of net worth, they are considered as financially constrained since these firms are likely to face an asymmetric information problem in financial markets. This leads to the result that it is hard for these firms to find enough external funds to finance their investment. Even if they can find external funds, these funds will be too expensive compared to the opportunity cost of internal funds. Whenever these firms financial position improves, lenders will be more willing to provide required funds, in turn, additional investment can be financed. As long as their financial position is weak, firms with financial problems will wait until they have enough funds to finance investment even if fundamentals are favorable to invest. Because of this, their investment process is non-linear in their response to fundamentals. Firms with high net worth, on the other hand, do not have an asymmetric information problem. They can find enough external funds to finance their capital adjustment and, as a result, they follow the investment process suggested by neoclassical investment models. Even though there is a large theoretical and empirical literature on the effects of both financial market imperfections and non-convex adjustment costs on investment, they have been rarely investigated together. 3 It is most likely that many firms face both frictions at the same time in their investment process. A model combining these two frictions can explain the investment process better since such a model can capture some features of investment that cannot be explained either only by models with different capital adjustment costs or only by models with financial market imperfections. Models with financial market imperfections, on the one hand, are incapable of explaining why the response of investment for financially relaxed firmsisnotlinear. 4 In these models, it is expected that investment follows fundamentals linearly in the absence of any financial problems since convex adjustment costs are the only source of friction in the absence of financial problems in these models. These models can be improved by introducing non-convex capital adjustment costs. In this way, the investment pattern will always be non-linear even in the absence of financial problems. Models with non-convex adjustment costs, on the other hand, are not successful in explaining 3 Whited (1998) empirically investigates how the performance of the investment Euler Equation changes for financially constrained firmsversusunconstrainedfirms in the presence of fixed adjustment costs. She shows that the performance of the Euler equation gets better when fixed adjustment costs are introduced. Pratap (1999) creates a model combining fixed adjustment costs with financial market imperfections in order to explain why sensitivity of investment to cash flow does not mean that firms face financial problems. But she does not solve the structural parameters of her model. She only simulates her model using exogenous parameters. The other difference from our model is that she investigates the effects of convex and non-convex adjustment costs separately instead of combining them. 4 Bayraktar (2002a) shows that the response of investment to fundamentals is always non-linear even for different groups of firms expected to be financially relaxed. 3

4 why the response of investment to the same level of fundamentals changes considerably for different firms. The inclusion of financial market imperfections can solve this problem by introducing a new source of heterogeneity in the investment process. As a result, a model simultaneously investigating the effects of financial market imperfections and non-convex adjustment costs on firms capital adjustment process, is constructed in this paper in order to improve both approaches. This model is an extension of Cooper and Haltiwanger s model (2002), which shows that both convex and non-convex adjustment costs are essential to explaining the relationship between the investment rate and fundamentals. The inclusion of financial market imperfections into this model introduces another source of heterogeneity among firms so that they may respond differently to the same level of fundamentals depending on their financial positions. The fundamental determinant of capital adjustment in this mixed model is idiosyncratic profitability shocks as the case in Cooper and Haltiwanger s model. 5 Financial market imperfections are introduced through the presence of a non-negativity constraint on dividends and the external finance premium. It is assumed that the premium is a linear function of the debt-to-capital ratio of firms. Since the capital stock is assumed to be the only collateral asset of a firm, as firm s debt-to-capital ratio increases, the financial position of this firm gets riskier. This causes lenders to charge a higher interest rate putting a premium on the risk-free interest rate. Following Cooper and Haltiwanger (2002), the model is solved by an indirect inference method. 6 Using this method, the structural parameters of the adjustment costs (both convex and non-convex components) and the structural parameter determining the external finance premium are chosen to reproduce the empirically observed econometric relationship between investment, profitability shocks, and the cash-flow-to-capital ratio. This econometric relationship is defined in a reduced form investment equation where the investment rate is the dependent variable and profitability shocks, their square terms, and the cash-flow-to-capital ratio are the independent variables. The square term of shocks is included in order to capture any non-linearity in the investment process. The reason for including the ratio of cash flow to capital is that this ratio is extensively used in the financial market imperfections literature in ordertounderstandhowsensitivefirms investment decision is to changes in internal funds. Themoresensitiveinvestmentistothecashflowratio,themoredependenttheyaretotheir 5 Bayraktar (2002a) compares the performance of alternative fundamentals such as Tobin s q, Fundamental Q, profitability shocks, and the gap measure between the desired and actual capital stocks. She finds that profitability shocks are more robust and better fundamental measure of investment. 6 This indirect inference procedure is advanced by Gourieroux, Monfort, and Renault (1993) and Smith (1993). The reason for not using analytical tools is that the presence of non-convex adjustment costs causes the dynamic optimization problem to be discontinuous. Because of non-convex adjustment costs, firms need to choose between investing and making no capital adjustment at all. 4

5 internal funds to finance their capital adjustment, in turn, the more financially constrained they are. The simulated data results are matched with the results obtained using a firm-level data set constructed from COMPUSTAT Database. The findings show that the model, in which financial market imperfections and nonconvex adjustment costs coexist, is more successful in reproducing the estimated coefficients of the reduced form investment equation when it is compared to two alternative models. The first alternative model is a representative of models with financial market imperfections. Frictions in this first alternative model consist of financial market imperfections and convex adjustment costs. The second alternative model represents models with different capital adjustment costs. It is based on both convex and non-convex adjustment costs. While the first alternative model is incapable of reproducing the estimated coefficients of shocks, the second alternative model is not successful in explaining the importance of the cash-flow-tocapital ratio in the investment process. But the mixed model manages to reproduce both features of investment. Investment behavior of financially constrained versus unconstrained firms is investigated using the simulated data produced by the mixed model. Financially unconstrained firms, on the one hand, follow fundamentals more closely in their investment decisions. The response of investment for financially constrained firms, on the other hand, is highly affected by changes in their internal funds. The rest of the paper is organized as follows. Section 2 gives brief information on the present literature. In Section 3, the features of investment data are presented. In Section 4, investment models with non-convex adjustment costs and financial market imperfections are introduced separately and their simulation results are presented. Section 5 presents the model combining financial market imperfections with non-convex adjustment costs and its simulation results. Section 6 concludes. 2 Related Work The literature on non-convex capital adjustment costs and financial market imperfections is quite large. Different features of investment have triggered development of these alternative approaches. After the recognition of the lumpy, infrequent and asymmetric nature of investment, models giving non-convex adjustment costs a central role in the investment process are developed. On the other hand, the success of cash flow and the failure of fundamentals such as Tobin s q in explaining investment are the basic reasons for introducing financial market imperfections. In this section, first of all, some studies in the non-convex adjustment costs literature are presented and then information on the financial market imperfections literature is given. 5

6 Cooper and Haltiwanger (1993) and Cooper, Haltiwanger, and Power (1999) investigate the machine replacement problem in the presence of non-convex adjustment costs. They characterize their solution by a hazard function where the probability of replacing capital is a function of the current capital stock and the aggregate state of productivity. The lower the level of current capital stock is (i.e. the older is capital), the higher the probability of investment is. This captures the infrequent nature of investment. The other result of these papers is that the longer you wait for replacing capital, the larger this adjustment will be. The reason is that the difference between the present and exogenously determined optimal capital level will be larger. This captures the lumpy nature of investment. The probability of investment may increase, decrease or be independent of the aggregate state of productivity depending on the nature of adjustment costs and the assumptions on the distribution of these shocks. Caballero and Engel (1994 and 1998) construct a model explaining non-linearities in the investment process by the help of the adjustment hazard approach. 7 The adjustment hazard function relates the probability of investment to mandated investment, which is defined as the log difference between the actual and the desired capital level where the latter is the stock of capital that an agent would like to hold if its adjustment costs are momentarily removed. The prediction of the model is that the higher the capital disequilibrium is, the higher the probability of investment is and, in turn, the higher the actual investment rate is. This means that there is a bunch of firms waiting for reaching to their trigger level of capital disequilibrium in order to adjust their capital stock (i.e. investment is infrequent) and this investment activity is associated with the large variations in their capital stock (i.e. investment is lumpy). These features are introduced by non-convex adjustment costs, which produce increasing returns to investment. Cooper and Haltiwanger (2002) compare models with alternative adjustment costs. The costs are the quadratic convex adjustment costs, fixed adjustment costs, and the adjustment costs associated with the presence of price wedge between the selling and buying price of capital. The models with only one type of adjustment cost are not successful in matching some features of investment. But the mixed model of non-convex and convex adjustment costs yields a investment pattern that matches much better with the actual one. 8 They use an indirect inference method to solve the structural parameters of this model in a way to reproduce the econometric relationship between profitability shocks and the investment rate. 9 7 Caballero, Engel, and Haltiwanger (1995) empirically investigate this model. 8 This investment pattern is defined by the relationship between the investment rate and idiosyncratic profitability shocks. 9 This method has been developed by Gourieroux, and Monfort (1996), Gourieroux, Monfort and Renault (1993), and has applied by Willes(1999), Adda and Cooper (2000), Cooper and Haltiwanger (2002) and Cooper and Ejarque (2001). 6

7 My study extends Cooper and Haltiwanger s model by introducing financial market imperfections, an important source of heterogeneity among firms during their capital adjustment process. The effects of financial market imperfections are also extensively studied in the investment literature. These studies show the importance of firms financial positions in shaping their investment decision besides fundamental determinants of investment. Empirical applications show that when firms are separated into different groups according to their financial characteristics, it is observed that investment behavior of financially constrained firmsisdif- ferent compared to financially relaxed firms. 10 At the microeconomic level, the basic idea about the effects of financial market imperfections on investment is related to the presence of asymmetric information problems between borrowers and lenders in debt markets. This affects the ability of financially constrained firms to obtain outside finance and, consequently, their allocation of real investment expenditure over time. The more the firm s wealth stock is (e.g. collateral assets and liquid assets), the healthier its financial position is, the less their investment decision will be affected by financial market imperfections. In macroeconomics, financial factors are used to magnify the initial shocks in order to explain the cyclical movements in the investment process and, in turn, in output. 11 Financial market imperfections are introduced into investment models following different ways. These ways might be collected in three different groups. The first group restricts the amount of debt that a firm can borrow. In the second group, even if firms can borrow as much debt as they want, the cost of debt may cause some restrictions. The external finance premium, which is defined as the gap between the interest rate that a firm will face and the market interest rate, is an example of this type of restriction. These two types of restrictions are mixed together in the third group of studies. These restrictions can be exogenous or a function of different firm specific or aggregate variables. 12 In this paper, 10 Some firm characteristics used in empirical studies in order to determine whether firms are financially constrained are as follows: firm age, firm size (Gertler and Gilchrist (1994)), whether the firm belongs to a cooperative industrial group (Hoski et al. (1991), Chirinko and Scheller (1995)), the ownership structure (Oliner and Rudebush (1992), Chirinko and Schaller (1995)), the amount of dividend payments (Fazzari et al. (1988)), the ratio of dividend over capital (Bond and Meghir (1994)), the debt to asset ratio, the interest coverage ratio and bond rating (Whited (1992)). 11 The accelerator model of Bernanke, Gertler, and Gilchrist (1996 and 1998) is an example of these macroeconomic studies. 12 Some of the studies based on constrainting the amount of debt that a firm can get and the determinants of these restrictions are: Evans and Jovanovic (1989) use initial wealth and entrepreneurial ability; Whited (1992) uses an exogenous restriction on debt; Bernanke, Gertler, and Gilchrist (1996), and Kiyotaki and Moore(1997) use collateral assets. Some examples of papers using the external finance premium as a source of financial imperfections and the determinants of this premium are: Greenwold, Kohn, and Stiglitz (1990) use produced output, assets, the price of output; Gilchrist and Himmelberg (1998) use the debt and capital stock, and productivity shocks; Bernanke, Gertler and Gilchrist(1998) use the net worth of firms. 7

8 financial market imperfections are introduced by the external finance premium and the nonnegativity constraint on dividends. The latter restriction is sufficient for debt to be marginal source of finance. The external finance premium is assumed to be a function of the leverage ratio as an indicator of financial health of firms. Firms leverage decision has important implications at both micro and macro levels as studied by Bernanke, Campbell, and Whited (1990). They study concerns about the change in the corporate leverage in 1987 and At the microeconomic level, workers, suppliers, and customers will be affected from the consequences of the financial distress as well as managers and owners of firms. At the macroeconomic level, the importance of how firms react to changes in economic activities is emphasized by the theories of aggregate demand externalities and multiple equilibria and by the traditional Keynesian models. Under this context, the more sensitive firms plans are to their current cash flow, the more unstable the macroeconomy will be. It has been shown both theoretically and empirically that when current cash flow falls, the pressure of debt service may cause highly leveraged firms to decrease their investment more severely compared to low-leveraged firms. This situation affects the stability of macroeconomy. Despite the success of the financial market imperfections literature in determining investment, there is a group of studies opposing to the importance of financial variables in the investment process. 13 They explain the importance of financial variables in determining investment by mismeasurement of investment fundamentals or imperfections in other markets. In this group of studies, Cooper and Ejarque (2001) is closely related to my study. They challenge to the idea that the statistical significance of profits in Tobin s q regressions is caused by the presence of financial market imperfections. They follow a structural empirical approach to analyze a dynamic programming problem for a firm with market power. The structural parameters are solved numerically to reproduce the econometric relationship between Tobin s q, the profit-to-capital ratio, and the investment rate by using the indirect inference approach. They find that profits enter to the investment regression significantly without introducing capital market imperfections. They also show that the estimated coefficients of the reduced form investment regression for small versus large firms can be obtained by slightly different values of the structural parameters. My paper is similar to Cooper and Ejarque (2001) in essence that both studies try to determine the relationship between the 13 Kaplan and Zingales (1995 and 1997) argue that some firms that were said to be financially constrained in the previous studies are not actually financially constrained after investigating the financial position of these firms in a detailed way. Cummins, Hassett, and Hubbard (1994) and Cummins, Hassett, and Oliner (1997) show that after calculating Tobin s q more accurately, the importance of financial variables decreases in the investment equation. Bayraktar (2002b) focuses on how successful financial variables are in explaining investment when investment opportunities are controlled for by profitability shocks and the gap between the desired and actual capital stock instead of Tobin s q. The results show that financial variables are still significant determinants of investment. However, their explanatory power for investment is lower. 8

9 investment rate, fundamentals, and the cash-flow-to-capital ratio. The difference is that they do not take capital market imperfections into account. However, one can obtain additional information on the relationship between the investment rate, cash flow, and fundamentals by simulating a model with financial constraints. The other difference is that while Cooper and Ejarque use only quadratic convex adjustment costs in their analysis. 14 In my model, I include both convex and non-convex adjustment costs. The chosen type fundamental of investment is the other source of difference. While they use Tobin s q measure, profitability shocksareusedinmystudy. 15 The other study opposing to the excessive importance of financial variables in the determination of investment is the paper of Gomes (2001). He introduces a finance cost for external funds and finds that capital market imperfections of this form can be summarized in Tobin s q. This provides support to the idea that the empirical success of cash flow in a reduced form investment regression equation is likely to be caused by measurement errors in Tobin s q. Asspecifiedinhispaper,thisdoesnotshowthatfinancial constraints are not important for investment, but they may not be as important as claimed to be in the financial market imperfections literature. My study provides a new viewpoint by including a different measure of fundamental and also by including capital adjustment costs, which are missing in Gomes s paper. In addition to these papers investigating the effects of financial market imperfections and non-convex adjustment costs separately, there are two papers taking these two frictions into consideration at the same time. Whited (1998) empirically investigates how the performance of the investment Euler Equation changes for financially constrained firmsversusuncon- strained firms in the presence of fixed adjustment costs. She shows that the performance of the Euler equation gets better when the fixed adjustment cost is introduced in a model. Pratap (1999) creates a model combining fixed adjustment costs with financial market imperfections in order to explain why the sensitivity of investment to cash flow does not mean that firms face financial problems. Her study is different from my study in a way that while she tries to relate cash flow to investment, my study tries to relate the investment rate, fundamentals, and cash flow. The other difference is that while she simulates her model using exogenous parameters, I estimate the structural parameters of my model. She also separately investigates the effects of convex and non-convex adjustment costs instead of combining them. 14 Cooper and Haltiwanger (2002) show that both convex and non-convex adjustment costs are important in determining investment. 15 Bayraktar (2002a) showthatprofitability shocks are better determinant of investment as a structural estimate compared to Tobin s q. 9

10 3 Features of Actual Data 3.1 Data Set The main data source in this paper is the COMPUSTAT firm-level database. The data set covers the period from 1983 to 1996 and the number of firms is 463. Details on the sample selection is presented in Appendix A.1. The definition of capital includes plant, property, and equipment. Investment is defined as capital expenditure net of sale of capital, which includes capital retirements. 16 The replacement value of capital is calculated using the perpetual inventory method: K t =(1 δ)k t 1 + I t (1) where K t is the real capital stock, I t is real investment obtained deflating its nominal value by the 4-digit investment price index. δ is the 2-digit depreciation rate from the Bureau of Labor Statistics (BLS) database. It is equal to the average value of the depreciation rate for the years 1981 to The investment rate is defined as the ratio of real investment to the replacement value of capital. The distribution function of the investment rate is presented in Figure 1 for the period. Since the definition of investment includes sale of capital, there are negative investment rate values corresponding to nearly 10 percent of the total observations. The cash flow variable is defined as sales plus operating income before depreciation minus cost of goods sold, interest payments, and taxes payable. When depreciation is subtracted from cash flow, we obtain net income before extraordinary items. This definition corresponds to the sum of items 14 and18 incompustatwhereitem14 is depreciation and amortization and item 18 is income before extraordinary items. Appendix A.2 gives detailed information on the definition of the series. The ratio of cash flow to capital is defined as the ratio of book value of cash flow to the book value of capital stock at the beginning of the period. Since we try to match the actual data results with the simulated data results, extreme data points may have a negative effect on this process. Because of this, profitability shocks and the cash flow ratio series are trimmed by 1 percentateachtail. Similarly,theinvestment rate greater than 400 percent and less than -100 percent is excluded. 16 As it is defined in COMPUSTAT User Guide, the sale of capital series contains retirements data in it only for some firms. But for the others the retirements data are available as a separate series. I combined the sale of capital and the retirements series in order to obtain a more uniform series. I added the retirements datatothesaleofcapitaldatawheneverthesaleofcapitaldatahavealowervaluethantheretirements data (assuming that retirements are not included in the sale of capital data). I also used the retirements data whenever the sale of capital data are missing. 10

11 Figure 1: Investment rate distribution Fr action of fir m s Investment rate 3.2 Summary Statistics Summary statistics are reported in Table 1. All statistics are calculated by pooling data for 463 firms and for the period of The average value of the investment rate is 12 percent. The autocorrelation of investment rate is It is a quite large number when it is compared to 0.007, which is found using plant-level data by Cooper and Haltiwanger (2002). The definition of the inaction region corresponds to the region in which the investment rate is between 2.5 percent and -2.5 percent. The fraction of firms in this region is percent. The investment rate is more than 20 percent for percent of observations. This number is 18 percent using plant-level data as presented by Cooper and Haltiwanger (2002). The fraction of firms investing less than -20 percent is 1.07 percent. This fraction is quite low compared to the fraction of firms investing more than 20 percent. This points out the presence of asymmetries. Summary statistics related to the cash flow ratio are also presented in Table 1. The standard deviation of the ratio is The correlation between the investment rate and the cash flow ratio is Fundamental Determinant of Investment: Profitability Shocks Fundamentals capture the present value of future returns on current capital adjustment. In the absence of any frictions, it is expected that the investment rate follows fundamentals closely. The most famous fundamental in the investment literature is Tobin s q, which is the 11

12 Table 1: Summary statistics Variable COMPUSTAT Mean of investment rate Autocorrelation between i t and i t i <2.5% 10.42% i > 20% 17.34% i < 0% 8.68% i < -20% 1.07% Correlation between CF_K and i Standard deviation of CF_K Note: All statistics are calculated pooling data for 498 firms and for the period i represents the investment rate. CF_K represents the ratio of the real value of cash flow to the replacement value of capital. ratio of the current value of a firm to the replacement value of its capital. The problem related to this measure is that it is not empirically successful in capturing investment opportunities, so it cannot explain investment in a statistically significant way. Even the improved versions of Tobin s q, for example, Fundamental Q measure created by Gilchrist and Himmelberg (1995), are not much successful. Alternative fundamentals are recently available in the literature. Profitability shocks and the gap measure between the desired and actual capital stock are examples of these new measures. As investigated in Bayraktar (2002a), they are more successful in explaining investment as a structural estimate compared to Tobin s q and Fundamental Q. Cooper and Haltiwanger (2002) use profitability shocks in their paper. They display that the empirical relationship between the investment rate and profitability shocks is nonlinear and asymmetric such that the response of investment to positive shocks is much stronger than the response of investment to negative shocks. Since the model used in this study is an extension of Cooper and Haltiwanger s model, profitability shocks are also used as a fundamental measure here. The profitability shocks are defined in the following firm-level profit function: Π(A it,k)=a it K θ it (2) 12

13 where A it is the profitability shock, θ is the curvature of the profit function,andk it is the firm level capital stock. θ is the estimated coefficient obtained regressing the natural log of net profit (net of cost of production) on the log of the replacement value of the capital stock using firm-level panel data. 17 There are two alternative ways of calculating the profitability shocks, A it (i represents firms and t represent the time period). The first way of calculating A it is through regressing profits on capital and taking the residuals. The second way of calculating A it is indirectly through using the first order condition for profit maximization with respect to employment. The second way allows avoiding possible measurement errors in profit data. I use the second way as it is the case in Cooper and Haltiwanger (2002). The first way is not preferred. The standard deviation of the shocks calculated using the first way is high compared to the standard deviation calculated using the second way. The high value of standard deviation causes the transition matrix of the shocks to be less informative. Given the fact that the transition matrix is quite essential in simulation of the models, the second way is preferred. A it contains both aggregate,a t,andfirm specific, ε it, components. After obtaining A it, aggregate shocks are calculated as the annual mean of the profitability shocks; the idiosyncratic component of the shocks is the deviation from that mean. In order to remove the fixed effects, the shocks are presented as deviated from the firm-level mean. In the following analysis, the idiosyncratic component of A it is called as profitability shocks for simplicity. Details are presented in Appendix B and in Bayraktar (2002a). The idiosyncratic shocks are used in the log form so that a it = ln(ε it ).Usingthisdefinition of shocks, the following reduced form investment equation is used throughout this paper: i it = α i + ψ 1 a it + ψ 2 (a it ) 2 + ψ 3 CF_K + u it where i it is investment at firm i in period t. (a it ) 2 is the square term of a it. This variable is included since it is known that the investment process is a non-linear function of fundamentals so this needs to be taken into account including higher moments of the fundamental measure. CF_K is the cash-flow-to-capital ratio. α i represents the firm dummies in order to remove fixed effects. 18 u it is the error term. This reduced form equation is standard in the investment literature. It can capture the non-linear nature of investment as well as the importance of financial position of firms in their capital adjustment process. The estimated coefficients are reported in Table 2. The estimation technique is the least square removing the fixed effects. The regression results show that both the level and the square term of the profitability 17 θ is assumed to be the same for each firm at each period. However, if there are structural differences across firms, they need to be removed from affecting the analysis. Consequently, we remove fixed effects in order to fixed the structural heterogeneity problem. 18 It should be noted that the time dummies are not included since it causes additional burden while calculating the structural parameters. 13

14 shocks are important in explaining investment. This can be presented as a support that the investment pattern of firms is non-linear. The coefficient of the cash-flow-to-capital ratio is also statistically significant. Changes in internal funds of firms are important determinants of investment even after investment opportunities are controlled for by the shocks. Table 2: Determinants of the investment rate Coefficients Es timated values a it (0.010) a it (0.035) CF_K it (0.016) Adjusted R-squared Number of observations 5569 Note: All statistics are calculated pooling data for 498 firms and for the period The estimation method is the least square. The dependent variable is the investment rate. a it represents the profitability shocks. a 2 it represents the square term of profitability shocks. CF_K it represents the ratio of the real value of cash flow to the replacement value of capital. The standard error is reported in the paranthesis. These results are comparable to the results of two other studies. Cooper and Haltiwanger (2002) estimate ψ 1 and ψ 2 as and , successively, using plant-level data. The investment rate at the plant level is more responsive to a it compared to the investment response at the firm level. Investment is, on the other hand, less responsive to a 2 it at the plant level. But despite these slight differences in the magnitude of the coefficients, the estimated coefficients can be considered close to each other. The second related study is 14

15 Cooper and Ejarque (2001). In this study, the reduced form regression equation is the one, in which the investment rate is regressed on the cash flow ratio and the Fundamental Q, which is an improved measure of Tobin s q. They use the actual data results taken from Gilchrist and Himmelberg (1995). The estimated coefficient of the Fundamental Q is not comparable to the coefficient of the profitability shocks but the coefficient of the cash-flowto-capital ratio can be compared to ψ 3. This coefficient is calculated as 0.24 by Gilchrist and Himmelberg (1995). This value is quite close to the value of ψ 3 estimated in this study, Figure 2: Investment rate and Profitability shocks (COMPUSTAT) Investment rate Shocks The overall aim of this study is to show how the investment rate is related to fundamentals and cash flow. In this regard, it is helpful to investigate the graphical relationship between the shocks and the investment rate. The non-linearity of the relationship between the shocks and the investment rate can be seen in Figure 2. Since a firm s specific behavior is not in the context of this paper, the fixed effects are eliminated by deviating the shocks and the investment rate series from their firm-level means. The nonparametric line is fitted to show the relationship between investment and the shocks. The application of the nonparametric approach starts with the creation of grid points of the fundamentals. 19 These grid points are 19 The results obtained here are almost identical to Kernel nonparametric regression with normal function with bandwidth value 1 (cubic polynomial). 15

16 calculated as follows. The shock series is divided into 100 equal bins between its minimum and maximum values. Then the average values of the observations in each bin are calculated. The depicted function connecting average values corresponds to a cubic polynomial fitted line of these 100 points. The figure presents that the investment rate is a convex function of the shocks. This finding supports that the investment process is non-linear. The response of investment to fundamentals is also asymmetric with respect to negative and positive values of fundamentals. The similar graph is presented by Cooper and Haltiwanger (2002) as Figure 2 on page 13. This graph is constructed using plant level data. However, they are quite similar to each other. Table 3 presents some statistical information about the relationship between the shocks, the cash flow ratio, and the investment rate. The correlation coefficient between the investment rate and the shocks is This correlation is using plant-level data as calculated by Cooper and Haltiwanger (2002). The correlation between the shocks and the cash flow ratio is 0.25, which is lower than the correlation between the investment rate and the shocks. As a reminder, the correlation coefficient between the investment rate and the cash flow ratio is 0.34, which is quite close to the correlation between the investment rate and the shocks. Table 3: Summary statistics related to the cash flow ratio Variable COMPUSTAT Correlation between i and ait Correlation between CF_K and ait Note: All statistics are calculated pooling data for 498 firms and for the period i represents the investment rate. CF_K represents the ratio of the real value of cash flow to the replacement value of capital. a it is the idiosyncratic profitability shocks. 4 Models In this section, models with different capital adjustment costs and with financial market imperfections are specified in order to understand how firms behave when they face different frictions one at a time. In this way, we can better understand the properties of the mixed model combining financial market imperfections with non-convex adjustment costs. This 16

17 mixed model will be presented in the next section. Thebaselinemodelwithfinancial market imperfections is constructed following the model of Gilchrist and Himmelberg (1998) and the base line models with different adjustment cost specifications are from Cooper and Haltiwanger (2002). In each model, it is assumed that there is a large and fixed number of monopolistically competitive firms. Firm i begins to period t with the inherited real capital stock, K it,which has been adjusted in the previous period, and the inherited net financial liabilities, B it,which summarizes both financial assets and liabilities (debt, cash, retained income etc.). If B it is positive, it can be thought as the debt stock borrowed in previous period. On the other hand, if B it is negative, it is considered as retained income from the previous period. It is assumed that debt contracts are for one period. Before making any investment decision, the firm learns about the current period aggregate and idiosyncratic profitability shocks. Given these state variables, the firm makes a decision on investment and on the amount debt that needs to be borrowed (or on the amount of dividend retention), depending on the nature of adjustment costs and the effects of financial markets. The aim of the firm manager is to maximize the present discounted value of dividends, D it. The profit functionhasacommonspecification in each model and parametrized in a following way: Π(A it,k it )=A it Kit θ (3) where θ is the parameter for the curvature of the profit function. If θ is less than one, this shows the decreasing marginal profitability of capital. This might be caused by some degree of monopoly power or decreasing returns in the technology. A it is the current period profitability shock. It contains both the idiosyncratic shocks, ε it, and aggregate shock, A t. 20 The price of output is normalized to one. It is assumed that capital is the only quasi-fixed factor of production and all variable factors have already been maximized out of the problem. In all models, β is the fixed discount factor and equals (1+r) 1 where r is the risk-free market interest rate. 4.1 Financial Market Imperfection Model In the presence of financial market imperfections, the dynamic programming model is: V (A it,k it,b it )= max D it + βe Ait+1 A it V (A it+1,k it+1,b it+1 ), (4) {K it+1, B it+1 } 20 Following Cooper and Haltiwanger (2002), I assume that A t is a first-order, two state Markov process with A t {A h,a l } where h and l denotes high and low value of shocks. The idiosyncratic shocks take eleven different values and also are serially correlated. 17

18 subject to the following constraints: Π(A it,k it ) C(K it,i it )+B it+1 (1 + r)(1 + η it (K it,b it ))B it when B D it = it > 0 Π(A it,k it ) C(K it,i it )+B it+1 (1 + r)b it when B it < 0 (5) I it = K it+1 (1 δ)k it (6) D it 0 (7) where V ( ) is a value function, βe Ait+1 A it V ( ) is the present discounted future value of the firm, η it ( ) is external finance premium, C( ) is the investment cost function, I it stands for investment, δ is the depreciation rate. The subscripts i and t denote the firm and the time period successively. In this model financial market imperfections are introduced by thepresenceofexternalfinance premium and the non-negativity constraint on dividends following Gilchrist and Himmelberg (1998). The cost function contains both the cost of investment and convex adjustment costs: C(K it,i it )=pi it + γ 2 Iit K it 2 K it (8) where p is the price of capital good, which is assumed to be fixed at each period. The second term on the right hand side of the equation shows the standard way of representing quadratic convex adjustment costs. γ is the structural parameter of the convex adjustment cost. The amount of firms internal funds may not be enough to finance desired capital adjustment for some of them. So they may need to borrow external funds where the cost of external funds will depend on their financial health. The external finance premium, which depends on the financial health of firms, is defined as the amount of additional interest that a firm needs to pay over the risk-free market interest rate. In the model, it is assumed that the leverage ratio (i.e. the debt-to-capital ratio) indicates the firm s financial health. The magnitude of this leverage ratio determines how strongly firms are affected by financial market imperfections. 21 The functional form of the external finance premium is given as: η it = α B it pk it (9) 21 There might be some concerns about whether high debt indicates that a firm faces with financial problems or it shows that firms have perfect excess to the debt market so that they have such a high level of debt. Many studies assume that the high debt stock relative to the capital stock is an indicator that firms are financially vulnerable since their net worth is low. Some examples of these studies are: Bernanke and Gertler (1990), Bernanke, Campbell and Whited (1990), Whited (1992), Hu and Schiantarelli (1998), and Gilchrist and Himmelberg (1998). When firms are financially fragile, lenders will take higher risk by lending fund to these firms, so they will charge a higher external finance premium to compensate this risk. 18

19 where B it pk it represents the leverage ratio. 22 The capital stock is in the denominator of the leverage ratio since it is assumed that capital is the only collateral asset that the firm has. This collateral asset can, at least partially, remove the asymmetric information between the firm and lenders. α is the structural parameter determining the magnitude of external finance premium and, in turn, the magnitude of the financial market imperfections. The expected sign of α is non-negative. This means that firms facing with a higher leverage ratio need to pay higher premium. In addition to the presence of external finance premium, it is required debt finance to be a marginal source of external finance rather than equity finance in order to incorporate financial frictions. It is sufficient to introduce a non-negativity constraint on dividends in order to guarantee this point. 4.2 Models with Different Adjustment Cost Structures In this section, the models with three different types of adjustment costs are presented. The types of adjustment costs are convex adjustment cost, fixed adjustment cost, and the presence of a price wedge between the selling and buying price of capital. As specified previously, these models are quite similar to the models presented in Cooper and Haltiwanger (2002). The difference is that debt is a choice variable in addition to investment. The reason is to keep the structural form of these models and of the models with financial market imperfections close to each other. It should be noted that, in the absence of financial frictions, the chosen debt level will not affect the investment rate Convex Adjustment Cost Models In this case, almost everything is the same as in the financial market imperfections model in Section 4.1. Equation (4) is maximized subject to equations (5) and (6). One difference is that α is zero so that D it = Π(A it,k it ) C(K it,i it )+B it+1 (1 + r)b it. The second difference is that D it 0 constraint does not exist. In this case, the debt stock can be chosen at any level independent of the financial position of firms. Because of this, it will not affect the investment decision of firms. 22 Gilchrist and Himmelberg (1998) use this kind of external finance premium. But they do not assign any functional form to it. Jaramillo, Schiantarelli, and Weiss (1996) use an explicit form of external finance premium, which is linear in the leverage ratio. In this study, the linear form is used too, for simplicity. 19