پویایی های سرمایه گذاری با هزینه های تعدیل ثابت سرمایه و عیوب بازار سرمایه

This paper examines the implications of financing frictions on capital stocks and on capital accumulation in the presence of non-convex costs of adjusting the capital stock. In this setup finance has an influence on both, the level of capital and the timing of investment. Finance and productivity are complements and finance influences investment the strongest when firms wish to significantly adjust capital for fundamental reasons. These theoretical considerations are confronted with UK data. While finance is mostly irrelevant for long-term capital decision, the short-run investment function shows a significant impact of finance, which is also strongest for strong fundamental investment incentives.

Economists’ knowledge of micro-level and aggregate investment is still far from being conclusive. Seemingly well established, however, is the view that the workhorse of the neoclassical theory of investment, the qq-model, has a hard time explaining empirically observed patterns of investment.1 Which of the assumptions of the neoclassical model actually leads to its failure remains to be answered. Beginning with Fazzari et al. (1988) the empirical literature has emphasized the role of financial factors in firm-level investment. More recently attention has been drawn to the role of non-convexities in the investment technology. This paper aims at merging both of these strands and shows that financial factors and non-convexities are both simultaneously important, since each significantly influences the effect of the other. This interaction has not been analyzed much, though recent contributions have drawn attention to the issue: Holt (2003) provides a theoretical real-options model of irreversible investment that shows how financial frictions and irreversibility of investment interact as complements, Caggese (2003) develops a formal test for financial constraints based on the irreversibility of fixed investment, and Whited (2006) provides evidence that firms which are identified as financially constrained exhibit investment spikes much less frequently. Our approach differs in both methodology and focus from these studies. With nonconvex adjustment costs, firms invest infrequently and lump their investment projects. We argue that this opens two ways for finance to affect investment: first, finance can alter the target level of capital to which a company adjusts and secondly, it can influence the timing of investment, the frequency at which projects are carried out. Our focus is to disentangle the two effects both theoretically and empirically. This makes Whited's (2006) paper most closely related, as her paper also analyzes the effect of finance on the timing of investment. However, she does not disentangle timing and level effects of finance, but only investigates if financially constrained firms adjust capital less frequently. Specifically, she estimates hazard rates for investment spikes as functions of the time elapsed since the last spike and performs this estimation for both, financially unconstrained and financially constrained firms. By contrast, our paper employs a “gap-approach” as developed in Caballero et al. (1995). This means that we estimate a non-linear error-correction model of capital which relates capital to productivity and finance. In relation to Whited's (2006) approach, this can be understood as a step towards structural estimation; tying the theoretical model more closely to the estimation. This step allows to separate timing and level effects of finance on investment. When we assess empirically which of the two effects is more important, the influence of finance on long-term target levels of capital or the influence of finance on the timing of investment, finance shows at best a minor influence on the long-term stocks of capital that companies hold. By contrast, finance has a significant influence on investment. In consequence, finance has only an intertemporal substitution effect—more liquidity speeds up investment. A similar result is found in Bayer (2004a), which extends the empirical analysis here to German data. In particular, Bayer (2004a) focuses on the discussion of potential endogeneity problems of finance and shows that the results are robust to a more detailed treatment of the problem. Also for the German data, finance influences investment timing but not long-term levels of capital. This result itself is already informative for identifying the actual form of frictions involved. Consider a convex adjustment cost model with wealth-dependent costs of capital, for example. In such model, one would expect the relative strength of both effects (level vs. frequency) to be just the reverse. Convex adjustment costs lead to partial adjustment of the current stock of capital to its target level every period and a change in finance translates into a change in the target level of capital. Consequently, our findings allow us to reject this model. While the interaction between finance and non-convex adjustment costs has not been analyzed much, non-convexities themselves—such as irreversibility or fixed costs of investment and other economies of scale—have been discussed widely and have been analyzed in a very general theoretical framework by Abel and Eberly (1994). Empirical evidence for non-convexities is mostly drawn from the longitudinal research database (LRD). Doms and Dunne (1998), for example, report that—at the plant-level—a small fraction of investment activities is associated with an overwhelmingly large fraction of changes in the capital stock. Cooper et al. (1999) use the LRD to estimate a hazard model of investment. They find a time-increasing investment hazard and thus evidence for non-convexities. A more direct approach has been taken by Caballero et al. (1995). These authors estimate “mandated investment” by imposing a long-run relation between earnings, capital employed and the costs of capital. Explaining actual investment by mandated investment in a second step, they empirically document the convex relationship predicted by the non-convex adjustment cost model of investment. Additional evidence for non-convexities has also been drawn from other data than the LRD.2 For instance, Caballero and Engel (1999) estimate a model of aggregate investment dynamics that rests on a microeconomic model which features stochastic non-convex adjustment costs. On the basis of two-digit industry level panel data they find significant fixed costs of investment and obtain a better fit with their structural model than with partial adjustment (convex cost) alternative models. Besides this strong emphasis that the investment literature has put on the role of non-convexities in investment decisions, it also has questioned some of the earlier papers on financial factors in investment.3 A series of papers has elaborated the problems of measurement errors and biased estimators that arise in qq-theoretical regressions and that may result in spuriously positive estimates of financial variables.4 The possibly most “discouraging” results for this branch of the literature are the results of Gomes (2001). He shows in a pecking order of finance framework that the presence of financial frictions is neither sufficient nor necessary to obtain a (seemingly) significant positive coefficient on cash-flow in a qq-theoretic investment regression. 5 Despite Gomes’ (2001) strong scepticism against including cash-flow inqq-regressions of investment to pick up financial frictions, Gomes’ (2001, p. 1279) contribution itself arguably calls for the inclusion of other measures of the financial status of a company in an investment regression with non-convex adjustment costs. He points out in particular that the investment behavior corresponding to a pecking order of finance model “[⋯⋯] is somewhat similar to those used in the investment with fixed cost literature” when not controlling for the financial status. This makes a departure from the standard “Tobin's qq plus cash-flow” model of investment necessary. Because of that, we modify Caballero and Engel's (1999) model, such that it captures most prominent specifications of financial frictions: wealth-dependent costs of capital, credit rationing, and the absence of external equity finance.6 From this model, we infer that the (expected) investment rate of a company is a function of only two variables: the firm's mandated investment and the firm's equity ratio, which is the book value of a firm's equity over the book value of its assets.7 In particular, our merged model predicts that finance influences the frequency of investment; that this influence is strong especially when there are strong fundamental incentives to adjust the stock of capital; and that investment is a convex function in fundamental investment incentives—like in the pure non-convex adjustment cost model. The direct effect of finance on the frequency of investment in the combined model can explain another apparent puzzle in the investment literature. In most data sets, including the one used in this paper, liquidity affects investment but not capital stocks in the long-run. This point has attracted little attention.8 Having analyzed the model theoretically, we then asses it empirically in an analysis that draws on the ideas developed in Caballero et al. (1995). Infrequent investment establishes a cointegration relation between the static optimal target level of capital and the actual capital a company employs. This allows to recover the gap between actual and desired level of capital from an estimation of a cointegrating vector between capital, total factor productivity, and the equity ratio. However, to minimize the influence of measurement errors in this estimation, we deviate from Caballero et al.'s (1995) procedure and combine their direct method of productivity measurement with the idea of Cooper and Haltiwanger (2002) to measure productivity indirectly. With our sample of UK companies, the Cambridge DTI database, this allows to generate three preliminary measures of productivity from which we then infer a final estimate of productivity as the common factor imbedded in all three of them. This common factor is non-stationary and cointegrated with the level of capital a company employs. By contrast to productivity, finance has no influence on the level of capital employed in the long run. The cointegration error of this long-run regression identifies the amount of mandated investment, which is the fundamental investment incentive. Having generated an estimate of mandated investment, the investment function is estimated non-parametrically as a function of the equity ratio and mandated investment. This second estimation shows that investment is a non-linear function of both finance and fundamentals. It is convex in fundamentals, it is significantly influenced by finance, and—in line with the theoretical prediction—this influence is the stronger, the stronger fundamental incentives are. The remainder of this paper is organized as follows: Section 2 develops a model that describes firm level investment under the assumption of capital market imperfections and fixed costs of investment. Within this section, Section 2.1 describes the company's choice problem whereas Section 2.2 discusses the properties of the investment function. Section 3 presents empirical evidence for the model and draws on firm level investment data from the Cambridge DTI database. Section 4 concludes and an appendix follows.

This paper has presented a model of investment that incorporates an imperfect capital market and fixed investment costs. The major result is to identify the difference between a short-run effect of liquidity on the frequency of investment and a long-run effect on the optimal stock of capital. While models that generate a finance and investment correlation primarily via agency or strategic motives—for example Myers (1977) or Brander and Lewis (1986)—predict the influence of finance through the stock of capital, the model in this paper rather emphasizes an alternative effect via the frequency of investment projects. This suggests a stronger short-term than long-term influence of finance in investment, and empirically, we find exactly this. Moreover, both our theoretical model as well as our empirical findings suggest a substantially non-linear form of the investment function. Fundamentals and finance interact, and with lumpy adjustment, investment is convex in fundamentals. For further empirical research, this result suggests a need for flexible functional approaches. This paper employed a generalized error correction model in which the short-run dynamics (or error-correction function) was estimated entirely non-parametrically.29 A step further could be to take a flexible (semi-)parametric approach to generalize the error-correction process. This could then be further integrated into an indirect inference approach that finally would allow to identify the economic primitives on the basis of the reduced form estimations.30 This might provide further insights, for example it would allow to analyze to what extent convex costs and to what extent fixed costs determine investment behavior. Our entirely non-parametric estimation is unable to distinguish there and can only rule out some model alternatives while being consistent with a class of other investment models. From a policy perspective, our findings have some implications. Suppose there are shocks to the balance sheet positions of firms—for example through exchange rates as in Céspedes et al. (2004), Aghion et al. (2001) or Devereux and Lane (2001)—then this paper's model predicts the real impact of such shocks to have a different timing and impact than the usual financial accelerator model of Bernanke and Gertler (1989) and Bernanke et al. (1998). Productive firms will delay investments, unproductive ones are more likely to sell capital to repay debt. The total effect comes much more up front than over time, the business cycle effect is much more pronounced. The total impact of a shock to balance sheets will depend on the distribution of capital imbalance in the economy in particular. Consider an economy without aggregate capital imbalance. First, assume that firms are heterogeneous in the sense that some firms need to increase their stock of capital, while others need to sell capital. In this situation, a deterioration of balance sheets will lead to a drop in aggregate investment. Now, assume that firms are homogeneous and no single firm wants to adjust its stock of capital for fundamental reasons. By contrast to the former situation, now an adverse shock to the financial situation will not be followed by any strong reaction of aggregate investment. Thus, if fixed adjustment costs are present, policies that influence the balance sheet will have different welfare implications depending on the distribution of capital imbalances across firms. The effects of finance and fundamentals cannot be considered separately, the magnitude of each effect depends on the state of the other variable. In other words, policy makers—for example central banks—need to observe the distribution of capital imbalances in order to predict the implications of their policies.