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Article Excerpt
Summary. In this paper we develop a general equilibrium model with heterogeneous, long-lived firms where financial factors play an important role in their production and investment decisions. When the economy is hit by monetary shocks, the response of small and large firms differs substantially, with small firms responding more than big firms. As a result of the financial decisions of firms, monetary shocks have a persistent impact on output. Another finding of the paper is that monetary shocks lead to considerable volatility in stock market returns.
Keywords and Phrases: Monetary policy, Firm financing, Propagation mechanism.
JEL Classification Numbers: E5, G3.
Introduction
Empirical studies of the financial decisions of firms have documented important differences in the behavior of large and small firms. It has been shown by Fazzari et al. (1988) and others that small firms are more profitable, pay fewer dividends, take on more bank debt, and invest more. Studies by Gertler and Gilchrist (1994), Gilchrist and Himmelberg (1996, 1998) have also shown that the investment decisions of small firms are more sensitive to cash flows and that they respond to monetary policy shocks very differently than do large firms. Because many of these authors identify small firms as a priori more likely to face financial constraints, these empirical features are widely interpreted as indirect evidence of frictions in financial markets. These frictions are conjectured to be an important channel for the propagation of monetary policy shocks.
To investigate how financial frictions affect the propagation of monetary shocks, we study an economy in which financial frictions lead to firm heterogeneity. Firms are heterogeneous in the amount of equity capital they have in their business which in turn affects their financial decisions and production scale. The capital structure of firms changes endogenously over time as a result of their financial decisions and in response to idiosyncratic shocks. The model is in the spirit of models by Jovanovic (1982) and Hopenhayn (1992), in that shocks affect the dynamics of firms over time. The key difference is that, in this environment, heterogeneity is not generated by technological differences. Rather, firms are heterogeneous because they face different financial conditions. (3)
All firms have access to the same decreasing return-to-scale technology for producing a single homogeneous good. The firm's production plan is financed with funds borrowed from a financial intermediary. In deciding the optimal amount of debt, the firm faces a trade-off: on the one hand, more debt allows them to expand the production scale and to increase the expected profits; on the other, the increase in the amount of debt implies a higher volatility of profits to which the firm is averse. The aversion to the volatility of profits derives from the fact that the value of the firm is a concave function of profits. This trade-off induces firms to choose a different amount of financial leverage (debt-equity ratio) depending on the amount of equity they have in their business. Firms with less equity choose a higher debt-equity ratio to take advantage of the higher return associated with smaller size. This feature of the financial decision of firms plays a crucial role in differentiating the responses of small and large firms to monetary shocks.
Firm financing and investment decisions determine how firms grow over time. Accordingly, any successful treatment of the financing decisions of heterogeneous firms should be consistent with an important set of observations about industry dynamics. Studies of the relationship between firm size and growth have overturned the conclusion of Gibrat's Law which holds that firm size and growth are independent. Studies by Hall (1987) and Evans (1987a), for example, show that the growth rate of manufacturing firms and their volatility is negatively associated with their initial age and size. Also, Davis et al. (1996) find that the rates of job reallocation are decreasing in the firm size and age. In Cooley and Quadrini (2001b) we study a similar environment but in a partial equilibrium setting and without aggregate shocks, and we establish that this model reproduces many of the salient features of industry dynamics that are observed in U.S. data. In particular, smaller firms grow faster, experience greater variability in their growth rates and they have higher rates of job reallocation. Moreover, the model is consistent with the observed financial and investment behavior of firms: we find that small firms take on more debt, distribute fewer dividends and their investment depends on the realization of cash flows, even after controlling for their future profitability.
In addition to replicating the observed features of industry dynamics, the model economy developed in this paper suggests that firm heterogeneity is an important channel of transmission for monetary policy. We find that small firms are much more responsive to monetary shocks than large firms. One consequence of this heterogeneous behavior is that a large fraction of the changes in aggregate output induced by monetary shocks derives from the reaction of small firms. Moreover, due to the persistence of this reaction, the response of the aggregate economy to monetary shocks is highly persistent with aggregate output that displays a hump-shape response.
The heterogeneous responses of firms to monetary policy occur for reasons related to the internal finance channel that has been analyzed in different contexts by Bernanke and Gertler (1989), Bernanke et al. (1998), Carlstrom and Fuerst (1997), Kiyotaki and Moore (1997). In these papers, however, firm heterogeneity is either exogenous or it does not play an important role. In contrast, in our model, firm heterogeneity is endogenous and it plays an key role in the transmission mechanism of monetary shocks.
The internal finance mechanism works as follows. The firm's ability to finance its production plan is related to the value of its assets. When the value of these assets increases--either because the price of the assets increases or because the firm reinvests more profits--the firm is able to expand its production plan. In our model, a fall in the nominal interest rate on loans decreases the interest payments of the firms and increases their profits. Because of reinvested profits, the next period financial capacity of firms increases, which in turn allows them to expand production. This mechanism, however, is more important for small firms because they are more levered.
The central role played by the financial structure in the transmission of monetary shocks highlights an important fact about the economic conditions under which the economy is more vulnerable to these shocks. Monetary shocks will have a larger impact during periods in which firms are more heavily indebted.
Although monetary shocks have real consequences in this economy, the effects are quantitatively small. This is consistent with the results of Sims (1992) and Leeper et al. (1996). In spite of their limited impact on the real sector of the economy, monetary shocks have a significant impact on stock market variables: monetary shocks generate fluctuations of stock returns that are much larger than the fluctuation of profits, dividends and aggregate output. This latter finding is consistent with the empirical evidence. (4) The main mechanism through which monetary shocks influence the volatility of stock returns is by altering the factor with which agents discount dividends. Because dividends are paid with cash at the end of the period, the shareholder has to wait until the next period before being able to use these dividends for consumption. Consequently, changes in the nominal prices affect the real values of the dividends paid with cash. Because monetary shocks affect the inflation rate, in addition to the nominal lending rate, they have a significant impact on the market value of the firms, and therefore, on the stock market return. Thus, monetary shocks have a far greater impact on financial markets than their impact on the real economy would seem to warrant. This may provide some insights on the excess volatility puzzle of stock market returns as emphasized in LeRoy (1989) and Shiller (1981).
In the next section we describe the model economy to be studied and the decision problems facing households, firms, and financial intermediaries. We then describe the problem of the firms and the households in some detail and define the competitive equilibrium. After describing the calibration of the model, we present the properties of the artificial economy. In that section we describe the channels through which financial factors induce heterogeneous behaviors of firms over the business cycle.
1 The model economy
There are three sectors: the production sector, the household sector and the financial intermediation sector. Financial intermediaries intermediate liquid assets (money) between households and firms. Shares of the financial intermediaries and firms are owned by the households.
1.1 Firms
At each point in time there is a continuum of firms that have access to the technology:
y = F(k, l, x, [phi]) (1)
where [phi] is a non-negative idiosyncratic shock, k is the input of capital that depreciates at rate [delta], l is the input of labor and x is an intermediate input purchased from other firms. The shock is observed after the choice of the inputs. To simplify the analysis we assume that labor and the intermediate input are perfect complements to capital. More specifically, per each unit of capital the firm employs [[gamma].sub.l] units of labor and [[gamma].sub.x] units of intermediate goods. Therefore, l = [[gamma].sub.l]k and x = [[gamma].sub.x]k. Given this, the production technology can be rewritten as y = F(k, [phi]).
The function F is strictly increasing and continuously differentiable in k and [phi], strictly concave in k, and satisfies F(0, [phi]) = F(k, 0) = 0. The assumption that the function F is concave in k implies that the production technology displays decreasing returns-to-scale. The shock [phi] is independently and identically distributed with probability density [GAMMA]([phi]). The distribution is assumed to be log-normal.
Firms are characterized by the amount of capital, e, that they own. Henceforth, this capital is referred to as equity. The amount of equity changes over time as firms reinvest profits. The value of a firm will thus depend on the realization of the idiosyncratic shock and its dividend policy. To keep the problem tractable, we assume that retained earnings is the only source of increased equity for the firm. We motivate this assumption by the observation that firms mainly rely on the reinvestment of earnings for increasing equity. (5)
In addition to the capital directly owned, firms can increase (decrease) the input of capital by renting it from (to) other firms...
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