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Article Excerpt
We study the dynamics of an industry subject to aggregate demand shocks where the productivity of a firm's technology evolves stochastically over time. To characterize the intertemporal evolution of the distribution of firms, we discuss in particular how exit decisions, aggregate output, profits, and distributions of firm productivities vary (a) across different demand realization paths; (b) along a demand history path, detailing the effects of continued good or bad market conditions; and (c) for different anticipated future market conditions. We show how poor demand conditions can lead to increased exit of low-productivity firms at all future dates and states and raise welfare due to the impact on exit decisions.
1. Introduction
* This article integrates aggregate demand uncertainty into a dynamic stochastic model of firm entry and exit, and derives the consequences both for the evolution of the distribution of firms and for individual firm decision making. The research builds on the dynamic stochastic equilibrium model of firm entry and exit developed by Hopenhayn (1990, 1992a, 1992b). Hopenhayn analytically characterized the individual exit and production decisions of firms according to their age, size, and productivity in the unique invariant steady-state equilibrium.
We extend that work to an environment with aggregate demand uncertainty. In particular, we determine how individual firm exit decisions, aggregate output, profits, and distributions of firm productivities vary (i) across different demand realization paths; (ii) along a demand history path, detailing the effects of continued good or bad market conditions; and (iii) for different anticipated future market conditions. We identify sufficient conditions under which the theoretical model can reconcile empirical regularities regarding counter-cyclical exit, correlations of exit rates with future GDP growth, and the relative length and extent of recessions and expansions.
Incorporating aggregate uncertainty together with individual stochastic heterogeneity-both necessary features of a rich model of industry dynamics--introduces formidable technical and modelling challenges. A significant contribution of this article is to characterize the distribution of firms, rather than simply calculate selected higher-order moments. In particular, we characterize the evolution of the distribution of firms following arbitrary histories of demand realizations, deriving conditions under which the distribution of firms can be ordered conditional on equilibrium exit decisions. We then consider such key questions as: does an economy with a better distribution of firms produce more output in all states? Will a more protracted period of high demand lead to a better distribution of firms, or worse?
A second contribution is to endogenize the value of exit by building in an opportunity cost to exit: a firm can exit and sell its resources to another firm, but this requires that the firm's resources go unutilized for a period while the resources are retooled so that they can be used by a potentially more efficient entrant. The amount an entrant is willing to pay for those resources reflects the profits that it expects to earn, and hence will vary with market conditions.
Endogenizing the value of exit complicates the characterization of the equilibrium evolution of the distribution of firms. Both the endogenous value of production and the endogenous value of exit vary pro-cyclically, both rising in higher aggregate demand states. Two basic issues must then be addressed: (i) does firm exit rise or fall in higher demand states?, and (ii) is the immediate impact of these exit decisions on the distribution of firm productivities preserved over time? In particular, does the effect of reduced exit on the distribution of firms persist, so that the distribution of firms is worse at all subsequent dates and states, or could this effect be reversed? Answering this question is fundamental to addressing the impact of recessions on the long- run productivity of the economy.
Obtaining analytical answers to these questions is difficult. The standard analytical tool for this class of models is to prove that the competitive economy corresponds to the solution of a social planner's problem. Here, even when the social planner's problem characterizes equilibrium, it is of limited help: the fact that the equilibrium solves a surplus maximization problem, does not ensure, in particular, that an improvement in the distribution of firms adversely affects all firms because of the endogenous effects on exit. Consequently, the social planner characterization does not help to shed light on issues such as whether an improvement in the distribution of firms is preserved at all future dates and states.
This leads us to identify conditions on the transition process for a firm's technology that ensure the aggregate distribution is always totally ordered in stochastic dominance terms, and we use this to prove that an improvement in the distribution of firms is preserved along every future demand path. This yields a strong characterization result: ceteris paribus, an economy with greater past exit produces more output at every future date and state.
With aggregate distributions comparable in stochastic dominance terms, it is possible to derive sufficient conditions for exit rates to be counter-cyclical. For standard production technologies (e.g., constant elasticity of substitution [CES]) and any two-state Markov demand process, the endogenous value of production varies more with market conditions than the endogenous value of exit. It follows that higher demand causes exit to fall. Combining this with the result that the effect of increased exit on future distributions of firm productivities is always preserved, yields the result that demand downturns increase future output and lead to better future distributions of firm productivities (ordered by stochastic dominance) at every future date and state.
These results permit a characterization of the effect of aggregate demand shocks on industry dynamics. We contrast outcomes across different demand realization paths, comparing exit decisions and their consequences for aggregate output, profits, and productivity distributions when one history of demand realizations is uniformly better than another. Following this, we study outcomes along a demand history path in order to describe the effect of continued good or bad market conditions on exit decisions and aggregate variables. In particular, we prove that as a demand contraction continues, the distribution of firms grows ever better, setting the stage for greater future output once demand improves. Conversely, firms in booming economies rest on their laurels, so that the distribution of firms grows ever worse as a boom continues, sowing the seeds for a greater fall in output when the demand boom ends. We then derive how anticipated future market conditions affect exit decisions and aggregate outcomes. Better anticipated future market conditions induce more exit and give rise to better distributions of firm productivities in the current period.
This theoretical model generates the pro-cyclical net entry (gross entry minus gross exit) found in the data (see Bilbiie, Ghironi, and, Melitz 2007), the correlations of exit rates with future GDP growth that are positive, economically large, persistent, and statistically significant (Campbell, 1998), and the observation that recessions are shorter and sharper than expansions, and is consistent with counter-cyclical gross turnover (gross exit plus gross entry) documented by Davis and Haltiwanger (1990, 1992) and Davis, Haltiwanger and Schuh (1996). The central tenent, that firm productivities vary stochastically, is necessary to reconcile the very different responses of firms to similar market conditions. Becker et al. (2004) find that about two thirds of all job creations and job destructions occur at establishments that shrink or grow by at least 10% in a quarter, whereas Cooper and Haltiwanger (2006) find investment rates exceeding 20% occur in 18% of their observations, accounting for 50% of total investment, whereas 8% of plants do not invest and 10.4% make negative investments. Dunne, Roberts, and Samuelson (1989a, 1989b, 1989c) document that, on an annual basis, entering and exiting firms account for about 40% of manufacturing firms, are on average one third the size of continuing firms, that exiting firms have higher costs, and that the conditional probability of exit declines with both age and size. These findings highlight the importance of firm-specific sources of uncertainty for firm survival and investment dynamics. Finally, we explore how the market for an exiting firm's specialized resources affects equilibrium dynamics. When the resources of an exiting firm are highly specialized, potential bidders are likely to attach very different values to them, so that the exiting firm's bargaining position is weak. As a result, the firm cannot expect to sell its specialized resources for close to their full value to the highest bidder. Empirically, Ramey and Shapiro (2001) find that the weak bargaining positions of exiting firms matter: "The process of selling capital results in significant declines in economic value (equipment sold for only one-third its inflation-adjusted book value, after accounting for normal annual depreciation).... Because of the large discounts experienced on the sale of capital, the option value of installed capital is very high." The exiting firm's weak bargaining position drives a wedge between the social and private opportunity cost of the resources so that "firms may rationally hold on to (under-utilized) capital for long periods of time," tying up valuable assets that can only be released upon exit. Becker et al. (2004) find related evidence that "the secondary market for capital for firms going through exit [is] much weaker than is implicitly assumed in our treatment of depreciation."
Thinner resale markets reduce the sensitivity of the endogenous value of exit to current market conditions. We show that in industries with more specialized inputs (where exiting firms have weaker bargaining positions), firms tend to be both larger and less productive, and there is less entry and exit. This is consistent with the substantial and persistent differences in entry and exit rates across industries that Dunne et al. (1989a) find. Finally, we show constructively that a downturn in demand can actually enhance total welfare because it narrows the wedge between the social and private opportunity cost of the plant, increasing exit. Thus, the Darwinian cleansing effect of a downturn on exit can raise future expected welfare by more than the immediate reduction in welfare due to the downturn.
Finally, we highlight what this article does not do. First, to focus on the impact of aggregate demand shocks, the model does not directly introduce productivity gains from adopting new and better methods of production (except to detail how incorporating such features into the model can generate predictions consistent with the empirical regularity that recessions are sharper and more asymmetric than booms). Levinsohn and Petrin (1999) find that the factors we model dominate. They empirically decompose aggregate industry productivity changes in Chile into the portion due to rationalization, that is, the replacement of losers by winners that we model, and the portion due to the adoption over time of better methods of production. They find "that very little of the increase in productivity was accounted for by firms actually becoming more productive. Rather than firms becoming more productive, reallocation of market shares to firms that were already more productive and net entry typically explain the increase in aggregate productivity." Indeed, our model predicts that newer firms should tend to be smaller, less efficient, and more likely to exit--precisely the features found in the data, and features that are hard to reconcile with environments in which dynamics are driven by entrants acquiring cutting-edge technologies. Second, to focus on the dynamics of the output market, we take input prices as constant as in Hopenhayn (1992a), and allow firms to enter only through the acquisition of another firm's plant. We briefly discuss when and how the qualitative findings extend if these assumptions are relaxed.
The outline of the article is as follows. The next section places this work in the literature. Section 2 describes the economic environment, Section 3 characterizes industry dynamics, and Section 4 considers how the resale market depth affects outcomes. Section 5 concludes. Most proofs are in the Appendix.
[] Related literature. Hopenhayn (1990, 1992a, 1992b) is most closely related to our work. Hopenhayn (1992a) characterizes the individual patterns of entry and exit in the invariant steady state of his economy, emphasizing the importance of (stochastic) heterogeneity across firms in explaining empirical regularities regarding the individual actions of firms.
Jovanovic (1982) explores entry and exit dynamics when firms learn about their profitability from past performance. In Jovanovic's model, the economy improves systematically over time, as better firms tend to be more successful, and hence remain in the industry, and there is no exit in the limiting economy. Jovanovic and MacDonald (1994b) explore the entry and exit dynamics of an industry following a theoretical innovation. Jovanovic and MacDonald (1994a) analyze a related environment in which there is no entry or exit, but firms choose how much to invest to try to acquire a superior technology.
Because of the analytical challenges involved, much of the literature relies on numerical characterizations. Ishwaran (2000) numerically investigates a version of Hopenhayn's model in which demand evolves according to a two-state Markov process and there is a single input, capital. She calculates moments conditioned on firm age and demand state. Our analysis highlights the importance of the path-dependent evolution of the economy. The entire history of demand shocks determines the equilibrium distribution of firms, and this distribution, in turn, impacts exit decisions. Her paper highlights the fact that the properties of industry dynamics that we derive cannot be addressed numerically (e.g., when does increased past exit or reduced demand lead to greater output at every future date and state?).
Campbell (1998) numerically analyzes a general equilibrium model of industry dynamics, melding a version of Hopenhayn's (1992a, 1992b) model with a vintage capital model that embodies aggregate uncertainty through innovations to the mean technology quality of new entrants. Campbell offers a complementary explanation to ours for the correlation between current exit and future GDP growth. He finds that greater future anticipated technical innovations lead to more firm exit in earlier periods because consumers respond by increasing savings and reducing current consumption.
Asplund and Nocke (2006) explore entry and exit in a stationary economy with heterogeneous firms in which the reduced-form structure of profits is assumed to have the feature that the impact of greater competition heightens the relative impact of having lower marginal costs on profits. As a result, increasing market size amplifies the impact of lower marginal costs on firm profits, raising both entry and exit. Asplund and Nocke then identify consistent supporting empirical evidence.
Jovanovic and Rousseau (2002) distinguish between "de novo" entry versus entry by merger in a stationary economy with heterogeneous firms. In their model, a "good" firm that takes over the capital of a "bad" firm transfers "its" productivity to that capital by incurring a fixed cost. Sufficiently bad firms either liquidate or sell their capital directly to sufficiently good firms.
Other papers turn to deterministic models. Caballero and Hammour (1994) simulate a model in which demand follows an exogenously specified cyclical path, new entrants are more productive, and there is a fixed cost of entry that depends exogenously on the measure of entrants. With sufficient entry cost externalities, when demand falls, the exit of old, unproductive firms rises by more than the entry of new productive firms falls, in which case average technology quality rises. Caballero and Hammour (1996) consider a variant with costly search.
Other papers assume that all prices are constant, which simplifies the analysis greatly, as the distribution of firms in the economy does not affect an individual firm's profits, and hence decision making. In such settings, Monge (2001) and Cooley and Quadrini (2001) explore the impact of interest rate shocks on the entry and exit of firms and aggregate output. In their models, firms borrow to finance capital, and firm productivities evolve stochastically. Cooley and Quadrini show that their model is consistent with the empirical regularities that smaller/newer firms have higher and more variable growth rates because they are credit rationed, yet they are more likely to exit.
Bergin and Bernhardt (2002, 2005) derive how dynamics are affected by the time- to-build feature of capital investment under the assumption that demand is sufficiently price elastic. By incorporating this feature of capital, they can distinguish between large firms and productive firms, and explain distinctly the size, productivity, and age patterns of profit, output,...
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