This paper develops a dynamic industry model with heterogeneous firms to analyze the intra-industry effects of international trade. The model shows how the exposure to trade will induce only the more productive firms to enter the export market (while some less productive firms continue to produce only for the domestic market) and will simultaneously force the least productive firms to exit. It then shows how further increases in the industry's exposure to trade lead to additional inter-firm reallocations towards more productive firms. The paper also shows how the aggregate industry productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a benefit from trade that has not been examined theoretically before. The paper adapts Hopenhayn's (1992a) dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the paper provides an extension of Krugman's (1980) trade model that incorporates firm level productivity differences. Firms with different productivity levels coexist in an industry because each firm faces initial uncertainty concerning its productivity before making an irreversible investment to enter the industry. Entry into the export market is also costly, but the firm's decision to export occurs after it gains knowledge of its productivity.

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The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

This Paper builds a dynamic industry model with heterogeneous firms that explains why international trade induces reallocations of resources among firms in an industry. The Paper shows how the exposure to trade will induce only the more productive firms to enter the export market (while some less productive firms continue to produce only for the domestic market) and will simultaneously force the least productive firms to exit. It then shows how further increases in the industry's exposure to trade lead to additional inter-firm reallocations towards more productive firms. These phenomena have been empirically documented but cannot be explained by current general equilibrium trade models, because they rely on a representative firm framework. The Paper also shows how the aggregate industry productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a benefit from trade that has not been examined theoretically before. The Paper adapts Hopenhayn's (1992a) dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the Paper provides an extension of Krugman's (1980) trade model that incorporates firm level productivity differences. Firms with different productivity levels coexist in an industry because each firm faces initial uncertainty concerning its productivity before making an irreversible investment to enter the industry. Entry into the export market is also costly, but the firm's decision to export occurs after it gains knowledge of its productivity.

https://papers.ssrn.com/sol3/Delivery.cfm/DP3381.pdf?abstractid=317300&mirid=1

Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. We estimate the parameters of a production function for the equipment industry and then use those estimates to analyze the evolution of plant-level productivity over this period. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Since firms choices on whether to liquidate and the on the quantities of inputs demanded should they continue depend on their productivity, we develop an estimation algorithm that takes into account the relationship between productivity on the one hand, and both input demand and survival on the other. The algorithm is guided by a dynamic equilibrium model that generates the exit and input demand equations needed to correct for the simultaneity and selection problems. A fully parametric estimation algorithm based on these decision rules would be both computationally burdensome and require a host of auxiliary assumptions. So we develop a semiparametric technique which is both consistent with a quite general version of the theoretical framework and easy to use. The algorithm produces markedly different estimates of both production function parameters and of productivity movements than traditional estimation procedures. We find an increase in the rate of industry productivity growth after deregulation. This in spite of the fact that there was no increase in the average of the plants' rates of productivity growth, and there was actually a fall in our index of the efficiency of the allocation of variable factors conditional on the existing distribution of fixed factors. Deregulation was, however, followed by a reallocation of capital towards more productive establishments (by a down sizing, often shutdown, of unproductive plants and by a disproportionate growth of productive establishments) which more than offset the other factors' negative impacts on aggregate productivity.

The Dynamics Of Productivity In The Telecommunications Equipment Industry

Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. Our empirical focus is on estimating the parameters of a production function for the equipment industry, and then using those estimates to analyze the evolution of plant-level productivity. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Firms' choices on whether to liquidate, and on input quantities should they continue, depended on their productivity. This generates a selection and a simultaneity problem when estimating production functions. Our theoretical focus is on providing an estimation algorithm which takes explicit account of these issues. We find that our algorithm produces markedly different and more plausible estimates of production function coefficients than do traditional estimation procedures. Using our estimates we find increases in the rate of aggregate productivity growth after deregulation. Since we have plant-level data we can introduce indices which delve deeper into how this productivity growth occurred. These indices indicate that productivity increases were primarily a result of a reallocation of capital towards more productive establishments.

/pdf/the-dynamics-of-productivity-in-the-telecommunications-4x42o22gre.pdf

The Dynamics of Productivity in the Telecommunications Equipment Industry

A dynamic stochastic model for a competitive industry is developed in which entry, exit, and the growth of firms' output and employment is determined. The paper extends long-run industry equilibrium theory to account for entry, exit, and heterogeneity in the size and growth rate of firms. Conditions under which there is entry and exit in the long run are developed. Cross sectional implications and distributions of profits and value of firms are derived. Comparative statics on the equilibrium size distribution and turnover rates are analyzed. Copyright 1992 by The Econometric Society.

Entry, exit, and firm dynamics in long run equilibrium

Recent empirical work indicates that job creation and destruction rates are large, implying significant amounts of job reallocation across firms. This paper builds a general equilibrium model of this reallocation process, calibrates it using data on firm-level dynamics, and evaluates the aggregate implications of policies that interfere with this process. We find that a tax on job destruction at the firm level has a sizable negative impact on total employment: a tax equal to 1 year's wages reduces employment by roughly 2.5 percent. More striking, however, are the welfare consequences: the cost in terms of consumption of this same tax is greater than 2 percent. The mechanism through which this welfare loss arises is apparently a decrease in average productivity, since this policy results in a decrease in average productivity of over 2 percent.

Job Turnover and Policy Evaluation: A General Equilibrium Analysis

This paper considers the design of an optimal unemployment insurance system. The problem is modeled as a repeated principalagent problem involving a risk‐averse agent‐the unemployed worker‐and a risk‐neutral principal, which cannot monitor the agent's search effort. The optimal long‐term contract subject to the associated incentive constraints is characterized. This contract involves a replacement ratio that decreases throughout the unemployment spell and a wage tax after reemployment that, under some mild regularity conditions, increases with the lenght of the unemployment spell. Some numerical results are presented that suggest that the gains from switching to this optimal unemployment insurance scheme could be quite large. The performance of this optimal contract is also compared to alternative liquidity provision mechanisms.

/pdf/optimal-unemployment-insurance-15j9cuq8hf.pdf

Optimal Unemployment Insurance

We develop a general model of lending in the presence of endogenous borrowing constraints. Borrowing constraints arise because borrowers face limited liability and debt repayment cannot be perfectly enforced. In the model, the dynamics of debt are closely linked with the dynamics of borrowing constraints. In fact, borrowing constraints must satisfy a dynamic consistency requirement: The value of outstanding debt restricts current access to short term capital, but is itself determined by future access to credit. This dynamic consistency is not guaranteed in models of exogenous borrowing constraints, where the ability to raise short term capital is limited by some prespecified function of debt. We characterize the optimal default-free contract - which minimizes borrowing constraints at all histories - and derive implications for firm growth, survival, leverage, and debt maturity. The model is qualitatively consistent with stylized facts on the growth and survival of firms. Comparative statics with respect to technology and default constraints are derived.

/pdf/optimal-lending-contracts-and-firm-dynamics-d3rvotg96p.pdf

Optimal Lending Contracts and Firm Dynamics

We develop a model of vintage human capital in which each technology requires vintage-specific skills. We examine the properties of a stationary equilibrium for our economy. The stationary equilibrium is characterized by an endogenous distribution of skilled workers across vintages. The distribution is shown to be single-peaked. Under general conditions, there is a lag between the appearance of a technology and its peak usage, a phenomenon known as diffusion. An increase in the rate of exogenous technological change shifts the distribution of human capital to more recent vintages, thereby increasing the diffusion rate.

Hugo A. Hopenhayn

Papers

Entry, exit, and firm dynamics in long run equilibrium

Job Turnover and Policy Evaluation: A General Equilibrium Analysis

Optimal Unemployment Insurance

Optimal Lending Contracts and Firm Dynamics

Vintage Human Capital, Growth, and the Diffusion of New Technology