The Pennsylvania State University The Graduate School MODELING AND QUANTIFYING INDUSTRY DYNAMICS UNDER AGGREGATE UNCERTAINTY. A Thesis in Economics by

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1 The Pennsylvania State University The Graduate School MODELING AND QUANTIFYING INDUSTRY DYNAMICS UNDER AGGREGATE UNCERTAINTY A Thesis in Economics by Hâle Utar c 2006 Hâle Utar Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2006

2 The thesis of Hâle Utar was reviewed and approved by the following: James R. Tybout Professor of Economics Thesis Advisor, Co-Chair of Committee Edward J. Green Professor of Economics Co-Chair of Committee Nezih Güner Assistant Professor of Economics Co-Chair of Committee Abdullah Yavas Elliott Professor of Business Administration James Jordan Professor of Economics Acting Head of the Department of Economics Signatures are on file in the Graduate School.

3 Abstract In this thesis, I empirically investigate the selection process and the evolution of an industry in response to aggregate shocks. In the first essay (Chapter 2), I develop a new way to quantify the effects of import competition on intra-industry patterns of job creation and destruction and productivity. It is based on a dynamic stochastic industry model with monopolistically competitive product markets, heterogeneous firms, and endogenous entry and exit. First, Colombian panel data on metal product producers are used to identify the model s parameters. Then several counterfactual trade policy experiments are conducted. In addition to quantifying the effects of openness on job turnover patterns, the model delivers predictions on the associated changes in the aggregate productivity, the nature of the transition process when openness changes, and the role of hiring and firing costs in shaping firms responses. In the second essay (Chapter 3), which is co-authored with J. Tybout and R. Bond, we analyze the firm-level consequences of a crisis-prone environment in the presence of capital market frictions. Balance of payments crises and banking crises are common in developing countries. Often they feed off one another, creating dramatic swings in the real exchange rate, real interest rates, and expectations about regime sustainability. We quantify the effects of these crises on industrial sector productivity distributions, size distributions and borrowing patterns. To do so, we first develop an industrial evolution model in which capital market imperfections link firms ability to borrow to the wealth of their owners. Then we fit our model to firm-level panel data and macro data from Colombia that span the debtcrisis period of the 1980s. Finally, using the estimated parameters, we simulate industrial evolution patterns under alternative assumptions about the stochastic processes for exchange rates and interest rates. iii

4 Table of Contents List of Figures List of Tables Acknowledgments vi vii viii Chapter 1 Overview 1 Bibliography 5 Chapter 2 Import Competition and Employment Dynamics Introduction Related Literature The Model Overview Production Demand Aggregate States Incumbents Decision Problem Potential Entrants Decision Problem Equilibrium The Methodology to Solve the Equilibrium: The Colombian Metal Products Industry Estimation Estimation of Aggregate Shocks Estimation of Structural Parameters Preliminary Estimates Preliminary Simulation Results Concluding Remarks and Future Work iv

5 Bibliography Appendix Construction of Industry Specific Average Imported Goods Prices Chapter 3 Industrial Evolution in Crisis-Prone Economies Introduction The Model Aggregate Environment The Household Optimization Problem Non-entrepreneurial Households Owner Households Potential Owner Households Industry Evolution Estimation Estimating the Profit Function Estimating Markov Process for Aggregate Variables Estimating the structural parameters Estimation Strategy Estimates Simulation Experiments The Effects of Volatility Long run effects Transition The Effects of Credit Market Imperfections Directions for Further Work Bibliography 76 v

6 List of Figures 2.1 Nominal Tariff Rates for the Structural Metal Products Industry (SIC 3813), Source: DANE Average Import Prices in Metal Products, Source: NBER Wages in Colombian Metal Products, Source: DANE Employment Growth ( ), Source: DANE Evolution of Industry-wide Employment Evolution of Industry-wide Productivity Colombian Exchange Rates and Interest Rates, Source: DANE Simulated Exchange Rates and Interest Rates, Source: DANE Number of Plants Mean Profitability Shock Covariance of Size and Profitability Size-weighted Average Productivity Debt-to-Capital Ratios Among Small Firms Debt-to-Capital Ratios Among Large Firms Credit Market Imperfections and Productivity Distributions Credit Market Imperfections and Wealth Distributions vi

7 List of Tables 2.1 Moments Import and Export in Colombian Metal Products Industry Metal Products Industry( ) Job Creation and Destruction in Colombian Metal Prod. Ind Net and Gross Flows in the Sample Data Expanding and contracting Plants Parameters of the VAR models Estimated Cost and Demand Parameters for the Colombian Metal Products Industry Model Fit Transitional Dynamics The Long-Run Comparison of Relatively Open vs Relatively Closed Environment Long-Run Effect of Lower Import Prices The Role of Severance Payments Estimation of Aggregate Shocks (from quarterly data) Operating Profit Function Parameters, Colombian Apparel producers,level form Operating Profit Function Parameters, Colombian Apparel Producers, difference form Switching VAR Parameters Estimation Results, Colombian Apparel Producers The Steady State Effect of Credit Market Imperfections vii

8 Acknowledgments I gratefully thank James Tybout for advice and guidance and for his confidence in me. I gratefully thank Edward Green for fruitful discussions, financial support and his efforts towards the success of this research. I gratefully thank Nezih Güner for fruitful discussions, support and help on many occasions. I especially thank Susanna Esteban for her kind encouragement and support. Fruitful collaboration with Eric Bond is gratefully acknowledged. Thoughtful comments from Barry Ickes, James Jordan, Mark Roberts, Andres Rodriguez-Clare, Neil Wallace, and Ruilin Zhou are acknowledged with appreciation. viii

9 Dedication This study is dedicated to the beautiful memory of my sister, Lale Utar, and of my father, H. Fahri Utar. ix

10 Chapter 1 Overview Even in narrowly defined industries, producers exhibit a great deal of heterogeneity. Each experiences idiosyncratic changes to its productive capabilities and demand for its goods, and each reacts differently to industry-wide changes in the economic conditions. Some grow, others shrink, and the set of producers itself frequently changes. These patterns of growth, contraction, entry and exit affect the economy in a number of important ways. They help to determine average efficiency levels, they drive patterns of job creation and destruction, and they interact with patterns of wealth accumulation. This thesis develops dynamic empirical models that characterize each of these phenomena. While these evolutionary processes are universal, their specific features depend on the business environment in which they occur. In particular, they reflect prevailing rules and regulations in the labor market, credit market, and international trade. For example, when firms that shed workers face large severance payments, patterns of job reallocations across firms and the turnover patterns of firms themselves will be affected. Similarly, when regulations make it costly to create a new firm, turnover is likely to be dampened. And when credit markets function poorly, or the macroeconomic environment makes profit streams volatile, the types of entrants are affected. The models developed herein thus devote particular attention to the relation between features of the aggregate environment and industrial evolution patterns. The analysis focuses on developing countries, both because trade restrictions and labor market regulations are common there, and because macroeconomic

11 2 volatility has often been important there. In particular, the research is designed to shed light on the implications of trade policies, labor market policies, and debt crisis-related volatility in Colombia. Among other things, I analyze how trade liberalization, severance laws, and macroeconomic volatility have combined to influence patterns of job creation and destruction, total factor productivity growth, and patterns of capital formation. To perform the analysis described above, I draw on the industrial evolution literature (Hopenhayn(1992), Jovanovic(1982), Ericson and Pakes (1995)). In this literature, each firm has its own productivity or profitability level, and each forms expectations regarding future market conditions and makes its decisions accordingly. Firms decide to enter or exit endogenously considering the costs associated with starting up the firm, the scrap value of their firms and the expectations regarding the future industry-wide and/or firm specific conditions. Ericson and Pakes (1995) and Pakes and McGuire (1994) develop a dynamic industry model with imperfect competition but since the computational burden increases exponentially with the number of firms, their algorithm is only feasible for a very limited number of firms. Here, in the first essay, I use an approximation method which is inspired by Krusell and Smith (1999) and the monopolistic competition assumption so that I am able to compute the model with a large number of firms. This approach, which I follow in this thesis 1, allows one to correctly deal with several important policy questions concerning the industry s response to aggregate shocks and transitionary dynamics. 2 Estimation of industrial evolution models is a field still under development. In this thesis I use simulated method of moments estimator to identify the models structural parameters. 3 1 In the third chapter we abstract from the interaction among firms and assume exogenous prices. That is, we disregard the feedback effect in order to simplify the model. As a result, aggregate uncertainty does not create extra complications in that essay 2 In the third chapter we abstract from the interaction among firms and assume exogenous prices. That is, we disregard the feedback effect in order to simplify the model. As a result, aggregate uncertainty does not create extra complications in that essay 3 The general idea of simulated method of moments estimator (SMM) is similar to calibration. It is based on matching the data moments constructed from plant-level panel data with the model moments where expectations are replaced by simulations. That is, I use the industry outcomes as an observation in this approach. In terms of efficiency, there is room for further refinement in the estimation methodology.

12 3 After I fit the models to the data, I analyze transition dynamics, and study the effects of aggregate shocks on industry-wide productivity distributions, job turnover and investment patterns. I also study the effect of different market regulations on industry responses to different macroeconomic environments. To my knowledge, modeling and estimating/calibrating industrial evolution model with monopolistic competition and ability to deal with transitionary dynamics constitute methodological contributions. In the chapter Import Competition and Employment Dynamics I quantify the effect of greater trade openness on the selection process, job creation and destruction patterns and profitability of an import-competing industry. In the chapter I also look at how the aggregate productivity and patterns of job flows are affected by hiring and firing restrictions. In the last chapter, Industrial Evolution in Crisis-Prone Economies we examine how industrial evolution and particularly selection and growth processes are affected by an environment combined with macroeconomic volatility and borrowing constraint. Simulation results in both chapters confirm that selection has an important effect on aggregate productivity. Selection effect represents the change in the productivity of the industry or the economy that arises from reallocation of the productive resources, e.g. capital, labor, etc., between less and more productive firms. The productivity gain through selection occurs when the relatively more productive firms over-represent themselves in the productivity distribution, or similarly, when the relatively less productive firms under-represent themselves in the overall productivity distribution. An important source of selection is entry and exit of firms. The exit of firms of less than average productivity, or the entry of firms with higher than average productivity will improve the aggregate productivity of the industry. Another source of selection is through market share reallocation of incumbent firms. This is the same type of resource reallocation but between heterogeneous incumbent firms. That is, aggregate productivity of the industry will improve if more productive firms become larger and attain a higher market share than the relatively less productive firms in the industry. Previous empirical studies have shown that the productivity gain through se-

13 4 lection is a very important source of aggregate productivity. 4 In this thesis, by developing a dynamic structural industry model, I am able to relate the productivity gain through selection to specific policies and changes in macroeconomic environments. In chapter 2 the significance of macroeconomic volatility and the flexibility of firms in firing and hiring are identified as a possible explanation to cross country differences in responses to trade liberalization. In chapter 3 it is suggested that a crisis-prone environment may have important implications on investment behavior and productivity distribution when combined with imperfect borrowing opportunities. 4 Pavcnik(2002) finds that aggregate productivity grew 31.9% between 1979 and 1986 in import-competing sectors of which selection effect for about 2/3 of total productivity growth in her study on Chilean economy.

14 Bibliography [1] Krusell, P. and A. Smith (1998), Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy 106: [2] Hopenhayn, H. (1992), Entry, Exit and Firm Dynamics in Long Run Equilibrium, Econometrica 60(2): [3] Ericson,R. and A. Pakes (1995), Markov-Perfect Industry Dynamics: A Framework for Empirical Work, Review of Economic studies, 62, [4] Jovanovic, B. (1982), Selection and the Evolution of an Industry Econometrica 50(3), [5] Pakes, A. and P. McGuire (1994), Computing Markov-perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model, Rand Journal of Economics,25(4), [6] Pavcnik, N. (2002) Trade Liberalization, Exit and Productivity Improvements: Evidence from Chilean Plants, Review of Economic Studies 69,

15 Chapter 2 Import Competition and Employment Dynamics 2.1 Introduction With the increase in globalization, the effect of intensified foreign competition on job flows becomes a concern for policy makers. Openness and the associated changes in the macroeconomic environment induce changes in the job creation and destruction patterns and aggregate productivity of industries. The relationship between trade openness and the employment dynamics is still not well understood. This paper develops and estimates a structural dynamic industrial evolution model that characterizes the relationship between intensified import competition and employment dynamics using plant-level panel data. It also characterizes interactions between market openness, labor regulation and exchange rate regimes. The relationship between trade openness and employment dynamics depends on a host of country and external conditions.[36] Additionally, in developing countries, trade liberalization often comes with other market reforms such as reforming labor codes or moving towards more flexible exchange rate regimes. Further, they are typically implemented as a partial response to serious macroeconomic shocks. To quantify the impact of openness on a domestic

16 7 labor market and industry productivity, it is, then, necessary to consider the interplay between the country or time specific macroeconomic environment, labor market regulations and the tariff policy. In order to do that, a structural model is needed where the agents correctly perceive the macroeconomic structure and the other market conditions and incorporate these conditions in their decision making process. Such an approach will have the additional advantage of providing further insight into the cross-country differences in the effects of trade liberalization. To the extend that cross-country differences are caused by labor market regulations or the aggregate volatility that surrounds the country under study, a structural model must be able to correctly deal with aggregate uncertainty or macroeconomic structure while isolating trade effect from the other factors. 1 Although there is a significant empirical literature on the relationship between import competition and employment dynamics which gives valuable patterns of correlation between import penetration rate, exchange rate movements and job creation and destruction, 2 these studies lack the structural foundation to do counterfactual experiments and thus to isolate the role of different regulations and/or of aggregate environments. Here, I use an an industrial evolution model with monopolistically competitive product markets, heterogeneous firms, stochastic wages and import prices, start-up costs for new firms, and asymmetric hiring and firing costs. As the processes that drive real wages and import prices unfold, and as individual firms realize their productivity shocks, the set of active producers and their employment levels respond. Each agent behaves optimally, given his/her beliefs about the exogenous processes and the behavior of his/her competitors. In equilibrium, each agent s beliefs are consistent with the actual behavior of all others. Explicitly modeling dynamics in an industrial evolution context, 3 also allows 1 See for example Levinsohn (1999) who concludes to his study of trade reform in Chile, that it is difficult to separate the effects of macroeconomic shocks from the effects of trade liberalization. 2 Relevant references include but are not limited to Freeman and Katz (1991), Revenga (1992),Gourinchas (1999). 3 In industrial evolution models, firms are seen as a part of the environment under which they operate. Heterogeneous firms, modeled as firm-specific productivity (Hopenhayn(1992),

17 8 us to deal with the role of expectations on macroeconomic conditions and with interaction among firms, which may play a significant role in the outcome of trade liberalization. Recent empirical studies found substantial reshuffling of resources within narrowly defined industries following trade liberalization. 4 These findings imply that intra-sectoral firm heterogeneity is an important dimension of response to openness. Thus the presence of heterogeneity will play an important role in driving job creation and destruction within sectors. Then it is important to incorporate the heterogeneity and endogenous entry and exit decision of firms in order to better understand the dynamics of productivity and employment in response to heightened foreign competition. Motivated by the empirical findings, the recent theoretical trade models have departed from representative firm assumption and provided a framework to explain the productivity gain through market share reallocation among continuing forms as well as entry and exit. (e.g. Melitz, 2003, Bernard, Eaton, Jensen and Kortum, 2003, and Melitz and Ottaviano, 2005) The model developed in this paper can be thought of as a dynamic empirical elaboration of the above mentioned recently emerged trade models with heterogeneous firms in terms of productivity operating in an imperfectly competitive industry of horizontally differentiated products. The model developed here differs from these studies by giving insight into the transitionary dynamics and the long-run equilibrium under aggregate uncertainty. Another difference is that this study focuses on the the effect of the import competition in the product market. 5 Opening up to international trade may alter the patterns of resource reallocation among heterogeneous plants and may cause increased aggregate productivity and/or increased uncertainty about the persistence of jobs in the labor Javonovic(1982)), have expectations regarding the future conditions and they make their decisions accordingly. Firms decide to enter or exit endogenously considering the costs associated with starting up the firm, scrap value of their firms and the expectations regarding the future industry-wide and/or firm specific conditions. Once they are estimated or calibrated, these models also allows us to do counterfactuals to quantify the effects of different environments on the evolution of the industry such as productivity, size distributions, cross-firm patterns of correlation in employment expansion and contraction. 4 See for example Pavcnik (2002). 5 It abstracts from exporting behavior. Although exporting an important source of self-selection mechanism, incorporating export will be a future research agenda.

18 9 market. On the other hand the flexibility of the labor market is an important factor in achieving efficient allocation of resources. Many developing countries have heavy regulations on the labor market. In this paper, I quantify the extent of hiring and firing frictions as well as the effect of these frictions on the response of an industry to a change in the trade regime. This model builds on Hopenhayn (1992) with a differentiated demand system and introduces foreign competition in the product market as well as aggregate uncertainty. Due to the presence of aggregate uncertainty, estimation of this model is not straightforward because some of the industry-wide variables that affect firms profits average prices and the number of producers evolve endogenously in response to the decisions of incumbent producers and new entrants. To overcome this problem I solve for an approximate equilibrium in which these industry-wide variables follow a Markov process that is consistent with individual behavior. This approach is motivated by the recent literature on models with heterogeneous agents in which distributions are approximated by their finite moments (Krusell and Smith, 1998). Applied to the Colombian metal products industry, the estimates of the key parameters are very plausible. First, sunk entry costs amount to about 15 per cent of the average total sales. These are the costs that are associated with starting up a business, such as government imposed legal expenses, installation and customization costs, and product development. Second, per-period fixed costs are estimated to be about 8 per cent of the average value of total sales in the industry. Finally, hiring costs amount to about 3 months wages, and firing costs to about 4.5 months wages. The latter numbers are particularly encouraging since, during the sample period, Colombian law mandated severance payments amounting to one month s wage per year worked based on a salary at the time of separation. The preliminary simulation results based on these parameters show, among other results, that switching to a more liberal trade regime is associated with a significant reduction in the number of jobs in the short-run. This is consistent with the findings of previous econometric studies (e.g. Freeman and Katz 1991). A substantial fraction of the total reduction in jobs is due to net

19 10 exit. Thus the model provides a structural explanation for the stylized fact that significant job destruction takes place on the entry/exit margin, and it suggests that studies based on panels of continuing firms are likely to miss a fundamental type of job flow. There are also productivity gains associated with the switch to a more liberal regime because of the selection effect. This, too, is consistent with econometric studies that show productivity gains in the aftermath of a trade liberalization due to the exit of inefficient plants (e.g., Pavcnik, 2002). Contrary to the short-run predictions of the model, there is no permanent job gain associated with the relatively protected trade regime in the long run. The reason is that both import prices and wages are higher under the relatively closed environment. Further, there is more volatility in the tariff-adjusted exchange rate, so the job turnover rates are actually higher. These results contrast with the industry s response to the lower import prices in the long run. So the external conditions play an important role in understanding the response of the industrial sector to the changes in commercial policy. The results altogether establish the importance of the macroeconomic environment surrounding the country on the effectiveness of the trade liberalization Related Literature Numerous studies have investigated the link between increasing foreign competition and domestic labor market. Some describe patterns of association using industry-level data and conclude that employment declines with the increase in import competition. 6 Similar conclusions emerge from Freeman and Katz (1991), Revenga (1992), and Sachs and Shatz (1994), who use industry level regressions to relate import competition to employment. Focusing on production rather than jobs, Bernard, Jensen and Schott (2005) documents patterns of correlation between import penetration rates and industry-specific 6 For example, Kletzer (1998, 2000) regresses industry-specific worker displacement rates on import-penetration rates, Davidson and Matusz (2003) regress job creation and destruction data on sector-specific foreign trade indices.

20 11 rates of plant survival and growth. Other empirical studies analyze the effect of exchange rate fluctuations and tariff reductions on the net employment fluctuations and gross job flows in firm-level econometric studies. Klein, Triest and Schuh (2003) analyze the impact of the real exchange rate movements on gross job flows using establishment level panel data. They find that changes in the trend of the real exchange rate affect reallocation but not net employment. Gourinchas (1999) uses firm level data, and finds that exchange rate appreciation reduces net employment growth as a result of lower job creation and increased job destruction. On the other hand, Bentivogli and Pagano (1999) find a limited effect of exchange rate fluctuations on job flows for a number of European countries. My paper contributes to this literature with its ability to correctly deal with the interaction between the commercial policy and the macroeconomic shocks. Pavcnik(2002) points out the significance of reallocation effects in accounting for growth in productivity in the Chilean manufacturing sector following trade liberalization. She aggregates productivity levels across plants in a given industry and finds that market share reallocation from less to relatively more productive units accounts for about 2/3 of the total productivity gain. Similar conclusions also emerge from Bernard, Jensen and Schott (2003) in their study using U.S. plant-level data. My paper contributes this literature with providing underlying structure of evolution of industry to be able to do counterfactual experiments. Another way of studying the effect of openness on job flows is focusing on inter-sectoral job reallocation based on search theory in a general equilibrium set-up. Davidson, Martin and Matusz (1999) investigate the implications of labor market turnover on international trade patterns in a general equilibrium model of trade where jobs are created and destroyed at exogenous rates. They consider two symmetric countries in terms of endowment and production technology. Then the labor turnover becomes an independent determinant of comparative advantage and determines the trade pattern between the two countries. Chaudhuri and McLaren (2003, 2004) develop a dynamic trade model where workers are subject to moving costs. Similarly, Kambaurov (2003) analyzes the effect of firing taxes in inter-sectoral labor mobility

21 12 in a general equilibrium competitive search model. My paper focuses on the intra-industry selection processes, instead of between sectoral differences and comparative advantage effect. Finally, without looking explicitly at trade issues, some analysts have developed structural models that describe the dynamics of job creation and destruction in the presence of adjustment costs. This literature is particularly relevant because it deals with uncertainty, and in some cases, firm heterogeneity. Bentolila and Bertola (1990) develop a partial equilibrium labor demand model of a monopolist which faces a stochastic demand function and asymmetric hiring and firing costs. They find that firing costs do not have large effect on hiring decisions, and that high firing cost do not reduce the average level of employment. Hopenhayn and Rogerson (1993) develop a general equilibrium model with endogenous entry and exit, competitive product markets and no aggregate uncertainty. In contrast to Bentolila and Bertola (1990), they find that severance costs equal to one year s wages decrease average employment levels by about 2.5 percent. Veracierto (2001) introduces a flexible form of capital into Hopenhayn and Rogerson s framework and studies the short-run affects of the severance cost. He finds that incorporating capital does not affect the long-run consequences of severance payment but it creates differences in the short-run depending on the elasticity of substitution between the two inputs. Finally, Cooper, Haltiwanger and Willis (2004), in an effort to reconcile the different characteristics of aggregate and plant-level data, estimate the general functional form of adjustment cost which consists of fixed cost, disruption cost and the quadratic cost using plant-level data. My paper deals with the cost of adjustment in an environment where firms interact with each other, rather than they are being treated as independent identities. In this paper, I adopt an industrial evolution approach to analyze the patterns of job creation and destruction and productivity patterns in response to heightened import-competition. This allows me to incorporate entry and exit decision of firms, which account for a large portion of job flows in the industry I study. It also allows me to study role of the expectations in shaping firms decisions and to perform counterfactual experiments. Finally, unlike the exist-

22 13 ing industrial evolution models that focus on job flows, I allow for imperfect competition. The remainder of the paper is organized as follows: Section 2 and Section 3 respectively introduce the model and the methodology that is used to solve the model. As this model is applied to Colombian metal products industry, Section 4 introduces the environment that surrounds this industry. In Section 5 the estimation methodology and the estimation results are presented. Finally Section 6 presents and discusses a few simulation experiments that I conducted to assess the effect of openness with focus on the role of expectations in shaping firms responses and the role of labor market policies. Concluding remarks follow in Section The Model Overview Assume that agents are infinitely lived and make their choices in discrete time. Each period, the economy consists of a number of monopolistically competitive heterogenous domestic producers and a number of potential entrants. Each firm is assumed to produce a uniquely differentiated variety and faces a downward sloping demand function. The demand function depends on the firm s own price, the average price in the industry, and the number of varieties currently produced. 7 The demand function for each firm is derived from the quasi-linear preferences of a representative consumer,who values varieties regardless of whether they are domestically produced or imported. As a result, the demand schedule for domestic producers depends on the number and prices of imported varieties since these affect the total number of varieties and the average price. It is assumed that prices as well as the number of imported varieties move stochastically over time. Domestic producers take these stochastic processes as given. 7 This is monopolistic competition in the Chamberlin sense where firms consider themselves too small to affect the industry aggregates.

23 14 At each point in time, an incumbent firm s operating profits depend on several firm-specific variables: its current productivity level, its current employment, and its previous period employment. The latter variable matters because the firm faces hiring and firing costs. Each firm s profits also depend on two endogenous market-wide variables: average output prices for domesticallyproduced varieties and the number of domestic producers. Finally current profits depend upon three exogenous market-wide variables: wages, the number of foreign varieties in the market, and the average price of imported varieties, which in turn depends upon commercial/tariff policy and the exchange rate regime. Note that it is not necessary to know the joint distribution of firms in order to calculate a firm s current profits; knowing average prices and the number of market participants is sufficient. Nonetheless, it is necessary to keep track of this distribution because the transition density for average prices and numbers of participants depends upon the number of firms in each individual state. In addition to incumbents, the model also describes the behavior of potential entrants. These firms are identical up to the entry costs that they draw. Once they observe these costs, they compare them with the expected value of being an incumbent next period. When the expected value of being an incumbent is higher than the entry cost, they decide to enter the industry. Following the entry decision, entrants draw their initial productivity realization from a commonly known distribution, and start to produce the next period. For any period, the sequence of actions is as follows. First, before the realization of firm-specific and aggregate shocks, last period s incumbents who decided to exit pay their labor adjustment cost and exit. Then, both incumbents and potential entrants observe the current realization of aggregate shocks. Given the aggregate state of the economy and their individual states, incumbent firms make their employment decisions. Finally, potential entrants decide whether to enter or stay out for the next period. Those that enter draw their productivity and join to the next period s incumbents. Given this setting, different firms have different reactions to common industrywide shocks. One reason is that different firms face different demand elastici-

24 15 ties and have different probabilities of exit. The response of firms facing higher demand elasticities will be more sensitive to the shocks. Due to policy distortions (e.g. hiring and firing costs ) industry-wide response will also differ across positive and negative shocks. It will be more costly for larger firms to contract or to exit in response to negative shocks, similarly it will be more costly for small firms to expand. It is important to note at this stage that the evolution of the firm distribution is not trivial in this economy. At any point in time, the economy will be populated by incumbents that differ in their current productivity shocks and past employment. Given aggregate variables and aggregate shocks, each producer will decide on its current employment and its entry/exit decision for the next period. These decisions together with the entry of new firms will determine the distribution of incumbents next periods. Hence, although an individual firm is only concerned about the evolution of industry aggregates, the way these aggregates evolve reflects individual decisions. Methodologically, this paper is in the spirit of Krusell and Smith (1998), who find that a Markov process for the mean of the wealth distribution is enough to approximate the equilibrium in a stochastic growth model with heterogeneous households. 8 I compute the equilibrium by assuming that agents forecast the evolution of the aggregates using a technique similar to Krusell and Smith s (1998) Production Each firm has access to the same production technology, up to a firm-specific productivity shock. The firms only input is labor. Firm i s production technology is given by f(l) = e µ it l θ it, 0 < θ 1, (2.1) 8 Similarly Khan and Thomas (2003) in their paper which analyzes the role of nonconvex adjustment cost in aggregate investment dynamics in a stochastic general equilibrium model finds it is enough to approximate the equilibrium close enough using only the two moments of the distribution of plants over capital and productivity.

25 16 where l it denotes labor input, and µ it is the firm-specific productivity shock. The firm-specific shock is assumed to follow a first order AR(1) process given by µ it = a 0 + a 1 µ it 1 + ε µ, ε µ N(0, σµ). 2 (2.2) The transition density for the firm specific productivity is denoted by M(µ it+1 µ it ). In each period t, firms pay w t for each unit of labor that they employ. It is assumed that there is an elastic supply of labor and firms behave as price takers in the factor market. In addition to the unit cost of labor, firms incur a hiring cost, c h, per new employee, and a firing cost, c f, per dismissed employee. Firms also pay a fixed per period cost f Demand The demand side of the product market is characterized by the quasi-linear preferences of a representative consumer over horizontally differentiated varieties q i, (i {1,..N}), and a numeraire good, q o. The utility function of a representative consumer is given by N U(q o, q 1, q 2,.., q N ) = q o + α q i 1 N 2 γ qi 2 1 N 2 η( q i ) 2. (2.3) i=1 i=1 i=1 This utility function has been previously used by Ottaviano, Tabuchi, Thisse (2002) and Melitz and Ottaviano (2004). As opposed to CES type of utility functions it allows the price elasticity of demand to vary with respect to average price and the number of differentiated goods. The parameters α, γ, and η are all positive. Parameters α and η index the degree of substitution between the varieties and the outside goods, while γ indexes the degree of product differentiation among the varieties.

26 17 Utility maximization and aggregation over L consumers, gives the demand for each variety q i as, Lα q i = ( ηn + γ L γ p i + ηn ηn + γ where P is the average price of all differentiated varieties. L P ). (2.4) γ The number of varieties produced domestically is denoted by N D, and the number of imported varieties is denoted by N F, i.e. N = N D + N F. Hence where P = N DP D + N F P F N D + N F, (2.5) P D denotes the average price among the domestic varieties and P F denotes the average price of imported varieties Aggregate States Three aggregate shocks that appear in this model are real wages, w t, the average price of imported varieties, P F,t, and the number of imported varieties, N F,t. The number of imported varieties are assumed to be iid, 9 N F,t = N F + ε t, ε t N(0, σ 2 ε). (2.6) The average price of imported varieties, P F,t and the wages, w t, are summarized by a vector s t = ( P F,t, w t ), and they jointly evolve according to a first order Markov Process. The associated transition density is denoted by Φ (s t+1 s t ). It is assumed that, s t is independent of ε t. Finally, let Γ t be time-t distribution of incumbents over their idiosyncratic productivity shocks and last period s employment levels. 9 The shocks to the number of foreign varieties can also be interpreted as iid demand/taste shocks. This assumption can also be justified by assuming fixed costs for exporting and negligible share of the industry in the global economy. Notice that, although the number of foreign varieties is iid, the domestic consumers will consume more of imported varieties as the average price of imported varieties decreases and the import penetration ratio which is defined as the total value of import divided by the total value of domestic consumption will respond to the heightened import competition in the price margin.

27 Incumbents Decision Problem The current state of an incumbent firm is given by its current productivity shock µ it, its last period s employment l it 1, aggregate shocks s t and Γ t. Incumbents problem is to choose the price and the associated level of employment imposed by the technology and the exit decision for the next period. Let Γ t+1 = H(Γ t, s t ) be a transition function that maps current distribution and aggregate shocks to tomorrow s distribution. The function H reflects firmlevel decisions and will be correctly understood by all agents in equilibrium. Given m, Φ, and H each incumbent has a well-defined problem characterized by the following Bellman equation, V (µ it, l it 1 ; Γ t, s t ) = Max lit P i (Γ t, l it, µ it )e µ it l θ it w t l it c(l it, l it 1 ) f +βmax(ev (µ it+1, l it ; Γ t+1, s t+1 µ it, s t ), c(0, l it ))(2.7) subject to Γ t+1 = H(Γ t, s t ), and c(l it, l it 1 ) = Max{c h (l it l it 1 ), c f (l it 1 l it )}. Here P i (Γ t, l it, µ it ) denotes the inverse demand function that a firm faces as it is determined by equation (2.4). I make use of the fact that firm s output, q i, will be a function of µ it, l it, and Γ t. This optimization problem will generate two policy functions, one for employment, l it = e(µ it, l it 1 ; Γ t, s t ) (2.8) and one for the exit decision χ(µ it, l it 1 ; Γ t, s t ) = { 0 if EV > c(0, lit ) 1 otherwise (2.9)

28 19 For a given (Γ t, s t, l it 1 ), the exit decision χ will give a cut-off level of productivity µ it = µ below which the firm will choose the exit Potential Entrants Decision Problem Each period, there is an exogenous pool of R ex-ante identical potential entrants. Entrants pay their sunk entry cost, F, before entering the market. At the beginning of each period, each potential entrant draws its entry cost from a commonly known distribution, denoted by Ψ(F ) with positive support on [F L, F H ]. Upon drawing an entry cost, each potential entrant decides whether to enter the market next period and pay the entry cost. Once the entry decision is made, entrants draw their productivity from a commonly known distribution denoted by M 0 (µ). Potential entrants make their entry decisions given the current market states, given the transition density for the initial productivity draws. Given an incumbent s problem defined in (2.7), each potential entrant s problem is given by subject to V E (Γ t, s t M 0 ) = βev (µ i,t+1, 0; Γ t+1, s t+1 ) (2.10) Γ t+1 = H(Γ t, s t ) It is assumed here that potential entrants enter with the level of employment which maximizes their expected value. Potential entrants will choose to enter if V E (Γ t, s t M 0 ) > F. (2.11) Condition (3.8) determines the number of entrants, denoted by E t = Ψ(V E t )R. (2.12)

29 Equilibrium Given M, M 0, Φ, Ψ, and H an equilibrium is a value function V for incumbents, a value function V E for potential entrants, and a set of decision rules e(.) and χ(.) such that 1. Given M, Φ, and H each incumbent solves (2.7) and the resulting decision rules are given by e(.) and χ(.). 2. Given V and H, V E characterizes the problem of potential entrants. 3. H is consistent with firm s optimal decision rules. 2.3 The Methodology to Solve the Equilibrium: The endogenous state variable of this economy, Γ t, is a high-dimensional object. To overcome the problem of dimensionality, I use the fact that an individual firm is concerned only with s t and with two industry aggregates, ] the number of producers N t, and the average price P t. Let m t = [P t N t denote these industry aggregates, and let H be a Markov chain on m t. Then, we can define the following dynamic programming problem for an incumbent: V (µ it, l it 1 ; m t, s t ) = Max lit P i (m t, l it, µ it )e µ it l θ it w t l it c(l it, l it 1 ) f + βmax(ev (µ it+1, l it ; m t+1, s t+1 µ it, s t ), c(0, l it )) subject to m t+1 = H(m t, s t ), and c(l it, l it 1 ) = Max{c h (l it l it 1 ), c f (l it 1 l it )}. We can redefine the potential entrants problem in a similar fashion.

30 21 In this alternative formulation, agents only use the information provided in H. Although an individual firm is only concerned with s t and m t and how these evolve over time, at any point in time the economy is characterized by a distribution of incumbents over their firm-specific productivity shocks and the last period s employment levels. Given Γ t and H, there are two aggregations in this approximate economy. First, given s t, m t and H, firms decisions determine an average price level for the current period. Let g(γ t, H, m t, s t ) denote the mapping from firm decisions to endogenous industry aggregates. The function g contains the information on spot market clearing that determines the average price level. In equilibrium we need the following fixed point condition m t = g(γ t, H, m t, s t ), t. Second, given m t, s t and H, there is a map from Γ t to Γ t+1. Let Γ t+1 = f(γ t, m t, H, s t ) denote this map. Hence, in equilibrium H must be consistent with f. The approximate equilibrium is solved using the following algorithm: 1. Choose number of grid points for P t and N t. 2. Guess H as a Markov process on P t and N t. 3. Given H, solve the incumbents and potential entrants optimization problems. 4. Use the resulting decision rules, simulate the industry over a long period, and generate the time series for the evolution of P t and N t. In order to simulate the economy, start with an initial Γ 0 and m 0. Using the optimal decisions update Γ t for t > 0. Furthermore, at each period t check if m t = g(γ t, m t, H, s t ) is satisfied, i.e. P t is determined by spot market clearing. 5. Use the stationary region of the time series to update the transition density, H. This is achieved by calculating the number of times the economy moves from (P i, N j ) to (P k, N k ) over a long period, and using this information to determine the relevant entries of H. 6. Check if the updated and old H are sufficiently close, if not return to step 3.

31 2.4 The Colombian Metal Products Industry 22 I estimate the model using data from Colombian structural metal product industry (SIC 3813) for the period 1977 through The choice of this particular country is motivated by data availability, and by the fact that Colombia is a small open developing country that has experienced significant swings in its foreign trade and exchange rate policies. Accordingly, it provides a natural candidate to study the firm-level consequences of trade related shocks. In this section, I describe the Colombian structural metal product industry and the macroeconomic environment surrounding this industry. At the beginning of the sample period, Colombia had a fairly liberal trade environment. In 1980, the average nominal tariff on manufacturing goods was about 26 per cent, and almost 70 per cent of all commodities did not require import licensing. 10 However, the economy became more protectionist after it suffered a severe economic crisis in the early 80s. In 1984, 83 per cent of all commodities required licences, and imports of some products were prohibited. The evolution of the nominal tariff rates and import prices for this industry is given in Figures 2.1 and 2.2. The period can be easily recognized in these figures. During the sample period, i.e. from , the average nominal tariff for the 4-digit metal products industry was about 30 per cent. Average nominal tariff rates fell to 19 per cent with the trade reforms in The Colombian labor market was considered rigid during the sample period. Employers were mandated to pay severance payments which amounted to one month salary per year worked based on the salary at the time of separation. Workers had the rights to advance payments of the amount they would potentially receive in case of a job break, with the restriction that the advance payments be used for education or housing. In case of a job break the advanced amounts were subtracted from the severance payment in nominal, not real, terms.[28] In the case of a voluntary quit, employers still were required to pay seniority premium. Colombia reformed its labor codes in After 1990, the fixed cost of firing were replaced with a monthly contribution to 10 For a more detailed discussion of the trade environment of the country, see Fajnzylber and Maloney (2000).

32 23 a capitalized fund, which would be accessible to the worker only in the case of separation. Moreover, the 1990 reform widened the legal definition of just cause dismissals to include economic conditions. 11 The metal products industry is an import-competing industry consisting mainly of small scale firms. 12 On average there are about 160 plants during the sample years, producing a range of metal products such as metal door handles, window frames, bolts, metal curtain walls, etc. These products are mainly used in construction. The assumption of horizontal differentiation is especially suitable for the metal fabrications used in architectural design, such as metal curtain walls or door handles. Although more structural metal fabrications such as metal sheets and bolts have similar standards, locational differences between the plants provide one dimension of differentiation. 13 On average, the plant turnover rate was about 23 percent per annum, and new entrants accounted for about 15 percent of the total output. High entry and exit rates suggest low barriers to entry, and thus support my assumption of monopolistic competition. The industry also exhibits very significant import penetration rates during the sample period. Table 3.2 reports the ratio of the M total value of imports to total domestic consumption, i.e., where Q, X, Q X+M and M denote the value of domestic production, the value of exports and the value ( of imports, ) respectively. Notice that in contrast, the export-orientation rate is quite low which allows me to ignore the export decision of X Q X+M firms in the model. In order to be able to talk about job flows in the sample data, I need to 11 See Kugler (2005) and Heckman and Pages (2000) for more details on the labor market regulations in Colombia. 12 The average number of employees was 36 during the sample years. 13 Product description of the industry 3813 as quoted from United Nations Statistic division, is the following: Manufacture of structural components, steel or other metal, of bridges, tanks, smoke stacks and buildings; metal doors and screens, window frames and sashes, metal staircases and other architectural metal work; metal sections for ships and barges; boiler shop products; and sheet metal components of buildings, stovepipes and light tanks. The assembly and installation at the site of pre-fabricated components into bridges, tanks, boilers, central air conditioning and other sheet-metal systems by the manufacturer of these components which can not be separately reported, is to be included in this group, along with the main manufacturing activity.

33 24 introduce some notation. Let L t be the total employment in the industry at period t. Let E t 1 and E t be the total number of employees in all expanding incumbent plants for the period t 1 to t, and similarly, let C t and C t 1 be the total number of employees in all contracting plants. Finally, let B t be the total number of employees in all entrants at period t, and let D t be the number of employees in all exiting plants. Then the net employment growth, ( Lt L t 1 ), can be decomposed into four parts, ( L t Et E t 1 = + B ) ( t Ct 1 C t + D ) t 1, L t 1 L t 1 L t 1 L t 1 L t 1 where the first bracketed term is job creation rate, and the second bracketed term is job destruction rate. Job creation has two sources: job creation that comes from expanding plants (E t E t 1 ),and that comes from entrants (B t ). Similarly, job destruction has two sources: from contracting plants, (C t 1 C t ) and from exiting plants, (D t 1 ). The summation of these four components is called the gross job flow. Table 2.4 shows evolution of these four components in the data and Table 2.5 shows the gross and net flows. The first thing to notice is that both net and gross employment flows fluctuate significantly. Gross job flows are also very large, averaging about 48 percent during the sample period. Furthermore, gross job flows from entry and exit dominate those from expansion and contraction in all but one sample year. So the data confirm that gross job flows are predominantly determined by the entry and exit of plants, therefore it is preferable to build a model based on entry and exit decisions of firms. In the crisis year of, 1983, there is a significant decline in the net employment, and most of the job destruction occurs on the exit margin rather than contraction. Following two years when the level of protection increased, we see net employment growth. This time, most of the action comes from the entry margin. 2.5 Estimation The model described above involves two types of parameters those that can be identified with macro data alone, and those that must be estimated with

34 25 plant-level panel data. My estimation thus involves two stages. First, I estimate a regime-switching VAR process for the exogenous macro variables, then I estimate all of the remaining parameters using a variant of generalized method of moments, (GMM). Details are provided below Estimation of Aggregate Shocks Changes in trade policy affect firms within an industry by affecting the prices of the imports, they compete with, and by affecting the factor prices, they face. The first task is to estimate the transition density for these two variables, Φ (s t+1 s t ). 14 During recent decades Colombia has experienced frequent crises, and the real exchange rate has undergone large swings. 15 Between 1977 and 1998, it also experienced a radical change in its tariff policies, major trade liberalization in These dramatic shifts lead me to choose a specification for Φ (s t+1 s t ) that allows for regime switching (e.g., Hamilton, 1994). The main motivation of the regime-switching VAR process is the possibility that the process could change again in the future since it has changed in the past. That is, the rational agents take the structural breaks into account when they forecast. So these changes in the regime can be thought as a random variable rather than deterministic events. The Markov-switching VAR modelling approach also allows the analysist to estimate transition probabilities governing the changes from one regime to another. So the deterministic case can be modeled as an extreme case where the second state is an absorbing state. The general idea behind switching models is that the parameters of the stochastic process are time-varying but constant conditional on an unobservable regime variable, r t. In particular, Hamilton (1990) proposed the idea of Markovian regime shifts. Estimation amounts to recovering the parameters that describe the stochastic process behind each regime together with the transition probabilities that characterize Markovian transition between 14 The details of constructing average import prices are given in the appendix. 15 See Bond, Tybout and Utar (2005) for a discussion about the Colombian macroeconomic environment. 16 Figure 2.3 and Figure 2.2 show the evolution of the industry-specific real wages and the average import prices during 1977 and 1998.

35 26 regimes. I estimate both linear VAR without allowing regime switching to constitute a base case and Markov-switching vector autoregressive models. Assuming that at any point in time, the economy is in one of the two regimes, the Markov-switching VAR model parameterizes the two regimes as (β r o, β r 1, Σ r ). When regime r {1, 2} prevails, s t = [ P F,t, w t ] evolves according to s t = β r o + β r 1s t 1 + ɛ r t, where E(ɛ r t ɛ r t ) = Σ r. Switches between regimes are governed by the transition matrix [ ] p11 p 12 Π =, p 21 p 22 where p ij, i {1, 2} is the probability of moving to regime j, given that the economy is currently in regime i. Notice that one can impose restrictions by allowing only intercept, or intercept and autocorrelation coefficients to be regime dependent. I estimated different model specifications from general (regime dependent intercept, autocorrelation coefficients and covariance matrix) to more restricted ones (regime dependence in some/none of the parameters). The likelihood ratio tests lead me to choose the Markov-switching vector autoregressive model with regime dependence in intercept and autocorrelation parameters. Using the Expectation Maximization Algorithm (the EM algorithm) 17 which is described in Hamilton (1994) I obtain the maximum likelihood estimates reported in Table Data on import prices and wages are available annually for 1977 through 1998, so I use this entire time period rather than limiting the analysis to the plant-level sample years. 19 The significantly higher log like- 17 The EM algorithm is first introduced by Demster, Laird and Rubin (1977) and it is designed for a general class of models where the observed time series depends on some stochastic unobservable variables. 18 I use the Ox Console MSVAR software package developed by Hans-Martin Krolzig. Details are available at on-line at: 19 Number of degrees of freedom is low in this estimation because of the data limitation. Monthly or quarterly data on import prices are not available. However, one can use exchange rate series to construct the import prices. I presented the results with the quarterly data with constructed import prices. In Table 2.14, I compare the model where all the parameters are regime dependent with one where I restrict the covariance matrix being independent from the regimes. Both log

36 27 lihood of Markov switching model indicates that this model performs better than the simple VAR, so hereafter I will focus on the Markov-Switching VAR results. However, because of the existence of nuisance parameters under the null hypothesis, the usual likelihood ratio test does not have a standard distribution. Davies (1977) derived an upper bound for the significance level of the likelihood ratio test statistics under nuisance parameters. In Table 2.7, I reported Davies statistic which is applied to test the null hypothesis of linearity (simple VAR) against the alternative of the Markov-switching model, it also indicates that simple VAR can be rejected in favor of Markov-switching VAR with two regimes. The estimated parameters indicate that in the first regime, import prices are lower and stable with lower wages. This corresponds to the period after The second regime picks up the period between 1984 and 1990, where both import prices and wages are higher with significant ups and downs in the average imported goods prices (see Figure 2.2 and Figure 2.3 for the actual series). 20 Below I refer to these regimes as relatively open and relatively closed respectively. 21 The transition probabilities also indicate that both regimes are highly persistent (The probabilities of staying in the same regime for regime 1 and 2 are.92 and.83 respectively) and there is higher probability of switching from regime 1 (relatively open regime) to regime 2 (relatively closed regime) Estimation of Structural Parameters As a first step, I normalize the lower bound of the distribution of sunk entry cost F L to zero. Furthermore, I assume that entrants draw their initial productivity from a lognormal distribution with mean z which is to be estimated and the variance σ 2 µ/(1 a 2 1). That is, I let entrants draw from likelihood and Davies favors the second model where all parameters are regime dependent. Future research is necessary for further refinement. 20 The average log price and log wage are about 4.29 and 4.16 respectively in the first regime and about 4.90 and 4.30 in the second regime 21 Based on the smoothed regime probabilities, the regime classification for the MSIAH model estimation is the following: Between 1978 and 1983 regime 1 is prevails with probability 1; between 1984 and 1990 regime 2 is prevails with probability.9994; and between 1991 and 1998 regime 1 is prevails with probability.9863.

37 28 a distribution which might differ from incumbents productivity distribution in mean. This leaves me with 13 parameters to estimate. They are the cost parameters, (F H, f, c f, c h ), demand parameters, (α, η, γ), parameters of the production function and productivity process for incumbents and entrants, (θ, a 0, a 1, σµ, 2 z) 22 and the foreign market parameter, (σε). 2 Given the stochastic processes for the aggregate shocks, I use the model to estimate remaining parameters. To estimate the remaining parameters, I embed the dynamic stochastic model defined above in a method of moments estimator. That is, I choose the set of parameters, [ ] FH f c f c h α η γ θ a 0 a 1 δ = σ 2 µ σ 2 ε z, (2.13) that minimizes a measure of distance between moments implied by model simulations and their sample counterparts. This is called a method of simulated moments estimator or simulated minimum distance estimator which is first proposed by Lee and Ingram (1990) in a time series model, then Duffie and Singleton (1993), Hall and Rust (2003) (simulated minimum distance estimator ), Gourieroux, Monfort and Renault (1993) (indirect inference). For any given parameter combination δ, I construct the distance measure as follows. First, using the candidate parameter vector and the estimated values for all of the other model parameters, and the initial set of beliefs on the evolution of market aggregates, I numerically solve for the value functions (2.7) & (2.10). Using the method described above I update the transition densities for the evolution of industry states and solve for the new value functions with updated transition densities until I reach an equilibrium with self-fulfilling expectations. Then, using the policy functions in combination with randomly drawn aggregate shocks (P F t, N ft, w t ), firm-level productivity shocks (µ it ), 22 There is also R which is the number of potential entrants that are giving entry decision at each period. I fixed this number in the estimation to 65, a value which is significantly bigger than the maximum number of entrants that I observe in the sample data. Fixing R to different numbers does not affect the results as long as this number is not finding. Identifying R would be difficult as the likelihood function would be too flat with respect to entry cost, F H, and the number of potential entrants, R.

38 29 and entry costs (F ), I repeatedly (50 times ) simulate patterns of industrial evolution. 23 I average over these simulations to construct the model moments. In the simulations, I use the same set of randomly drawn errors. Finally, I calculate the measure of distance between the sample and simulated moments as, X(δ) = (d m(δ)) W (d m(δ)), (2.14) where d and m denote the data and model moments respectively, and W is a conformable matrix of weights. I use pattern search methods in the minimization routine. 24 Any weighting matrix which is positive semidefinite will give consistent estimates. However due to efficiency concerns, I calculate the weighting matrix by bootstrapping the data. Bootstrap treats the sample data as if they were the population. So I resample the data 500 times. To do that, I assign a plant id to each plant in the original sample. Then I randomly select the observations from the original data with replacement. If a plant is chosen in a particular year then I added the entire time series for this plant to the new sample, so the resampling is random across plants but not across time. Simulation based estimators are useful especially for models where the likelihood function is intractable or impossible to formulate. However, one disadvantage is the lack of a formal selection criterion for the appropriate set of moments, or the auxiliary parameters. The table below gives the 21 moments/statistics that are used in the estimation. Since I am especially interested in matching the employment characteristics of the data, more than half of the moments are employment characteristics of the industry including mean of job creation through entry, job creation through expansion of existing firms, 23 The asymptotic variance of the SMD or SMM estimator is multiplied by a factor (1+1/S) where S is the number of simulations. That means that there is an efficiency gain of running additional simulations because it reduces the variance of the estimator. When you compare the variances where you let the number of simulations go to infinity with the one where you use only one set of simulation, you will get a twice as large variance. This increase in the variance might be small in comparison the benefit that comes with the significant reduction in the computational burden as noted by Hall and Rust (2003). So some researchers even use just one set of simulation. 24 For a detailed review and the proof of convergence of patternsearch methods, see Kolda, Lewis, Torzcon (2003).

39 30 Table 2.1. Moments Mean Job Creation comes from Entry Mean Entry Rate Variance Log Employment Mean Job Creation comes from Expansion Variance Entry Rate Mean % of Plants with No Change in Emp. Mean Job Destruction comes from Exit Mean Exit Rate Covariance of Emp. Growth & Log Profit Mean Job Destruction comes from Contraction Variance Exit Rate Covariance of Log Emp and Log Profit Mean Employment Growth Mean Log Profit Mean Number of Plants Variance Employment Growth Variance Log Profit Variance Number of Plants Mean Import Penetration Rate Mean Log Employment Covariance of Lagged LogEmp &LogEmp job destruction through exit, job destruction through contraction of existing firms. In addition to that, I use general industry characteristics such as entry and exit rates, the number of operating firms, operating profits in order to be able identify parameters such as entry cost, and fixed costs. In order to identify hiring and firing costs and the persistence of the productivity parameter I use three covariance moments Preliminary Estimates Table 2.8 reports the preliminary estimation results for the structural parameters. Standard errors are created using the bootstrapped covariance matrix. I estimate the upper bound for the distribution of sunk entry cost, F H, to be 5,786,900 peso. 25 Since I normalize the lower bound of the distribution to be 0, this estimate pins down the mean sunk entry cost which amounts to 2,893,50 pesos ($US 61,562). This cost amounts to 14.5% of the average value of total sales in the industry. The sunk entry cost covers all the costs that are associated with starting-up a business and that cannot be recovered upon exit. These include government imposed legal costs, installation and customizing costs, and opportunity cost of managerial time during the set-up period. The per period fixed cost f is estimated to be 1,234,900 pesos ($US 26,276 ). Since there is no capital in the production function, this cost reflects all the cost paid to fixed capital and the other per period fixed expenditures which are paid regardless of the production level, such as insurance and mortgage 25 All values are in 1977 pesos if expressed in pesos or in 1977 USD if expressed in dollar.

40 31 payments. (This cost amounts to approximately 8.5% of the average value of total sales.) Hiring costs (c h ) are estimated to be 16,000 pesos ($US 340), which amounts to approximately 3 months wages, while firing costs (c f ) are estimated to 23,200 pesos ($US 493), or 4.5 months wages. Hiring costs cover all the advertising and recruitment expenditure associated with hiring workers as well as the training costs for the new employee. Probably the most significant component of the firing cost is the severance payment imposed by the government policies. Before the labor market reform in 1990, the severance payment amounted to one month s wage per year worked based on a salary at the time of separation. Estimated productivity process parameters indicate that the productivity process is persistent, (the root is approximately.9), with variance,.10. The high persistence of productivity mitigates the effect of hiring and firing costs on firms employment decisions. The mean value for the entrants productivity distribution is estimated.98. This estimate indicates that entrants are on average less productive than the overall average. In the estimation, I fixed the market size, which is the multiplicative term in the equation (2.4) to be With this normalization, the estimate of α is 5475 and that of η is Parameter γ, which is the index for the substitutability, is This estimate gives the slope of the demand curve that each domestic firm faces which is about Table 2.9 shows how well the model performs in fitting the data. The model performs very well in matching entry and exit rate, operating profit and sizes, as well as job flows. It does not do a good job in matching import penetration rate, mainly because I fixed the number of varieties to an arbitrary number, which is I will add this parameter into the estimation process in later versions. 26 This is just a normalization, since this term is unidentifiable. 27 The average number of domestic varieties during the sample period which is implied by the model is 160.

41 Preliminary Simulation Results Given all the estimated parameters, I next conduct several experiments to quantify the effects of changes in the economic environments on the importcompeting industry. First, I use the estimated switching model to simulate industrial evolution and job flow patterns in an environment that bumps stochastically between the relatively inward-oriented and the relatively open regime. That is, firms correctly perceive the current regime, the regime-specific transition densities for the macro shocks, and the transition density for the regimes reported in Table 2.7. The first step in this exercise is to discretize the two VAR processes identified as two regimes in the MSIAH model, using the methodology described in Tauchen and Hussey(1991). Then, using the discretized version of the MSIAH model, I solve the industrial evolution model and find the equilibrium transition density for industry aggregates as well as the optimal decisions. Finally, given the simulated path for the aggregate shocks, I simulate 250 trajectories for the industry and take the averages over those trajectories. The exercise I report in Table 2.10 compares average industry characteristics during the period corresponds to the relatively open regime with average characteristics during the relatively closed regime. Thus, for both types of statistic, I am describing performance in the aftermath of a regime switch rather than the long run effects of keeping an industry in a single regime indefinitely. This comparison will give insights into the short-run, transitionary dynamics of the model. The model predicts that switching to the liberal regime is associated with a significant (29 percent) reduction in the number of jobs, which is consistent with the reduced-form econometric studies reviewed in section 1 (Table 2.10). 28 The number of active firms also drops by roughly 30 percent, so a substantial fraction of the total reduction in jobs is due to net exit. Thus the model provides a structural explanation for the stylized fact that significant job destruction takes place on the entry/exit margin, and it suggests that 28 The predicted total employment for the regime 2 is 6305, and it falls to 4472 in the short-run (mean employment in data during the sample period is 6279)

42 33 studies based on panels of continuing firms are likely to miss a fundamental type of job flow. Because exit takes place disproportionately at the low end of the productivity distribution, there are also productivity gains associated with the switch to a more liberal regime. More precisely, productivity increases by 31 percent on average. This, too, is consistent with econometric studies that show productivity gains in the aftermath of a trade liberalization due to the exit of inefficient firms (e.g., Pavcnik, 2002). Together, these results confirm that the model I have developed is capable of replicating the patterns of correlation familiar from other studies. But given that I have modeled the underlying structure that generates these patterns, it is possible to perform counterfactual experiments. One interesting exercise is to compare two hypothetical economies one permanently stuck in a liberal regime, and one stuck in a protected regime. That is, now the probability of changing regime is zero, so the agents perceive each regime as permanent. The industry level results of this exercise are reported in Table Notice that there is no significant job gain associated with protection, even though we are limiting our attention to an import-competing industry. The reason is that, in addition to higher output prices under the protected regime, wages are higher too. Further, there is more volatility in the tariff-adjusted exchange rate, so the rates of job turnover are actually higher both because of higher turnover in the number of plants, and more contraction and expansion among continuing plants. Hence, if the pattern of association between volatility and protection that emerges in Colombia is typical of developing countries, it is not necessarily in the long run interests of workers in import-competing sectors to lobby for protection. In order to isolate the role of commercial policy from the associated macroeconomic environment, I compare the two economies with the differences in the mean of import prices but otherwise the same stochastic process for the aggregate shocks. The simulation averages of the industry level results of this exercise are reported in Table 2.12.

43 34 Lower import prices cause lower level aggregate employment and lower average profit. Intensified foreign competition also increases mean gross flows and the mean firm turnover. This experiment shows the importance of macroeconomic environment in response to commercial policy. Another interesting question that has received considerable attention in the literature is the role of labor adjustment costs. Table 2.13 reports the simulation averages of the industry aggregates in the economy when the firing costs are removed. The immediate effect of eliminating firing costs is to increase the rate of job destruction. But it also increases the hiring propensity of firms, and the net effect is positive with about 6 percent increase in the aggregate employment. Removing firing costs also increases the firm turnover by about 1 percent. The productivity increase is about 1.5 percent. There are two sources of this productivity gain. One is that increased turnover rate and the other is the market share reallocation among incumbents. Firing costs distort efficient market share reallocation as it delays the response of firms to the changes in productivity levels. These findings are in line with those of Hopenhayn and Rogerson (1993). Let us consider the importance of firing costs in the transition process. Figure 2.5 and Figure 2.6 show the evolution of the aggregate employment and aggregate productivity respectively in the regime switching environment. I use the Markov Switching VAR process in these figures. The sudden decline in the aggregate employment and the associated big jump in the aggregate productivity is due to the transition to the relatively open regime. Aggregate employment follows a more volatile path as expected when there are no firing costs. When there are firing costs, firms adjustment is more dominated by exit rather than adjustment in size in the transitionary period. This is reflected in Figure 2.6. The productivity gain in the economy with firing costs, which mainly stems from exit of firms, is higher than the productivity gain in the economy without firing costs, which mainly stems from adjustment in size. This finding provides a rationale for the common practice of developing countries to reform their labor market codes before lowering trade barriers.

44 2.7 Concluding Remarks and Future Work 35 In this paper I build a dynamic industrial evolution model with import competition where heterogeneous firms adjust their employment levels in response to each others behavior and to the degree of foreign competition. Counterfactual experiments establish the link between the macroeconomic environment and the response of the industry to greater openness. In particular, the industrial sector response depends on the macroeconomic volatility and the expectations to the regime sustainability as well as the underlying labor market policies. Exporting opportunities becoming available with trade liberalization is one important channel in the selection process. Relatively efficient firms in the domestic market gain access to the foreign markets and increase their market. In this paper I do not consider export and apply this paper to an industry where firms mostly serve the domestic industry. Adding export to the model is one important future extension envisioned. Productivity gain in the model comes only from selection, which is empirically shown to be a very important source of the aggregate productivity after trade liberalization. But another channel which might also be important is intrafirm productivity gain. It would be interesting to add the possibility of intrafirm productivity gain, through e.g. technology adoption. One other valuable extension would be the incorporation of capital into the model. In general, falling tariffs and exchange rate movements alter the relative prices of capital and labor, and might change the substitution patterns between labor and capital.

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47 38 [21] Hopenhayn, H. (1992), Entry, Exit and Firm Dynamics in Long Run Equilibrium, Econometrica 60(2): [22] Hopenhayn, H. and R. Rogerson (1993), Job Turnover and Policy Evaluation: a general equilibrium analysis, Journal of Political Economy 96: [23] Kambaurov, G. (2003), Labor Market Restrictions and the Sectoral Reallocation of Workers: The Case of Trade Liberalizations, Mimeo: University of Toronto. [24] Khan, A. and J. Thomas (2003), Nonconvex factor Adjustments in Equilibrium Business Cycles Models: Do Nonlinearities Matter?, Journal of Monetary Economics 50: [25] Klein, Triest and Schuh (2003), Job Creation, Job Destruction and real Exchange Rate, Journal of International Economics, 59: [26] Kolda, T.G., R. M. Lewis, and V. Torczon (2003), Optimization by direct search: New perspectives on some classical and modern methods, SIAM Review, 45: [27] Krusell, P. and A. Smith (1998), Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy 106: [28] Kugler, A. D. (2005), Wage-shifting effects of severance payments savings accounts in Colombia, Journal of Public Economics 89: [29] Levinsohn, J. (1999), Employment responses to international liberalization in Chile, Journal of International Economics 47: [30] Melitz, M. and G. Ottaviano (2005), Market Size, Trade and Productivity, NBER Working Paper # [31] Melitz, M. (2003), The impact of trade on intra-industry reallocations and aggregate industry productivity, Econometrica 71: [32] Ottaviano, G., T. Tabuchi, and J. Thisse (2002), Agglomeration and Trade Revisited, International Economic Review, 43: [33] Pavcnik, N. (2002) Trade Liberalization, Exit and Productivity Improvements: Evidence from Chilean Plants, Review of Economic Studies 69, pp

48 39 [34] Revenga, A. L., (1992), Exporting Jobs? The Impact of Import Competition on Employment and Wages in U.S. Manufacturing, Quarterly Journal of Economics 107, [35] Revenga, A. L., (1997), Employment and Wage Effects of Trade Liberalisation: The Case of mexican Manufacturing, Journal of Labor Economics, 15, [36] Rodriguez, F., and D. Rodrik (2000), Trade Policy and Economic Growth: A Skeptic s Guide To The Cross-National Evidence,, Working Paper. [37] Sachs, J.D., H. J. Shatz (1994), Trade and Jobs in U.S. Manufacturing, Brooking Papers on Economic Activity 1994, 1-65 [38] Tauchen, G. and R. Hussey (1991), Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models, Econometrica, 59: [39] Veracierto, M. (2001), Employment Flows, Capital Mobility and Policy Analysis, International Economic Review 42: Appendix Construction of Industry Specific Average Imported Goods Prices International trade data which is available online as the part of the NBER Trade Database is used to construct the average imported goods prices for the Colombian structural metal product industry. 29 This requires matching SIC (standard industrial classification)code for the industry under study with the SITC (standard international trade classification)codes of the products and constructing the group of products which are produced in this industry. The prices in the data set are in terms of dollar but they are reported by 29 The dataset covers the years , and is constructed from United Nations trade data by Robert Feenstra and Robert Lipsey, under a grant from the National Science Foundation to the NBER.

49 40 the importing country, Colombia. So exchange rate pass-through, if any, is already included in these prices. 30 Price series are converted into peso using Colombian nominal exchange rate, and the consumer price index using, P F,t = DP F,t (1 + τ t )( e t Pt CP I ), (2.15) where DP F,t denotes the average price of imported varieties in dollar term, τ t denotes the tariff rate for the four digit industry, e t denotes the nominal exchange rate, Pt CP I denotes the consumer price index at period and subscripts t denotes the time. Notice that the real exchange rate variation is going to be picked up by the last term, e t Pt CP I. 30 Empirical research showed that the domestic prices of imported products do not fully respond to exchange rates. See Goldberg & Knetter (1997) for a good survey on exchange rate passthrough.

50 41 Table 2.2. Import and Export in Colombian Metal Products Industry Export Orientation Ratio Import Penetration Ratio Table 2.3. Metal Products Industry( ) avg output share of entrants avg entry rate avg exit rate % 15 % 22 % 21 Table 2.4. Job Creation and Destruction in Colombian Metal Prod. Ind. Year Expansion Contraction Entry Exit ((E t E t 1 )/L t 1 ) ((C t C t 1 )/L t 1 ) (B t /L t 1 ) (D t 1 /L t 1 ) Source: DANE, author s calculation.

51 Figure 2.1. Nominal Tariff Rates for the Structural Metal Products Industry (SIC 3813), Source: DANE 42

52 43 Figure 2.2. Average Import Prices in Metal Products, Source: NBER Figure 2.3. Wages in Colombian Metal Products, Source: DANE

53 44 Year Table 2.5. Net and Gross Flows in the Sample Data Net ( Change ) ( ) Gross ( Turnover ) ( Et E t 1 + Bt C t 1 Ct + D t 1 Total Et E t 1 + Bt C t 1 Ct Lt 1 Lt 1 Lt 1 Lt 1 Lt 1 Lt 1 Lt 1 + D t 1 Lt 1 ) Total Source: DANE, author s calculation.

54 45 Table 2.6. Expanding and contracting Plants Year Expanding Plants Contracting Plants Plants with No Change in Emp Data source is DANE, Author s calculation. Figure 2.4. Employment Growth ( ), Source: DANE

55 46 Table 2.7. Parameters of the VAR models Simple VAR Markov Switching VAR P F w P F w β (1.7) (0.69) (0.59) (0.69) β (4.72) (0.52) β (0.19) (0.07) (0.07) (0.08) (0.35) (0.14) (0.13) (0.15) β (0.51) (0.06) (1.08) (0.12) Σ e e e e e e e e-003 Σ e e e e-003 Π Log Likelihood LR Linearity Test DAVIES ** Data source: IFS, DANE, and Feenstra (2000). Standard deviations are in parentheses.

56 47 Table 2.8. Estimated Cost and Demand Parameters for the Colombian Metal Products Industry Parameters Standard Errors Mean Sunk Entry Cost ( F H Fixed Cost, f Firing Cost, cf Hiring Cost, ch Demand Parameter, α Demand Parameter, η Demand Parameter, γ Production Function Parameter Incumbents Productivity Process, intercept (a0µ) Incumbents Productivity Process, root, (a1µ) Incumbents Productivity Process, variance (σ µ) Entrants Productivity Distribution,mean (z) Variance of Imported Varieties, (σ ε) In thousand 1977 pesos.

57 48 Table 2.9. Model Fit Simulated Data Moments Moments Expected Value of Log Employment Variance of Log Employment Expected Value of Log Profit Variance of Log Profit Expected Growth in Employment Variance of Growth in Employment Expected Entry Rate Expected Exit Rate Variance of Entry Rate Variance of Exit Rate Covariance of L Employment and Lagged L Empl Covariance of Log Employment and Log Profit Covariance of Employment Growth and Log Profit Expected Log Number of Firms Variance of Log Firms Expected % of Firms with No Change in Employ Expected Job Creation Through Entry Expected Job Destruction Through Exit Expected Job Creation Through Expansion Expected Job Destruction Through Contraction Expected Import Penetration Rate

58 49 Table Transitional Dynamics Relatively Closed Environment Relatively Open Environment Total Employment Mean Gross Flows Variance Gross Flow Mean Productivity of Incumbents Mean Number of Firms Mean Entry Rate 21% 20% Mean Exit Rate 5% 23% Mean Log Profit Mean Log Size Mean Import Price Mean Domestic Price

59 50 Table The Long-Run Comparison of Relatively Open vs Relatively Closed Environment Relatively Closed Relatively Open Total Employment Mean Gross Flows Variance Gross Flow Mean Productivity of Incumbents Mean Number of Firms Mean Entry Rate 22% 20% Mean Exit Rate 22% 20% Mean Log Profit Mean Log Size

60 51 Table Long-Run Effect of Lower Import Prices High Tariff Low tariff Total Employment Mean Gross Flows Variance Gross Flow Mean Log Profit Mean Number of Firms Mean Entry/Exit 22% 26% Table The Role of Severance Payments With Firing Costs No Firing Costs Total Employment Mean Gross Flows Variance Gross Flow Mean Log Profit Mean Log Size Mean Productivity Mean Entry 22% 23% Mean Exit 22% 23% Mean Layoff Costs $15, 908 0

61 52 Figure 2.5. Evolution of Industry-wide Employment Figure 2.6. Evolution of Industry-wide Productivity

62 53 Table Estimation of Aggregate Shocks (from quarterly data) Markov Switching VAR Model 1: MSIA Model 2: MSIAH P F w P F w β e e e e 001 β e e e e β e e e e e e e e 001 β e e e e e e e e 001 Σ e e e e e e e e 004 Σ e e e e e e e e 003 Π Log Likelihood Log Likelihood (linear) Likelihood ratio linearity test DAVIES * Based on data from NBER Trade Database, IFS, and DANE. Standard deviations are in parentheses.

63 Chapter 3 Industrial Evolution in Crisis-Prone Economies by Rick Bond, James Tybout, and Hale Utar 3.1 Introduction Balance of payments crises and banking crises are common in developing countries. 1 Often they feed off one another, creating dramatic swings in the real exchange rate, real interest rates, and expectations about regime sustainability. The effects of these macro crises on productivity and wealth distributions can be severe, particularly in countries where credit markets function poorly and stock markets are thin. They can discourage investment overall, and favor firms with ample collateral. 2 Similarly, they can change patterns of job 1 In a panel of 20 countries from Asia, Europe, Latin America and the Middle East, Kaminsky and Reinhart (1999) document 25 banking crises and 71 balance of payments crises during the period Volatility may also change the types of capital goods that firms invest in. For example, uncertainty about the future can induce firms to avoid specialized technologies that are very efficient in some states of nature and very inefficient in others (Lambson, 1991). Also, by increasing the risk of a liquidity constraint in the future, volatility can discourage long-term investments in favor of shorter term, lower productivity alternatives (Aghion, et al, 2005). Our analysis does not deal with these phenomena.

64 55 destruction and business failure, weakening the link between firms real-side performance and their chances of survival. Our objective is to model and quantify these relationships. We first develop an industrial evolution model in which capital market imperfections link firms ability to borrow with the wealth of their owners. Then we fit our model to firm-level panel data and macro data from Colombia that span the debt-crisis period of the 1980s. Finally, using the estimated parameters, we simulate industrial evolution patterns under alternative assumptions about the stochastic processes for exchange rates and interest rates. In particular, we explore the effects of crisis-prone environments on entry and exit patterns, cross-firm investment patterns, industry-wide productivity, and wealth distributions. The simulations yield a variety of results. Among other things, we find that heightened macro volatility reduces average productivity because of the selection effects it creates. Households with modest wealth are unable to bridge periods of temporary losses by borrowing, and are discouraged from operating businesses because of their risk-aversity. Also, in the immediate aftermath of a shift from a stable regime to a crisis regime, heightened uncertainty creates greater incentives for large, poorly-performing firms to delay exit in the hope that things will improve. The associated industry-wide productivity losses can range from 3 to 5 percent during the early years of a crisis. In addition to exploring the effects of volatility, we quantify the effects of credit market imperfections. Our simulations suggest that improvements in loan contract enforcement would lead to more borrowing, larger firms, more entrepreneurship among households with modest wealth, and a more egalitarian distribution of income. 3.2 The Model Our industrial evolution model has several key features. First, to approximate financial market conditions in developing countries, we assume that securities markets are negligible, so households hold their wealth as bank deposits

65 56 and/or investments in proprietorships. Second, households can borrow to finance some of their business investments, but their loans must be sufficiently small that they pose no default risk to lenders. Third, households are forwardlooking, infinitely-lived, and risk-averse. Fourth, they are also heterogeneous in terms of their ability to generate business income, which is subject to serially correlated, idiosyncratic shocks. Fifth, all firms produce traded goods, so changes in the real exchange rate result in changes in output prices for firms. Finally, exchange rates and interest rates evolve jointly according to an exogenous Markov process. Given this setting, households with different entrepreneurial abilities and wealth levels react differently to macro shocks. One reason is that they have different expectations regarding the gross earnings potential of their businesses. But other factors play a role as well. For example, owner-households with ample wealth can borrow to weather periods of exchange rate appreciation, while poorer households may be induced to shut down their firms. Also, risk-aversity declines with increase in wealth, so wealthy households are relatively tolerant of volatility in business income, and are more inclined to hold business assets in their portfolios. Thus macro crises affect firm ownership patterns, firm size distributions, productivity distributions, borrowing patterns, and cross-household wealth distributions. We now turn to model specifics Aggregate Environment Three macro variables appear in our model-the real exchange rate, e, the lending rate, r, and the deposit rate, r µ. The interest spread µ is parametrically fixed, so we can summarize the state of the macro economy at any point in time by the vector s = (e, r). This vector evolves according to an exogenous Markov process, ψ(e t+1, r t+1 e t, r t ), which characterizes the extent to which the economy is crisis-prone.

66 The Household Optimization Problem Households fall into one of three categories: owner-households, which own incumbent firms, potential owner-households, which have the option to start a firm, and non-entrepreneurial households, which owned firms in the past but sold them. Potential owner-households can become owner-households by paying the sunk costs of creating a firm, and owner-households can become non-entrepreneurial households by selling their firms assets and shutting them down. To keep the model tractable we assume that non-entrepreneurial households cannot re-establish a firm once they exit. However, the stock of potential owner-households is augmented each period by the exogenous arrival of new potential owner-households. All households share a common CRRA utility function, U(c it ) = (c it) 1 σ, where c it is consumption by household i at time t. Each period, households choose their savings rate, next-period type (if choices are available), and business investments (if they have chosen to own a proprietorship). They make these decisions with the objective of maximizing their discounted expected utility streams,e t τ=t U(c it)β τ t, subject to borrowing constraints. (Here E t is an expectations operator conditioned on information available in period t, and β is a discount factor that reflects the rate of time preference.) Outcomes are uncertain because the macro economy evolves stochastically, and because owner-households experience idiosyncratic shocks to the return on their business investments. 1 σ Non-entrepreneurial Households We now characterize the optimization problems faced by the various types of households. We begin with non-entrepreneurs, which face the simplest problem because they cannot change their type. Let a it denote the wealth held by household i at the beginning of period t, and let y i0 denote its exogenous, non-asset income. Then non-entrepreneurial household i consumes c it = y i0 + (r t µ)a it (a it+1 a it ) in period t, and it maximizes the expected present value of its utility stream when the macro state is s t by choosing the savings

67 58 rate that solves the following dynamic programming problem: V E (a it, y i0, s t ) = max a 0 U(y i0+(r t µ)a it (a a it ))+β s ψ(s s t )V E (a, y i0, s ) (3.1) Owner Households Owner-households face a more complicated decision problem because they must choose whether to continue operating their proprietorships and given that they continue how much of their wealth to hold as investments in their firms. The business income (before fixed costs and interest payments) generated by household i s proprietorship is given by: π(k it, e t, ν it ), π k > 0, π kk < 0, π e < 0, π ν > 0, (3.2) where k it is the firm s stock of productive assets and ν it is an idiosyncratic shock that captures managerial skills and investment opportunities. We assume that ν it evolves according to the discrete Markov process φ(ν it+1 ν it ) that it is independent of the macroeconomic state vector s t. Several features of the function (3.2) merit comment. First, business income is decreasing in e because we treat an increase in the exchange rate as an appreciation, which makes imports cheaper and reduces the return to exporting. Second, firms incomes are not affected by the behavior of their domestic competitors because we assume that each firm s product has many substitutes in foreign markets, making the effects of entry, exit or price adjustments by domestic producers insignificant. Finally, diminishing returns to productive assets, π kk < 0, reflect our assumption that span-of-control issues are important. That is, each entrepreneurial household has finite managerial resources, and has increasing difficulty overseeing its proprietorship as it grows larger. Owner-households can invest all of, more than, or less than their entire wealth in their business s asset stock. If household i invests all of its wealth in its firm, a it = k it and it has neither bank deposits nor loan obligations. If it invests less than all of its wealth, it holds the balance a it k it as bank deposits, which

68 59 yield r t µ. If it invests more than its wealth, it must satisfy the no-default constraint, and it finances the excess k it a it with a loan at rate r t. 3 Combining these possibilities, the i t h household earns or pays out (a it k it )(r t it ) in 1 if a it k it > 0 interest during period t, where D it = is a dummy variable 0 otherwise indicating whether households hold bank deposits. Accordingly, its period t consumption amounts to c it = y i0 + π(k it, e t, ν it ) f + (a it k it )(r t it ) (a it+1 a it ), where f is the per-period fixed cost of operating a business. Given the above, the expected present value of owner-household i s utility stream is determined by its beginning-of-period wealth,a it, the macroeconomic state,s t, and its idiosyncratic profitability shock, ν it. If the household sells off its productive assets, pays off its debts, and shuts down its firm, it reaps the expected utility stream of a non-entrepreneur, V E (a it, y i0, s t ). Alternatively, if it continues to operate, it reaps current utility U(y i0 +π(k it, e t, ν it ) f +(a it k it )(r t µd it ) (a a it )) and it retains the option to continue producing next period. Accordingly, the unconditional expected utility stream for an owner-household in state (a it, s t, ν it ) is: V it (a it, y i0, s t, ν it ) = max[v I (a it, y i0, s t, ν it ), V E (a it, y i0, s t )], (3.3) where V I (a it, y i0, s t, ν it ) = max [U(y a i0 + π(k it, e t, ν it ) f + (a it k it )(r t µd it ) (a a it )) 0,k it >0 + β V (a, y i0, s, ν )ψ(s s t )φ(ν ν t )], ν s and the maximization in (3.4) is subject to: (3.4) V I (a it, y i0, s t, ν it ) V E (θk it, y i0, s t ) (3.5) 3 Households never borrow to acquire bank deposits because, with µ > 0, this amounts to giving money away to the bank.

69 60 Here, V I (a it, y i0, s t, ν it ) is the expected utility stream for a continuing producer who does not shut down, and (3.5) ensures that households with debt have no incentive to default on their loans. The borrowing constraint (3.5) merits further explanation. We assume that lenders are perfectly informed about the current profitability of their borrowers firms, ν it, but they are unable to observe the uses to which these borrowers puts their loans. If the i th household borrows an amount (k it a it ), she can either invest that amount in the firm or sell the firm s capital stock and abscond with θk it. The parameter θ (0, 1) captures all of the monetary and psychic costs of taking the money and running, including the possibility of future punishment. 4 Owner-households that shut down their firms are excluded from future firm investment opportunities, so the payoff to defaulting is simply the valuation of a non-entrepreneurial household with assets θk it, and an owner household will not default on its loans as long as (3.5) is satisfied. The limiting cases of θ = 0 and θ = 1 correspond to perfectly enforceable debt contracts and costless default, respectively. The wealth of the household serves as collateral that relaxes the no default constraint. This problem captures two senses in which household wealth facilitates the financing of firms. First, because of the wedge µ between the borrowing and lending rate for firms, it becomes more attractive for households to accumulate assets because of the higher return available when a it > k it. The second is due to the fact that increases in household wealth will relax the no default constraint in (3.5) Potential Owner Households We conclude our description of the model by characterizing the entry decision into the industry. Each period, an exogenously given number of households, N, become potential entrants to the industry. One can think of this influx as 4 No default constraints of this type have been used by Banerjee and Newman (1993, 2001) to examine the role of capital market imperfections. Cooley and Quadrini (2001) examine a model of capital market imperfections with costly state verification, where expected productivity of the firm is observable to lenders but the current period realization of the cash flow can only be observed with a positive cost.

70 61 reflecting either the entry of new entrepreneurs into the population and/or the random arrival of new entrepreneurial ideas in the population. If a potential entrant household chooses to enter, it must pay start-up costs, F, and draw an initial ν it from the distribution q 0 (ν), which is common to all entrants. Given this ν it, the household then chooses initial k it and (a it+1 a it ) values, subject to the appropriate no-default constraint. If a potential entrant household chooses not to enter, it allocates its current income of y i0 +(r t µ)a it between consumption and asset accumulation, and it retains the option of entering in the future. If household i creates a firm with profitability ν and capital stock k it in period t, and if it holds asset stock a it and saves a a it, the present value of its expected utility stream will be: Ṽ N (a it, y i0, k it, s t ν) =U(y i0 + π(k it, e t, ν) f F + (a it k it )(r t µd it ) (a a it )) + β ν s V (a, y i0, s, ν )ψ(s s t )φ(ν ν t ) (3.6) Accordingly, the value of entry to a household with assets a it and exogenous income y i0 is: V N (a it, y i0, s t ) = ν subject to max Ṽ N (a it, y i0, k it, s t ν)q 0 (ν) a 0,k it 0 Ṽ N (a it, y i0, k it, s t ν) > V E (θk it, y i0, s t ) (3.7) and it will create a new proprietorship if: where: V N (a it, y i0, s t ) > V O (a it, y i0, s t ), (3.8) V O (a it, y i0, s t ) = max [U(y a i0 + (r t µ)a it (a a it ))+ 0 β max[v N (a, y i0, e, r ), V O (a, y i0, e, r )]ψ(s s t )]. e s (3.9)

71 62 Note that the value of entry is not conditioned on because the firm s productivity is only observed after the entry cost has been incurred. Potential entrants might choose to postpone entry for two reasons. One possibility is that the current macroeconomic state makes entry unattractive, so that the household waits until conditions improve to enter. A second possibility is that the potential entrant has a low level of initial wealth holdings. Such a household might choose to accumulate assets for one or more periods prior to entering in order to increase the probability of success by relaxing the borrowing constraint it will face upon entry Industry Evolution The solutions to the optimization problems described above can be used to characterize the evolution of the industry over time. The solution to ownerhousehold optimization problem (3.3)-(3.5) yields two policy functions. The one, ã(a it, s t, ν it ) describes an incumbent firm s asset choice for the next period and exit function, χ(a it, s t, ν it ) that is equal to one if the household chooses to exit. Given an initial distribution of incumbent owner-households, h I (a it, ν it ), these policy functions will generate an expected frequency distribution over (a it, ν it ) space. Similarly, the solution to the potential entrant optimization problem (3.6-VO) yields a saving-policy function ã N (a it, s t ) for households that choose to enter, a saving-policy function ã N (a it, s t ) for households that choose to postpone entry, and an exit function χ N (a it, s t )that is equal to 1 if the household enters. Given an initial distribution of potential entrant firms over asset levels h N (a it ), these policy functions can be used to generate an expected frequency distribution over (a it, ν it ) for entering firms and an updated distribution of asset levels among potential entrants.

72 Estimation To give our model empirical content, we exploit Colombian time series on interest rates and exchange rates for the period , and we exploit plant-level panel data on apparel producers for the period We choose this particular country, time period and industry partly for reasons of data availability. But our choices also reflect the fact that these data exhibit the kind of variation we wish to study. The country and time period suit our purposes because exchange rates and interest rates exhibited major swings during the debt crisis period of the early 1980s, and they exhibited relative stability thereafter. Thus the data span a crisis period and a stable period. The apparel industry suits our purposes because apparel products are highly tradeable, and the entry costs for new apparel producers are low. Thus our assumption that prices are determined in global markets is defensible, and low entry costs make our assumption of monopolistic competition reasonable. The lack of entry barriers also ensure that small, closely held firms are the dominant business type. Fitting the model to the Colombian data involves three basic exercises. First, we use annual plant level panel data on apparel producers to estimate the business earnings function π(k it, e t, ν it ) and the transition density φ(ν it+1 ν it ). Second, we use monthly time series on exchange rates and interest rates for the period to estimate the transition density ϕ(s t+1 s t ) and the interest rate spread, µ. Finally, with these results in hand, we use the dynamic implications of our model and various industry-wide summary statistics to estimate entry costs (F ), per-period fixed costs (f), and the credit market imperfection index (θ). (Our data do not contain much information about taste parameters, so we follow convention and fix them to σ = 0.5 and β = 0.9.) Each step in the estimation process is described below Estimating the Profit Function To obtain estimates of the earnings function π(k it, e t, ν it ) and the transition density φ(ν it+1 ν it ), we must impose additional structure on our model. Let the

73 64 production function for firm i be Q it = exp(u it )kitl α γ it, where u it is a productivity index and l it is an index of variable input usage (labor, intermediates, and energy). Given an exogenous world price (P it ) for the i th firm product and an exogenous price for a unit bundle of its variable inputs (w it ), this production function implies that the profit-maximizing values for total revenue (G it) and total variable costs (Cit) are : 5 G it = γ 1 e u it(1 γ) 1 w it ( γp it ) (1 γ) 1 k w it α (1 γ) it (3.10) Cit = e u it(1 γ) 1 w it ( γp it ) (1 γ) 1 k w it α (1 γ) it (3.11) Prices for inputs and outputs are not observable at the plant level, so we express w it ( γp it w it ) 1 (1 γ) as a Cobb-Douglas function of a time trend, the real exchange rate, and firm-specific shocks. Similarly we express u it as a time trend and firm-specific shocks. This allows us to write 3.10 and 3.11 as: G it = γ 1 e η 0+η1e t+η 2 t+µ it +ε E it k η 3 it, (3.12) C it = e η 0+η1e t+η 2 t+µ it +ε E it k η 3 it, (3.13) where η 3 = α. Business earnings amount to revenues less variable costs and 1 γ depreciation expenses, so π(k it, e t, ν it ) = exp(η 0 + η 1 e t + ν it )(γ 1 1)(k it ) η 3 δk it, where ν it = µ i + η 2 t + ε E it. We impose no particular distribution on the fixed effects, but we assume that ε E it is normally distributed and follows the same AR(1) process for all firms. Our industrial survey data provide plant-specific information on the value of output and expenditures on labor, intermediates and materials, capital stocks, and current period depreciation. So equations 3.12 and 3.13 provides a basis for 5 Alternatively, one can begin from a monopolistic competition model in which each firm faces a downward sloping demand function. However, this specification would complicate the solution algorithm because it would require that firms anticipate the evolution of an economywide aggregate that depends upon all other firms pricing decisions.

74 65 estimating the parameters of the earning function and the transition density φ(ν it+1 ν it ). To allow for noise in the data, particularly due to discrepancies between true variable costs and measured expenditures, we assume that reported revenues and costs are measured with serially-correlated error: G it = G ite εg it, Cit = Cite εc it, where (ε G it, ε C it) is a vector of orthogonal, normal AR(1) processes that are uncorrelated with ε E it. Substituting 3.12 and 3.13 into these expressions, taking logs yields: To identify (η 1, η 2, η 3 ), equations 3.12 and 3.13 can be estimated as a system, either in level form or in first differences. (The latter is appropriate if the disturbance terms include a permanent source of heterogeneity.) Because the profit disturbance is common to both equations while measurement errors are not, this estimation strategy also identifies the parameters of the transition density φ(ν it+1 ν it ). The depreciation rate (δ) can be estimated separately as the simple average (across all observations on active firms) of current depreciation expenses to capital stocks. Doing so yields δ = Table 3.1 reports preliminary results for the remaining earnings function parameters. Here, both level-form and differenced-form estimates are fit to the population of producers appearing in the annual manufacturing survey for a least one year between 1981 and Also, to allow for the possibility that new entrants draw their initial productivity shock from a different distribution, we include a dummy for plants in their first year of operation. Increases in the capital stock increase revenues, costs, and profits, as expected. However, the coefficient on capital is smaller for the differenced-form estimator. Most likely this is because capital is measured with error, and differencing the data exacerbates the associated bias (Griliches and Hausman, 1986). None of the other coefficients is very sensitive to differencing the data. The exchange rate coefficient implies each percentage point of devaluation reduces earnings, costs and profits by about one-third of one percent. Clearly, plant-specific profitability shocks are serially correlated the root of this process is around 0.94, and is highly significant. However, profitability shocks exhibit very little trend. Finally, serially-correlated measurement errors appear to be present in both revenues and total variable costs.

75 Estimating Markov Process for Aggregate Variables Our methodology for estimating the transition density Ψ(s t+1 s t ) comes from the econometric literature on regime switching, which was developed to characterize macroeconomic processes that change dramatically during certain periods (e.g. Hamilton, 1994, chapter 22). The notion is that the observed time series actually reflect multiple regimes. Estimation amounts to recovering the parameters that describe the stochastic process behind each regime, and recovering the transition probabilities that characterize movements between regimes. A variety of specifications have been used for switching models, and it is not obvious ex ante which one is appropriate for our purposes. 6 Accordingly, we fit several models with different degrees of generality and compare them. First, to provide a base case, we estimate a simple VAR in the real exchange rate and the real interest rate. Second, we estimate a switching model that allows for Markov-switching heteroskedasticity (MSH). That is, the covariance matrix for the innovations are regime-specific, but nothing else is. Finally, we estimate a more general model in which all parameters of the VAR (intercepts, roots and covariance matrix) are allowed to be regime dependent (MSIAH). We assume that at any point in time, the economy is in one of two macro regimes. When regime m {1, 2} prevails, s t = ( e t ) r t evolves according to β0 m + β1 m s t 1 + υt m, where E(υt m υt m ) = Σ m. Thus our base case model is a simple VAR, in which there is a single regime (and all superscripts could be dropped); the MSH model parameterizes the two regimes as (β 0, β 1, Σ 1 ) and (β 0, β 1, Σ 2 ); and the MSIAH model parameterizes the two regimes as (β 1 0, β 1 1, Σ 1 )and (β 2 0, β 2 1, Σ 2 ). Switches between regimes are governed by the transition matrix p = {p mn }, where p mn is the probability of moving to regime m, given the economy is currently in regime n. 6 Applications to exchange rates include Engel and Hamilton (1990) and Bollen, et al (2000). Applications to interest rate processes include Gray (1996). Although we are unaware of papers that apply switching estimators to the joint evolution of exchange rates and interest rates, the methodology for estimating multivariate switching models is well developed (e.g., Clarida et al, 2003, Krolzig (1997)).

76 67 Figure 3.1 presents monthly series on the Colombian real exchange rate and real interest rate, respectively (IMF,2004). Lower exchange rate values correspond to a cheaper Colombian peso. Both series suggests the Colombia was in one regime during the early 1980s, when the debt crisis was at its most severe, and another regime thereafter. The data also suggest that month-tomonth volatility is much different from year-to-year volatility, and that when crises hit, the macro volatility that they create is often concentrated within relatively short periods. Therefore, it seems preferable to estimate the models with monthly data; in fact, for the MSH specification it proved infeasible to do otherwise. Using a variant of the EM algorithm described in Clarida et al (2003) we obtain the maximum likelihood estimates reported in table 2. Likelihood ratio tests indicate that the MSH model and the simple VAR model can be rejected in favor of the MSIAH model, so we focus our attention on this latter specification. The two regimes it describes differ in terms of both roots and volatility. Regime 1, which is very likely to continue from one month to the next (p11 = 0.966), exhibits strong serial correlation in both exchange rates and interest rates. It also exhibits relatively small variance in the process innovations (refer to ), and relatively little interdependence between interest rates and exchange rates (refer to the off-diagonal elements of ). Regime 2 is relatively unlikely to occur, and when it does occur, it is relatively unlikely to persist (p 22 = 0.384). It is characterized by much weaker serial correlation, substantially higher variance in the process innovations, and substantial, positive interdependence between the exchange rate and the interest rate. This latter regime thus appears to correspond to the debt crisis years that occur during the first part of the sample period, and we will think of an increase in the volatility of macro conditions as an increase in the probability that the economy spends time in regime 2. It remains to discuss the spread between the lending rate and the deposit rate, µ. This differential is a fixed parameter in our model, so we simply estimate it as the mean difference between these two series over the sample period, obtaining µ =

77 Estimating the structural parameters Estimation Strategy To approximate the remaining parameters (entry costs (F ), fixed costs(f), and the credit market imperfection index (θ))we embed our behavioral model in a method of moments estimator. That is, we choose the (θ, F, f) combination that minimizes a measure of distance between moments implied by model simulations and their sample counterparts. For any given (θ, F, f) combination, we construct the distance measure as follows. First, using the candidate (θ, F, f) vector and the estimated values for all of the other model parameters, we numerically solve for the value functions characterized in section IIB. Second, using these functions in combination with randomly drawn macro shocks (υ) and firm-level profitability shocks (ε E ), we repeatedly simulate patterns of industrial evolution. Third, we average over these simulations to construct the expected entry rates, exit rates, and other moments implied by the candidate (θ, F, f) vector. Fourth, calling the vector of simulated moments m(f, f, θ) and their sample counterparts m, we calculate our measure of distance between the sample and simulated moments as X(F, f, θ) = (m m(f, f, θ)) W (m m(f, f, θ)), where W is a conformable matrix of weights. In addition to the mean entry rate and the mean exit rate, the moments we base our estimator upon include the mean rate of growth in capital stocks among incumbents, and the mean, variance and pair-wise covariance of each of the following variables: log capital stock among incumbents, log operating profit among incumbents, log indebtedness among indebted firm/households. We also include the covariance of current and lagged log capital stocks to better capture the persistence in firm sizes. Several issues arise in constructing our simulations. First, we must discretize our variables in order to use standard solution techniques for firms dynamic optimization problem. We do this using Tauchen s (1991) method. Second, we must impute an annual transition density for lending rates and exchange rates from our monthly transition densities in table 3.3. We do this by simulating

78 69 long sequences of realizations from our table 12 estimates and then forming averages within 12 month blocks. Frequency counts on transitions among these averages provide our annual transition probabilities. Third, we must invent an initial cross-household distribution for profitability shocks (ν it ), exogenous income (y i0 ), and assets (a it ). We base the (ν it ) distribution on the steady state distribution for the profitability shocks (ε E, it s) from our estimated of profit function, we set at the approximate mean per capita Colombian income for all households, and we base the distribution on an invented log-normal distribution. Although this asset distribution is arbitrary, we throw out the first 150 years of our simulations before constructing the vector m(f, f, θ) in order to minimize its influence. (Note that this 150 year burn-in period induces correlation between assets and the profitability shocks, even though none is present in the initial year.) Finally, given that we cannot observe the number of households that might potentially start new apparel firms, we must make some arbitrary assumptions. In the initial period we assume that there are 60 owner-households and 20 additional are available to start new firms. Also, since our model presumes that households cannot re-enter the apparel industry once they have left, we add 20 new households to the population each period in order to avoid running out of entrants. (The asset stocks and initial realizations for new households are randomly drawn from the distributions described in the previous paragraph.) These figures essentially serve to fix the number of active firms. Experiments show that, holding other parameters fixed, variations in the number of new potential entrants per period have very little effect on the simulated moments. A final issue is what algorithm to use when searching (θ, F, f) space. Exploratory grid searches indicate that is neither smooth nor concave, so gradient-based algorithms fail to find global minima. We have experimented with both Nelder-Meade and genetic search algorithms; the results discussed below are based on the former. Bootstrap standard errors have not yet been generated.

79 Estimates Table 3.4 reports our estimates for (θ, F, f) in the upper panel; the simulated moments that they imply are juxtaposed with corresponding data-based moments in the lower panel. Note that, in addition to the parameters of interest, we estimate the nuisance parameter, λ. This parameter is necessary to reconcile the concept of productive assets that appears in our model (k) with the fixed assets measure that appears in our data. Although our data set does not provide information on establishments debts, it does include total interest payments. We therefore impute total debt for each observation as interest payments divided by the market lending rate. Turning to the parameters of interest, we estimate that sunk entry costs amount to 71, pesos ($US 3,960), or about 14 percent of the value of the fixed capital stock for a firm of average size. Thus, entrepreneurs who shut down average-sized firms typically recoup about 86 percent of their investment. One can think of this magnitude as reflecting installation and removal costs, as well as any customizing of equipment and facilities that does not add to their market value. The relatively low magnitude of this figure is probably traceable to the fact that it is identified by entry and exit patterns, which are dominated by small firms. We estimate fixed costs to be 1,997, pesos ($US 111,300). These expenditures are incurred every year, regardless of production levels. They reflect the opportunity costs of the owner s time and various overhead expenses like insurance, marketing, and legal representation. Also, to the extent that the intercept term in our profit function was overestimated because of selection bias, this figure partly reflects an offsetting adjustment. Our estimate for the credit market imperfection parameter, θ, is nearly unity, suggesting that banks view households as capable of absconding with nearly the entire value of their firms productive assets. Thus, our model implies there are severe enforcement problems in Colombian credit markets, and suggests that borrowing is consequently infeasible for many entrepreneurs.

80 71 The moments reported at the bottom of Table 3.4 show how well the model does in fitting the sample. It does an excellent job of matching the sample entry and exit rates, partly because we have given these moments heavy weight by expressing them in terms of percentages. It also does well in terms of matching the typical firm size, although it under-predicts firm heterogeneity. All simulated moments except one match their sample counterparts in sign, and many are reasonably close. Overall, given the small number of free parameters, the amount of structure imposed by the model, and the large number of moments considered, we view the fit as reasonably good. 3.4 Simulation Experiments Given all of the parameters estimates discussed above, we can now use simulations to characterize the effects of crisis-prone macro environments on industrial evolution patterns. Similarly, we can explore the consequences of imperfect credit markets The Effects of Volatility Long run effects Our first exercise is to quantify the effects of volatility on the performance of the Colombian apparel industry, holding other parameters constant across regimes. To do so, we first simulate industrial evolution patterns under the assumption that macro variables are governed by the MSH process reported in table 3.3 (the base case ). Then we re-simulate evolution patterns after increasing the degree of macro volatility by setting all elements of the transition probability matrix, p, to 0.5 (the counterfactual ). For both cases, we simulate patterns of industrial evolution over a 250 year period, 50 times. Throwing out the initial 50 years, we average our results to obtain the figures presented in Table 4. Because we are using the MSH switching model for this exercise, mean values of the log exchange rate and the interest rate are the same in both columns.

81 72 However, these variables both exhibit higher variance under the counterfactual assumptions. This heightened volatility has little effect on the number of firms, but it leads to more variation in the number of firms through time. It also induces firms to rely more heavily on debt( 0.28 percent do so in the counterfactual environment, while only 0.13 percent do so in the base case.) This reflects households desire to smooth their business income over periods of exchange rate fluctuation. Heightened volatility also reduces average profitability (η 0 + ν it ) among active firms by about 0.01, which translates into a one percent loss in productivity. One possible explanation is that wealthy households diversify risk by holding some relatively low productivity firms; another explanation is that some households with high quality firms and little collateral are unable to borrow during periods of exchange rate appreciation. Finally, because it slightly increases turnover, heightened volatility slightly reduces the average age of active firms Transition In addition to looking at long run differences between industrial evolution patterns in these two environments, it is interesting to examine the transition dynamics induced by a change in environment. For this exercise we compare our base case scenario with a scenario in which volatility suddenly increases. More precisely, after putting households in the base case environment for 50 years, we suddenly confront them with the more volatile environment and we examine the transition path over the following 50 years. (Although the switch is modeled as a surprise when it occurs, the new macro process is presumed to be understood by all agents thereafter.) Figure 3.2 shows the average time paths followed by interest rates and exchange rates over this transition period; period 0 corresponds to the first year of the high-volatility macro environment. When firms are suddenly confronted with heightened volatility, they become less inclined to exit (figure 3.3). That is, with the future less predictable, producers who are doing poorly perceive an increased option value to sticking around. Consequently, the number of active firms is initially larger when

82 73 volatility increases, and average productivity levels are initially lower (figure 3.4). Interestingly, this option value effect is stronger among the larger poorly performing firms because they sacrifice a more valuable option when they abandon the market.(for example, a given movement in the exchange rate translates into a relatively large absolute change in business income for a firm with a relatively large capital stock.) Hence the correlation between profitability and size falls during the early years (figure 3.5), and size-weighted average profitability falls by 3 to 5 percent (figure 3.6). The option value effect weakens over time because firms that continue to do poorly eventually exit. Finally, patterns of borrowing depend upon regime volatility, but in a way that varies with firm size. Among smaller firms, extra volatility induces extra borrowing to help them through lean periods. But among larger firms, whose owners have less absolute risk aversion and more ability to self-finance, there is no obvious tendency to increase debt (figure 3.7) The Effects of Credit Market Imperfections As a final exercise, we investigate the effects of credit market imperfections by comparing our base case simulations with a counterfactual in which ownerhouseholds lose their entire capital stocks if they default on their loans. This case, which we shall refer to as perfect credit markets, amounts to setting θ = 0. Elimination of the option to abscond with borrowed funds induces banks to lend to some owner-households that would have otherwise defaulted. Thus it relaxes the borrowing constraint faced by households with little wealth and/or poor realizations (refer to equation 3.5). To characterize the macro environment, we use the estimates for our most general model (MSIAH). Once again we throw out a burn-in period of 50 years, and we base our analysis on the following 100 years. The results are summarized in Table 5. Note first that switching to perfect credit markets increases debt finance, and more than doubles the average firm size. In logs, the mean capital stock

83 74 increases from approximately 5.9 to 7.2. So credit market imperfections can have a dramatic effect on the size distribution. Interestingly, although firms get much larger with improvements in credit markets, the average wealth of owner-households falls nearly 15 percent (Table 3.5 and figure 3.3). This is because better functioning credit markets allow households with modest wealth to create new firms by relying partly on debt finance. Some of this extra entry allows owner-households to exploit fleeting profit opportunities, and so exit rates rise as well, and the average age of active firms falls. Thus, although one would expect well-functioning credit markets to improve firms ability to survive lean periods, this effect on longevity appears to be dominated by the additional short-horizon investment that they facilitate (Table 3.5). Surprisingly, the effects of improved credit markets do not dramatically affect mean profitability shocks among active firms. The unweighted average value of profitability does increase by 0.02 when θ drops to zero, presumably reflecting better access to finance among relatively poor households with high-return investment opportunities (Table 3.5 and figure 3.10). However, these small firms account for a small fraction of total output, so the size-weighted average profitability fails to improve. 3.5 Directions for Further Work Although our model is already rather complex, there are a number of ways in which it might be made more realistic. First, capital stock adjustment costs could be added, making owner-households pay extra to rapidly adjust the size of their firm. Preliminary experiments with quadratic costs suggest that this would improve the ability of the model to explain the persistence in capital stocks that we find in the data (refer to the moments in Table 3.3). It would also create incentives for firms to borrow during periods in which they otherwise would have scaled back their operations. Second, we have assumed that firms can only borrow in one currency. But in a number of macro crises, the currency denomination of firms debt has

84 75 been an important determinant of their profitability and ability to survive. In principle, it would be possible to add this dimension to the model. Third, we have not exploited any information on the characteristics of ownerhouseholds because such information was not available from Colombian manufacturing surveys. However, it may be possible to obtain information on the wealth, income and ownership patterns of Colombian households from other surveys. Among other things, this would allow us to introduce heterogeneity in, and to perhaps to better characterize the population of potential entrants. Finally, and most ambitiously, it might be possible to adopt a more realistic characterization of market structure. By assuming that all products are tradeable, and by relying on a span of control assumption to induce diminishing returns to capital investments, we have made it possible to ignore the number of competing firms as a profit determinant, and to analyze each household s behavior in isolation. For apparel, these assumptions may not be too unreasonable. But for other, less tradeable goods it would be better to adopt the assumption of monopolistic competition in domestic markets and move to a multi-agent optimization problem.

85 Bibliography [1] Aghion, Philippe, George-Mario Angeletos,Abhijit Banerjee, and Kalina Manova (2005) Volatility and Growth: Credit Constraints and Productivity-Enhancing Investment, NBER Working Paper [2] Albuquerque, Rui and Hugo Hopenhayn (2004), Optimal Lending and Firm Dynamics, Review of Economic Studies, 71 (2) [3] Banerjee, Abhijit and Andrew Newman (1993) Occupational Choice and the Process of Development, Journal of Political Economy, 101, [4] Banerjee, Abhijit and Andrew Newman (2003) Inequality, Growth and Trade Policy, MIT Working Paper, Cambridge, MA. [5] Bollen, Nicolas, Stephen Gray, and Robert Whaley (2000). Regime Switching in Foreign Exchange Rates: Evidence from Currency Option Prices, Journal of Econometrics, 94, [6] Clarida, Richard, Lucio Sarno, Mark Taylor, and Giorgio Valente (2003), The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors, Journal of International Economics 60 (1) [7] Cooley, Thomas and Vincenzo Quadrini (2001), Financial Markets and Firm Dynamics, American Economic Review, 91 (5), [8] Cooper, Russell and John Haltiwanger (2000) On the Nature of Capital Adjustment Costs, NBER Working Paper No

86 77 [9] Engel, Charles and James Hamilton (1990), Long Swings in the Dollar: Are They in the Data and Do Markets Know It? American Economic Review, 80 (4), [10] Gray, Stephen (1996) Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process, Journal of Financial Economics, [11] Griliches, Zvi and Jerry Hausman (1986) Errors in Variables in Panel Data, Journal of Econometrics 31 (1), [12] Gourieroux, Christian, Alain Monfort and Eric Renault (1993) Indirect Inference, Journal of Applied Econometrics, 8, [13] Hamilton, James. (1994) Time Series Analysis. Princeton: Princeton U. Press. [14] Kaminsky, Graciela and Carmen Reinhart (1999), The Twin Crises: The Causes of Banking and Balance of Payments Problems, American Economic Review, 89 (3), [15] Lambson, Val (1991) Industry Evolution with Sunk Costs and Uncertain Market Conditions, International Journal of Industrial Organization, Vol. 9, No. 2, pp [16] Rustichini, Aldo. (1998). Dynamic Programming Solution of Incentive- Constrained Problems, Journal of Economic Theory 78(2), pp [17] Smith, A. (1993) Estimating Non-Linear Time Series Models Using Vector Autoregressions, Journal of Applied Econometrics 8, S63-S84. [18] Tauchen, George (1991) Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models, Econometrica, Volume 59, No. 2, pp

87 78 Table 3.1. Operating Profit Function Parameters, Colombian Apparel producers,level form Coefficient Std. Error Z-ratio Level-form estimator exchange rate capital stock trend term initial year dummy intercept, revenue equation intercept, cost equation Variance of innovation in ε E process Root of ε E process Variance of innovation in ε C process Root of ε C process Variance of innovation in ε R process Root of ε R process Number of observations 2,640 Table 3.2. Operating Profit Function Parameters, Colombian Apparel Producers, difference form Coefficient Std. Error Z-ratio Difference-form estimator exchange rate capital stock trend term initial year dummy intercept, revenue equation intercept, cost equation Variance of innovation in ε E process Root of ε E process Variance of innovation in ε C process Root of ε C process Variance of innovation in ε R process Root of ε R process Number of observations 2,640

88 79 Table 3.3. Switching VAR Parameters Linear VAR Markov Switching VAR MSH MSIAH e r e r e r β (0.072) (0.41) (0.03) (0.01) (0.03) (0.014) β (0.75) (0.27) β (0.009) (0.035) (0.006) (0.02) (0.006) (0.02) (0.004) (0.017) (0.002) (0.011) (0.003) (0.01) β (0.16) (0.44) (0.06) (0.16) Σ e e e e e e e e e e e e-5 Σ e e e e e e e e-4 Π Log Likelihood LR Linearity Test DAVIES ** ** Based on monthly IFS data for Colombia, 1982 through Standards errors are in parentheses. Standard deviations are in parentheses.

89 80 Table 3.4. Estimation Results, Colombian Apparel Producers Parameter Standard Error Sunk entry costs (F ) n.a. Fixed costs (f) n.a. Credit market imperfection index (θ) n.a. Ratio of total firm assets to fixed capital (λ) n.a. Objective function (X) Simulated Sample Moment Moment Expected value of log capital stock Variance of log capital stock Expected value of log operating profits Variance of log operating profits Expected value of log debt (given debt is positive) Variance of log debt (given debt is positive) Expected growth in capital stock (net of deprec.) Variance of growth in capital stock (net of deprec.) Expected entry rate (expressed as a percentage) Expected exit rate (expressed as a percentage) Variance of entry rate Variance of exit rate Covariance of log capital and log operating profits Covariance of log capital and lagged log capital Covariance of log debt and log capital Covariance of log debt and log profits Covariance of capital growth rate and log profits Covariance of capital growth rate and log capital

90 81 Table 3.5. The Steady State Effect of Credit Market Imperfections Base Case Perfect Credit (θ =.995) Markets (θ = 0) Aggregate shocks Mean log exchange rate Variance, log exchange rate Mean lending rate Variance, interest rate 1.23e e-04 Industry Characteristics Mean number of firms Variance, number of firms Mean rate of investment Mean profit shock among active firms Size-weighted profit shock Mean entry rate Mean exit rate Mean age of active firms Mean debt to capital ratio among borrowers Percent of firms with positive debt Owner-household characteristics Mean log wealth of firms Variance, log wealth of firm owners

91 Figure 3.1. Colombian Exchange Rates and Interest Rates, Source: DANE 82