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

TL;DR: This paper developed a dynamic industry model with heterogeneous firms to analyze the intra-industry effects of international trade and showed how the exposure to trade will induce only the more productive firms to enter the export market (while some less productive firms continue to produce only for the domestic market).

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

Summary

1 Introduction

• Recent empirical research using longitudinal plant or Þrm-level data in several countries has overwhelmingly substantiated the existence of large and persistent productivity differences among establishments in the same narrowly deÞned industries.
• Evidence reported in Roberts and Tybout (1996) and Davis and Haltiwanger (1999) conÞrms that these patterns are not speciÞc to the U.S. and that substantial within sector reallocations between heterogeneous Þrms are also prevalent in developing countries.
• On the other hand, if the reallocations are related to Þrm characteristics, then the nature of the link between the two signiÞcantly affects several important aspects of industry performance.
• The paper then shows how further increases in the industry s exposure to trade (driven either by trade liberalization or the addition of new trading partners) lead to additional inter-Þrm reallocations towards more productive Þrms.
• Neither of these studies Þnds evidence supporting this hypothesis.

2 Model Background

• Incorporating heterogeneity in a dynamic industry setting, where forward looking Þrms make entry and export decisions, necessarily increases the technical complexity of this model vis-a-vis its representative Þrm counterparts.
• The main forces explaining the impact of trade on an industry are nevertheless quite intuitive.
• The model draws heavily from Hopenhayn s (1992a, 1992b) work on Þrm and industry productivity dynamics to explain the endogenous selection of heterogeneous Þrms in an industry.
• Forward looking, Þrm entry decision, it greatly simpliÞes 5As was previously mentioned, one of the robust empirical patterns emerging from recent industry studies is that new entrants are much more likely to have lower productivity and exit than do older incumbents.
• This equilibrium therefore does not respond to changes in the entry cost while being overly sensitive to the magnitude of the losses incurred by Þrms who exit the industry.

Demand

• The measure of the set Ω will represent the mass (or alternatively, the number) of available goods.
• (1) These aggregates can then be used to derive the optimal consumption decisions over individual varieties using q(ω) = Q µ p(ω).

Production

• Production requires only one factor, labor, which is inelastically supplied at its aggregate level L (which also indexes the size of the economy).
• Firm technology is represented by a cost function that exhibits constant marginal cost with a Þxed overhead cost.

Aggregation

• Using the same weighted average function deÞned in (9), let ϕ = ϕ(ϕ∗) and ϕx = ϕ(ϕ∗x) denote the average productivity levels of, respectively, all Þrms and exporting Þrms only.
• The average productivity across all Þrms, ϕ, is based only on domestic market share differences between Þrms (as reßected by differences in the Þrms productivity levels).
• If some Þrms do not export, then this average will not reßect the additional export shares of the more productive Þrms.

4 Firm Entry and Exit

• There is a large pool of prospective entrants into the industry.
• Upon entry with a low productivity draw, a Þrm may decide to immediately exit and not produce.
• He then shows how these Þrm level productivity dynamics give the equilibrium distribution of productivity levels µ(ϕ) a different shape than the ex-ante distribution g(ϕ), and determine the ex-ante survival probabilities for a Þrm, conditional on successful entry.
• On the other hand, the range of productivity levels, and hence the average productivity level, are endogenously determined.
• Modeling an additional time discount factor would not qualitatively change any of the results.

Zero Cutoff ProÞt Condition

• This will not be the case in the current situation.
• The model thus does not differentiate between cohorts of incumbent Þrms.
• This cohort is then critically differentiated from that formed by new entrants, whose distribution of productivity levels is given by g(ϕ).

Free Entry and the Value of Firms

• Since all incumbent Þrms other than the cutoff Þrm earn positive proÞts, the average proÞt level π̄ must be positive.
• If this value were negative, no Þrm would want to enter.
• In any equilibrium where entry is unrestricted, this value could further not be positive since the mass of prospective entrants is unbounded.

5 Equilibrium in a Closed Economy

• A stationary equilibrium is deÞned by constant aggregate variables over time and the free entry of Þrms into the industry.
• Me of new entrants in every period, such that the mass of successful entrants, pinMe, exactly replaces the mass δM of incumbents who are hit with the bad shock and exit: pinMe = δM.
• The labor used by these new entrants for investment purposes must, of course, be reßected in the accounting for aggregate labor L, and affects the aggregate labor available for production: L = Lp+Le where Lp and Le represent the aggregate labor used for production and investment (by new entrants).
• In equilibrium, the aggregate return Π equals the aggregate investment cost Le in every period so there is no net investment income (this would not be the case with a positive time discount factor).

Existence and Uniqueness of the Equilibrium

• The free entry (FE) and zero cutoff proÞt (ZCP) conditions represent two different relationships between the average proÞt level π̄ and the cutoff productivity level ϕ∗ (see (12)).
• I Þrst summarize their important properties for the determination of the equilibrium values of ϕ∗ and π̄: In (ϕ,π) space the FE curve is increasing and is cut by the ZCP curve only once from above .
• As the cutoff level ϕ∗ goes to zero, the revenue of the cutoff Þrm also goes to zero.
• If g(ϕ) belongs to most of the common families of distributions (including the lognormal, exponential, Gamma, or Weibull distributions or truncations on (0,∞) of the normal, logistic, extreme value, or Laplace distributions), then k(ϕ) will monotonically decrease to zero on (0,∞).
• These regularity conditions ensure that an increase in the cutoff level ϕ∗ redistributes the mass of incumbent Þrms towards the cutoff level.

Analysis of the Equilibrium

• As was just shown, the equilibrium productivity cutoff level, ϕ∗, and average Þrm proÞt, π̄, do not depend on the country size L. Hence, the equilibrium distribution of productivity levels µ(ϕ) and average productivity level ϕ will also be independent of country size.
• The large country will just have more Þrms in an amount proportional to its country size.
• Once ϕ and π̄ are determined, the aggregate outcome predicted by this model is identical to one generated by an economy with representative Þrms who share the same productivity level ϕ and proÞt level π̄.
• In the following sections, I argue that the exposure of a country to trade creates precisely the type of shock that induces reallocations between Þrms and generates increases in aggregate productivity.
• These results can not be explained by representative Þrm models where the aggregate productivity level is exogenously given as the productivity level common to all Þrms.

6 Overview and Assumptions of the Open Economy Model

• I now examine the impact of trade in a world (or trade bloc) that is composed of countries whose economies are of the type that was previously described.
• The transition to trade will thus not affect 19Consumers in every country have access to the same bundle of goods at the same aggregate price index.
• The current model is modiÞed by allowing the elasticity of substitution to endogenously increase with product variety.
• Bernard and Jensen (1999a), Clerides, Lach and Tybout (1998), Roberts and Tybout (1997a), and Roberts, Sullivan and Tybout (1995) all introduce a Þxed export cost into the theoretical sections of their work in order to explain the self-selection of Þrms into the export market.
• Countries who differ only in country size can exhibit different wage rates in the equilibrium with trade.

7 Equilibrium in the Open Economy

• The symmetry assumption ensures that all countries share the same wage, which is still normalized to one, and also share the same aggregate variables.
• Firms who export will set higher prices in the foreign markets that reßect the increased marginal cost τ of serving these markets: px(ϕ) = τ ρϕ = τpd(ϕ).
• The analysis of these equilibria is left for future work.
• (16) If some Þrms do not export, then there no longer exists an integrated world market for all goods.

Firm Entry, Exit, and Export Status

• All the exogenous factors affecting Þrm entry, exit, and productivity levels remain unchanged by trade.
• Prior to entry, Þrms face the same ex-ante distribution of productivity levels g(ϕ).
• In a stationary equilibrium, any incumbent Þrm with productivity ϕ earns variable proÞts rx(ϕ)σ in every period from its export sales to any given country.
• If ϕ∗x > ϕ∗, then some Þrms (with productivity levels between ϕ∗ and ϕ∗x) produce exclusively for their domestic market.

Determination of the Equilibrium

• As in the closed economy case, a stationary equilibrium is uniquely determined by the triplet (ϕ∗, P,R) satisfying the free entry and zero cutoff proÞt conditions.
• The equilibrium ϕ∗, in turn, determines the export productivity cutoff ϕ∗x as well as the average productivity levels ϕ, ϕx, ϕt, and the ex-ante successful entry and export probabilities pin and px.
• As was the case in the closed economy equilibrium, the free entry condition and the aggregate stability condition30 (pinMe = δM) ensure that the aggregate payment to the investment workers.
• Le equals the aggregate proÞt level Π. As shown in (18), the aggregate price index is determined by the aggregate number of goods available in each country (Mt) and the average productivity level across all Þrms selling these goods ( ϕt).

8 The Impact of Trade

• The result that the modeling of Þxed export costs explains the partitioning of Þrms by export status and productivity level is not exactly earth-shattering.
• On the other hand, such a model would be ill-suited to address several important questions concerning the impact of trade in the presence of export market entry costs and Þrm heterogeneity:.
• It is nevertheless possible, when the export costs are high, that these foreign Þrms replace a larger number of domestic Þrms (if the latter are sufficiently less productive).

The Reallocation of Market Shares and ProÞts Across Firms

• I now examine how the impact of trade on individual Þrms changes with the Þrm s productivity level.
• Additionally, in this equilibrium with trade, rd(ϕ)R represents the Þrm s share of its domestic market (since rd(ϕ) is the Þrm s domestic revenue and R also represents aggregate consumer expenditure in the country).
• Thus, a Þrm who exports increases its share of industry revenues while a Þrm who does not export loses market share.
• (The market share of the least productive Þrms in the autarky equilibrium with productivity between ϕ∗a and ϕ∗ drops down to zero as these Þrms exit.).
• 25 Summarizing these results on the Þrm level impact of trade by stating that the beneÞts of trade are not equally spread across Þrms would be quite an understatement!.

Why Does Trade Force the Least Productive Firms to Exit?

• The most obvious cause explaining the exit of the least productive domestic Þrms would be the new competition from the entry of the more productive Þrms into the domestic market.
• With C.E.S. product differentiation, the new import competition affects domestic Þrms with different productivity levels in similar ways, and translates only into a reduction in aggregate sales for all domestic Þrms.
• On the other hand, if the model were amended to allow for the opening of new export markets without any import competition, then distributional changes very similar to those described for the symmetric trade case would occur (and the least productive Þrms would be forced to exit the industry).
• In equilibrium, an increase in the proÞts of more productive Þrms relative to less productive Þrms leads to more entry and a higher cutoff productivity level.
• It is therefore the pull of the export markets, rather than the push of import competition that forces the least productive Þrms to exit.

9 The Impact of Trade Liberalization

• The preceding analysis compared the equilibrium outcomes of an economy undergoing a massive change in trade regime from autarky to trade.
• The current model is well-suited to address several different mechanisms that would produce an increase in trade exposure and plausibly correspond to observed decreases in trade costs over time or some speciÞc policies to liberalize trade.
• These three scenarios involve comparative statics of the open economy equilibrium with respect to n, τ , and fx.
• The main impact of the transition from autarky to trade was an increase in aggregate productivity and welfare generated by a reallocation of market shares towards more productive Þrms (where the least productive Þrms are forced to exit).
• The increased exposure to trade will also unequivocally deliver welfare gains.

Increase in the Number of Trading Partners

• Throughout this comparative static exercise, I use the notation of the open economy equilibrium to describe the old equilibrium with n countries.
• I then add primes (0) to all variables and functions when they pertain to the new equilibrium with n0 > n countries.
• Thus, both market shares and proÞts are reallocated towards the more efficient Þrms.

Decrease in Trade Costs

• A decrease in the variable trade cost τ will induce almost identical effects to those just described for the increase in trading partners.
• 0 < τ (again I use primes to reference all variables and functions in the new equilibrium) will shift up the ZCP curve and induce an increase in the cutoff productivity level ϕ∗0 > ϕ∗.
• As before, the increased exposure to trade will force the least productive Þrms to exit, but it will now also generate the entry of new Þrms into the export market (who did not export with the higher τ).
• As before, the exit of the least productive Þrms and the market share increase of the most productive Þrms both contribute to an aggregate productivity gain and an increase in welfare.
• 40 38There is a transitional issue associated with the exporting status of Þrms with productivity levels between ϕ∗x and ϕ∗0x .

10 Conclusion

• This paper has described and analyzed a new transmission channel for the impact of trade on industry structure and performance.
• Since this channel works through intra-industry reallocations across Þrms, it can only be studied within an industry model that incorporates Þrm level heterogeneity.
• The paper shows how the existence of export market entry costs drastically affects how the impact of trade is distributed across different types of Þrms.
• In fact, only a portion of the Þrms the more efficient ones reap beneÞts from trade in the form of gains in market share and proÞt.
• It is therefore important to have a model that can predict the impact of trade policy on inter-Þrm reallocations in order to design accompanying policies that would address issues related to the transition towards a new regime.

Figures

Figure 3: The reallocation of market shares and proÞts.

Figure 2: Representative Firms as a Limiting Equilibrium When fe → 0.

Figure 1: Determination of the Equilibrium Cutoff ϕ∗ and Average ProÞt π̄

Full text

NBER WORKING PAPER SERIES
THE IMPACT OF TRADE ON INTRA-INDUSTRY REALLOCATIONS
AND AGGREGATE INDUSTRY PRODUCTIVITY
Marc J. Melitz
Working Paper 8881
http://www.nber.org/papers/w8881
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
April 2002
The author thanks, without implicating, Alan Deardor, Jim Levinsohn, and Elhanan Helpman for helpful
comments and discussions. Funding from the Alfred P. Sloan Foundation is gratefully acknowledged. The
views expressed herein are those of the author and not necessarily those of the National Bureau of Economic
Research.
© 2002 by Marc J. Melitz. All rights reserved. Short sections of text, not to exceed two paragraphs, may
be quoted without explicit permission provided that full credit, including © notice, is given to the source.

The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity
Marc J. Melitz
NBER Working Paper No. 8881
April 2002
JEL No. F1
ABSTRACT
This paper builds a dynamic industry model with heterogeneous firms that explains why
international trade induces reallocations of resources among firms in an industry. The paper shows how
the exposure to trade will induce only the more productive firms to enter the export market (while some
less productive firms continue to produce only for the domestic market) and will simultaneously force
the least productive firms to exit. It then shows how further increases in the industry's exposure to trade
lead to additional inter-firm reallocations towards more productive firms. These phenomena have been
empirically documented but can not be explained by current general equilibrium trade models, because
they rely on a representative firm framework. The paper also shows how the aggregate industry
productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a
benefit from trade that has not been examined theoretically before. The paper adapts Hopenhayn's (1992a)
dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the
paper provides an extension of Krugman's (1980) trade model that incorporates firm level productivity
differences. Firms with different productivity levels coexist in an industry because each firm faces initial
uncertainty concerning its productivity before making an irreversible investment to enter the industry.
Entry into the export market is also costly, but the firm's decision to export occurs after it gains
knowledge of its productivity.
Mark J. Melitz
Department of Economics
Littauer Center
Harvard University
Cambridge, MA 02138
and NBER
mmelitz@harvard.edu

1 In troduction
Recent empirical research using longitudinal plant or Þrm-level data in several countries has ov er-
whelmingly substan tiated the existence of large and persistent productivit y differences among es-
tablishments in the same narrowly deÞned industries. Foster, Haltiwanger and Krizan (1998)
summarize this research by concluding that “... within sector differences dwarf betw een sector
differences in behavior.” In related work, Haltiwanger (1997, Table 1) reports that 4-digit industry
effectsexplainlessthan10percentoftheoverallvariationinthegrowthratesofoutput,em-
ployment, capital stocks, and productivity across establishments in the U.S. from 1977 to 1987.
Complementing this evidence on the extent of within sector heterogeneit y, other studies hav e sho w n
that the bulk of resource reallocations across Þrms remains internal to the speciÞc sector. Davis
and Haltiwanger (1999) summarize this evidence for the U.S. and report that less than 1 in 10 job
reallocations reßect employment shifts acro ss sectors. Levinsohn (1999) reports similar numbers for
most industries in Chile following wide-reaching trade liberalization. Evidence reported in Roberts
and T ybout (1996) and Davis and Haltiwanger (1999) conÞrms that these patterns are not speciÞc
to the U.S. and that substantial within sector reallocations between heterogeneous Þrms are also
prevalent in developing countries.
If these large intra-industry reallocations w ere unrelated to the heterogeneous characteristics of
Þrms, then their separate existence would not necessarily make them important determining factors
of industry performance. On the other hand, if the reallocations are related to Þrm characteristics,
then the nature of the link between the tw o signiÞcantly affects several important aspects of industry
performance. Although the analysis of this link between Þrm characteristics and industry evolution
is an ongoing research program, enough evidence has b een collected to demonstrate its existence and
relevance for industry performance. The main Þrm characteristic found to be empirically linked to
in tra-industry reallocations is Þrm productivit y.
1
The strongest evidence of this link pertains to Þrm
entry and exit decisions. Productivity differences between entering and exiting Þrms signiÞcan tly
cont ribute to aggregate industry productivit y c hanges over time. Additionally, a large number of
studies have documented a strong correlation bet ween Þrm exit and lo w productivit y (Þrm age
is also correlated with exit: younger Þrms have disproportionately high failure rates). Finally,
some studies have also found evidence that reallocations unrelated to entry and exit contribute to
1
Firm age and capital vintage are other importan t explanatory characteristics that hav e been highlighted in some
studies, although their impact may be limited to their effect on productivity.
1

industry productivity growth b y redistributing market shares among incumbent Þrms.
2
A similar
reallocation process has also been studied at a higher level of aggregation: Basu and Fernald
(1997) Þnd that U.S. aggregate productivit y changes across the business cycle are partly driven
b y expenditure reallocations across sectors with differen t average productivity lev els. The inherent
inabilit y of representative Þrm industry models to explain the contribution of reallocations to
industry performance has prompted the development of a theoretical literature of industry dynamics
that emphasizes the role of Þrm level heterogeneit y. This literature, along with the previously
mentioned empirical evidence, is reviewed in Foster, Haltiwanger and Krizan (1998) and Tybout
(2002).
This paper adapts one of these recen t industry models with heterogeneous Þrms in order to an-
alyze the role of international trade as a catalyst for inter-Þrm reallocations within an industry. It
then describes how these reallocations affect both industry performance and welfare. The business
press often assumes the existenc e of this catalyst role of trade when describing how exposure to
trade has both enhanced the growth opportunities of some Þrms while simu ltaneously cont ribut-
ing to the down fall or “downsizing” of other Þrms in the same industry. Similarly, protection from
trade is reported to shelter inefficient Þrms. Rigorous empirical work has recently corroborated this
anecdotal evidence. Bernard and Jensen (1999a) (for the U.S.), Aw, Ch ung and Roberts (2000) (for
Taiw an), and Clerides, Lach and T ybout (1998) (for Colom bia, Mexico, and Morocco) all Þnd evi-
dence that the causation of the correlation between Þrm productivity and export status runs from
theformertothelatter: moreproductiveÞrms self-select into the export market. Aw, Chung and
Roberts (2000) also Þnd evidence suggesting that exposure to trade forces the least productive Þrms
to exit the industry (Þrms with higher productivity levels relativ e to the incumbent average exit
after the exposure to trade). Both of these selection effects (into the export market and out of the
industry) obviously reallocate market shares from less productive Þrms(whoexit)tomoreproduc-
tive ones (who export) and therefore contribute to industry productivity growth.
3
P av cnik (2002)
directly looks at the contribution of market share reallocations to sectoral productivity growth
follow ing trade liberalization in Chile. She Þnds that these reallocations signiÞcan tly contribute to
productivity growth in the tradable sectors. In a related study, Bernard and Jensen (1999b) Þnd
that within-sector mark et share reallocations towards more productive exporting plants accounts
2
The importance of this phenomenon varies across studies and is cyclically sensitive (see Foster, Haltiwanger and
Krizan (1998))
3
Forces other than trade also affect the reallocation of resources within an industry. Olley and Pakes (1996) Þnd
that deregulation in the U.S. telecommunications industry increased productivity predominantly through this channel
rather than through intra-Þrm productivity gains.
2

for 20% of U.S. manufacturing productivity gro wth.
By relying on a representative Þrm framew ork (at least at the level of the industry), general
equilibrium trade models have largely ignored these intra-industry reallocations and focused instead
on other consequences of trade, such as inter-industry reallocations or phenomena affecting all Þrms
in similar ways.
4
This paper attempts to Þll this gap by providing a general equilibrium model
with heterogeneous Þrms that explains how trade induces these selection effects and in tra-industry
reallocations. This model shows how exposure to trade will induce only the more productive Þrms
to enter the export markets (while some less productive Þrms continue to produce only for the
domestic market) and will sim u ltaneously force the least productive Þrms to exit. The paper then
shows how further increases in the industry’s exposure to trade (drive n either by trade liberalization
or the addition of new trading partners) lead to additional inter-Þrm reallocations towards more
productive Þrms. The model th u s explains how trade can generate industry productivity growth
without necessarily affecting in tra-Þrm efficiency. It also provides a theoretical foundation for
the recent empirical Þndings described above and rigorously shows how trade can contribute to
the Darwinian evolution of industries — forcing the least efficient Þrms to con tract or exit while
promoting the growth and success of the more efficient ones.
Another recen t paper by Bernard, Eaton, Jenson and Kortum (2000) also introduces Þrm-level
heterogeneity into a model of trade b y adapting a Ricardian model to Þrm-speciÞccomparative
advantage. Both papers predict the same basic kinds of trade-induced reallocations, although the
ch annels and motiv ations behind these reallocations vary. In addition, Bernard et al. (2000) sho w
how their model can be calibrated to provide a good ÞttoacombinationofmicroandmacroUS
data patterns. Ho wev er, subsequent work b y Brooks (2001) has sho wn that this feature is not
robust across countries. The current paper relies on the previously docume nted empirical micro
patterns and focuses on the theoretical explanations and motivations behind these patterns.
4
This last category includes models that assume a direct link between trade and Þrm lev el efficiency. In these
models, exposure to trade typically increases the efficiency level of all Þrms through a variety of channels: learning
effects, increased scale of production, increased innovation, higher quality or diversity of intermediate inputs, reduction
of agency problems between owners and managers. Clerides, Lach and Tybout (1998) and Bernard and Jensen (1999a)
speciÞcally test whether new exporting Þrmsbecomemoreefficient. Neither of these studies Þnds evidence supporting
this hypothesis. Tybout and Westbrook (1995) test and reject the hypothesis that increased productivity in Mexico’s
growing export industries was driven by increases in the scale of plant production.
3

Frequently asked questions

Q1. What are the contributions in "Nber working paper series the impact of trade on intra-industry reallocations and aggregate industry productivity" ?

This paper builds a dynamic industry model with heterogeneous firms that explains why international trade induces reallocations of resources among firms in an industry. The paper shows how the exposure to trade will induce only the more productive firms to enter the export market ( while some less productive firms continue to produce only for the domestic market ) and will simultaneously force the least productive firms to exit. The paper also shows how the aggregate industry productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a benefit from trade that has not been examined theoretically before. The paper adapts Hopenhayn 's ( 1992a ) dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the paper provides an extension of Krugman 's ( 1980 ) trade model that incorporates firm level productivity differences. It then shows how further increases in the industry 's exposure to trade lead to additional inter-firm reallocations towards more productive firms. 

Q2. What are some other important explanatory characteristics that have been highlighted in some studies?

some studies have also found evidence that reallocations unrelated to entry and exit contribute to 1Firm age and capital vintage are other important explanatory characteristics that have been highlighted in some studies, although their impact may be limited to their effect on productivity. 

Q3. How does the probability of entry increase?

As ϕ∗ increases, the probability of successful entry (pin = 1−G(ϕ∗)) decreases average proÞts must therefore increase for Þrms to remain indifferent about entry. 

Q4. What is the effect of the export market selection effect on the productivity of rms?

This export market selection effect and the domestic market selection effect (of Þrms out of the industry) both reallocate market shares towards more efficient Þrms and contribute to an aggregate productivity gain. 

Q5. What is the ratio of the average to cutoff rm revenue?

Since the average revenue level is always positive (even when ϕ∗ → 0), the ratio of the average to cutoff Þrm revenue becomes inÞnite as ϕ∗ goes to zero: 

Q6. What is the main reason why trade-induced reallocations are so important?

These trade-induced reallocations towards more efficient Þrms explain why trade may generate aggregate productivity gains without necessarily improving the productive efficiency of individual Þrms. 

Q7. What is the effect of the decrease in product variety on welfare?

Although the direction of the change in product variety is ambiguous (product variety will decrease so long as the ZCP curve is downward sloping), the decrease in aggregate productivity is enough to unambiguously entail a welfare loss (see appendix for proof). 

Q8. What is the main reason for the absence of an upper bound on productivity?

The absence of an upper bound on productivity is assumed only for simplicity; an upper bound can be incorporated in the analysis without qualitatively changing any of the main results. 

Q9. What is the main force that drives the hypothesis that increased productivity in Mexico s growing export industries?

Tybout and Westbrook (1995) test and reject the hypothesis that increased productivity in Mexico s growing export industries was driven by increases in the scale of plant production. 

Q10. How does Hopenhayn explain the rm productivity dynamics?

Hopenhayn shows how these dynamics shape the equilibrium distribution of Þrm productivity and analyzes the impact of these dynamics on Þrm value and the performance of cohorts of Þrms over time.