exports, innovation and production growth: a dynamic ... · exports, innovation and production...

Exports, Innovation and Production Growth:

A Dynamic Heterogeneous Firm Model with Learning and

Entry Costs

Helen Ruohan Wu∗†

The Ohio State University

November 13, 2012

Abstract

In this paper, I analyze a dynamic model of a firm’s joint decisions to export and

innovate, allowing both decisions to affect the firm’s production in accordance with self-

selection and learning-by-exporting theories of firm-level export and production dynamics.

I calibrate the model using Chilean manufacturing plant data from 2005 to 2007 and

find that self-selection and learning-by-exporting alone cannot adequately explain the

observed cross-sectional relationship between firm level exports and production, favoring

instead a model that requires both mechanisms to work in tandem. Counterfactual policy

analysis indicates that the impact of trade liberalization depends on the maturity of

the industry, the rate at which liberalization occurs, and the nature of the dominant

adjustment mechanism governing firm-level export-production dynamics.

JEL Classification: C61; C82; F17; F43; F63; O14; O32.

Keywords: Exports; Production; Innovation; Self-Selection; Learning-by-Exporting;

Heterogeneity; Trade Liberalization.

∗Email: [email protected]; Address: Department of Economics, The Ohio State University, Arps Hall 410,1945 North High Streeet, Columbus, OH 43210-1172.†I am grateful to Professor Mario Miranda, Professor Paul Evans, and participants in The Ohio State

University Department of Economics Macroeconomic Theory Seminar for helpful comments on earlier draftsof this paper. I would also like to thank the National Statistics Institute of Chile for providing the data usedin this paper and Alexander Gotthard-Real for helping me to understand the data.

1 Introduction

It is well documented that firms that export are more productive than firms that do not export.

Two theories have been proposed to explain this observed phenomenon. Self-selection theory

maintains that exporting is a consequence of high firm production. Specifically, exporting

is profitable. However, to enter the export market, a firm incurs unrecoverable entry costs

and typically faces higher fixed-costs of production over time. Entry into the export market

is therefore sensible only if the firm is sufficiently productive to generate the high volume of

exports needed to cover the entry costs and the higher continuing fixed costs.

Learning-by-exporting theory, on the other hand, maintains that high firm production is

a consequence of exporting behavior. Specifically, upon entering the export market, firm

production will grow at a faster rate. Various explanations have been used to justify this

claim, including that exporters become more productive as a result of intense yet informative

global competition and that they have greater access to state-of-the-art technology.

However, exporting may not be strictly a cause nor strictly a consequence of a firm’s

production. That is, exporting and production may mutually reinforcing, in which case nei-

ther self-selection theory nor learning-by-exporting theory alone will adequately explain the

complex relationship between exports and production.

To study the relationship between exports and firm production, I develop a dynamic

optimization model of an individual firm that allows for both self-selection and learning-by-

exporting. Following Melitz (2003) [20] and Constantini & Melitz (2008) [14], the firm faces

unrecoverable export market entry costs, but enjoys faster production gains when it becomes

an exporter. Each period, the firm faces three key decisions. First, facing an unrecoverable

cost of entering the export market, the firm must decide whether to enter. Second, if the firm

enters or has previously entered the export market, it must then decide how much to export

and how much to sell in domestic markets. Third, the firm, whether an exporter or non-

exporter, must decide how much to invest in production-enhancing innovation, the benefits

of which may depend on the export status of the firm.

My model makes a novel contribution to the self-selection and learning-by-exporting lit-

eratures by allowing export and innovation decisions to be continuous. Specifically, unlike

existing models in which innovation and exportation are modeled as discrete one-time choic-

es, I allow a firm that has entered the export market to sell its product in both the domestic

and export markets to degrees that may vary over time and firm production. Innovation is

also viewed as a continuous action whose costs may depend explicitly on whether the firm is

or is not an “exporter”.

I extend my representative firm model to consider an industry consisting of many firms

that are heterogeneous with respect to age, production, and exporter status. Specifically, each

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period, a fixed percentage of existing firms are forced to exit the industry for purely exogenous

reasons. Simultaneously, a fixed number of new, as yet non-exporting firms enter the industry

with an initial production drawn from a fixed probability distribution. I calibrate the model

using Chilean manufacturing plant data from 2005-2007 obtained from the Annual National

Industrial Survey of the National Statistics Institute of Chile (INE, Instituto Nacional de

Estadisticas Chile).

In my heterogeneous firm industry model, aggregate production, exports, and innovation

vary over time, but eventually converge to a steady state. I perform simulations to compare the

dynamic adjustments of the industry and the eventual steady-states achieved by the industry

under three distinct scenarios: a benchmark scenario that allows for both self-selection and

learning-by-exporting, a scenario that allows for self-selection but not learning-by-exporting,

and a scenario that allows for learning-by-exporting but not self-selection. I also perform

simulations to assess the impacts of trade liberalization on the industry at different stages of

industry development, ranging from an infant industry to a mature industry.

I find that self-selection and learning-by-exporting influence firm growth in different ways.

Specifically, without learning-by-exporting, self-selection leads to unrealistically low levels of

exports; without self-selection, however, all non-exporters instantly become exporters. Both

mechanisms jointly are needed to explain the stylized facts of Chilean manufacturing. I also

find that trade liberalization that raises the effective price received by exporters will have a

more profound impact on the level of exports in the short- and medium-run if the industry

relatively young than when it is mature.

This paper is organized as follows. Section 2 develops a model of a representative firm’s

joint decisions to export and innovate. Section 3 describes and summarizes the benchmark

parameter values employed in the study and the data from which the parameter estimates were

drawn. In section 4, I analyze the optimal export and innovation policies of a representative

firm under the benchmark parameterization. In section 5, I examine the two polar cases in

which either self-selection and learning-by-exporting mechanisms, but not both, are operant.

In section 6, I report findings from a counterfactual analysis of trade liberalization. Section 7

concludes the paper.

1.1 Literature Review

There is an extensive body of empirical research that supports the hypothesis that investment

in innovation and technology can reasonably explain the observed correlation between firm

production and exports. Hallward-Driemeier et al. (2002) [15], Baldwin and Gu (2004) [6],

Bustos (2005) [11], and Aw et al. (2007) [4] find that firms’ exports are related to research

and development (R&D) investment or adoption of new technology. The key insights drawn

from these studies is that innovation and exportation are correlated and that both influence

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the firm’s production growth. Numerous theoretical studies on the role of innovation in

exporting decisions have complemented the empirical studies. Atkeson & Burstein (2010) [3]

and Constantini & Melitz (2008) [14] find that trade liberalization increases the rate of return

to a firm’s R&D investment, and thus leads to production growth. In both papers, firms

are distinguished only by their production. Wu (2011, 2012) [26] [27], using industry-level

and plant-level data, finds that significant learning-by-exporting effects are present only when

industries are investing substantial amounts in innovation.

Self-selection theory (Melitz 2003 [20]; Bernard et al. 2003 [8], 2006 [9]) has enjoyed

widespread theoretical and empirical support. Empirical tests of learning-by-exporting theory

(Marin 1992 [19]; Ben-David 1993 [7]), however, have met with mixed results. Empirical tests

based on different data sets have yielded conflicting conclusions, indicating that the theory

may be case-sensitive. For example, studies using data from Indonesia (Amiti & Konings

2004 [2]), Canada (Baldwin & Gu 2004 [6]), Britain (Blalock et al. 2004 [10]) and Chile

(Alvarez & Lopez 2005 [1]) find strong evidence that exporting firms are more productive.

However, Clerides et al. (1998) [13], using plant-level data from Mexico, Columbia and

Morocco, find no evidence that production costs are affected by entering the export market.

Using the data of Canadian plants, Lileeva et al. (2010) [18] find significant learning effect

only among those induced by the tariff cuts to start exporting or to export more. To resolve

the apparent conflict, recent studies (Bustos 2011 [12]; Verhoogen 2004 [24]; Aw, Roberts &

Winston 2007 [4]) have suggested that learning-by-exporting is possible only if firms make

sufficiently high investment in innovation.

Other recent research has compared the mechanisms hypothesized by self-selection and

learning-by-exporting theories. Wagner (2007) [25] performed a review of the empirical lit-

erature, finding strong support for self-selection theory and mixed support for learning-by-

exporting theory. He concluded that “exporters are more productive than non-exporters, and

the more productive firms self-select into export markets, while exporting does not necessarily

improve production”. Imbruno (2008) [16] tested for both mechanisms using Italian manufac-

turing firms, finding that self-selection, rather than learning-by-exporting, is responsible for

high production among exporters. Other researchers have combined both mechanisms in a

single model to study export-production dynamics. Constantini & Melitz (2008) [14] and Aw

et al. (2008) [5], for example, treat firm-level exporting and innovation as discrete all-or-none

decisions.

2 Model

The representative firm begins each period either as an established exporter i = 1 or non-

exporter i = 0, with a predetermined production q ≥ 0, namely how much a firm produces.

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Being in a competitive market, the firm takes the domestic market price P0 and the export

market price P1 as given (hereafter, P = (P0,P1) indicates the joint price vector). The firm

must then decide whether to assume exporter status j = 1 or not j = 0 for the current period,

and, if it assumes exporter status, what proportion y of its production q to export, selling the

remainder domestically.

The firm must also decide how much to invest in innovation that would enhance productive

capacity next period. Specifically, the firm’s production in the following period

q′ = (1− γ)q + x (1)

is a function of its current production q, the amount it invests in innovation x ≥ 0, and

per-period rate of production depreciation γ ∈ (0,1).

Each period the firm faces a fixed cost κ1 if it is an exporter (j = 1) and a fixed cost κ0

if it is not an exporter (j = 0), where κ1 > κ0 > 0. A non-exporter that wishes to become

an exporter must make a fixed investment K > 0 which is unrecoverable. To economize on

notation, we let ηij denote the sum of fixed production and export market entry and exit costs

associated with the firm choosing exporter status j this period, given it begins the period in

exporter status i. Thus the export-status switching cost is:

ηij =

{κ1 +K if i = 0, j = 1

κj if otherwise.

The firm also incurs a quadratic variable production and marketing cost:

D(q, y) = d0(q(1− y))2 + d1(qy)2; (2)

and incurs a variable innovation cost:

Cj(x) = cjxβ. (3)

with β > 0. I assume that exporting production and marketing is more expensive than the

domestic one (d1 > d0 > 0) and, to capture learning-by-exporting, that an exporter faces

lower innovation costs than a non-exporter (c0 > c1 > 0).

The firm maximizes the present value of current and expected future profits over an

infinite horizon, given that it faces a probability µ of going bankrupt and ceasing to exist

at the beginning of each period. The firm’s dynamic decision problem is characterized by a

Bellman equation whose value function specifies the maximum present value of current and

expected future profits Vi(q) attainable by the firm, given its export status i and production

q at the beginning of the period:

Vi(q) = maxj=0,10≤y≤jx≥0

{P0q(1− y) + P1qy − Cj(x)−D(q, y)− ηij + δ(1− µ)Vj((1− γ)q + x)}. (4)

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Here, δ ∈(0 1) is the firm’s per-period discount rate.

The industry is assumed to consist of many firms that behave as the representative firm,

but which differ with respect to age and initial production. Specifically, a fixed proportion µ

of firms exit the industry randomly in any period but are replaced by a fixed number of new

firms with production drawn randomly from a known distribution. Specifically, I assume that

a new firm’s initial production, or production is drawn randomly from gamma distribution

Γ(q|k, θ) with shape parameter k and scale parameter θ. Idiosyncratic variation in initial

production and time of death produces an industry with firms that are heterogenous with

respect to production and export status; the total number of firms in the industry increases

until the number of firms exiting equals the number of firms entering.

3 Data and Parameterization

Table 1 reports the benchmark values of the model parameters used in model simulation-

s. In our parameter specification, we normalize the domestic price P0 to 1 and express all

other prices and costs relative to it. The remaining model parameters can be divided into

three classes. First, parameters estimated directly from from data, which include the export

price, fixed cost of exporters and non-exporters, depreciation rate, the death probability and

the initial production distribution parameters. Second, parameters whose values are drawn

from econometric estimates, which include the non-exporters’ innovation cost parameter, the

production cost function parameters, and the innovation cost rate. Column “Range” shows

the 95% credit interval of the estimation results. Third, parameters that are chosen through

calibration, that is, chosen so that simulated values of prescribed endogenous variables match

empirically observed values; these parameters include exporters’ innovation cost, and the

export market entry cost.

To parameterize the model, I use 2005-2007 Chilean manufacturing plant data obtained

from the National Industrial Survey conducted by the Chilean National Statistics Institute

(INE, Instituto Nacional de Estadisticas). The annual INE survey includes plants that began

operating during that year and excludes those that closed for any reason. In the survey,

production, exports, overseas business connections, and other manufacturing information are

collected at the plant level. Although firms may own more than one plant, most plants in the

survey are single-firm plants.1 Table 4 in Appendix B provides the descriptive statistics of

the observed plants.

I use the average income tax rate on firms as the fixed cost κ0 faced by a non-exporting

firm. I add the average tax rate on exports to generate an estimate the fixed cost κ1 faced

by exporting firms. To calibrate export market entry costs and exporter innovation cost

1According to Pavcnik (2002) [23], more than 90% of Chilean manufacturing firms have only one plant.

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Table 1: Parameterization

Description Symbol Benchmark Value Range

Domestic Price P0 1.0

Export Price P1 2.0

Exporting Start-Up Cost K 1.12

Fixed Cost - Non-Exporter κ0 1.0

Fixed Cost - Exporter κ1 2.0

Innovation Cost Parameter - Exporter c1 0.18

Innovation Cost Parameter - Non-Exporter c0 0.9 0.98 ∼ 1.00

Production Cost Parameter - Exporting Products d1 0.85 1.02 ∼ 1.31

Production Cost Parameter - Domestic Products d0 0.2 0.20 ∼ 0.24

Innovation Cost Rate β 10 9.12 ∼ 12.19

Production Distribution Shape Parameter k 2.5 2.48 ∼ 2.66

Production Distribution Scale Parameter θ 0.2 0.20 ∼ 0.22

Death Probability µ 0.15 0.11 ∼ 0.17

Production Depreciation Rate γ 0.2

Discount Rate δ 0.9

parameters, I use two targets from the data: relative exporting supply, namely the ratio

between aggregate exports and domestic marketings QS1 /QS0 ; and the exporter percentage.

Among the observed Chilean manufacturing plants, the relative exporting supply is 0.19.

And among all the 6,614 observations, there are only 1,624 (25%) plants being exporters. I

then calibrate K and c1 to match both of these targets.

Other parameters estimates were drawn from Wu (2012) [27], who used an extended

Olley-Pakes method to estimate plant-level productivity from the INE data set. The Olley-

Pakes (Olley & Pakes 1996 [22]) method employs a semi-parametric algorithm to remove

simultaneity and endogeneity from the unobserved production shock and capital input. The

conventional estimation method treats investment and capital as quasi-fixed inputs; Wu (2011,

2012) [26] [27] extends estimation by including two additional variables: the export ratio and

the export growth rate. In this paper, I use the production to indicate how productive a firm

is. Thus hereby I use the firms’ estimated productivity to represent their production levels.

The death probability µ and the parameters of the new plant production Γ distribution were

directly estimated from the 2005-2007 ENIA data, which tracks the number of firms that

enter and exit each year (See Figure 18 of Appendix C). The comparison of productivities

between non-exporters and exporters are shown in Figure 19 of Appendix C. The density

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histogram of the production distribution of the exporters’ productivity is given with a much

higher median, and a more right-skewed shape.

4 Firm-Level Simulations

I begin with an analysis of the representative firm’s optimal export and innovation policies

and the evolutionary path taken by an individual firm that follows these policies.

The Bellman equation (4) is solved using the method of collocation (Judd 1998 [17];

Miranda and Fackler 2002 [21]). The collocation method calls for the value functions Vi(q) to

be approximated using a linear combination of n known basis functions φj :

Vi(q) ≈∑

j=1...n

ςijφj(q) (5)

The 2n unknown coefficients ςij are then fixed by requiring the value function approximate

to satisfy the Bellman equation (4), not at all production levels q, but rather at n judiciously

chosen collocation nodes qj . The collocation method replaces the Bellman functional equations

with a set of 2n nonlinear equations with 2n unknowns that are solved using Newton’s method.

The collocation method can generate highly accurate approximate solutions to the Bellman

equation, provided the basis functions and collocation nodes are chosen judiciously and their

number n is set adequately high. For this paper, I chose linear orthogonal polynomial basis

functions and n = 150 linear nodes to compute the approximate solutions for the Bellman

equations. The solution was computed using the CompEcon 2010 Toolbox routine dpsolve

(Miranda and Fackler 2002 [21]).

Figure 1: Conditional Value Functions for Non-Exporter

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4.1 Optimal Policy

Figure 1 illustrates the conditional value functions for a non-exporter under the benchmark

parameterization. The horizontal axis represents the production q, while the vertical axis

represents the value. For a current non-exporter, the value associated with becoming an

exporter is the red line, while the value of remaining a non-exporter is the blue line. The

two curves intersect each other at a critical production q∗ = 2.81 at which a non-exporter

becomes an exporter. On the left side of q∗, the value of becoming an exporter exceeds the

value of remaining a non-exporter.

Figure 2 illustrates the representative firm’s optimal innovation policy (left panel) and

optimal export policy (right panel). On both panels the horizontal axis represents production

q.

As seen in the right panel of Figure 2, if q < q∗, the firm remains a non-exporter; if

q > q∗, the firm becomes an exporter. For an exporter, the proportion of production exported

declines with production due to rising production and marketing costs.

Figure 2: Optimal Policy

As seen in the left panel of Figure 2, optimal innovation initially declines with production,

but begins to rise in an irregular manner as production approaches the critical level q∗ at

which the firm becomes an exporter. This issue is addressed specifically in Figure 3. Those 5

kinked points corresponds to 5 specific critical q’s. Point q∗5 = 1.56 means if a firm starts as a

non-exporter with a q on the left hand side of q∗5, it needs more than 5 periods to jump and

start to export. Point q∗4 means if a firm starts as a non-exporter with a q on the right side

of q∗5 and on the left of q∗4 (= 1.95), it needs more than 4 periods to jump. If it starts with a

q between q∗4 and q∗3 (= 2.23), it needs 4 periods to jump. A firm starts with a q between q∗3

and q∗2 (= 2.43) needs only 3 periods to jump; between q∗2 and q∗1 (=2.60) needs 2 periods to

jump. Once a firm starts with a q that is higher than q∗1 yet lower than critical q∗, the firm

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will jump after only 1 period. Between each q∗m (m = 1, 2, . . . , 5) the optimal innovation will

decrease as q increases; the more productive a firm is, the less innovation it needs to make.

Figure 3: Optimal Policy of an Ex-Post Non-Exporter

At the critical production level q∗, innovation makes a discrete jump. However, for an

exporter, the level of innovation subsequently decreases with production, eventually falling

to zero as the production exceeds 4.73. For a highly-productive firm, it does not invest in

innovation anymore. Instead, the firm will let the production fall and cut back its production

and marketing expenditure. Eventually its production will converge to the steady-state value

3.59, with the steady-state innovation investment 0.72.

4.2 Individual Firm Dynamics

Consider now a firm that starts as a non-exporter with initial production q = 0.1 and lives

forever. As seen in Figure 4, the firm innovates from the outset and its production grows.

In period 9, the firm’s production reaches the critical level q∗, at which point it becomes an

”exporter”. From that point forward, the firm’s production continues to grow, but at a de-

clining rate, eventually approaching a steady-state of 3.59. Any firm, if it survives sufficiently

long, will become an exporter and approach this steady-state, regardless of its production at

inception.

The dynamics of exports and innovation for the representative firm are illustrated in Figure

5. As seen on the left panel, the firm does not export until the 9th period; once this happens,

the proportion of production exported jumps to its highest level. However, the export ratio

subsequently declines gradually as production increases because of the increasing production

cost, eventually converges to its steady-state.

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Figure 4: Path of An Individual Firm’s Production

As seen on the right panel of Figure 5, a nascent non-exporting firm innovates, but ini-

tially at a declining rate due to rising costs of innovation. However, as a firm’s production

approaches the critical level q∗ at which the firm becomes an exporter, the firm’s production

begins to rise as the firm anticipates becoming an exporter and being able to take advantage

of the lower innovation cost that would bring. Innovation reaches the maximum in the period

the firm becomes an exporter. Once the firm becomes an exporter, its innovation begins to

decline, again due to rising marginal cost of innovation, eventually dropping to its steady-state

value, the level of innovation needed to cover depreciation of production in its steady-state.

Figure 5: Paths of An Individual Firm’s Exports and Innovation

In the long run, the distributions of the q, x and y across all the different firms will

converge to steady-states. Under the benchmark parameter setting, at the steady-state the

aggregate domestic supply is 1.80, while the aggregate exports is 0.34. The relative export

supply is 0.19, and 25% of the firms are exporters. Both targets are successfully replicated.

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5 Self-Selection vs. Learning-by-Exporting

How does self-selection and learning-by-exporting affects firms’ and industries’ dynamics re-

spectively? What is the specific role each of them plays? To unravel the effects of self-

selection and learning-by-exporting, I now simulate the model under two extreme cases: one

with self-selection but no learning-by-exporting, and one with learning-by-exporting but no

self-selection. Previously under the benchmark model, both relative exporting supply and

exporter percentage were managed to be replicated. In this section, I will examine how well

each extreme case behaves. If I remove one mechanism from the consideration, will the model

still be able to replicate both targets? If not, what results can be attained?

5.1 Pure Self-Selection Model

I eliminate learning-by-exporting from my model by setting the innovation cost for the ex-

porters c1 and the innovation cost for non-exporters c0 equal to one another. Under this

assumption, the firm’s export market participation has no influence on its costs of innovation.

The only remaining cost consideration for a firm contemplating entering the export market is

the cost of entry associated with self-selection theory.

Next I recalibrate the model to see how it can replicate the stylized facts. I choose two

empirical targets: the relative export supply as the ratio between aggregate export supply and

aggregate domestic supply, and the exporter percentage on the entire industry. To replicate

the stylized facts, I adjust the parameterization; specifically, production cost for domestic

products d1 needs to be raised by 10%. As a result, the steady-state export ratio increases,

while innovation and production decreases. Without the learning benefit from exporting,

the innovation behavior is discouraged. Even with a higher export ratio, pure self-selection

mechanism leads to a lower production.

However, only the exporter percentage can be successfully matched with the data. Because

of the lack of the learning effect, the export supply is discouraged; even with the same exporter

percentage, the amount of the products supplied to the overseas decreases. As a result, the

relative export supply decreases by 21%. The pure self-selection can not thoroughly replicate

the stylized facts. Compared with the benchmark model, the export intensity will be greatly

discouraged in terms of less export supply. Without learning-by-exporting mechanism, the

positive correlation between exports and production can only be partially explained. As a

result, the exporting behavior of an industry will be much more shrunk, which is not what

the current globalization indicates.

Figure 16 in Appendix C depicts the simulated growth path of a firm beginning from q =

0.1. It still takes 9 periods for this firm to become an exporter, the same as in the benchmark

model. Notice that under this circumstance, the innovation investment reaches its peak at

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the 8th periods, one period before the switching moment. Afterwards the innovation declines

gradually because of the increasing marginal cost. Production smoothly increases with a

decreasing rate, yet experience a bump at the 8th period because of the innovation peak.

Other than these differences, all the other findings are similar to the benchmark results.

Self-selection mechanism therefore separates domestic market from the export market. At

the steady-state, the export ratio rises by 6%; the innovation decreases by 8%, so does the

steady-state production. On the industry-level, the exporter percentage is replicated, however

the relative export supply decreases 21%. Without learning-by-exporting, the export inten-

sity of an industry declines. Therefore, the learning-by-exporting mechanism can effectively

encourage the export intensity of an industry.

5.2 Pure Learning-by-Exporting Model

To eliminate self-selection mechanism I will equalize the fixed cost of entering both domestic

and export market, and make the extra starting-up exporting cost K to be 0. This way the

threshold to the export-market is removed, and the firms can enter the export market under

the same condition as the domestic one. To be specific, I have ηij = κ0, ∀i, j. Under this

circumstance both high export prices and learning-by-exporting drives firms’s incentive to

export.

Next I recalibrate the pure learning-by-exporting model to replicate the stylized facts.

It is found that as long as we have a higher expor price, non-exporters will always jump

immediately. Even with no lower innovation cost and therefore no learning effect, an exporter

status is highly desirable due to the higher export profit. To replicate the empirical targets,

I need to allow a lower export price. Specifically, P1 should be 86% of P0. At the same time,

the learning effect must be shrunk significantly; specifically domestic innovation cost should

be only 0.3% higher than export innovation cost.

Based on this renewed parameterization, the pure learning-by-exporting can now success-

fully replicate the relative export supply. However, even with the same supply ratio, there

are much more exporters under this extreme case. The exporter percentage will increase to

80%, while in the data it is only 25%. Therefore, compared with the benchmark model, the

export intensity will be greatly encouraged in terms of a soaring number of exporters on the

market. Without self-selection mechanism and higher export price, the positive correlation

between exports and production can be partially explained with an unconvincingly high ex-

porter percentage. As indicated by the data, even after decades of globalization, exporting

behavior is not considered common among producers nowadays.

Figure 17 in Appendix C depicts the simulated growth path of a firm beginning from q

= 0.1. It now takes 2 periods for a non-exporter to jump. Born as a non-exporter, a firm

will wait for only one period before it starts the exporting. Even with a lower export profit,

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Table 2: Pure Self-Selection vs. Pure Learning-by-Exporting

Description Benchmark Pure SS Mech. Pure LBE Mech.

Time to Jump1 9 9 2

Critical q∗ 2.79 2.73 0.35

Steady-State Firm-Level Results:

Innovation 0.72 0.66 0.60

Exporting Ratio 0.32 0.34 0.17

Production 3.59 3.30 2.99

Data Replication Results:

Relative Exporting Supply QS1 /Q

S0 0.19 0.15 0.19

Exporter Percentage 25.03 25.00 80.00

1: It indicates how many periods for a firm starting with q = 0.1 to switch from anon-exporter to an exporter.

being an exporter is still very desirable because of a lower innovation cost. The innovation

investment is the highest at the very first period, then gradually decreases due to the increasing

marginal cost. All the steady-state values on the firm level are much lower compared with

the benchmark model; the innovation investment and production both decrease by 17%, and

the export ratio decreases by 47%. On the market level, the relative export ratio can be

replicated, but the exporter percentage is as much as 3.2 times in the data. Therefore, the

self-selection mechanism can slow down the export-status switching process, and keep the

industry’s export intensity under control.

Table 2 summarizes the results. The steady-state innovation, export ratio and produc-

tion are on firm-level; the steady-state relative export ratio and exporter percentage are on

aggregate-level. Generally speaking, self-selection mechanism works in a sense of aggregate-

level adjustment, and allows more productive firms into the export market. By establishing

a export-entry threshold, the self-selection mechanism allows time for a non-exporter to grow

until it starts to export, thus separate the domestic market from the export market. On

the other hand, the learning-by-exporting mechanism works in the sense of individual-level

development; after a firm starts to export, it benefits from a lower innovation cost — as an

important motivation to jump. Without either mechanism the model fails to replicate the

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data adequately enough. Pure self-selection can only replicate the exporter percentage but

with a lower relative export supply; pure learning-by-exporting can only replicate the relative

export supply but with a much higher exporter percentage. Only with both mechanisms can

the model adequately explain both stylized facts.

6 Trade Liberalization

In this section I will make counterfactual analysis of trade liberalization. Assume now an

exogenous trade liberalization happens, and the firms face a lower transportation cost. To be

specific, recall that in the benchmark model, the iceberg transportation cost τ was normalized

to be 1. Now τ is considered to be variable. Under a trade liberalization, I assume that

this transportation cost decreases by 10%. As a result, the real export price P1/τ increases

exogenously from 2 to 2.2. This liberalization can happen abruptly within one period, or

can gradually happen over several periods. I will analyze the changes of firm-level dynamics

under different scenarios in details. I then make comparison between the counterfactual and

the previous benchmark results to determine the influence of different liberalizations.

6.1 Mature Industry

The first counterfactual case is a liberalization after the aggregate industry has reached its

steady state. In the benchmark model, at the 39th period the industry will be stabilized. Now

assume that a industry is mature enough to have already achieved stabilization, then it is

disturbed by a decrease of the transportation cost. As a result, the real export price is raised

by 10%. Because of this change, the firms will make different decisions on their innovation

and export ratio. This will lead to changes in aggregate supplies and exporter percentage

from time to time. Panel A of Table 3 shows these changes over different periods.

Difference cases in Panel A explain different liberalization scenarios: first, when the real

export price rises abruptly within one period; second, P1/τ rises gradually for 5 periods, each

period increases by 0.04; third, P1/τ rises gradually for 10 periods, each period increases

by 0.02. Now compare these scenarios at the same period after the liberalization finishes.

Across different cases there are no changes in the exporter percentage over time, and only

slight difference in the relative export supply. In the middle run, after 25 periods of the

liberalization, a longer liberalization brings a lower QS1 /QS0 , meaning that the less products

are supplied to the export market. However this decrease of relative export supply is only

around 0.02% between different scenarios. In the long run, there are no significant differences

of exporter percentage across these scenarios either. If trade liberalization happens to mature

industry which is already stabilized, then whether the change happens abruptly or gradually

won’t matter; the export intensity of the industry will increase slowly period by period. To

14

Table 3: Trade Liberalization Counterfactual Dynamics

Panel A Trade Liberalization for a Mature Industry (after the 39th period)

Case 1a Case 1b Case 1c

Abrupt Change Gradual 5 Periods Gradual 10 Periods

QS1 /Q

S0 Exporter % QS

1 /QS0 Exporter % QS

1 /QS0 Exporter %

Short Run (1 period later) 0.191 26.15 0.191 26.22 0.192 26.26

Middle Run (5 periods later) 0.192 26.22 0.192 26.26 0.192 26.28

Mid-Long Run (25 periods later) 0.292 30.29 0.292 30.30 0.292 30.30

Long Run (30 periods later) 0.299 31.30 0.299 31.30 0.299 31.30

Panel B Trade Liberalization for a Young Industry (the 8th period)



QS1 /Q

S0 Exporter % QS


1 /QS0 Exporter %





Panel C Trade Liberalization for a Young Industry (the 5th period)



QS1 /Q

S0 Exporter % QS


1 /QS0 Exporter %





15

be specific, after 30 periods the relative export supply will grow by 57.37%, and the exporter

percentage will grow by 25.20%.

6.2 Young Industry

Now assume a trade liberalization happens before the aggregate industry reaches its initial

steady state. Specifically, P1/τ rises when the industry is still at its initial stage of growth.

I then look into how the dynamics of the industry differs across scenarios with different

liberalization patterns.

I consider two cases: first, liberalization upon a young industry, which is at its 8th period of

growth; second, liberalization upon a even younger industry, at its 5th period. The dynamics

of supply ratio and exporter percentage over time are shown in Panel B and C of Table 3.

In Panel B when the trade liberalization happens, only partial firms in the industry have

started exporting. After the abrupt liberalization takes place, immediately the the exporter

percentage will rise. Unlike the previous results in section 6.1, the relative export supply will

be lower compared with the benchmark results at the same period. As time goes by, the

relative export supply starts to rise and 30 periods later, it ends up at a higher level (9.30%

higher) than the contemporaneous benchmark result. The exporter percentage, on the other

hand, will consistently increase. At the 30th period after the liberalization, the exporter

percentage ends up being 8.46% higher than the benchmark level.

If the liberalization takes 5 periods to gradually finish, right after the change happens the

relative export supply QS1 /QS0 will be 1.57% lower than the benchmark result, however the

exporter percentage will not change. As time goes by, both the relative export supply and

the exporter percentage will increase, and 30 periods later the export supply ratio is 6.18%

higher than the contemporaneous benchmark result. Interestingly enough, at this moment

the exporter percentage happens to be the same as the benchmark result.

If the liberalization takes 10 periods to finish, things are again different. Immediately

both relative export supply and exporter percentage will be lower than contemporaneous

benchmark results. As time goes by, both of them will rise. However not both of them can be

as high as the benchmark results even after a long while. To be specific, after 30 periods the

relative export supply will be only 0.81% higher than the contemporaneous benchmark result,

while the exporter percentage will be 1.86% lower. To sum up, if trade liberalization happens

to a young and unstabilized industry, it does not necessarily increase the export intensity of

the industry. The result depends on how the change takes place; if it takes place abruptly

then both relative export supply and exporter percentage will rise. If it takes as long as 10

periods to complete, then the exporter percentage will even be lower than a no-liberalization

level for a very long time.

In Panel C, the trade liberalization happens to a even younger industry at its 5th period,

16

when no exporters appear yet. If the change takes place abruptly, then immediately there

will be exporters. Again, the relative export supply as well as the exporter percentage will

be higher than the contemporaneous benchmark results. As time goes by the relative export

supply gradually rises. After 30 periods of the liberalization, the relative export supply is as

1.64 times as much in the benchmark level, while the exporter percentage is 1.37 times as

much as in the benchmark level. However, if the change takes place gradually, there will be

much less exporters right after the liberalization finishes. As time goes by the relative export

supply and the exporter percentage will both increase. After 30 periods, neither of them

is as high as the contemporaneous benchmark results. To be specific, if the liberalization

lasts for 5 periods, in the long run the relative export supply will be 10.29% lower, and the

exporter percentage will be 16.25% lower. If the liberalization lasts for 10 periods, in the long

run the relative export supply will be 33.68% lower while the exporter percentage 25.24%

lower. Therefore surprisingly, if the liberalization happens to an industry that is so young

that no exporters have appeared yet, the longer the trade liberalization lasts, the lower export

intensity the industry will have for a long time.

To sum up, the dynamics of the export intensity varies across different exogenous trade

liberalization patterns. First, if the liberalization happens to mature industry which has

already reached its steady state, across various liberalization patterns no significant difference

will happen. Second, if the liberalization happens to a young industry with partial firms

as exporters, the longer the liberalization takes, the higher relative export supply will be.

In other words, the relative export supply is lower because of a slower trade liberalization.

Third, if the liberalization happens to a even younger industry with no exporters yet, the

relative export supply and the exporter percentage will both instantly increase at once if the

change is abrupt. But if the change takes 5 or 10 periods for the change to gradually finish,

the relative export supply and the exporter percentage will both be lower compared with

contemporaneous benchmark results, and the export intensity of an industry will be reduced

significantly for a long time. Finally, through comparing between different cases, we can find

that the abrupt liberalization takes effect much faster for a young industry than a mature

industry.

Therefore, to determine whether an exogenous trade liberalization can encourage the ex-

porting behavior in an industry, we need to consider when the change happens, and how long

it lasts. If policymakers want to use a trade liberalization to effectively encourage the export-

ing behavior in an industry in terms of export supply and the number of exporters, there are

important things they should keep in mind: either wait until the industry is stabilized, and

the liberalization pattern won’t matter. If the industry is still very young, then implement the

liberalization as fast as possible; otherwise the export intensity will probably be discouraged

instead for a long period. Under this circumstance, the industry’s export intensity will be

17

encouraged much faster than in a mature industry.

Figures 20, 21 and 22 in Appendix C depict the distribution of firms’ innovation, export

and production after 40 periods. Each figure shows the comparison among different distribu-

tions under a specific trade liberalization pattern. Liberalization after the steady state brings

no change of the distribution across figures under different patterns. If the liberalization takes

place even before any firm starts to export, variations are the most significant when it comes

to the distribution of production and exporting ratio. Specifically, the earlier and the slow-

er the liberalization happens, more firms will have lower production, and there will be less

exporters on the industry.

7 Conclusion

In this paper, I have developed a dynamic model of a firm’s joint decisions to export and

innovate, allowing both decisions to affect the firm’s production in accordance with self-

selection and learning-by-exporting theories of firm-level export and production dynamics.

The model is extended to allow for an industry containing many firms that are heterogenous

with respect to age, export status, and production.

I find that both self-selection and learning-by-exporting critically influence the dynamic

evolution of a firm, an thus the dynamic evolution of an industry. On the one hand, models

that allow only for self-selection can replicate the percentage of firms that export, but predict a

much lower volume of exports than is observed. On the other hand, models that allow only for

learning-by-exporting can replicate the relative volume of exports, but predict unrealistically

high percentage of firms involved in exporting. To adequately capture the stylized facts

embodied in Chilean manufacturing from 2005 to 2007, both mechanisms must be posited to

be effective.

In a counterfactual policy analysis, I find that the effects of trade liberalization depend

critically on the age of the industry. One the one hand, liberalization trade for a mature in-

dustry encourages exports. However if the trade liberalization happens to a young industry at

its initial stage of production evolvement, and it takes long enough to finish the liberalization,

the export intensity of the industry will be reduced.

Also, there remain may potentially interesting extension of the work presented in this

paper. For example, the model’s predictions regarding the impacts of trade liberalization

can be carried out. Another theoretical extension would be to allow firms to shut down

temporarily, rather than shutting down forever. Finally, one could extend the model by

explicitly incorporating a production function and factor pricing. This would allow us to

study the influence of wages on firm- and industry-level dynamics and the impacts of labor

immigration and wage policies.

18

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20

A Policy Analysis

In this section I will perform a policy analysis of the model. That is to analyze the influence

of relevant parameters on the computational results, given potential policies that vary these

parameters. The analysis is targeting on these seven variables: the period for a initially non-

exporter starting with q = 0.1 to jump; the firm-level steady-state innovation investment,

export ratio, and production; the aggregate-level steady-state aggregate domestic supply,

export supply and exporter percentage.

A.1 Export Price P1

Previously in Section 5 I have already done counterfactual analysis based on change of P1.

Here are more details of how it changes the economy. Keep the domestic price P0 to be equal

to 1, and all the other parameters to be the same as the benchmark model; now suppose the

government is imposing an export subsidy or tax on the exporters so that the real export

price received is varying. Figure 6 reports all the relevant difference P1 can make. Panel (a)

depicts how an individual firm starting with q = 0.1 will be affected by changing P1, while

panel (b) how the entire market will be affected.

Figure 6: Simulation Result of a Representative Firm and a Market –Sensitivity analysis of Export Price P1

If P1 is less than 1.96, then a non-exporter will never become an exporter since there is not

enough profitability of exporting. In this case the steady state innovation investment, export

ratio as well as production will keep constant. If P1 equals 1.96, a non-exporter beginning

with q = 0 will be able to jump. If P1 increases further, a non-exporter needs fewer and

21

fewer periods to jump. Intuitively speaking, as the profitability of exports increases, it is

more attractive and more affordable for a firm to start exporting sooner than later. Thus the

steady-state export ratio will also rise as P1 rises; an exporter will eventually choose to export

more out of its entire production. Meanwhile, the steady-state innovation investment will be

much higher and start to rise once a firm is capable to jump, and so will the steady-state

production.

As for the steady-state of an entire market, if P1 < 1.96, there will be neither exporters

nor export supply; the steady-state aggregate production is the aggregate domestic supply,

which is fixed. As the export price exceeds 1.96, the steady-state domestic supply start to

drop; the export supply rises, and so does the exporter percentage. The more subsidy the

government gives to the exporters, the more exporters there will be on the market.

Figure 7: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Innovation Cost Parameter - Exporter c1

A.2 Innovation Cost Parameter - Exporter c1

Now let’s look into how c1 — the innovation cost for the exporters — influences the steady-

state values. Figure 7 shows the results. Suppose the government impose an additional tax on

the exporters so that their innovation become more expensive (c1 rises). It costs the exporters

more in innovation. In this case, it takes longer for a non-exporter to start exporting. The

steady-state innovation will decrease due to the higher production cost; so will the steady-

state production level. Yet the steady-state exporting ratio will rise, even though it means

more costly investment in the innovation. As for an entire market with heterogeneous firms,

as c1 increases there will be a decrease in both export supply and exporter percentage, due

22

to the rising production cost. The steady-state domestic supply will also decline slightly.

A.3 Innovation Cost Parameter - Non-Exporters c0

c0 is the innovation cost for the non-exporters. Figure 8 shows how this parameter influences

the results. Now suppose the government impose a tax on non-exporters’ innovation and c0

rises. It means it costs non-exporters more to invest in innovation. Because of the higher

cost, it makes non-exporters grow slower, and takes longer to start exporting. But as long

as the firms can eventually become exporters, the steady-state innovation, exporting ratio as

well as the steady-state production will not be affected. Varying between 0.5 and 3, c0 allows

this jump to happen. Yet as for the market, the total domestic and export supply will drop

due to the higher cost, and so will the exporter percentage.

Figure 8: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Innovation Cost Parameter - Non-Exporter c0

A.4 Production Cost Parameter - Exporting Products d1

Figure 9 shows the influence of d1, the production cost for exporting products. As it increases,

it costs more to produce the exporting products. The more a firm exports, the more it needs

to pay for production. Under the benchmark parameter setting, non-exporters will be able

to jump eventually when d1 < 0.86. As d1 rises, non-exporters will need more time to start

exporting. Also, the firm’s steady-state export ratio will decrease as d1 increases because of

the higher cost. Also, the firm’s steady-state innovation will decrease, leading us to a lower

production. As d1 rises, the exporters’ export behavior will be hindered and the total export

23

supply as well as exporter percentage will both drop. The total domestic supply will rise, on

the other hand.

Figure 9: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Production Cost Parameter - Exporter d1

Once d1 > 0.86, a non-exporter can never make the jump, and its steady-state innovation

and production will be at a much lower level. Also, in this case, its steady-state innovation

and production cannot be changed by d1 since d1 does not affect the firm’s decision anymore.

The market will also be unaffected by d1 via a constant domestic supply and no exporting

activities.

A.5 Production Cost Parameter - Domestic Products d0

d0 is the production cost for domestic products. Every firm, except those 100% exporters, will

be influenced by it. As described in Figure 10, as d0 increases, the more costly a firm’s domestic

production becomes. Non-exporters will be never jump when d0 < 0.16 since producing purely

domestically is more profitable. In this case as d0 rises, non-exporters will decrease their

steady-state innovation due to the higher cost, resulting in a lower production. The total

domestic supply in the market will slightly fall.

Once d0 > 0.16, a non-exporter will now start to export, since purely domestically pro-

duction is becoming more expensive. Interestingly, the firms’ steady-state innovation and

production will start from a higher level, then decrease as d0 increases. Also, its steady-state

export ratio is rising as it costs more and more to produce domestic products, and it takes

fewer periods for a non-exporter to jump. As a result, total export supply as well as the

exporter percentage will both increase.

24

Figure 10: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Production Cost Parameter - Non-Exporter d0

A.6 Production Depreciation Rate γ

Figure 11 shows the analysis based on γ, the depreciation rate of production from today to

tomorrow. Suppose there is an economic recession which increases γ and creates an unfavor-

able environment for the firms to grow. Consequently q will grow slower. Specifically, as γ

increases below 0.23, the periods it takes for a non-exporter to jump to be an exporter will

increase, since it will take more time for a firm’s production to evolve.

Figure 11: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Production Depreciation Rate γ

25

Furthermore, the rising γ will increase the steady-state innovation and export ratio. A

firm is urged to innovate and export more, so as to keep its production from falling too fast.

However because of the rising depreciation rate, its steady-state production is still declining

even though the firm increases its innovation and exporting effort. As a result, there are fewer

and fewer exporters on the market.

Once γ exceeds 0.23, non-exporters can never make the jump and there will be no exporters

eventually. The firm’s steady-state innovation and production will both sharply fall to a much

lower level. As γ keeps rising, the firm will increase its innovation effort even though now

it can no longer learn from exporting. But still, its steady-state production keeps falling

due to the higher depreciation rate. The total domestic supply always keeps decreasing as γ

increases.

A.7 Fixed Cost - Exporter κ1 and Exporting Start-Up Cost K

κ1 is the fixed cost a firm needs to pay once it enters the exporting market. Assume the

foreign tariff rises, so does the cost. In Figure 12, as κ1 increases, a domestic firm has to

pay more to enter the exporting market. Therefore, when κ1 < 2.03 a non-exporter is able

to jump eventually. As long as the jump happens, as κ1 rises it will take more time for a

non-exporter to grow until it reaches the exporting threshold. The more a firm needs to pay

for its entry to the exporting market, the longer it must wait until it can afford this cost. The

steady-state values of innovation and production will not change.

Figure 12: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Fixed Cost - Exporter κ1

Once κ1 > 2.03, the fixed exporting cost will be so high that a non-exporter can never

26

make the jump, and there will be no exporters on the market in the steady-state. Once a

non-exporting firm can never afford the switch, its steady-state innovation will drop sharply;

as a non-exporter, without any learning from exporting, its production will also drop. Also,

if a firm always stays as a non-exporter, its steady-state innovation and production will not

change as κ1 changes.

The analysis of the exporting start-up cost K has the similar results, which are depicted

in Figure 13. If K < 1.40, non-exporters can make the jump. As K increases, it costs more

for a non-exporter to enter the exporting market, therefore it takes longer for it to jump.

There will be less exporters on the market, and the domestic supply will increase. Firms’

steady-state innovation, exporting ratio and production will keep the same if non-exporters

can make the jump, and keep the same at another lower level if no jumps can ever happen.

To sum up, if the exporting entry threshold changes, the steady-states of individual firms

will not be affected unless this change forbids exporting behavior. Only the steady states of

aggregate economy will be different.

Figure 13: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Exporting Start-Up Cost K

A.8 Innovation Cost Rate β

Let’s look at how β affects the steady-state results of the model. β is a firm’s innovation cost

rate. Notice that the steady-state innovation is always below one. The higher β becomes, the

less it costs a firm, no matter a non-exporter or an exporter, to pay for the same innovation

investment. In Figure 14, as I increase β from 6 to 12, it costs less to innovate. The periods

it takes for a new-born firm to jump will decrease, thus makes the firm to innovate more and

27

grow faster. Meanwhile, increasing β can increase a firm’s exporting ratio, because the firm

needs to resort to exports to keep growing. Thus steady-state production will increase as β

rises.

Figure 14: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Innovation Cost Rate β

Assume the government offers subsidies to firms’ innovation investment, and this policy

cut the innovation cost greatly. In the aggregate market, because higher β and lower cost, both

domestic and exporting supply will increase, and the exporter percentage will also increase

fast.

A.9 Death Probability µ

µ is the probability of a firm being forced to exit the market. In other words, each period a

firm will have a chance of µ to stop production and discontinue its existence on the market. As

this probability varies, the steady-state policies and production of a firm will not be affected;

individual decision of how much to innovate and export will be not affected by the death rate.

As in Figure 15, only the aggregate steady-states of an entire economy will be different

because of the change of µ. Assume the government decides to increase the liquidity of the

market, so that the frequency of firms’ in-flow and out-flow increase. Thus µ goes higher, and

it is more likely for a firm to be forced out of the market; each period more firms die and

more new firms enter. What’s more, under the benchmark parameter setting Q < q1, which

means the new firms are all born as non-exporters. Thus the less the total supply to both

domestic and foreign market will become, and the less exporters there will be.

28

Figure 15: Simulation Result of a Representative Firm and a Market –Sensitivity Tests of Death Probability µ

A.10 Summary & Discussion

There is a major finding based on the above sensitivity tests. The steady-state values of

the production all experience a sharp increase once a firm seizes its opportunity to become

an exporter. Compared with an eternal non-exporter, a firm that ends up as an exporter

will have a significantly higher production. Correspondingly, the steady-state innovation and

exporting ratio will both be significantly higher. The virtuous circle will promote the growth

of an exporter much further. Again, this finding supports the learning-by-exporting theory

— the exporters can experience faster production growth compared with the non-exporters.

Furthermore, a major finding based on the benchmark model is that once an exporter,

always an exporter. However in the real life, as what the data indicate, there are almost as

many firms switching forward to be exporters as those switching back to be non-exporters. To

explained the firms’ withdrawal from the exporting market, changes should occur to relevant

parameters, e.g. exporting price P1, or production depreciation rate γ. In the benchmark

model all these parameters are given, therefore the firms will always keep their exporting

status. But if a new trade agreement is made, and some industries suddenly suffers from a

declining exporting price; or during a recession the production depreciation rate is soaring

high. Then the withdrawal from exporting will happen and certain firms will switch back and

never become exporters again.

29

B Table

Table 4: Descriptive Statistics, 2005 to 2007

Exporters of the year Non-Exporters of the year

Number Percentage Number Percentage

A. TOTAL NUMBER OF PLANTS 1,624 100.00 4,990 100.00

B. CAPITAL PROPORTION

Foreign Capital Proportion = 0 1,321 81.34 4,872 97.64

Foreign Capital Proportion ∈ (0 50%) 49 3.02 42 0.84

Foreign Capital Proportion ∈ [50% 100%) 86 5.30 39 0.78

Foreign Capital Proportion = 100% 168 10.34 37 0.74

C. Technical Assistance

Foreign Tech Assistance Ratio = 0 1,321 81.34 4,872 97.64

Foreign Tech Assistance Ratio ∈ (0 5.0e-6) 167 10.28 43 0.86

Foreign Tech Assistance Ratio ∈ [5.0e-6 1.0e-5] 47 2.89 11 0.22

Foreign Tech Assistance Ratio > 1.0e-5 89 5.48 64 1.28

D. SIZE

Small (10-49 Workers) 669 41.19 4,377 87.71

Median (50-149 Workers) 895 55.11 595 11.92

Large (≥ 150 Workers) 60 3.69 18 0.36

E. VALUE ADDED RATIO

< 0 12 0.74 37 0.74

∈ [0 0.5) 1,088 67.00 3,095 62.02

≥ 0.5 524 32.27 1,858 37.23

F. INNOVATION ON ASSETS

Innovation on Buildings > 0 122 7.51 163 3.27

Innovation on Vehicles > 0 15 0.92 30 0.60

Innovation on Machines > 0 101 6.22 144 2.89

Innovation on Land > 0 7 0.43 14 0.28

No Innovation 1,436 88.42 4,711 94.41

G. Productivity

a ∈ [0 0.5) 56 3.45 1,252 25.09

a ∈ [0.5 1.5) 391 24.07 2,149 43.07

a ∈ [1.5 3) 1145 70.50 1,563 31.32

a ≥ 3 32 1.97 26 0.52

Source: ENIA (Annual National Industry Survey), National Institute of Statistics of Chile.

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C Figures

Figure 16: Simulation Results of the Growth Path of a Firm Starting with q = 0.1

Figure 17: Simulation Results of the Growth Path of a Firm Starting with q = 0.1

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Figure 18: Density of Productivity of New-Born Firms

Figure 19: Density of Productivity of Exporters vs. Non-exporters

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Figure 20: Cumulative Distribution of Firm Production 40 Periods Later:Abrupt Trade Liberalization within 1 Period

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Figure 21: Cumulative Distribution of Firm Production 40 Periods Later:Gradual Trade Liberalization for 5 Periods

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Figure 22: Cumulative Distribution of Firm Production 40 Periods Later:Gradual Trade Liberalization for 10 Periods

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exports, innovation and production growth: a dynamic ... · exports, innovation and production...

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