# Learning, Incomplete Contracts and Export Dynamics: Theory and Evidence from French Firms

Romain Aeberhardt, Ines Buono, Harald Fadinger

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Direction des Études et Synthèses Économiques

G 2011 / 16

Learning, Incomplete Contracts and Export Dynamics:
Theory and Evidence from French Firms

Romain AEBERHARDT - Ines BUONO - Harald FADINGER

Document de travail
INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

Série des documents de travail
de la Direction des Études et Synthèses Économiques

G 2011 / 16

Learning, Incomplete Contracts
and Export Dynamics:
Theory and Evidence from French Firms

Romain AEBERHARDT* - Ines BUONO**
Harald FADINGER***

OCTOBRE 2011

Les auteurs remercient Andrew BERNARD, Paola CONCONI, Alejandro CUNAT, Jonathan EATON, Pauline GIVORD, Michael GREINECKER, Isabelle MÉJEAN, Raùl SAMPOGNARO et Sandro SHELEGIA pour leurs suggestions ainsi que les participants aux séminaires de Banca d'Italia, Insee, Institute for Advanced Studies, WIIW et des conférences 2009 CEPR-ERWIT, 2009 SED meeting, 2009 ESEM et 2009 ETSG annual meeting pour leurs commentaires. Toutes les erreurs restantes sont les nôtres. Les opinions exprimées ici sont celles des auteurs et ne représentent en aucun cas celles de leurs institutions respectives.

<footnote>* Département des Études Économiques d'Ensemble - Division « Marchés et Stratégies d'Entreprise »
Timbre G230 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX</footnote>

<footnote>** Banca d'Italia, via Nazionale 91, 00184, Rome, Italy</footnote>

<footnote>*** Department of Economics, University of Vienna, Hohenstaufengasse 9, A-1010 Vienna, Austria</footnote>
# Learning, Incomplete Contracts and Export Dynamics:
## Theory and Evidence from French Firms

**Abstract**

We consider a model where exporting requires finding a local partner in each market. Contracts are incomplete and exporters must learn the reliability of their partners through experience. In the model, export behavior is state-dependent due to matching frictions, although there are no sunk costs. Better legal institutions alleviate contracting frictions especially in sectors with large contracting problems. Thus, measures of legal quality help reduce the risk that a match between an exporter and a local distributor splits, and they are all the more effective in sectors that are more exposed to hold-up problems. Moreover, the breaking risk declines with the age of the relationship, as unreliable partners are weeded out. We find strong evidence in favor of the model's predictions when testing them with a French dataset that includes information on firm-level exports by destination country.

**Keywords:** Trade Dynamics, Learning, Incomplete Contracts, State dependence, Firm-level Trade Data

## Apprentissage, contrats incomplets et dynamique des exportations :
### Modèle théorique et application empirique
### sur un échantillon d'entreprises françaises

**Résumé**

Nous construisons un modèle dans lequel exporter nécessite de trouver un partenaire local. Les contrats sont incomplets et les exportateurs font évoluer leurs croyances quant à la fiabilité de leur partenaire au fur et à mesure de la relation. Dans ce modèle, les frictions d'appariement génèrent de la dépendance d'état bien qu'il n'y ait pas de coûts échoués. De meilleures institutions réduisent ces frictions, en particulier dans les secteurs où les risques de défaut sur les contrats sont les plus importants. Par conséquent, des mesures de politique publique visant à améliorer la qualité des institutions réduisent d'autant plus le risque de rupture de la relation que les secteurs sont plus exposés aux risques de défaut. De plus le risque de rupture moyen diminue avec l'âge de la relation en raison de l'éviction progressive des partenaires les moins fiables. Ces faits stylisés sont en adéquation avec les résultats empiriques obtenus sur un échantillon de firmes françaises pour lesquelles on dispose de données individuelles sur les pays de destination des exportations.

**Mots-clés:** Dynamique des exportations, Apprentissage, Contrats incomplets, Dépendance d'état, Données microéconomiques, Douanes, BRN

**Classification JEL:** F12, F14, L14
# 1 Introduction

How do firms establish new export relations and what determines the dynamics of exports at the firm level? The most prominent models of export dynamics rely on sunk fixed costs to enter the export market. Such costs can explain why only a few very productive firms export (Melitz, 2003), why firms’ export statuses are very persistent over time and why the probability that a firm exports is determined primarily by its past export status (see Roberts and Tybout, 1997, among others). However, a growing number of micro studies on export dynamics (Eaton, Eslava, Kugler and Tybout, 2007; Buono, Fadinger and Berger, 2008; Lawless, 2009) have revealed evidence that is at odds with this view.

First, export values are usually small when a firm breaks into a new market. Second, most export flows have a very short duration (one or two years), few survive for a longer period and these export relationships with longer durations grow fast. This leads to hazard rates of export relationships that sharply decrease over time and fast growing export values conditional on survival. Finally, a novel stylized fact, which we uncover in the present paper, is the positive relation between persistence of export flows and the quality of legal institutions in the destination country.

We argue that it is crucial to consider that exports at the firm level are relationship-specific in order to explain these observations. Most exporters neither sell a perfectly homogeneous good that can be sold in an organized exchange nor own a distribution network in the export destination. As a result, exporters need to rely on partners in each market. These are either trade intermediaries, distributors that locally market the exporter's product, or foreign firms that import the exporter's product to use it as an intermediate input.

In our model, firms that want to start exporting to a specific country have to search for a partner in that destination. When an exporter is matched with an importer, she is initially uncertain about the importer's reliability. Contracts are incomplete, so that some partners may try to hold up the exporter. Whether an importer has incentives to do so depends on the value of the short term gains from holding up the partner relative to the value of maintaining a long term relationship. This depends – among other things – on the importer's type (patient or impatient), the exporter's productivity, the extent of sectoral contracting frictions and the quality of legal institutions in the destination country. Patient importers sufficiently value
future profits from any relationship to respect contracts with all exporters. On the other hand, impatient importers try to renegotiate contracts *ex post* if contracting frictions are severe (the payoff from renegotiation is large), legal institutions are weak (the opportunity to renegotiate is strong) and exporters are relatively unproductive (the expected value of future profits is low). Since exporters have to learn their partners’ type through experience, uncertainty is initially large and thus export values are small. As an exporter observes that the contract is respected she becomes more confident that her partner is reliable and the value of exports grows.

The combination of these ingredients leads to several interesting patterns. Here, we focus on the more important ones. First, matching frictions generate persistence (state dependence) in export decisions, even though there are no sunk costs in the model. An exporter is unwilling to give up a partner unless she is sure that the importer is unreliable. Second, better legal institutions make it more likely that a given relation survives from one period to the next. As a consequence, better legal quality leads to more state dependence and reduced hazard rates. Moreover, this effect is larger the more severe contracting frictions are in a given sector. Similarly, larger destination market size or higher exporter productivity imply that a given relationship is more valuable for importers and thus makes it more likely that they will honor the contract. Hence, state dependence is larger (and hazards are lower) in destinations with larger markets and for more productive exporters. Moreover, hazard rates decrease with the age of the relationship because partnerships involving unreliable importers are sorted out, while relations with reliable partners survive in the long run.

We use a panel of roughly 6,600 French manufacturing exporters over 13 years to test these predictions. Our dataset allows us to improve upon the econometric methodology of previous research on firm export dynamics (such as Roberts and Tybout, 1997; Bernard and Jensen, 2004). This is because we observe the export value of each plant by destination country, while other studies only had information on the plants’ aggregate export status available. First, we relate state dependence to institutional quality as measured by four different indicators. First, as our main measure of legal institutions, we employ *rule of law* by Kaufmann, Kraay and Mastruzzi (2006), as given in Nunn (2007).<fnref n="1" /> Second, we use *legal quality* by Gwartney and

<footnote n="1">¹This is a weighted average of a number of variables (perceptions of the incidence of crime, the effectiveness and predictability of the judiciary, and the enforceability of contracts) that measure individuals’ perceptions of the effectiveness and predictability of the judiciary and the enforcement of contracts in each country between</footnote>
Lawson (2003).<fnref n="2" /> Finally, we make use of a set of variables collected by the World Bank (World Bank, 2004). We use data on *number of procedures* and *official costs* required to collect an overdue debt. Both variables are scaled and transformed by Nunn (2007) in order to make them increasing in judicial quality.<fnref n="3" /> Basic statistics for the different institutional quality variables are reported in Table 1.

We find that there is strong evidence that state dependence of export decisions is positively related to institutional quality. Figure 1 illustrates this positive relationship. It presents a plot of the estimated effect of past export status on today's export probability by destination country against a measure of the legal quality of the destination country.<fnref n="4" /> It is apparent that the coefficients of past export status are larger for countries with higher quality legal institutions. Second, we find that hazard rates of trade flows are negatively correlated with the destination countries' legal quality and strongly decrease with the age of the relationship. Figure 2 visualizes these observations by plotting a non-parametric estimate of the hazard for different quartiles of legal quality. The hazard has a strongly negative slope. While the probability that a trade flow stops is around 20 percent in the beginning, for trade flows that survive for 9 years the hazard drops to around five percent. Moreover, note that the hazard is lower for higher quartiles of legal quality. Third, export values are initially small and grow with the age of the relationship. In Figure 3 we depict box plots by age of the relationship.<fnref n="5" /> The figure shows nicely that median export sales are initially very small (around 10,000 euros). As relationships get older export

<footnote n="1997">1997 and 1998. The variable ranges from 0 to 1, increasing according to the quality of the institutions.</footnote>

<footnote n="2">²This index, which ranges from 1 to 10, measures the legal structure and the security of property rights in each country in 1995.</footnote>

<footnote n="3">³*Number of procedures* is the total number of procedures mandated by law or court regulation that require interaction between the parties or between them and the judge or court office. *Number of procedures* is obtained as 60 minus the total number of procedures, thus a higher number indicates less procedures and a more efficient judicial system. This variable ranges from 2 to 49 in our sample. *Official costs* is the sum of attorney fees and court fees during the litigation process, divided by the country's per capita income. The transformed variable ranges from 1 to 4.5.</footnote>

<footnote n="4">⁴We use a linear probability model and regress the current export status of each plant on the export status in the previous year by destination country. This figure is meant to be purely illustrative. We provide more formal econometric evidence for this relation in the empirical section of this paper.</footnote>

<footnote n="5">⁵The box plot depicts the median and the 25th and 75th percentiles of the distribution of export values, as well as the minimum and maximum export value. Note that the distribution has a long right tail, with most of the mass of the distribution being concentrated at very low values.</footnote>
values increase substantially.<fnref n="6" />

We now turn to a discussion of the related literature. While there is a growing body of research on the firm-level dynamics of exporting, we are not aware of an alternative explanation that can explain all the empirical facts emphasized in this paper. A large empirical literature, which builds on the classical hysteresis models by Baldwin and Krugman (1989) and Dixit (1989), focuses on sunk costs as the main reason for state dependence of exporting decisions. The seminal contribution is Roberts and Tybout (1997) using data on Colombian exporters, followed, among other studies, by similar evidence for the US by Bernard and Jensen (2004). These papers estimate reduced form models for export decisions and show that past export status is an important predictor for current export status. In an influential study, Das, Roberts and Tybout (2007) perform a structural estimation of a model with heterogeneous firms and sunk costs to quantify the size of sunk entry costs to start exporting. They estimate these costs to be substantial for Colombian exporters (around $US 400,000). More recently, Ruhl and Willis (2008) show that the standard model of firm heterogeneity with sunk costs predicts export values which are too large upon entry and hazard rates that increase over time, which is at odds with the empirical evidence. The intuition for these counterfactual predictions is that in such a model firms enter the export market when they are productive enough to overcome the sunk cost entry hurdle.

A more recent line of research is motivated by the empirical observations that entry into export markets usually occurs with small values and that hazards decline with the age of the relationship. To explain these facts, Eaton, Eslava, Krizan, Kugler and Tybout (2008a) develop a model of Bayesian learning. In this setting, firms are initially uncertain about their demand in the export market and therefore start small. If they discover that demand is large they spend resources in order to reach more consumers and their exports grow fast. This idea is related to our paper but – since firms sell directly to consumers – their model remains silent on the role of institutions and contractual frictions for export dynamics.<fnref n="7" />

Our paper is also strongly related to the literature on relationship-specific trade. In Rauch

<footnote n="6">⁶Similar evidence has also been reported by Eaton et al. (2007) for Colombian exporters.</footnote>

<footnote n="7">⁷Other papers that emphasize learning about local demand are Arkolakis and Papageorgiou (2009), as well as Segura-Cayuela and Vilarrubia (2008) and Albornoz, Pardo, Corcos and Ornelas (2009), who focus on learning from other exporters (export destinations).</footnote>
and Watson (2003) importers are uncertain about the reliability of foreign suppliers. They test the waters by initially placing small orders, which are followed by large orders if the test is successful. This leads to small import values at the beginning of the import relationship that grow as the relationship matures. Besedes and Prusa (2006) find empirical support for this using highly disaggregated product-level import data for the US.

The paper most closely related to ours is Araujo and Ornelas (2007). They consider a model where exporters have to match with a distributor, whose type is unknown and has to be learned through experience. Some distributors run away with exported goods if they can. As a consequence, export values are initially small and increase as exporters become more confident about the reliability of their partners. They also derive results on the role of institutions on firm-level and aggregate trade flows but they do not investigate their model's predictions regarding state dependence. Our main theoretical contribution is to extend their homogeneous firm setup to a setting with heterogeneous firms. This extension is crucial to bringing the model to the data. The reason is that most of our comparative statics results depend on firm heterogeneity because they are based on composition effects. For example, the predictions that state dependence is larger in larger markets, or that institutional quality is less important for more productive firms are consequences of firm heterogeneity. In addition, we focus on an incomplete contract interpretation of their setup and we allow sectors to differ in the extent of their contracting frictions. This gives the prediction that the impact of legal institutions on state dependence or hazard rates is larger in sectors that are more exposed to contracting frictions and allows us to also exploit the cross-sectoral variation of our data in the empirical section. Most importantly, the main contribution of this paper compared to Araujo and Ornelas (2007) is our careful empirical test of the model's predictions regarding export dynamics.

Summing up, the contribution of our paper is to provide a micro-foundation for the dynamics of exporting at the firm level that highlights the importance of both informational and contracting frictions. Our model generates state dependence of exporting decisions without relying on sunk costs, while also being consistent with other stylized facts about exporting dynamics. In addition, the model has implications for the interaction between state dependence/hazard rates and the quality of legal institutions that differentiate it from alternative explanations. We show that these predictions are strongly supported by empirical evidence.
In the next section we motivate our assumptions on the relationship-specificity of exports and discuss the model. We also derive a set of testable predictions. In section 3 we present the data and test the predictions derived in the theory section. The final section concludes.

## 2 A Model of Exporting and Learning

In standard trade models exporting is not different in nature from being active in the domestic market – firms can directly sell their goods to consumers. In reality, however, exporters usually sell their products to a very small number of importers in each foreign market. These are either distributors who locally market and sell the exporters’ products, trade intermediaries, or foreign firms that use these products as intermediate inputs.

Empirically, many – especially smaller – exporters use importers to sell their goods in foreign markets. Few products are sufficiently standardized in order to be sold on an organized market. Thus, if an exporter wants to penetrate a foreign market she can either market the product herself – which entails substantial costs for getting to know the local business environment and setting up a distribution network – or she has to rely on a local partner. Hence, trade is relationship-specific, since it involves a bilateral relation between an exporter and an importer.

Regarding evidence on the relationship-specificity of trade, Eaton et al. (2008a) combine Colombian firm-level export data with US import data and show that each Colombian exporter is involved in a very small number of trade relations with the US. On average, Colombian firms that export to the US have 1.4 trade relations in the US, 80% of Colombian exporters to the US have only one relation and 90% at most two relations, providing strong support for the hypothesis that most trade is relationship-specific. Blum, Claro and Horstmann (2010) provide similar evidence for Chilean exporters linked to Colombian importers – the median exporting firm from Chile has only one importer in Colombia. In our model, we abstract from direct exports to consumers, setting up a distribution network and other forms of intra-firm trade, an option that is viable only for very large exporters because it requires substantial amounts of fixed investments.<fnref n="8" />

Informational frictions about the quality and reliability of local partners are important obstacles for exporters, who want to establish in new markets. For example, the U.S. department

<footnote n="8">⁸Felbermayr and Jung (2009) report that only 4% of German exporters have wholesale affiliates.</footnote>
of commerce (U.S. Commerce Department, 2000) advises that “a proper channel of distribution needs to be carefully chosen for each market,” warning potential exporters that they “should investigate potential representatives or distributors carefully before entering into an agreement.” Some local partners may behave opportunistically if they have incentives to do so and this depends to a large extent on the quality of the local legal system. Reputation may help to overcome institutional weaknesses, but it takes time to build up. We now turn to a description of the model.

## 2.1 Setup

Consider an economy with two countries, Home and Foreign, and many sectors $j = 1, ..., J$.

In Home there is a measure $M \gg 1$ of infinitely lived producers in each sector $j$, which discount the future at rate $\beta_E$. Producers, indexed by $f$, face a constant marginal cost $c$ to produce,<fnref n="9" /> which is firm-specific and drawn from a distribution $G(c)$ with support on $(0, \infty)$. Each firm produces a differentiated variety and is a monopolist for that specific variety. If a producer wants to export she cannot sell her goods directly to Foreign consumers but needs to form a partnership with an importer located in Foreign.

Since we are mainly interested in the formation of export relationships and because the export decision is independent of behavior in the domestic market (as marginal costs are constant), we disregard the activities of producers in their domestic market.

In each sector, Foreign aggregate demand for each variety produced by a Home exporter is described by a constant price elasticity demand function $q(p) = Ap^{-\varepsilon}$, where $A$ is a summary measure of Foreign market size in sector $j$.<fnref n="10" />

In each sector, Foreign is populated by a measure one of infinitely lived firms that can distribute goods produced by Home producers to Foreign consumers, which we call importers.<fnref n="11" /> Each of them can sell any imported good in that sector to Foreign consumers but cannot

<footnote n="9">⁹We omit indices for notational ease whenever this does not cause confusion.</footnote>

<footnote n="10">¹⁰Such a demand function can be derived in an environment where Foreign consumers love variety and have Dixit-Stiglitz preferences. We take the Foreign price index and expenditure on each sector as given, implicitly assuming that the share of Home exporters in Foreign is small so that their impact on the sectoral price level in Foreign is negligible.</footnote>

<footnote n="11">¹¹Alternatively, importers can be interpreted as Foreign manufacturing firms that import intermediate inputs.</footnote>
distribute more than one good simultaneously.<fnref n="12" /> Importers may be of two types that differ in terms of their discount factor.<fnref n="13" /> There are patient importers, indexed by $H$, with discount factor $\beta_H$ and impatient importers, indexed by $L$, with discount factor $\beta_L$, where $\beta_L < \beta_H$. The type of the importer $\in \{H, L\}$ is private information. The fraction of impatient importers in the population is $\theta_0$ in each sector.

In every period, exporters and importers that are not in an export relation decide whether to look for a partner or to remain inactive. We assume that exporters are in excess supply, so that the number of exporters that can find an importer is limited by the number of importers.<fnref n="14" /> If importers decide to search for a partner they meet an unmatched exporter with exogenous probability $x$.

Before a partnership is formed, exporters' marginal cost is unobservable to importers, so that matching occurs randomly. Only once matched, the importer discovers the marginal cost of her partner. At the beginning of every period, matched exporters and importers can both decide whether to maintain the partnership or to dissolve it. If they decide to dissolve it, both the exporter and the importer cease to be active and are replaced by another set of firms of the same type.<fnref n="15" />

<footnote n="12">¹²The predictions of the model would not change if importers could distribute more than one good as long as exporters cannot observe the success of other exporters matched with a particular importer. If exporters could infer the importer's reliability by observing other exporters the model would become far more complex. Exporters would try to match with importers that are successful with other firms. This would mitigate uncertainty and reduce the role of contracting frictions. Thus, our model can be seen as an extreme case of uncertainty. Nevertheless, our empirical results show that legal institutions play an important role for the state dependence and survival of export relationships.</footnote>

<footnote n="13">¹³While we do not need to take a stand on where differences in the level of patience come from, one possible micro-foundation is credit market frictions – if some importers are credit constrained and face higher borrowing costs they discount future profits at a higher interest rate than importers who do not need to rely on external funds. Alternatively, we could model importers with different fixed distribution costs that are unobserved by exporters and we would still obtain similar predictions.</footnote>

<footnote n="14">¹⁴This assumption simplifies some of the algebra but is not important for the main results. We could alternatively assume that importers are in excess supply.</footnote>

<footnote n="15">¹⁵The assumption that exporters and importers cannot reenter the pool of unmatched firms simplifies some of the analysis but is innocuous given that in equilibrium the pool of available importers and exporters deteriorates weakly over time. Thus, importers and exporters never have an incentive to wait for a better partner or to break a relationship because the available pool of partners has improved.</footnote>
In each period – if they decide to continue the relationship for another period – the partners write a simple one-period contract. The contract specifies an export quantity and an exogenous split of the current period’s surplus.<fnref n="16" /> The exporter receives an exogenous fraction α of the current surplus and the remaining fraction goes to the importer. The surplus consists in the revenue of exporting minus the fixed cost to export. In the next stage, exporters produce the quantity of goods specified in the contract and pay the fixed cost, and importers make a transfer equal to their fraction of the fixed cost. After that, the importer may try to hold up the exporter by renegotiating the split of current revenues if it pays to do so. Importers can make a take-it-or-leave-it offer in order to appropriate an additional sector-specific fraction $\gamma_j \in [0, 1]$ of the part of current revenues that the contract originally assigned to the exporter. $\gamma_j$ measures how sensitive a sector is to hold-up problems. This depends on whether the good has been specifically designed for the export market. The exporter’s outside option is to sell the good through a partner in the domestic market with the same revenue split but for a fraction $(1 - \gamma_j)$ of the original price. The lower price in the domestic market reflects the extent to which the good has been tailored to the export market. If $\gamma_j = 0$, the importer cannot appropriate any of the exporter’s share of revenues if she tries to renegotiate because the exporter could easily sell the good in the domestic market for the same price as in the current relationship. If $\gamma_j = 1$, on the other hand, the good is worthless outside the relationship and the importer can appropriate all the revenues by renegotiating the contract. We assume that the exporter always accepts the importer’s proposal since she is indifferent between accepting and her outside option.

Moreover, the possibility to renegotiate the contract also depends crucially on the quality of the Foreign legal system, $\lambda$. Importers are ex ante uncertain whether they will find an opportunity to renegotiate. They are able to do so with probability $(1 - \lambda)$. For example, they may need to bribe a public official in order to get around the conditions stipulated in the contract and they are unsure whether they can do this successfully. If renegotiation occurs it is observed by the exporter.<fnref n="17" /> In the last stage, the exporter ships the quantity of goods specified

<footnote n="16">¹⁶Since we want to focus on the role of reputation for trade relations we do not allow for contracts that can be used to screen between patient and impatient importers.</footnote>

<footnote n="17">¹⁷Araujo and Ornelas (2007)'s interpretation for a very similar setup is that importers may try to default on exporters and run away with the revenues from the sales of shipped goods. This requires that shipments are made before goods are paid for (trade credit). If importers try to default, they can steal exporters' revenues and are successful with probability $(1 - \lambda)$. Here $\lambda$ is again a measure of the quality of the local legal system. In</footnote>
in the contract, goods are sold and the importer transfers a fraction of revenues to the exporter.

Finally, at the end of each period there is a positive probability of exogenous separation,
$s \in [0, 1]$.

## 2.2 Nash Equilibrium

In this section we study a perfect Bayesian Nash equilibrium of the game between exporters and importers described above that involves the following considerations.

In each period $t$ potential exporters decide whether to enter the export market in order to search for a partner. If an unmatched exporter meets an importer she decides optimally whether to accept the partner or to continue the search given her marginal cost, her belief about the partner's type and the strategies of the importers. Any exporter that has a partner decides at the beginning of each period whether to continue the relation for another period or to terminate it given her beliefs about the type of the importer. If she decides to continue the relation, she chooses the optimal quantity to export given her marginal cost $c$, her beliefs about the type of the importer and the strategies of the importers.

Importers face a similar set of decisions. If an importer meets an exporter she decides optimally whether to accept this match and form an export relation or to continue the search given her belief about the partner's type and exporters' strategies. An importer that has a partner decides optimally whether to try to renegotiate or to honor the contract given her type, the exporter's marginal cost and her strategy.

Even though in this infinite-horizon setup many perfect Bayesian Nash equilibria exist, we focus on a Markov-perfect equilibrium, which is especially plausible because of its simplicity. In any period, beliefs about the importers' type, which follow a Markov process, are sufficient to describe the current state. The equilibrium strategies of exporters and importers depend only on current beliefs and on current actions.

Given this setup, we show that the equilibrium is characterized as follows: exporters enter the export market as long as they expect to make non-negative profits given their marginal

this case, one could interpret $\gamma_j$ as the fraction of revenues financed with trade credit but we did not find any empirical evidence that measures of sectoral dependence on trade credit have any impact on state dependence or hazard rates. Thus, we prefer the explanation given in the main text and we will focus on the incomplete contract interpretation of our setup in the empirical section.
cost, their beliefs, and the importers' strategies. Impatient and patient importers as well as exporters initially accept any match. Once a match is formed, impatient importers try to renegotiate contracts with unproductive exporters and honor contracts with sufficiently productive exporters; in fact, we show that there is a threshold $\bar{c}$, such that they try to renegotiate the contract if and only if $c > \bar{c}_t$. Patient importers, on the other hand, always honor their contracts with any type of exporter. Exporters who have a partner choose the optimal quantity to export given the split of the surplus, their beliefs about the type of their partner and the strategy of importers. Having observed the behavior of their partners, exporters update their belief about the type of the importer at the end of the period using Bayes' rule. If the exporter discovers that she is matched to an importer who tries to renegotiate the contracts, her expected profits become negative and she terminates the relationship.

These equilibrium strategies and beliefs imply that sufficiently productive exporters are indifferent to the type of their partner, while less productive exporters fear that an impatient partner will hold them up if she has the chance. Since exporters cannot distinguish between patient and impatient importers unless they observe that the contract is renegotiated successfully, they stick to the importer as long as the contract is respected. The longer importers have honored their contracts, the more confident exporters become that their partner is patient.

We now analyze this equilibrium in more detail. Most proofs are relegated to the Appendix. We start out with the evolution of beliefs.

### 2.2.1 Beliefs

For the most productive exporters, it is never in the interest of importers to renegotiate a contract, because immediate profits made by expropriating the exporter are always outweighed by the expected gains of maintaining the relationship with the exporter. For the less productive ones, the expected future gains are smaller and it can be in the interest of the importer to renegotiate. In general, there must therefore exist a threshold $\bar{c}$ such that it is beneficial for an impatient importer to renegotiate when $c > \bar{c}$.

Beliefs are modelled only for unproductive exporters ($c > \bar{c}$) since for the productive ones ($c < \bar{c}$), all importers are equivalent and therefore they are indifferent between them.

In equilibrium, exporters with $c > \bar{c}$ maintain a partnership as long as they are not certain
that their partner is impatient. Every period they update their beliefs about the probability that their partner is impatient according to Bayes' rule.

Let $\tilde{\theta}$ be the subjective probability for these exporters that the importer is impatient and therefore might not honor the contract. Conditional on having observed a violation ($v$) of the contract and given the equilibrium strategies of importers, $\tilde{\theta}(v) = 1$. Conversely, conditional on having observed that the contract was respected ($r$) in the previous period, and since impatient importers honor their contracts with unproductive exporters with probability $\lambda$, $\tilde{\theta}(r) = \frac{Prob(L \cap r)}{Prob(r)} = \frac{\lambda \tilde{\theta}}{\lambda \tilde{\theta} + 1 - \tilde{\theta}} < \tilde{\theta}$. If no renegotiation occurs this does not reveal any information about the type of the importer to the exporter, so $\tilde{\theta}(r) = \tilde{\theta}$. More generally, let $\tilde{\theta}_{it}$ be the subjective probability of an exporter with $c > \bar{c}$ that the importer is impatient in a relationship of age $i$ that started in period $t$, then $\tilde{\theta}_{it} = \frac{\lambda^i \tilde{\theta}_{0t}}{\lambda^i \tilde{\theta}_{0t} + 1 - \tilde{\theta}_{0t}}$ if no renegotiation has occurred for any $i \in \{0, ..., i-1\}$ and $\tilde{\theta}_{it} = 1$ otherwise.

In equilibrium, beliefs must be consistent with the actual probabilities of getting an impatient partner, such that initial subjective probabilities equal the true fraction of impatient importers in the number of unmatched importers that are searching for an exporter, $\tilde{\theta}_{0t} = \theta_{0t}$. Next, we determine the exporters' optimal strategies given the strategies of importers and exporters' beliefs.

### 2.2.2 Exporters

In every period, each exporter chooses the optimal export quantity given her type $c$, her belief about the type of the importer and the importers' strategies. Remember that in the Nash equilibrium we are considering, impatient importers try to renegotiate the contracts with firms with $c > \bar{c}_t$ and that renegotiation is successful with probability $1 - \lambda$.

The maximization problem of any exporter with $c > \bar{c}_t$ is therefore given by

$$ \max_{p} \Pi(\tilde{\theta}, c > \bar{c}_t) = \max_{p} \alpha \{\tilde{\theta}[\lambda + (1-\lambda)(1-\gamma)] + (1-\tilde{\theta})\} p^{1-\varepsilon}A - p^{-\varepsilon}Ac - \alpha f. \quad (1) $$

These exporters face an impatient importer with subjective probability $\tilde{\theta}$, who does not respect the contract with probability $(1 - \lambda)$. If the importer does not stick to the contract she can appropriate a fraction $\gamma$ of the exporter's share of revenues. Variable production costs and a fraction $\alpha$ of the fixed costs always have to be incurred by the exporter.
The optimal price and quantity for these exporters are given by $p^*(\tilde{\theta}_t, c > \bar{c}_t) = \frac{\varepsilon}{\varepsilon-1} \frac{c}{\alpha[1-\tilde{\theta}\gamma(1-\lambda)]}$, $q^*(\tilde{\theta}_t, c > \bar{c}_t) = \left\{\frac{\varepsilon-1}{\varepsilon} \frac{\alpha[1-\tilde{\theta}\gamma(1-\lambda)]}{c}\right\}^{\varepsilon} A$.

Total revenue is given by $Rev^*(\tilde{\theta}_t, c > \bar{c}_t) = \left\{\frac{\varepsilon-1}{\varepsilon}\alpha[1 - \tilde{\theta}\gamma(1-\lambda)]\right\}^{\varepsilon-1} c^{1-\varepsilon}A$, while exporters' profits are $\Pi^*(\tilde{\theta}_t, c > \bar{c}_t) = \frac{\alpha}{\varepsilon}[1 - \tilde{\theta}\gamma(1-\lambda)]Rev^*(c > \bar{c}_t) - \alpha f$.

Note that prices are inefficiently high while export quantities and revenues are too low compared with a monopolist who can directly export his product to Foreign. This reflects the facts that exporters face the full marginal costs of production while receiving only a fraction $\alpha$ of revenues and their uncertainty about the importer's type. *Ceteris paribus*, an improvement in the quality of legal institutions (higher $\lambda$) increases export quantities and revenues because it implies less uncertainty about the exporter's behavior.<fnref n="18" /> Moreover, more severe contracting problems (higher $\gamma$) lower export quantities and revenues, since exporters have more to lose in the case of successful renegotiation.

Similarly, the maximization problem of exporters with $c \le \bar{c}_t$ is

$$ \max_{p} \Pi(c \le \bar{c}_t) = \max_{p} \alpha p^{1-\varepsilon} A - p^{-\varepsilon} Ac - \alpha f, \quad (2) $$

with solution $p^*(c \le \bar{c}_t) = \frac{\varepsilon}{\varepsilon-1} \frac{c}{\alpha}$, $q^*(c \le \bar{c}_t) = \left(\frac{\varepsilon-1}{\varepsilon} \frac{\alpha}{c}\right)^{\varepsilon} A$, total revenues $Rev^*(c \le \bar{c}_t) = \left(\frac{\varepsilon-1}{\varepsilon} \alpha\right)^{\varepsilon-1} c^{1-\varepsilon}A$ and profits $\Pi^*(c \le \bar{c}_t) = \left(\frac{\alpha}{\varepsilon}\right) Rev^*(c < \bar{c}_t) - \alpha f$.

These exporters charge lower prices and sell higher quantities than exporters with $c > \bar{c}_t$ both because they are more productive and because they face no risk that impatient importers may violate the contract.

The implication of incomplete information is that the longer exporters observe no contract violation, the more confident they become that their partner is patient. As a consequence, they put more at stake and increase the quantity they export. At the same time, for firms with $c \le \bar{c}$, learning plays no role because even impatient importers honor their contracts with these exporters. Thus, we can state the following lemma.

**Lemma 1:** Export revenues are increasing in the age of the relationship as long as $c > \bar{c}_t$ and constant for $c \le \bar{c}_t$.

**Proof:** See Appendix.

<footnote n="18">¹⁸There is also an indirect effect of $\lambda$ through its impact on equilibrium beliefs, $\tilde{\theta}$, which are increasing in $\lambda$.</footnote>
Next, define $\theta^*(c)$ as the level of $\theta$ such that exporters with $c > \bar{c}_t$ make zero per period profits given their marginal cost $c$ and importers' equilibrium strategies: $\Pi(c, \theta^*(c)) = 0$. Then we can state the following lemma:

**Lemma 2:** Let $\tilde{\theta}_{0t}$ be non-decreasing in $t$. Then given importers' equilibrium strategies and exporters' equilibrium beliefs there is a unique value $\bar{\theta}(c) \in [\theta^*(c), 1)$ such that for all $t$ an exporter with marginal cost $c > \bar{c}_t$ accepts any importer she meets as long as $\tilde{\theta}_{0t} \le \bar{\theta}(c)$. Moreover, she maintains a partnership if and only if the importer does not violate the contract. Exporters with $c \le \bar{c}_t$ accept any partner for $\tilde{\theta}_{0t} \in [0, 1]$ and maintain a partnership as long as the importer does not violate the contract given importers' equilibrium strategies and exporter's equilibrium beliefs.

**Proof:** See Appendix.

Lemma 2 states that given her marginal cost an exporter only enters Foreign if her belief about the probability of meeting an impatient importer is sufficiently low. Moreover, if the exporters' subjective probability at the beginning of the relationship that the importer is impatient increases weakly over time, it never pays off to wait for a better partner. The reason is that the expected value of finding a partner in the future is lower than that of finding a partner today because exporters' per period profits and the probability for the relation to survive are decreasing in initial beliefs $\tilde{\theta}_{0t}$. In addition, an exporter sticks to any importer as long as she does not observe a violation of the contract. This is because as long as the contract is respected, she cannot be certain whether her partner is patient or whether the importer did not manage to violate the contract despite trying to. Each time an importer honors the contract, the exporter becomes more confident that her partner is patient and increases exports, which in turn increases the value of the relationship. Consequently, it does not make sense to terminate a relation before a violation of the contract occurs. Very productive exporters with $c < \bar{c}$, on the other hand, do not fear that contracts are not respected by impatient importers. Thus, their beliefs about the probability that their partner is impatient do not influence their decision to form a relationship.

The least productive exporter that enters the export market and accepts an importer makes zero profits in expected terms. This defines a cutoff marginal cost $\tilde{c}_t$ such that $\tilde{\theta}_{0t} = \bar{\theta}(\tilde{c}_t)$. Thus exporters accept a match if and only if $c \le \tilde{c}_t$. To make things interesting, we assume that
$\tilde{c}_t > \bar{c}_t$. Since impatient importers try to violate contracts with exporters with $c \ge \bar{c}_t$, the cutoff marginal cost level is implicitly defined by the following zero profit condition:

$$V_E(\tilde{c}_t, \tilde{\theta}_{0t}) = \Pi(\tilde{c}_t, \tilde{\theta}_{0t}) + \sum_{i=1}^{\infty} (\beta_E(1-s))^i \Pi(\tilde{c}_t, \tilde{\theta}_{it}) \prod_{j=0}^{i-1} (1 - \tilde{\theta}_{jt} + \tilde{\theta}_{jt}\lambda) = 0. \quad (3)$$

Here, $V_E(\tilde{c}_t, \tilde{\theta}_{0t})$ is the value function for a match for exporters with $c = \tilde{c}_t$. Future profits are discounted by the exporters' discount factor $\beta_E$, the probability of no exogenous separation occurring, $1-s$, and the subjective probability that the contract is not violated before the relationship reaches age $i$, $\prod_{j=0}^{i-1}(1 - \tilde{\theta}_{jt} + \tilde{\theta}_{jt}\lambda)$. This means that the least productive firms that match are willing to incur initial losses because if contracts are respected export revenues grow over time and allow these firms to break even in expectations. The following lemma summarizes the free entry condition.

**Lemma 3:** Given equilibrium strategies and beliefs there is a $\tilde{c}_t$ such that exporters enter the export market if and only if $c \le \tilde{c}_t$.

Since per period profits, $\Pi(\tilde{c}_t, \tilde{\theta}_{it})$, and the probability that the relationship survives until age $i$, $\prod_{j=0}^{i-1}(1 - \tilde{\theta}_{jt} + \tilde{\theta}_{jt}\lambda)$, are both decreasing in the subjective probability that the partner is impatient in the period of the match, $\tilde{\theta}_{0t}$, we can establish the following:

**Lemma 4:** Let $\tilde{\theta}_{0t}$ be non-decreasing in $t$. Then the cutoff marginal cost $\tilde{c}_t$ is non-increasing in $t$.

Having described the exporters' equilibrium strategies, we now turn to importers.

### 2.2.3 Importers

Initially, importers accept any partner because they do not observe the exporters' marginal cost before they match and because the value of waiting is always smaller than the value of accepting a partner today. This is because the expected value of a match decreases over time for two reasons: first, the surplus from any relation decreases the later the relation starts because exporters' initial subjective probability that importers are impatient increases; second, the expected marginal cost of unmatched exporters, $E_t(c)$, increases over time and this reduces per period expected surplus. Lemma 5 summarizes this behavior.
**Lemma 5:** Let $\tilde{\theta}_{0t}$ be non-decreasing in $t$ and let $E_t(c)$ be non-decreasing in $t$. Then, given the equilibrium strategies and beliefs, importers initially accept any partner.

**Proof:** See Appendix.

In equilibrium, impatient importers honor contracts with low cost exporters and try to violate contracts with high cost exporters. Given a sufficiently high level of patience, $\beta_L$, renegotiating contracts with productive exporters is not profitable because the loss of future shared revenues is too large compared to current profits from violating the contract. Conversely, when impatient importers face a less productive partner, future surplus from the relation is not large enough to compensate for impatience, so impatient importers try to violate the contract.

**Lemma 6:** Given the equilibrium strategies and beliefs and if $\beta_L$ is sufficiently large, impatient importers try to violate contracts if and only if $c > \bar{c}_t$.

**Proof:** See Appendix.

Patient importers, on the other hand, value the future sufficiently in order not to renegotiate contracts with high cost exporters. They would only renegotiate contracts with producers with extremely high marginal costs, which do not enter the export market in equilibrium.

**Lemma 7:** Given the equilibrium strategies and beliefs, patient importers honor contracts with all exporters that enter.

**Proof:** See Appendix.

## 2.3 Industry Equilibrium

In this section we determine how the measure of impatient importers that search for an exporter, $v_{Lt}$, and the measure of patient importers that search for an exporter, $v_{Ht}$, evolve over time since they determine $\tilde{\theta}_{0t}$ and therefore agents' beliefs. In addition, we establish the evolution of the distribution of unmatched exporters that are searching for an importer, $G_t^u(c)$, which determines the expected marginal cost of unmatched exporters, $E_t(c)$.

Given the laws of motion for $v_L$ and $v_H$, which are derived in the Appendix, one can show that $\theta_t = \frac{v_{Lt}}{v_{Lt}+v_{Ht}}$ is weakly increasing over time and converges to the steady state value $\theta_{SS}$. The
intuition is that relations with impatient importers are dissolved both for exogenous and en-
dogenous reasons, while relations with patient importers are dissolved exclusively exogenously,
so that the proportion of impatient importers in the population of unmatched importers in-
creases over time. This verifies the assumption on $\tilde{\theta}_t$ made in order to derive exporters' and
importers' equilibrium strategies.

**Lemma 8: $\theta_t$ is weakly increasing in t.**

**Proof:** See Appendix.

Moreover, in the Appendix we also derive the law of motion of the distribution of unmatched
exporters and show that the average cost of unmatched exporters $E_t(c)$ is weakly increasing
over time. This confirms the assumption made in previous lemmata. Lemma 9 states this
formally.

**Lemma 9: $E_t(c)$ is weakly increasing in t.**

**Proof:** See Appendix.

Finally, the industry equilibrium is given by the two difference equations that describe
the evolution of unmatched patient and impatient importers, as well as the law of motion of
the distribution of exporters matched with patient importers $G^H(c)$, the law of motion of the
distribution of exporters matched with impatient importers $G_L(c)$ and an equation relating
the population distribution of productivity to the distribution of matched and unmatched
exporters.<fnref n="19" /> All equations can be found in the Appendix.

## 2.4 Comparative Statics

Having described the industry equilibrium, we derive a number of comparative statics re-
sults that we will test in the empirical section of the paper. Our main interest is to relate
export dynamics to firm characteristics (productivity), industry characteristics (the severity of
sectoral contracting frictions), destination characteristics (legal institutions, market size) and
their interaction. Thus, we now interpret our model as applying to a world with many export
destinations. We investigate the effect of firm, industry and destination characteristics on the

<footnote n="19">¹⁹Thus, this is a system of 5 difference equations in $v_L, v_H, G^H(c), G^L(c)$ and $G^u(c)$.</footnote>
state dependence of export decisions and on hazard rates. For all comparative statics we assume that the economy is in the steady state, which implies that $\bar{c}$ and $\tilde{c}$ are independent of time.

### 2.4.1 State dependence

Our model predicts that state dependence, defined as the specific effect of having exported to a destination the previous year on the probability of exporting there in the current year, is systematically related to firm and destination characteristics. Econometrically, state dependence is captured by the marginal effect of a change in the last period's export status (which is either one, if a firm has exported to a destination in the last period, or zero otherwise) on the current export status conditional on firm and destination characteristics.

Let $Y_t$ be an indicator variable that equals one if a firm exports to a given destination in period $t$ and zero otherwise. Given this definition the conditional probabilities of exporting are:<fnref n="20" />

$$P(Y_t = 1 | Y_{t-1} = 0, c \in (0, \tilde{c})) = \frac{x(v_H + v_L)}{M^u},$$

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (0, \bar{c}]) = 1 - s,$$

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (\bar{c}, \tilde{c}]) = \frac{(1-s) \left[ 1 + \lambda \frac{(\theta_0 - v_L)}{(1-\theta_0 - v_H)} \frac{g^L(c)}{g^u(c)} \right]}{1 + \frac{(\theta_0 - v_L)}{(1-\theta_0 - v_H)} \frac{g^L(c)}{g^u(c)}},$$

where $v_H$ ($v_L$) are the steady state measures of unmatched (im)patient importers, $M^u$ is the total measure of unmatched exporters, $g^L(c)$ is the density function of exporters matched with impatient importers and $g^u(c)$ is the density function of unmatched exporters.

Thus, state dependence is defined as:

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (0, \bar{c}]) - P(Y_t = 1 | Y_{t-1} = 0, c, c \in (0, \bar{c}]) = 1 - s - \frac{x(v_H + v_L)}{M^u}, \quad (4)$$

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (\bar{c}, \tilde{c}]) - P(Y_t = 1 | Y_{t-1} = 0, c, c \in (\bar{c}, \tilde{c}]) =$$

$$\frac{(1-s) \left[ 1 + \lambda \frac{(\theta_0 - v_L)}{(1-\theta_0 - v_H)} \frac{g^L(c)}{g^u(c)} \right]}{1 + \frac{(\theta_0 - v_L)}{(1-\theta_0 - v_H)} \frac{g^L(c)}{g^u(c)}} - \frac{x(v_H + v_L)}{M^u}.$$

From the above expressions for state dependence we immediately obtain the result that state dependence is larger for exporters with low marginal costs (with $c \in (0, \bar{c}]$) than for those with

<footnote n="20">²⁰The derivations can be found in the Appendix.</footnote>
high marginal costs (with $c \in (\bar{c}, \tilde{c}]$) because importers always honor contracts with sufficiently productive exporters, while there are endogenous separations from exporters with high marginal costs.

**Proposition 1: State dependence is larger for exporters with lower marginal costs.**

Next, we establish how state dependence is affected by the export destinations' market size. We show in the Appendix that state dependence increases according to the market size of the destination. The reason is that $\bar{c}$ is increasing in market size ($A$) – a larger market increases the value of a given export relationship and therefore makes it easier to sustain cooperation. As a consequence, a given level of $c$ is more likely to lie below the level $\bar{c}$ from where impatient importers try to violate contracts. Thus, a given relation is more likely to survive from one period to the next. We summarize this result in the following proposition.

**Proposition 2: State dependence is increasing in the market size of the export destination.**

**Proof: See Appendix.**

We now derive a relation between state dependence and the destinations’ legal quality $\lambda$. An improvement in legal quality increases $\bar{c}$ and thus makes it more likely that a relation involving an exporter with a given $c$ is not affected by endogenous separation and survives from one period to the next. This is because a higher $\lambda$ lowers the probability that renegotiation is successful and makes renegotiation less attractive. As a consequence, impatient importers honor contracts with less productive exporters.<fnref n="21" />

Moreover, the quality of legal institutions only matters for state dependence for those relations that involve less productive exporters – contracts with sufficiently productive exporters are honored by both types of importers independently of institutional quality. These points are summarized by the following proposition:

**Proposition 3: State dependence is increasing in the quality of the export destinations' legal institutions. Moreover, the impact of legal institutions on state dependence is larger for exporters with higher marginal costs.**

**Proof: See Appendix.**

<footnote n="21">²¹In addition, this also increases the probability that a given relationship survives, even if the importers’ strategy does not change.</footnote>
Finally, we compare the impact of an improvement in legal institutions for two sectors that differ in the extent of their contracting frictions $\gamma$. To consider an extreme case, if $\gamma = 0$, importers cannot extract anything from the exporters' share of the surplus. Thus, they always honor contracts independently of legal quality and an increase in $\lambda$ has no effect on their equilibrium strategies and on state dependence. If, however, $\gamma$ is large, an improvement in legal quality implies a large reduction of importers' incentives to renegotiate contracts. As a consequence, many relationships, for which endogenous separations could occur before the change in $\lambda$, are no longer at risk of being endogenously destroyed and state dependence increases discretely. The following proposition makes this point more generally:

**Proposition 4:** *The positive impact of legal institutions on state dependence is larger in sectors with larger contracting frictions (sectors with higher levels of $\gamma$).*

**Proof:** See Appendix.

### 2.4.2 Hazard Rate

A further prediction of our model is on the conditional hazard rate, i.e. the probability that a relationship ends in period $i$ conditional on the exporter's marginal cost $c$.

The hazard rate is defined as the ratio between the measure of relationships which are dissolved and the measure of relations at risk. The measure of relations of age $i-1$ at risk between exporters with cost $c$, with $c > \bar{c}$, and impatient importers is $v_L x g^u(c) \lambda^{i-1} (1-s)^{i-1}$, while the measure of relationships at risk between these exporters and patient importers is $v_H x g^u(c) (1-s)^{i-1}$. At the same time, the measure of relations of age $i$ that are dissolved in period $i$ between exporters with cost $c$, with $c > \bar{c}$ and impatient importers is $v_L x g^u(c) \lambda^{i-1} (1-s)^{i-1} [(1-s)(1-\lambda) + s]$ and the measure of dissolved relations of age $i$ between those exporters and impatient importers is $v_L x g^u(c) (1-s)^{i-1} s$.

Thus, the hazard conditional on $c$ for $c \le \bar{c}$ is:

$$H(c, c \le \bar{c}) = \frac{v_L x g^u(c) (1-s)^{i-1} s + v_H x g^u(c) (1-s)^{i-1} s}{v_L x g^u(c) (1-s)^{i-1} + v_H x g^u(c) (1-s)^{i-1}} = s. \quad (5)$$
Similarly, the hazard conditional on $c$ for $c > \bar{c}$ is:

$$ H(c, c > \bar{c}) = \frac{v_L x g^u(c) [(1-s)(1-\lambda) + s] (1-s)^{i-1} \lambda^{i-1} + v_H x g^u(c) (1-s)^{i-1} s}{v_L x g^u(c) (1-s)^{i-1} \lambda^{i-1} + v_H x g^u(c) (1-s)^{i-1}} \quad (6) \\ = \frac{v_L [(1-s)(1-\lambda) + s] \lambda^{i-1} + v_H s}{v_L \lambda^{i-1} + v_H} = s + \frac{v_L (1-s)(1-\lambda) \lambda^{i-1}}{v_L \lambda^{i-1} + v_H}. $$

We now state a number of comparative statics results on the hazard rate.

**Proposition 5: The conditional hazard is decreasing in the age of the relationship for $c > \bar{c}$**.

**Proof:** See Appendix.

The mechanism behind this result is a composition effect – since relations with impatient importers have a higher probability of separation than those with patient ones, the older the relationship, the smaller becomes the fraction of surviving relationships that involve impatient importers.

As can be seen directly from the formula of the conditional hazard, the hazard rate is lower for more productive exporters. This is because importers do not violate contracts with productive exporters and all separations from these exporters are exogenous, while impatient importers try to violate contracts with unproductive exporters, so that there are both exogenous and endogenous separations. Thus, we can state the following proposition:

**Proposition 6: The conditional hazard is increasing in firms’ marginal cost.**

We can also establish that the conditional hazard is lower in larger markets. The reason is that in these markets, relations with any given exporter have a larger value because demand is higher. Thus, the larger the market, impatient importers are more likely to honor contracts for a given marginal cost of the exporter. This reduces the probability of endogenous separation for a given $c$ and therefore decreases the hazard.

**Proposition 7: The conditional hazard is decreasing in the market size of the export destination.**

**Proof:** See Appendix.

The next proposition establishes a relation between the hazard and the destination country’s legal institutions.
**Proposition 8:** The conditional hazard is decreasing in the quality of the export destination's legal institutions for sufficiently young relationships. Moreover, for these relationships an increase in the quality of legal institutions leads to a larger decrease in the conditional hazard in sectors with larger contracting problems.

**Proof:** See Appendix.

The intuition for this proposition is as follows. An increase in $\lambda$ increases the cutoff, $\bar{c}$, and also reduces the probability of successful contract violation for a given relation for $c > \bar{c}$. However, for sufficiently old relationships with $c > \bar{c}$ there is also a composition effect that goes in the opposite direction – more relationships with impatient importers survive and this tends to increase the hazard.

To understand the mechanism behind the second part of the proposition note that when $\gamma$ is zero (importers cannot appropriate any of the exporters' revenue share), institutions have no impact on firms' strategies and thus no effect on the hazard. When $\gamma$ becomes positive, this is no longer true. In particular, the higher $\gamma$, the more likely an exporter is to be affected by endogenous separations for a given marginal cost. As a consequence – since better legal institutions decrease the probability that a given relation lies above the cutoff $\bar{c}$ and also reduce contract violation of importers that are matched with exporters with $c > \bar{c}$ – an increase in $\lambda$ has a particularly strong negative effect on the hazard in high $\gamma$ sectors.

# 3 Empirical Analysis

## 3.1 Data

We use a panel of 6,594 French manufacturing firms that exist continuously and export at least once in the period from 1993 to 2005. The dataset is administered by the French Statistical Institute (INSEE) and merges two data sources. One is the customs (Douanes) database which allows us to precisely observe the exports of each firm to any potential destination.<fnref n="22" /> The customs data include records of the value (measured in euros) of all the extra EU shipments and all the intra EU trade of French firms above a certain value by firm, destination country and year. Because the reporting threshold for intra-EU trade changed several times over the

<footnote n="22">²²Regrettably, we do not have information whether trade flows are intra-firm.</footnote>
sample period, we exclude EU destinations from our main sample to avoid spurious results but we include them in robustness checks.<fnref n="23" /> We select the destination countries for which we have the additional information we need to carry out our analysis. Thus, the final data set includes 75 countries. The other source is the Bénéfices Réels Normaux (BRN) database, which provides very detailed firm-level data on a variety of balance-sheet measures. This allows us to calculate and control for firm characteristics such as labor productivity. Each firm is assigned to one of 55 manufacturing sectors using the French NES classification system.<fnref n="24" /> Table 6 reports descriptive statistics of the firm-level variables for our sample.

We also use several control variables that come from other sources. Data on average real GDP, real GDP per worker and bilateral real exchange rates for the sample period are from the Penn World Tables (Mark 6.2) and data on distance from Paris are taken from Rose (2004). The different measures of the quality of legal institutions are described in Section 1.

Moreover, we construct two measures of sectoral relationship-dependence. The first measure uses data collected by Rauch (1999), who classifies the output of different sectors according to its standardization. Rauch assigns the goods produced by each 4-digit-SITC sector to one of the three following categories: traded on an organized exchange, reference priced, or neither. Nunn (2007) argues that this classification is a good measure for the severity of hold-up problems in a sector, since goods that are neither traded on an organized exchange nor reference priced are likely to be tailor-made for a specific partner and have little value outside this relationship. The second measure comes from Nunn (2007) and measures the fraction of inputs used by a sector that are neither reference priced nor traded on an organized exchange at the 3-digit ISIC

<footnote n="23">²³The reporting threshold for intra EU trade changed several times in the sample period. It went from 250,000 FF to 650,500 FF in 2001 and then was changed to 100,000 Euros in 2002. For extra EU trade, the threshold is close to 1000 Euros.</footnote>

<footnote n="24">²⁴Our data source is the same as that of Eaton, Kortum and Kramarz (2004) and Eaton, Kortum and Kramarz (2008b). They report 34,035 exporters for the year 1986 that sell to 113 destinations outside France. We have less exporters in our dataset for several reasons. First, we exclude intra-EU trade. Second, we require exporters to exist continuously during the sample period. Third, we have less export destinations. Fourth, we drop exporters for whom the sector information was missing and we require firms to be both in the Douanes and in the BRN database and to have info on value added and employment. Finally, we focus on manufacturing and drop a number of manufacturing sectors for which we are not able to construct the sector-specific variables discussed below.</footnote>
level. This is a measure of relationship-dependence of sectoral inputs rather than outputs, but sectors that use a lot of specific inputs tend to also produce strongly differentiated outputs<fnref n="25" /> and Nunn's measure has more variation. We convert both measures to the French NES classification. Table 7 lists both measures of relationship-dependence by sector.

## 3.2 State Dependence

In this subsection we describe our econometric methodology to measure state dependence of exporting decisions and we present our empirical results on the correlation between state dependence and firm, sector and country-characteristics mentioned in the introduction and derived from our model.

In our main specification, we use a linear probability model to estimate state dependence. The main difficulty when estimating the impact of the past export status on the current one, is to disentangle the true state dependence from the spurious one. Indeed, when the residuals are auto-correlated, a naive regression of the export status on its past value would essentially capture the persistence of unobservables rather than a true effect of the past export status. One reason why one might think of auto-correlated residuals comes from unobserved heterogeneity at the firm or country level that is constant over time, such as firms' average productivity or the market size of the export destination.<fnref n="26" /> Exploiting the three-dimensional nature (firms, destinations, time) of our dataset we can also take time-varying firm-level as well as time-varying destination-specific unobserved heterogeneity into account. Firm-level time-varying unobserved heterogeneity refers to firm-level supply shocks, such as changes in productivity, managerial ability, or firm's strategy which may affect a firm's decision to export. Destination-

<footnote n="25">²⁵The correlation between Rauch's and Nunn's measure in our sample is 0.66. For example, most subcategories of both *Textile Products* and *Electrical Equipment NEC* fall into Rauch's category “neither” (this fraction is 0.76 in both sectors with Rauch's classification), even though electric equipment is probably more likely to be made specifically for a trade partner than a carpet, so the hold up problem should be more severe in the first case (Nunn's measure for the fraction of differentiated inputs is 0.76 for *Electrical Equipment NEC* against 0.48 for *Textile Products* at the NES level.).</footnote>

<footnote n="26">²⁶Previous articles, which only had information on firms’ aggregate export status available, have dealt with this problem in different ways. For example Bernard and Jensen (2004) estimated a linear probability model in first differences using the Arellano-Bond panel IV procedure. Others, such as Roberts and Tybout (1997) instead used a dynamic random effect probit strategy.</footnote>
specific time-varying unobserved heterogeneity captures country characteristics like market size, openness policies, movements in the exchange rate, or other demand shifts which may influence the probability of a firm exporting to a given country.

As a first step we investigate whether current export status depends on past export status, even when we control for firm- and destination-specific shocks.

Our basic specification is:

$$ Pr(Y_{fkt} = 1|Y_{fkt-1}, X_{fkt}) = E(Y_{fkt}|Y_{fkt-1}, X_{fkt}) = \beta_0 + \beta_1 Y_{fkt-1} + \delta_{ft} + \delta_{kt}. \quad (7) $$

Here $Y_{fkt}$ is a dummy that equals one whenever firm $f$ exports to destination $k$ in period $t$, whereas $\delta_{ft}$ and $\delta_{kt}$ are firm-time- and destination-time-specific fixed effects. The coefficient $\beta_1$ of equation (7) is a measure of state dependence, since it captures the marginal effect of past export status on the probability that a firm currently exports to a destination.

To implement the regression, we use a standard double within-transformation. Let $K_{ft}$ be the total number of destinations of firm $f$ in period $t$, let $F_{kt}$ be the total number of firms that export to destination $k$ in period $t$, let $K$ be the total number of possible destinations and let $F$ be the total number of firms. Moreover, let $\bar{Y}_{ft} = 1/K \sum_{k=1}^{K} Y_{fkt} = K_{ft}/K$ be the probability that firm $f$ exports to an average destination in period $t$, let $\bar{Y}_{kt} = 1/F \sum_{f=1}^{F} Y_{fkt} = F_{kt}/F$ be the probability of exporting to destination $k$ for an average firm in period $t$ and let $\bar{\bar{Y}}_t = 1/(FK) \sum_{k=1}^{K} \sum_{f=1}^{F} Y_{fkt} = R_t/(FK)$, be the average probability of exporting in period $t$, where $R_t$ is the total number of relationships at time $t$. Then define $\ddot{Y}_{fkt} \equiv Y_{fkt} - \bar{Y}_{ft} - \bar{Y}_{kt} + \bar{\bar{Y}}_t = Y_{fkt} - K_{ft}/K_t - F_{kt}/F_t + R_t/(F_t K_t)$. This transformed variable measures the export status of firm $f$ to destination $k$ in period $t$ as a deviation from firm $f$'s probability of exporting to an average destination and the probability of exporting to destination $k$ for an average firm, adding the average probability to export. Note that this transformation eliminates $\delta_{ft}$ and $\delta_{kt}$ from specification (7). Defining $\ddot{Y}_{fkt-1}$ and $\ddot{u}_{fkt}$ analogously, we can estimate the transformed linear probability model by ordinary least squares.<fnref n="27" />

$$ \ddot{Y}_{fkt} = \beta_0 + \beta_1 \ddot{Y}_{fkt-1} + \ddot{u}_{fkt}. \quad (8) $$

The first column of Table 2 tests for state dependence. Indeed, $\hat{\beta}_1$ is positive and significant

<footnote n="27">²⁷Note that since we do not rely on the time dimension of the panel for our transformation, the lagged dependent variable does not cause any problems for consistency and we need not use a dynamic panel estimator.</footnote>
at the one-percent level. Having exported to a destination in the previous period increases the probability of exporting in the current period by 64 percentage points compared to a firm that did not export in the previous period, even when controlling for unobserved effects at the firm-time and destination-time level.

We now specify the empirical model to test our hypotheses regarding the relation between state dependence and the quality of legal institutions, market size and firm productivity.

$$ Pr(Y_{fkt} = 1|Y_{fkt-1}, X_{fkt}) = \beta_0 + \beta_1 Y_{fkt-1} + \beta_2 Y_{fkt-1} * Prod_{ft} + \beta_3 Y_{fkt-1} * A_k + \beta_4 Y_{fkt-1} * IQ_k + \delta_{ft} + \delta_{kt}. \quad (9) $$

Here, $Y_{fkt-1}*Prod_{ft}$ is the interaction between last period's export status and firm productivity (measured as the log of value-added per worker), $Y_{fkt-1}*A_k$ is the interaction between past export status and effective market size proxies – GDP and distance<fnref n="28" /> (all in logs) and $Y_{fkt-1}*IQ_k$ is the interaction between last period's export status and one of the measures of the quality of legal institutions. We also control for any interaction between past export status and GDP per capita (in logs) to make sure that our institutional variables do not pick up the effect of that variable on state dependence.

According to Proposition 1, state dependence is higher for more productive firms. Thus, we expect $\beta_2 > 0$. Proposition 2 states that state dependence is increasing in market size, so we expect GDP to have a positive and distance to have a negative impact on state dependence. Finally, Proposition 3 implies that state dependence is increasing in legal quality. Therefore, we expect $\beta_4 > 0$.

Columns (2) to (5) of Table 2 present results for regression (9).<fnref n="29" /> Each specification employs a different measure of institutional quality. Turning first to the effect of firm productivity on state dependence, we find that $\hat{\beta}_2$ is always positive and significant at the one percent level. Moving from the 25th (minimum) to the 75th percentile (maximum) of productivity increases the marginal effect of the past export status by 3 percentage points (43 percentage points).<fnref n="30" /> As for the interactions of past export status and the market size controls, distance has a

<footnote n="28">²⁸It is straightforward to incorporate transport costs, which have a negative effect on effective market size, into the model.</footnote>

<footnote n="29">²⁹All standard errors are clustered by firm-year.</footnote>

<footnote n="30">³⁰$0.03 \approx 0.051 * (4.2 - 3.6), 0.43 \approx 0.051(11.7 - (-3.2))$.</footnote>
significantly (at the one-percent level) negative impact on the effect of past export status, while GDP has a significantly positive effect (also at the one percent level).

In all specifications, $\hat{\beta}_4$, the coefficient of the interaction term between past export status and the different measures of legal institutions, is positive and significant at the one-percent level. In terms of economic magnitudes, the effect of institutions on state dependence is also sizeable. For example, moving from the 25th percentile of *rule of law* to the 75th percentile increases the effect of past export status on the probability of exporting in the current period by roughly 2.4 percentage points, while moving from the country with the worst institutions to the one with the best increases the effect of past export status by around 8 percentage points.<fnref n="31" /> Note also, that the level of development (measured by $log(GDP \ per \ capita)$) has a significantly positive impact on state dependence.

In columns (6) to (9) of Table 2 we add triple interaction terms between past export status, the different measures of legal quality and firm productivity. According to Proposition 3 we expect this interaction term to be negative since legal institutions should have a smaller impact on state dependence if exporters are more productive. Indeed, we find that in all specifications the interaction terms are negative and significant at the one-percent level, supporting our hypothesis. The other coefficients remain largely unaffected, apart from the coefficient of past export status, which now turns negative for some specifications. Note, however, that when we evaluate all the explanatory variables at their sample mean, past export status still has a large and significant positive effect on current export status.

Next, we test the prediction of Proposition 4, which states that the effect of legal quality on state dependence is larger in sectors that are more relationship-dependent. To this end, we specify the following econometric model:

$$ Pr(Y_{fkt} = 1 | Y_{fkt-1}, X_{fkt}) = \beta_0 + \beta_1 Y_{fkt-1} + \beta_2 Y_{fkt-1} * IQ_k + \beta_3 Y_{fkt-1} * RD_j + \beta_4 Y_{fkt-1} * IQ_k * RD_j + \beta_5 Y_{fkt-1} * X_k + \beta_6 Y_{fkt-1} * X_k * RD_j + \delta_{ft} + \delta_{kt}, \quad (10) $$

where $Y_{fkt-1} * RD_j$ is the interaction between last period's export status and our measures of sectoral relationship-dependence and $Y_{fkt-1} * IQ_k * RD_j$ is the triple interaction between last

<footnote n="31">³¹The 25th percentile (minimum) of *rule of law* is 0.4 (0.2) and the 75th percentile (maximum) is 0.6 (0.9) and $\hat{\beta}_2 = 0.114$, so the change in the effect of past export status is given by $0.114(0.6 - 0 - 4) = 0.0236$ and $0.114(0.9 - 0.2) \approx 0.08$.</footnote>
period's export status, legal quality and relationship-dependence. Finally, $Y_{fkt-1} * X_k$ is the interaction between past export status and other country controls and $Y_{fkt-1} * X_k * RD_j$ is the triple interaction between last period's export status, other country controls and relationship-dependence.

This specification implies that $\frac{\partial \Pr(Y_{fkt}=1|Y_{fkt-1}=1, X_{fkt}) - \Pr(Y_{fkt}=1|Y_{fkt-1}=0, X_{fkt})}{\partial I_{Q_k}} = \beta_2 + \beta_4 RD_j$, so we expect $\beta_2 > 0$ and $\beta_4 > 0$. An additional advantage of this specification is that it is less likely to suffer from some form of omitted variable bias than the regressions that only use explanatory variables at the destination level interacted with past export status. Even if there are omitted country-specific variables that are correlated with institutional quality, there is no reason to expect $\beta_4 > 0$, unless this omitted variable has a larger effect in relationship-dependent sectors. To exclude even this possibility, we interact the sector-specific effect of past export status with other country controls, such as log(GDP per capita).

Table 3 presents the results for these regressions using both Rauch's and Nunn's measure of relationship-dependence and our two main measures of the quality of legal institutions, rule of law and legal quality. The first two specifications use rule of law and do not control for the triple interaction with other country variables. Again, $\hat{\beta}_2$, that measures the direct effect of institutions on state dependence when $RD_j$ is zero, is positive and strongly significant. Also, $\hat{\beta}_3$, that measures the impact of relationship-dependence on state dependence when rule of law is zero, is negative as expected. More importantly, the coefficient of the triple interaction, $\hat{\beta}_4$, is positive and significant at the one percent level. This implies that legal institutions have a larger positive impact on state dependence in more relationship-dependent sectors.

In columns (3) and (4) we add a triple interaction with $log(GDP \ per \ capita)$ as an additional control variable. While $\hat{\beta}_2$ maintains its positive and significant sign only in column (4), $\hat{\beta}_4$ remains positive and significant at the one percent level in both specifications. Finally, columns (5)-(8) repeat the previous specifications using legal quality. Results are robust to using this alternative measure of legal institutions.

In the Appendix we show that all results are robust to 1) including EU-destinations in the sample; 2) using an Arellano-Bond dynamic panel estimator to control for firm-destination unobserved heterogeneity; 3) estimating a dynamic random effects Probit model. We conclude that there is strong evidence in favor of propositions 1-4 and now turn to the predictions on hazard rates.
3.3 Survival Analysis

Our theoretical model makes several predictions on the correlations between hazard rates
of export relations and firm as well as country characteristics. In order to test them, we use
survival analysis methods. An observation is now defined as a spell – the duration of a firm-
country export relation. Before going into the details of our econometric strategy, let us discuss
two features of the data that we have to take care of: existence of multiple spells and right and
left censoring of spells.

First, there are many multiple spells in our sample, i.e., the same firm exports to a given
country repeatedly in different time intervals and each of these relations may have a different
duration. In our analysis we treat each spell as independent, which is consistent with our
theoretical analysis.<fnref n="32" />

Second, the original data are censored on both sides. There are right-censored observations because we observe data until 2005 and many relations are still active in that year. There are also left-censored observations since in the first year in our sample we cannot distinguish between relations which start before that year and new ones. We deal with the left-censoring problem by considering only those firms that start exporting in the second year for which we have information in our database or later. Right-censoring is taken into account through the Cox model, and we add time dummies to control for the different starting dates of the relationships.

We start out with a description of the duration of trade relations. Table 11 reports the frequency of observations for each possible length of the relations’ duration: 77% of all relations last less than 4 years, with one-year relations accounting for slightly more than half of the observations. This confirms that the majority of trade relations have a short duration.

In order to test the predictions of the model on the relation between firm productivity and
the hazard rate (Proposition 6), market size and the hazard rate (Proposition 7), as well as
the relation between legal quality and the hazard rate (Proposition 8), we perform a set of Cox
regressions.

<footnote n="32"><sup>32</sup>In the model, having previously exported to a destination does not provide any advantage to a firm that wants to re-enter a destination over a firm that tries to export to a destination for the first time, since it has to find a new importer. Nevertheless, we take care of the multi-spell problem in the robustness checks.</footnote>
The assumption of the Cox proportional hazard model is that the hazard is separable between an arbitrary function of time, $h(t)$, and a part that depends on a vector of explanatory variables, $X$. Our specification is the following:

$$h(t, X\beta) = h(t)\exp(\beta_0 + \beta_1\text{Prod}_f + \beta_2A_k + \beta_3\text{IQ}_k + \delta_t + \delta_j), \quad (11)$$

where $\text{Prod}_f$ is the firm average of log value added per worker, the vector $A_k$ contains the logs of GDP, GDP per capita and distance. $\text{IQ}_k$ is again one of our measures of legal institutions (measured in logs); $\delta_t$ is a dummy for the starting year of each relation, which is the standard treatment for right-censoring; $\delta_j$ takes care of time-invariant sector characteristics that may drive different durations of export relations. Note that since the log of the hazard is linear and the explanatory variables are measured in logs, coefficients can be interpreted as elasticities.

Results for these regressions are reported in Table 4. As predicted, the hazard is strictly decreasing in all the measures of the quality of the legal system (all variables are significant at the one-percent level) and strictly decreasing in firm productivity (also significant at the one percent level). We also find that the market size proxies have the expected sign and are strongly significant.<fnref n="33" /> As for the magnitude of our results, we find that an increase of *rule of law* by 100% decreases the hazard by roughly 6%, while a 100% increase in productivity decreases the hazard by around 10%.

Next we turn to the second part of Proposition 8, which states that the negative impact of legal institutions on the hazard should be larger in more relationship-dependent sectors. In order to test this prediction we specify the following hazard:

$$h(t, X\beta) = h(t)\exp(\beta_0 + \beta_1\text{Prod}_f + \beta_2A_k + \beta_3\text{IQ}_k + \beta_4RD_j * \text{IQ}_k + \delta_t + \delta_j) \quad (12)$$

In this case the marginal effect of $\text{IQ}_k$ on the log-hazard is $\beta_3 + \beta_4RD_j$, so we expect $\beta_3 > 0$ and $\beta_4 > 0$. Table 5 presents the results for these regressions using our main measures of legal institutions, *rule of law* and *legal quality* and both Nunn's and Rauch's measure of relationship-dependence. In the first two columns we just use sector and start dummies as additional controls. $\hat{\beta}_3$ is negative and significant at the one-percent level, while $\hat{\beta}_4$ is negative but only

<footnote n="33">³³We cluster standard errors at the country-level (in the regressions that focus on country-level dependent variables) and at the firm level (in the regressions that focus on firm-level dependent variables), and we use robust standard errors in those specifications which include both firm and country characteristics.</footnote>
significant with Nunn's measure. When adding additional country and firm controls in columns (3) and (4), $\hat{\beta}_3$ remains negative but becomes insignificant, while the interaction term $\hat{\beta}_4$ remains stable and becomes significant at the 5% level for both measures of relationship-dependence. Results remain similar but are somewhat less significant when using *legal quality* instead of *rule of law* (columns (5)-(8)).

Our last prediction on hazard rates is that relations become more stable as they mature, so the hazard should be decreasing with the age of the relation (Proposition 5). Since the Cox method for estimating the parameters of the proportional hazard model does not require the specification of the time dependent part of the hazard, there is no parameter that pins down time dependence. Thus we refer to Figure 4, which plots a kernel smoothing of the estimated hazard contributions derived from (11) against time. Clearly, the estimated hazard is decreasing over time. We conclude that the probability for a trade relation to be destroyed indeed decreases with the age of the relation.<fnref n="34" />

Finally, we show in the Appendix that results are robust to including EU destinations and to estimating the model only with single spells. Thus, also the model's predictions on hazard rates are strongly supported by the data.

## 3.4 Discussion

One may wonder to what extent our empirical findings can be explained by alternative mechanisms rather than one-to-one matching between exporters and importers with incomplete information. If exporters can match with more than one importer, this should reduce the influence of institutions on state dependence and hazard rates, since firms can continue to export even when relations with one specific partner break up. As Blum et al. (2010) show, one-to-many matching is only relevant for big exporters. Our finding that institutions matter less for state dependence and hazards if exporters are more productive is thus also consistent with one-to-many matching. Alternatively, this result could be explained by the fact that big exporters are more likely to have their own distribution network and do not need to rely on

<footnote n="34">³⁴We have also estimated parametric duration models, such as the Weibull model. These models gave very similar results for the impact of institutional quality and productivity on the hazard, and estimates implied mostly negative time dependence. Results are available on request.</footnote>
local partners in each market. Thus, their export flows should be more persistent and should
depend less on local institutions.

State dependence that is increasing in institutional quality could also potentially be due to sunk entry costs that are increasing in institutional quality. Still, besides the fact that it would be difficult to come up with an intuition as to why it should be more costly to enter a market with better legal institutions (rather than cheaper), a model with sunk costs would imply that hazard rates should be increasing over time instead of decreasing. State dependence of export decisions and hazard rates that are decreasing over time are also consistent with models of learning about local demand (Eaton et al., 2008a; Arkolakis and Papageorgiou, 2009; Albornoz et al., 2009). However, these models have nothing to say about the role of institutions and contracting frictions. Finally, one may be concerned that trade flows stop because trade is replaced by horizontal FDI, which we can not observe in our data. If this mechanism were important for trade dynamics, however, we would observe hazard rates that would be increasing over time instead of decreasing. Thus, overall, the empirical evidence lends strong support for the specific mechanism emphasized in the model.

4 Conclusions

In this paper we have explored the links between export dynamics, on the one hand, and destination countries’ institutional quality, firm productivity and sector-specific contracting frictions, on the other. We have developed a model in which exporting requires firms to find a partner in each market. Incomplete information and imperfect enforcement of contracts give room for reputation and lead to learning by exporters about the reliability of their partners.

This framework leads to several interesting patterns. Matching frictions imply state de-
pendence of exporting decisions in the absence of sunk fixed costs. State dependence is larger
and hazard rates are lower in markets with better legal institutions. Moreover, the impact of
legal institutions on state dependence and on hazard rates is larger in sectors that are more
exposed to hold-up problems. We test these predictions using a large panel of French exporters
that provides information on individual firms’ exports by destination country. Overall, we
find strong support for our model – specifically, export relations are more stable and there is
more state dependence in countries with better legal institutions, and these effects are larger
in sectors with more severe contracting frictions. These facts shed light on the importance of
relationship-specificity for explaining the dynamics of trade.
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# A Proofs

In this section we present proofs for the results in the main text.

**Lemma 1:** Export revenues are increasing in the age of the relation as long as $c > \bar{c}_t$ and constant for $c \le \bar{c}_t$.

**Proof:**

Note that as long as $c > \bar{c}_t$, $\tilde{\theta}$ is decreasing in $i$ and revenues are decreasing in $\tilde{\theta}$. Hence, revenues are increasing in $i$. For $c \le \bar{c}_t$ there is no learning and therefore revenues are independent of the age of the relation.

**Lemma 2:** Let $\tilde{\theta}_{0t}$ be non-decreasing in $t$. Then given the importers' equilibrium strategies and equilibrium beliefs there is a unique value $\bar{\theta}_t(c) \in [\theta^*(c), 1)$ such that for all $t$ an exporter with marginal cost $c > \bar{c}_t$ accepts any partner whenever she meets an importer and $\tilde{\theta}_{0t} \le \bar{\theta}(c)$. Moreover, she maintains a partnership if and only if the importer respects the contract. Exporters with $c \le \bar{c}_t$ accept every partner for any $\tilde{\theta}_{0t} \in [0, 1]$ and maintain a partnership as long as the importer respects the contract given importers' equilibrium strategies.

The proof of Lemma 2 requires the following assumptions: For all $\lambda < 1$, $\gamma > 0$ exporters expect to make losses in every period if their subjective probability that their partner is impatient equals one and impatient importers violate the contract if they can: $\Pi(v, \tilde{\theta} = 1, c) = Ac^{1-\varepsilon}(\varepsilon - 1)^{\varepsilon-1}[\lambda + (1-\lambda)(1-\gamma)]^\varepsilon (\frac{\alpha}{\varepsilon})^\varepsilon - \alpha f < 0$. We also assume that there exists a $c^* > 0$ such that for all $c \le c^*$ it holds that $\Pi(r, \tilde{\theta} = 0, c \le c^*) = Ac^{1-\varepsilon}(\varepsilon - 1)^{\varepsilon-1} (\frac{\alpha}{\varepsilon})^\varepsilon - \alpha f \ge 0$. This means that sufficiently productive exporters make profits in each period when they believe that importers are patient with probability one and patient importers respect contracts.

**Proof:**

Let $\text{Pr}(0|c)_{it}$ be the subjective probability that the contract is respected for a relation of age $i$ that started in period $t$ given firm's marginal cost $c$, so that $\text{Pr}(0|c \le \bar{c}_t)_{it} = 1$ and $\text{Pr}(0|c > \bar{c}_t)_{it} = (1 - \tilde{\theta}_{it} + \lambda\tilde{\theta}_{it})$.

Then $\tilde{V}_E(\tilde{\theta}_{0t}, c) = \max\{V_E(\tilde{\theta}_{0t}, c), \beta_E W_E(\tilde{\theta}_{0t+1}, c)\}$, where $V_E(\tilde{\theta}_{0t}, c) = \Pi(\tilde{\theta}_{0t}, c) + \beta_E(1-s)\text{Pr}(0|c)_{0t*} * V_E(\tilde{\theta}_{1t}, c)$ is the expected value of entering a partnership and $W_E(\tilde{\theta}_{0t+1}, c) = \tilde{V}_E(\tilde{\theta}_{0t+1}, c)x(v_{Ht} + v_{Lt})/(M_t^u) + W_E(\tilde{\theta}_{0t+2}, c)(1 - x(v_{Ht} + v_{Lt})/(M_t^u))$ is the expected value of not entering the partnership in period $t$ and waiting for a new business opportunity in the next period.
By substituting recursively, $V_E(\tilde{\theta}_t, c)$ can be written as:

$$V_E(\tilde{\theta}_{0t}, c) = \Pi(\tilde{\theta}_{0t}, c) + \sum_{i=1}^{\infty} \beta_E^i (1-s)^i \Pi(\tilde{\theta}_{it}, c) \prod_{j=0}^{i-1} \text{Pr}(0|c)_{jt}$$

Then $\frac{\partial V_E(\tilde{\theta}_{0t}, c > \bar{c}_t)}{\partial \tilde{\theta}_{0t}} < 0$, since $\frac{\partial \Pi(\tilde{\theta}_{it}, c > \bar{c}_t)}{\partial \tilde{\theta}_{0t}} = \frac{\partial \Pi(\tilde{\theta}_{it}, c > \bar{c}_t)}{\partial \tilde{\theta}_{it}} \frac{\partial \tilde{\theta}_{it}}{\partial \tilde{\theta}_{0t}} < 0$ and $\frac{\partial \text{Pr}(0|c > \bar{c}_t)_{jt}}{\partial \tilde{\theta}_{0t}} = \frac{(1 - \tilde{\theta}_{it} + \lambda \tilde{\theta}_{it})}{\partial \tilde{\theta}_{0t}} < 0$. At the same time, $\frac{\partial V_E(\tilde{\theta}_{0t}, c \le \bar{c}_t)}{\partial \tilde{\theta}_{0t}} = 0$, since no importer cheats on these exporters. Hence, since $\tilde{\theta}_{0t}$ is non-decreasing in $t$, it is always worth accepting a partner immediately because rejecting a partner and starting a partnership tomorrow has a weakly lower expected value. Consequently, we can write $\tilde{V}_E(\tilde{\theta}_{0t}, c) = \max\{V_E(\tilde{\theta}_{0t}, c), 0\}$. Now, since by assumption $V_E(\tilde{\theta}_{0t} = 0, c) = \frac{\Pi(\tilde{\theta}_{0t} = 0, c)}{1 - \beta_E(1-s)} \ge 0$ for all $c \le c^*$ and $V_E(\tilde{\theta}_{0t} = 1, c) = \frac{\Pi(\tilde{\theta}_{0t} = 1, c)}{1 - \lambda \beta_E(1-s)} < 0$ for all $c > \bar{c}$ and since $V_E(\tilde{\theta}_{0t})$ is strictly decreasing in $\theta_{0t}$, we have that for all $c > \bar{c}$ there is a unique $\bar{\theta}(c)$ such that $\tilde{V}_E(\tilde{\theta}_{0t}, c) \le 0$ if $\tilde{\theta}_{0t} \ge \bar{\theta}(c)$ and $\tilde{V}_E(\tilde{\theta}_{0t}, c) > 0$ if $\tilde{\theta}_{0t} < \bar{\theta}(c)$. Thus, exporters never deviate to maintaining the relationship in any period $t + i$ if $\tilde{\theta}_{it} = 1$ and return to their equilibrium strategy in the following period because they would make losses in the deviation period $t + i$, since $\Pi(\tilde{\theta}_{it} = 1, c) < 0$. Moreover, they would also not deviate to ending the relation as long as $\tilde{\theta}_{it} < \bar{\theta}(c)$ because they would forego positive profits.

Similarly, for exporters with $c \le \bar{c}$, if a renegotiation occurs, they set $\tilde{\theta}_{it} = 1$, $\text{Pr}(0|c \le \bar{c}_t) = 0$ and expect profits $V_E(\tilde{\theta}_{it} = 1, c) = \frac{\Pi(\tilde{\theta}_{it} = 1, c)}{1 - \lambda \beta_E(1-s)} < 0$. Hence exporters stay in a partnership as long as there is no renegotiation.

**Lemma 5:** Let $\tilde{\theta}_{0t}$ be non-decreasing in $t$ and let $E_t(c)$ be non-decreasing in $t$. Then, given the equilibrium strategies and beliefs, importers initially accept any partner.

**Proof:**

Impatient importers face the following problem. Let $\tilde{V}_L(\tilde{\theta}_{0t}) = \max\{V_L(\tilde{\theta}_{0t}), \beta_L W_L(\tilde{\theta}_{0t+1}, c)\}$, where $V_L(\tilde{\theta}_{0t}) = [\lambda(1 - \alpha) + (1 - \lambda)(1 - \alpha + \alpha\gamma)] E(Rev(\tilde{\theta}_{0t}, c)|\bar{c}_t < c \le \tilde{c}_t)(1 - G_t^u(\bar{c}_t)) + (1 - \alpha)E(Rev(c)|c \le \bar{c})G_t^u(\bar{c}_t) - (1 - \alpha)f + \beta_L(1 - s)[G_t^u(\bar{c}_t)E(V_L(\tilde{\theta}_{1t}, c)|c \le \bar{c}_t) + \lambda(1 - G_t^u(\bar{c}_t))E(V(\tilde{\theta}_{1t}, c)|c > \bar{c}_t)]$ is the expected value of entering a partnership in period $t$ and $W_L(\tilde{\theta}_{0t+1}, c) = x\tilde{V}_L(\tilde{\theta}_{0t+1}) + (1 - x)W_L(\tilde{\theta}_{0t+2})$ is the expected value of not entering the partnership in period $t$ and waiting for a new business opportunity in the next period. Then it is straightforward to show that $\tilde{V}_L(\tilde{\theta}_{0t})$ is decreasing in $t$. The first reason is that $\tilde{\theta}_{0t}$ is weakly increasing in $t$, which reduces export revenues $Rev(\tilde{\theta}_{0t}, c)$ for a given $c$. The second reason is that $E_t(c)$ is weakly increasing in $t$ and this reduces expected revenues as well. Finally, we
show in the section on industry equilibrium that the probability of matching with an exporter with $c < \bar{c}$, $G_t^u(\bar{c})$, is decreasing in $t$. Hence, it is always optimal to accept a given partner.

Similarly, for a patient importer we have $\tilde{V}_H(\tilde{\theta}_{0t}) = \max\{V_H(\tilde{\theta}_{0t}), \beta_H W_H(\tilde{\theta}_{0t+1})\}$, where $V_H(\tilde{\theta}_{0t}) = (1-\alpha)[E(Rev(\tilde{\theta}_{0t}, c)) - f] + \beta_H(1-s)E(V_H(\tilde{\theta}_{1t}, c))$ is the expected value of entering a partnership and $W_H(\tilde{\theta}_{0t+1}) = x\tilde{V}_H(\tilde{\theta}_{0t+1}) + (1-x)W_H(\tilde{\theta}_{0t+2})$ is the expected value of not entering the partnership in period $t$ and waiting for a new business opportunity in the next period. Patient importers accept any partner for the same reason as impatient ones. Waiting does not pay off because the average revenue of exporters is weakly decreasing in $t$ both because $\tilde{\theta}_{0t}$ is weakly decreasing in $t$ and the pool of available exporters weakly deteriorates over time.

**Lemma 6:** Given the equilibrium strategies and beliefs and if $\beta_L$ is sufficiently large, impatient importers try to violate contracts if and only if $c > \bar{c}_t$.

**Proof:** The strategy of impatient importers is:

1. to honor contracts for $c \le \bar{c}$ given that exporters believe that contracts are honored. At $\bar{c}$ they are indifferent between violating and honoring contracts given these beliefs. Thus, we assume that impatient importers stick to honoring them.

2. to violate contracts for $c > \bar{c}$ given that exporters believe that contracts are violated. At $\bar{c}$ they are indifferent between violating contracts and honoring them given these beliefs. Thus, we assume that impatient importers deviate to honoring them.

**Proof of 1:** Consider a deviation to violating a contract in period $t$, and playing the equilibrium strategy in all other periods given that exporters play their equilibrium strategy and their equilibrium beliefs.<fnref n="35" /> Such a deviation is not profitable whenever $V_t(r, c) \ge \lambda(1-\alpha)Rev_t(c) + (1-\lambda)(1-\alpha+\alpha\gamma)Rev_t(c) - (1-\alpha)f + \beta_L(1-s)\lambda V_{t+1}(r, c)$. Since $V_t(r, c) = (1-\alpha)(Rev_t(c)-f)$, we can write the previous condition as $\beta_L(1-s)V_{t+1}(r, c) \ge \alpha\gamma Rev_t(c)$. Because $V_{t+1}(r, c) = \frac{(1-\alpha)(Rev(c)-f)}{1-\beta_L(1-s)}$ and using the expression $Rev(c) = (\frac{\varepsilon-1}{\varepsilon}\alpha)^{\varepsilon-1}Ac^{-(\varepsilon-1)}$, we can express this condition as $c^{\varepsilon-1} \le \ddot{c}^{\varepsilon-1} = (\frac{\varepsilon-1}{\varepsilon}\alpha)^{\varepsilon-1} A[\frac{\beta_L(1-s)(1-\alpha+\alpha\gamma)-\alpha\gamma}{\beta_L(1-s)(1-\alpha)f}]$. Note that $\ddot{c}$ is independent of $\lambda$ and that $\ddot{c} > 0$ if and only if $\beta_L > \frac{\alpha\gamma}{(1-s)(1-\alpha+\alpha\gamma)}$.

<footnote n="35">³⁵This is the one stage deviation principle for dynamic games. This principle applies also to games with incomplete information (see Hendon, Jacobsen and Sloth, 1996).</footnote>
Proof of 2: Consider a deviation to honoring the contract in period *t* and playing the equilibrium strategy in all other periods given that exporters play their equilibrium strategy and have their equilibrium beliefs. Such a deviation is not profitable whenever $V_t(v, c) \ge (1-\alpha)(Rev_t(c) - f) + \beta_L(1-s)V_{t+1}(v, c)$. Since $V_t(v, c) = (1-\lambda)(1-\alpha + \alpha\gamma)Rev_t(c) + \lambda(1-\alpha)Rev_t(c) - (1-\alpha)f + \beta_L(1-s)\lambda V_{t+1}(v, c)$, we have that $\alpha\gamma Rev_t(c) \ge \beta_L(1-s)V_{t+1}(v, c)$. Thus, $V_{t+1}(c) = \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i \{[(1-\alpha) + (1-\lambda)\alpha\gamma]Rev_{t+1+i} - (1-\alpha)f\}$ and $Rev_{t+1+i}(c) = (\frac{\varepsilon-1}{\varepsilon}\alpha)^{\varepsilon-1} A[1 - \tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-1}c^{-(\varepsilon-1)}$.

Substituting this, the previous condition becomes $\alpha\gamma (\frac{\varepsilon-1}{\varepsilon}\alpha)^{\varepsilon-1} A[1 - \tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-1}c^{-(\varepsilon-1)} \ge \beta(1-s) (\frac{\varepsilon-1}{\varepsilon}\alpha)^{\varepsilon-1} A[(1-\alpha) + (1-\lambda)\alpha\gamma] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i [1 - \tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-1} - \frac{\beta_L(1-s)(1-\alpha)f}{1-\beta_L(1-s)\lambda}$. Solving for *c*, we obtain

$$c^{\varepsilon-1} \ge \bar{c}^{\varepsilon-1} = \left[ \frac{1 - \beta_L(1-s)\lambda}{\beta_L(1-s)(1-\alpha)f} \right] \left( \frac{\varepsilon-1}{\varepsilon}\alpha \right)^{\varepsilon-1} A* \left[ \beta_L(1-s)[(1-\alpha) + (1-\lambda)\alpha\gamma] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i [1 - \tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-1} - \alpha\gamma[1 - \tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-1} \right].$$

Note that a sufficient condition for the term in brackets to be positive can be found by setting $\tilde{\theta}_{t+1+i} = \tilde{\theta}_t$. Sufficient is $\beta_L > \frac{\alpha\gamma}{(1-s)(1-\alpha+\alpha\gamma)}$, which is the same condition as for $\ddot{c}$.

Proof that $\bar{c} \le \ddot{c}$:

It is easy to show that $\bar{c}(\lambda = 0) < 0$ and $\bar{c}(\lambda = 1) = \ddot{c}$. It remains to show that $\bar{c}(\lambda < 1) < \bar{c}(\lambda = 1) = \ddot{c}$. First, we need to show that $\bar{c}$ is decreasing in $\tilde{\theta}$. Ignoring the constant before the term in square brackets, we have

$$\frac{\partial \bar{c}}{\partial \tilde{\theta}_t} = \beta_L(1-s)[1-\alpha+(1-\lambda)\alpha\gamma] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i (\varepsilon-1)[1-\tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-2}\gamma(1-\lambda) \left(-\frac{\partial \tilde{\theta}_{t+1+i}}{\partial \tilde{\theta}_t}\right) - \alpha\gamma(\varepsilon-1)[1-\tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-2}\gamma(1-\lambda)(-1).$$

Since $\frac{\partial \tilde{\theta}_{t+1+i}}{\partial \tilde{\theta}_t} = \frac{\lambda^{i+1}(1-\tilde{\theta}_t)}{[(\lambda^{i+1}-1)\tilde{\theta}_{t+1}]^2} > 0$, the above expression is smaller than $-\beta_L(1-s)[1-\alpha + (1-\lambda)\alpha\gamma](\varepsilon-1)[1-\tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-2}\gamma(1-\lambda) + \alpha\gamma(\varepsilon-1)[1-\tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-2}\gamma(1-\lambda)$. This expression is negative whenever $\beta_L > \frac{\alpha\gamma}{(1-s)[1-\alpha+(1-\lambda)\alpha\gamma]}$. Hence, this is a sufficient condition for $\bar{c}$ to be decreasing in $\tilde{\theta}$. Therefore, we have that for any $\lambda > 0$: $\bar{c}(\lambda, \tilde{\theta}_t) < \bar{c}(\lambda, \tilde{\theta}_t = 0) = \bar{c}(\lambda = 0, \tilde{\theta}_t \ge 0) = \ddot{c}$. Since $\ddot{c}$ does not depend on $\lambda$ and $\tilde{\theta}$, it follows that for any $\tilde{\theta} > 0$: $\bar{c}(\lambda < 1, \tilde{\theta}_t) < \bar{c}(\lambda = 1, \tilde{\theta}_t) = \ddot{c}$.

**Lemma 7:** Given equilibrium strategies and beliefs, patient importers always honor their contracts.
**Proof:**

We show that in equilibrium patient importers honor their contracts with all types of exporters, that is, there exists a $\check{c}_t > \bar{c}_t$ such that for all $c \le \check{c}_t$ we have that profits from honoring the contract forever are larger than those of a one period deviation from the equilibrium strategy. The proof is analogous to Lemma 5. It is straightforward to show that $\check{c}_t > \bar{c}_t$. Since $\check{c}_t$ is increasing in $\beta$ and $\beta_H > \beta_L$, we have that $\check{c}_t > \check{c}_t \ge \bar{c}_t$. Moreover, we assume that parameters are such that $\check{c}_t > \tilde{c}_t$, so that patient importers honor contracts with all exporters that enter.

**Lemma 8:** $\theta_t$ is weakly increasing in t.

**Proof:**

The law of motion for the measure of impatient importers that are searching for an exporter is given by:

$$v_{Lt+1} = (1-x)v_{Lt} + [s + (1-s)(1-\lambda)Pr(\bar{c}_t)](\theta_0 - v_{Lt}) \quad (13)$$

A fraction $(1-x)$ of the population of currently unmatched impatient importers $v_{Lt}$ does not find an exporter and therefore remains inactive. Moreover, a proportion $s$ of the measure of matched impatient importers is dissolved exogenously. Out of the remaining proportion $(1-s)$ of the relations that involve exporters with marginal costs larger than $\bar{c}$, $Pr(\bar{c}_t)$, a fraction $(1-\lambda)$ is dissolved endogenously. $Pr(\bar{c}_t) = \sum_{i=0}^{t-1} \frac{\mu_{it\bar{c}}}{(\theta_0 - v_{Lt})}$ is the total probability that relations involve a partner with $c > \bar{c}_i$ conditional on $c \le \tilde{c}_i$, taking into account that the threshold marginal cost as of which impatient importers try to violate contracts, $\bar{c}$, depends on time. Here, $\mu_{it\bar{c}} = v_{Li}x\lambda^{t-i-1}(1-s)^{t-i-1}(1-G_i^u(\bar{c}_i))$ is the measure of matches of impatient importers with unproductive exporters formed in period $i$ that survive until period $t$.

A similar difference equation describes the evolution of the measure of unmatched patient importers:

$$v_{Ht+1} = (1-x)v_{Ht} + s(1-\theta_0 - v_{Ht}) \quad (14)$$

It is easy to show that $v_{Lt}$ and $v_{Ht}$ are both strictly decreasing sequences that converge to $v_L = \frac{\theta_0[s+(1-\lambda)(1-s)Pr(\bar{c})]}{x+s+(1-\lambda)(1-s)Pr(\bar{c})}$ and $v_H = \frac{s}{x+s}(1-\theta_0)$ respectively.

Note that in order to show that $\theta_t$ is weakly increasing in $t$ it is sufficient to show that $\frac{v_{Lt}}{v_{Ht}}$ is weakly increasing in $t$. Hence, we need to show that $\frac{v_{Lt+1}}{v_{Ht+1}} = \frac{(1-x)v_{Lt}+[s+(1-s)(1-\lambda)Pr(c_t)](\theta_0-v_{Lt})}{(1-x)v_{Ht}+s(1-\theta_0-v_{Ht})} \ge$
$\frac{v_{Lt}}{v_{Ht}}$. It is easy to show that this inequality is satisfied whenever $\frac{\theta_0}{1-\theta_0} \ge \frac{v_{Lt}}{v_{Ht}}$. We show next that this is always the case.

Suppose, on the contrary, that $\frac{\theta_0}{1-\theta_0} < \frac{v_{Lt}}{v_{Ht}}$. Then we must have that $(1-\theta_0)v_{Lt}[1-x-(1-s)(1-\lambda)Pr(c_t)] + \theta_0 v_{Ht}(x+s-1) > \theta_0(1-\theta_0)[s-(1-s)(1-\lambda)Pr(c_t)]$. Since $v_{Lt} \le \theta_0$ and $v_{Ht} \le (1-\theta_0)$ it holds that $(1-\theta_0)\theta_0[s-(1-s)(1-\lambda)Pr(c_t)] \ge (1-\theta_0)v_{Lt}[1-x-(1-s)(1-\lambda)Pr(c_t)] + \theta_0 v_{Ht}(x+s-1)$. Hence we have that $(1-\theta_0)\theta_0[s-(1-s)(1-\lambda)Pr(c_t)] > (1-\theta_0)\theta_0[s-(1-s)(1-\lambda)Pr(c_t)]$, which contradicts the initial assumption. Thus, $\frac{\theta_0}{1-\theta_0} \ge \frac{v_{Lt}}{v_{Ht}}$ must hold, which implies that $\frac{v_{Lt}}{v_{Ht}}$ is weakly increasing in $t$.

**Lemma 9:** $E_t(c)$ is weakly increasing in $t$.

**Proof:**

We first turn to the law of motion of the distribution of unmatched exporters. Let $M^u \equiv MG(\tilde{c}) - (1-v_L - v_H)$ be the measure of unmatched exporters that are looking for an importer. There are four types of exporters searching for an importer:

* There are $M^u - x(v_L + v_H)$ exporters which do not find an importer. Those have a distribution $G^u(c)$.

* There are $s(1 - \theta_0 - v_H)$ exporters that have been exogenously separated from patient importers, with a distribution $G^H(c)$.

* There are $s(\theta_0 - v_L)$ exporters that have been exogenously separated from an impatient importer, with a distribution $G^L(c)$.

* Finally, there are $(1-s)(1-\lambda)(\theta_0 - v_L)$ exporters that have been endogenously separated from an impatient importer, with conditional distribution $\frac{G^L(c)-G^L(\bar{c})}{1-G^L(\bar{c})}1_{\{c>\bar{c}\}}$.

Thus, the distribution of unmatched exporters evolves according to the following law of motion:

$$G_{t+1}^u(c) = \left(1 - \frac{x(v_{Lt} + v_{Ht})}{M_t^u}\right) G_t^u(c) + \frac{(1 - \theta_0 - v_{Ht})s}{M_t^u} G_t^H(c) + \frac{s(\theta_0 - v_{Lt})}{M_t^u} G_t^L(c) + \frac{(1 - s)(1 - \lambda)(\theta_0 - v_{Lt})}{M_t^u} \frac{G_t^L(c) - G_t^L(\bar{c})}{1 - G_t^L(\bar{c})} 1_{\{c>\bar{c}\}} \quad (15)$$

Note that since $G_t^u$ is a c.d.f., $G_t^u(0) = 0$ and $G_t^u(\tilde{c}_t) = 1$. Assume for a moment that $\bar{c}$ and $\tilde{c}$ are independent of time. Then it becomes clear that the pool of unmatched exporters is
worsening over time, because the relative mass of unproductive exporters is increasing over time. This is because endogenous destruction of relations with impatient importers occurs only for unproductive exporters (the last term on the right hand side is present only for $c > \bar{c}$), while exogenous separations – which affect both relations with impatient and with patient importers – are random. Thus, the probability mass of the distribution of unmatched exporters shifts toward the right tail over time. This conclusion continues to hold even if $\bar{c}_t$ decreases over time. Hence, the average cost of unmatched exporters, $E_t(c) = \int_0^{\bar{c}_t} cdG_t^u$, is increasing in $t$ as long as $\tilde{c}$ does not decrease so much that it more than compensates for the shift in the probability mass to the right tail of $G_t^u$. We assume that this condition holds and that therefore $E_t(c)$ is increasing in $t$.

**Lemma A1:** $\bar{c}$ is increasing in $A$.

**Proof:**

The proof is straightforward from inspecting the expression for $\bar{c}$. First, there is a direct positive effect of $A$ on $\bar{c}$. Moreover, there is an indirect effect: an increase in $A$ implies an increase in $G^u(\bar{c})$ (see Lemma A.9) and this implies a drop in $v_L$. To see this, note that $v_L$ can be written as $\frac{\theta_{0SS}s^2+\theta_0(1-s)(1-\lambda)s}{x[s+(1-s)(1-\lambda)G^u(\bar{c})]+s^2+(1-\lambda)(1-s)s}$. Since $G^u(\bar{c})$ increases in $A$ because $\bar{c}$ increases in $A$, it follows that $v_L$ is decreasing in $A$. The decrease in $v_L$ implies a drop in $\theta_{SS}$ and thus in $\tilde{\theta}$. This also increases $\bar{c}$ for sufficiently large $\beta_L$.

**Lemma A2:** $\bar{c}$ is increasing in $\lambda$.

**Proof:**

We show that $\bar{c}$ is monotonically increasing in $\lambda$ ($\lambda > \lambda' \Leftrightarrow \bar{c}(\lambda) > \bar{c}(\lambda')$): Consider the expression for $\bar{c}$:

$$ \bar{c}^{\varepsilon-1} = \left[ \frac{1 - \beta_L(1-s)\lambda}{\beta_L(1-s)(1-\alpha)f} \right] \left( \frac{\varepsilon-1}{\varepsilon} \alpha \right)^{\varepsilon-1} A \left[ \beta_L(1-s)[(1-\alpha) + (1-\lambda)\alpha\gamma] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i [1 - \tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-1} - \alpha\gamma[1 - \tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-1} \right]. $$

Note that $\tilde{\theta}_{t+1+i}(\lambda) = \frac{\lambda^{i+1}\theta_{SS}(\lambda)}{(\lambda^{i+1}-1)\theta_{SS}(\lambda)+1}$ is decreasing in $\lambda$ ($\theta_{SS}$ is decreasing in $\lambda$ – see Proposition 3) and converges to zero as $i$ goes to infinity. Consider the terms in the infinite sum in the expression for $\bar{c}$: $\beta^{i+1}(1-s)^{i+1}\lambda^{i+1}[1 - \tilde{\theta}_{t+1+i}(\lambda)\gamma(1-\lambda)]^{\varepsilon-1} > \beta^{i+1}(1-s)^{i+1}\lambda'^{i+1}[1 - \tilde{\theta}_{t+1+i}(\lambda)\gamma(1-\lambda)]^{\varepsilon-1}$.
$\tilde{\theta}_{t+1+i}(\lambda')\gamma(1-\lambda')^{\varepsilon-1}$. Hence, the first term is larger than the second for any $i$ and the distance between the terms becomes smaller as $i$ increases. Hence, a sufficient condition for $\bar{c}$ to be increasing in $\lambda$ is (setting $\tilde{\theta}_{t+1+i} = 0$):

$$ \left[ \frac{1 - \beta_L(1-s)\lambda}{\beta_L(1-s)(1-\alpha)f} \right] \left\{ \frac{\beta_L(1-s)[1 - \alpha + (1-\lambda)\alpha\gamma]}{1 - \beta_L(1-s)\lambda} - \alpha\gamma[1 - \theta_{SS}(\lambda)\gamma(1-\lambda)]^{\varepsilon-1} \right\} > \\ \left[ \frac{1 - \beta_L(1-s)\lambda'}{\beta_L(1-s)(1-\alpha)f} \right] \left\{ \frac{\beta_L(1-s)[1 - \alpha + (1-\lambda')\alpha\gamma]}{1 - \beta_L(1-s)\lambda'} - \alpha\gamma[1 - \theta_{SS}(\lambda')\gamma(1-\lambda')]^{\varepsilon-1} \right\} $$

Rearranging and simplifying, we obtain

$$ [1 - \beta_L(1-s)\lambda']\alpha\gamma[1 - \theta_{SS}(\lambda')\gamma(1-\lambda')]^{\varepsilon-1} - [1 - \beta_L(1-s)\lambda]\alpha\gamma[1 - \theta_{SS}(\lambda)\gamma(1-\lambda)]^{\varepsilon-1} > \\ \beta_L(1-s)(\lambda - \lambda')\alpha\gamma. $$

A sufficient condition for this condition to hold is: $[1 - \theta_{SS}(\lambda')\gamma(1-\lambda')]^{\varepsilon-1}\beta_L(1-s)(\lambda - \lambda') > \beta_L(1-s)\alpha\gamma(\lambda - \lambda')$, or, rearranging: $\theta_{SS} < \frac{1-(\alpha\gamma)^{1/(\varepsilon-1)}}{(1-\lambda)\gamma}$.

**Lemma A3:** $\bar{c}$ is decreasing in $\gamma$.

**Proof:**

We want to show: $\gamma > \gamma' \Leftrightarrow \bar{c}(\gamma) < \bar{c}(\gamma')$.

We have that

$$ \bar{c}(\gamma)^{\varepsilon-1} = \left[ \frac{1 - \beta_L(1-s)\lambda}{\beta_L(1-s)(1-\alpha)f} \right] \left( \frac{\varepsilon - 1}{\varepsilon} \alpha \right)^{\varepsilon-1} A \\ \left[ \beta_L(1-s)[(1-\alpha) + (1-\lambda)\alpha\gamma] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i [1 - \tilde{\theta}_{t+1+i}\gamma(1-\lambda)]^{\varepsilon-1} - \alpha\gamma[1 - \tilde{\theta}_t\gamma(1-\lambda)]^{\varepsilon-1} \right] $$

and

$$ \bar{c}(\gamma')^{\varepsilon-1} = \left[ \frac{1 - \beta_L(1-s)\lambda}{\beta_L(1-s)(1-\alpha)f} \right] \left( \frac{\varepsilon - 1}{\varepsilon} \alpha \right)^{\varepsilon-1} A \\ \left[ \beta_L(1-s)[(1-\alpha) + (1-\lambda)\alpha\gamma'] \sum_{i=0}^{\infty} \beta_L^i (1-s)^i \lambda^i [1 - \tilde{\theta}_{t+1+i}\gamma'(1-\lambda)]^{\varepsilon-1} - \alpha\gamma'[1 - \tilde{\theta}_t\gamma'(1-\lambda)]^{\varepsilon-1} \right]. $$

We also know that $\tilde{\theta}_{t+1+i}(\gamma) = \frac{\lambda^{i+1}\theta_{SS}(\gamma)}{(\lambda^{i+1}+1)\theta_{SS}(\gamma)+1}$ and that $\theta_{SS}(\gamma)$ is increasing in $\gamma$ since $v_L$ is increasing in $\gamma$. Therefore, the term $[1 - \tilde{\theta}_{t+1+i}(\gamma')\gamma'(1-\lambda)]^{\varepsilon-1} > [1 - \tilde{\theta}_{t+1+i}(\gamma)\gamma(1-\lambda)]^{\varepsilon-1}$ and the distance between the terms converges to zero as $i$ goes to infinity. Hence, a sufficient condition for $\bar{c}(\gamma) < \bar{c}(\gamma')$ is:
$$ \frac{(1-s)[1-\alpha+(1-\lambda)\alpha\gamma]}{1-\beta_L(1-s)\lambda} - \alpha\gamma[1-\theta_{SS}(\gamma)\gamma(1-\lambda)]^{\varepsilon-1} < \frac{(1-s)[1-\alpha+(1-\lambda)\alpha\gamma']}{1-\beta_L(1-s)\lambda} - \alpha\gamma'[1-\theta_{SS}(\gamma')\gamma'(1-\lambda)]^{\varepsilon-1} \\ \Leftrightarrow (1-s)(1-\lambda)\alpha(\gamma-\gamma') < [\alpha\gamma[1-\theta_{SS}(\gamma)\gamma(1-\lambda)]^{\varepsilon-1} - \alpha\gamma'[1-\theta_{SS}(\gamma')\gamma'(1-\lambda)]^{\varepsilon-1}][1-\beta_L(1-s)\lambda] $$

Which can also be written as:

$$ \beta_L(1-s)\lambda < 1 - \frac{(1-s)(1-\lambda)\alpha(\gamma-\gamma')}{\alpha\gamma[1-\theta_{SS}(\gamma)\gamma(1-\lambda)]^{\varepsilon-1}-\alpha\gamma'[1-\theta_{SS}(\gamma')\gamma'(1-\lambda)]^{\varepsilon-1}} $$

This is strictly smaller than $1 - \frac{(1-s)(1-\lambda)\alpha(\gamma-\gamma')}{\alpha[\gamma-\gamma'][1-\theta_{SS}(\gamma')\gamma'(1-\lambda)]^{\varepsilon-1}}$.

Therefore a sufficient condition for monotonicity is $\beta_L(1-s)\lambda < 1 - \frac{(1-s)(1-\lambda)}{[1-\theta_{SS}\gamma'(1-\lambda)]^{\varepsilon-1}}$ or $\beta_L < \frac{1}{[(1-s)\lambda] - \frac{(1-s)(1-\lambda)}{\lambda[1-\theta_{SS}\gamma'(1-\lambda)]^{\varepsilon-1}}}.$

**Lemma A4:** $\tilde{c}$ is increasing in A.

**Proof:**

Note that $\tilde{c}$ is defined by:

$$ V_E(\tilde{c}_t, \tilde{\theta}_{0t}) = \Pi(\tilde{c}_t, \tilde{\theta}_{0t}) + \sum_{i=1}^{\infty} (\beta_E(1-s))^i \Pi(\tilde{c}_t, \tilde{\theta}_{it}) \prod_{j=0}^{i-1} (1 - \tilde{\theta}_{jt} + \tilde{\theta}_{jt}\lambda) = 0. $$

We have that $\Pi(\tilde{c}) = (\frac{\alpha}{\varepsilon}) (\alpha \frac{(\varepsilon-1)}{\varepsilon})^{\varepsilon-1} [1 - \tilde{\theta}(1 - \lambda)\gamma]^\varepsilon c^{1-\varepsilon} A - \alpha f$. Thus, $\Pi(\tilde{c})$ increases in A because of the direct effect of A and because $\tilde{\theta}$ decreases in A (see Lemma A.1).

**Lemma A5:** $\tilde{c}$ is increasing in $\lambda$.

**Proof:**

Note that $\tilde{c}$ is defined by:

$$ V_E(\tilde{c}_t, \tilde{\theta}_{0t}) = \Pi(\tilde{c}_t, \tilde{\theta}_{0t}) + \sum_{i=1}^{\infty} (\beta_E(1-s))^i \Pi(\tilde{c}_t, \tilde{\theta}_{it}) \prod_{j=0}^{i-1} (1 - \tilde{\theta}_{jt} + \tilde{\theta}_{jt}\lambda) = 0. $$

We have that $\Pi(\tilde{c}) = (\frac{\alpha}{\varepsilon}) (\alpha \frac{(\varepsilon-1)}{\varepsilon})^{\varepsilon-1} [1 - \tilde{\theta}(1 - \lambda)\gamma]^\varepsilon c^{1-\varepsilon} A - \alpha f$.

Hence, $\frac{\partial\Pi(\tilde{c})}{\partial\lambda} = (\frac{\alpha}{\varepsilon}) (\alpha \frac{(\varepsilon-1)}{\varepsilon})^{\varepsilon-1} c^{1-\varepsilon} A\varepsilon [1 - \tilde{\theta}(1 - \lambda)\gamma]^{\varepsilon-1} [\tilde{\theta}\gamma - \frac{\partial\tilde{\theta}}{\partial\lambda}(1 - \lambda)\gamma]$.

Here, $\tilde{\theta}\gamma$ is the direct effect of higher $\lambda$ on profits through less contract violations and $\frac{\partial\tilde{\theta}}{\partial\lambda}(1 - \lambda)\gamma$ is the indirect effect through change in beliefs.

Note that $\frac{\partial\tilde{\theta}_i}{\partial\lambda} = \frac{i\lambda^{i-1}\theta_{SS}(1-\theta_{SS}) + \frac{\partial\theta_{SS}}{\partial\lambda}\lambda^i}{[(\lambda^{i-1})\theta_{SS}+1]^2}$. $i\lambda^{i-1}\theta_{SS}(1 - \theta_{SS})$ is the positive effect of $\lambda$ on beliefs, because of lower learning speed, while $\frac{\partial\theta_{SS}}{\partial\lambda} < 0$ is the negative effect on beliefs through lower steady state value of $\theta$. We assume that the second effect dominates the first one, so that
the sign of the derivative is negative. Moreover, $\frac{\partial \Pi_{j=0}^{i-1}(1-\tilde{\theta}_{jt}+\tilde{\theta}_{jt}\lambda)}{\partial \lambda} > 0$, since $\frac{\partial(1-\tilde{\theta}_{jt}+\tilde{\theta}_{jt}\lambda)}{\partial \lambda} = \tilde{\theta}_j - \frac{\partial \tilde{\theta}_j}{\partial \lambda}(1-\lambda) > 0$.

**Lemma A6:** $\tilde{c}$ is decreasing in $\gamma$.

**Proof:**

Since $\Pi(\tilde{c}) = (\frac{\alpha}{\epsilon}) (\alpha(\frac{\epsilon-1}{\epsilon}))^{\epsilon-1} [1-\tilde{\theta}(1-\lambda)\gamma]^\epsilon c^{1-\epsilon} A - \alpha f$, we have that $\frac{\partial \Pi(\tilde{c})}{\partial \gamma} = (\frac{\alpha}{\epsilon}) (\alpha(\frac{\epsilon-1}{\epsilon}))^{\epsilon-1} c^{1-\epsilon} A \epsilon * [1 - \tilde{\theta}(1-\lambda)\gamma]^{\epsilon-1} [-\tilde{\theta}(1-\lambda) - \frac{\partial \tilde{\theta}}{\partial \gamma}(1-\lambda)\gamma] < 0$. This follows, since $\frac{\lambda^i \partial \tilde{\theta}_{SS}}{\partial \gamma} = \frac{\lambda^{i-1} \partial \tilde{\theta}_{SS+1}}{\partial \gamma} > 0$. Moreover, $\frac{\partial \Pi_{j=0}^{i-1}(1-\tilde{\theta}_{jt}+\tilde{\theta}_{jt}\lambda)}{\partial \gamma} < 0$, since $\frac{\partial(1-\tilde{\theta}_{jt}+\tilde{\theta}_{jt}\lambda)}{\partial \gamma} = -\frac{\partial \tilde{\theta}_j}{\partial \gamma}(1-\lambda) < 0$.

**Steady State Distribution of Exporters**

Let $G^u(c)$, $G^L(c)$ and $G^H(c)$ be, respectively, the distributions of exporters which are un-
matched, matched with patient importers and matched with impatient importers. In the
steady state, the distribution of exporters matched with patient importers is described by
$G^H(c) = sG^u(c) + (1-s)G^H(c)$. Thus $G^u(c) = G^H(c)$, which is logical at the steady state
because all separations are exogenous.

The distribution of exporters matched with impatient importers is described as follows. There
are 4 different groups: 1) exporters which have been replaced after exogenous separation:
proportion $s$ and distribution $G^u(c)$; 2) exporters which were not exogenously separated with
proportion $(1-s)$. Out of those $(1-s)G^L(\bar{c})$ have $c \le \bar{c}$ and $(1-s)(1-G^L(\bar{c}))$ have $c > \bar{c}$; 3) those
which were replaced after endogenous separation: $(1-s)(1-G^L(\bar{c})) (1-\lambda)$ with distribution
$G^u(c)$; 4) those which were not endogenously separated: proportion $(1-s)(1-G^L(\bar{c}))\lambda$.

We further distinguish between $c \le \bar{c}$ and $c > \bar{c}$:

For exporters with $c \le \bar{c}$ we have $G^L(c) = sG^u(c) + (1-s)G^L(c) + (1-s)(1-G^L(\bar{c})) (1-\lambda)G^u(c)$,
while for exporters with $c > \bar{c}$: $G^L(c) = sG^u(c) + (1-s)G^L(\bar{c}) + (1-s)(1-G^L(\bar{c})) (1-\lambda)G^u(c) +
(1-s)\lambda(G^L(c) - G^L(\bar{c}))$. Hence, $G^L(z)$ is different from $G^u(z)$ because impatient importers get
rid of the less efficient exporters.

Finally, we can write the population distribution as a weighted average of the distribution of
the three types of exporters:

$$
\begin{align}
MG(\bar{c}) &= (\theta_0 - v_L)G^L(\bar{c}) + (1 - \theta_0 - v_H)G^H(\bar{c}) + M^u G^u(\bar{c}) \tag{16} \\
&= (\theta_0 - v_L)G^L(\bar{c}) + (M^u + 1 - \theta_0 - v_H)G^u(\bar{c}) \nonumber
\end{align}
$$
At $\bar{c}$ we can express $G^H(\bar{c}) = G^u(\bar{c})$, $G^L(\bar{c}) = \frac{G^u(\bar{c})[s+(1-s)(1-\lambda)]}{s+(1-s)(1-\lambda)G^u(\bar{c})}$, $v_L = \frac{\theta_0[s+(1-s)(1-\lambda)(1-G^L(\bar{c}))]}{x+s+(1-\lambda)(1-s)(1-G^L(\bar{c}))}$, $M^u = MG(\tilde{c}) - (1 - v_H - v_L)$. Substituting this into (16), we obtain a quadratic equation in $G^u(\bar{c})$, that implicitly defines $G^u(\bar{c})$:

$$MG(\bar{c})\Phi = [G^u(\bar{c})]^2 \{\Omega[MG(\tilde{c}) - \theta_0]\} + G^u(\bar{c}) \{\Omega\theta_0 + MG(\tilde{c})\Phi - MG(\bar{c})\Omega\}, \quad (17)$$

where $\Phi = (x+s)s + (1-s)(1-\lambda)s$ and $\Omega = (1-s)(1-\lambda)x$.

**Lemma A7: $G^u(c)$ is increasing in $\lambda$**.

**Proof:**

Implicitly differentiating (17) and rearranging, we can write

$$\frac{\partial G^u(\bar{c})}{\partial \lambda} = \left\{ \left[ \frac{\partial G(\bar{c})}{\partial \lambda} - \frac{\partial G(\bar{c})}{\partial \lambda} G_u(\bar{c}) \right] B + D \right\} / E,$$

where

$$E = \Omega[2G^u(\bar{c})(MG(\tilde{c}) - \theta_0) - (MG(\bar{c}) - \theta_0)] + \Phi MG(\tilde{c}),$$

$$B = MG_u(\bar{c})\Omega + M\Phi,$$

$$D = (1-s)sM[G^u(\bar{c})G(\tilde{c}) - G(\bar{c})] + (1-s)xG^u[G^u(MG(\tilde{c}) - \theta_0) - (MG(\bar{c}) - \theta_0)].$$

This derivative is positive provided that the following sufficient conditions hold. A sufficient condition for $E > 0$ and $D > 0$ is $G^u(\bar{c}) > \frac{G(\bar{c})}{G(\tilde{c})}$, implying that the fraction of unmatched exporters that lie below the contract violation cutoff must be sufficiently larger than the fraction of firms in the population distribution below this cutoff. Sufficient for $[\frac{\partial G(\bar{c})}{\partial \lambda} - \frac{\partial G(\bar{c})}{\partial \lambda} G_u(\bar{c})] > 0$ is $g(\bar{c})\frac{\partial \bar{c}}{\partial \lambda} > g(\tilde{c})\frac{\partial \tilde{c}}{\partial \lambda}G^u(\bar{c})$, implying that the contract violation cutoff $\bar{c}$ must be sufficiently responsive to a change in $\lambda$ compared to the entry cutoff $\tilde{c}$.

**Lemma A8: $G^u(c)$ is decreasing in $\gamma$**.

**Proof:**

Implicitly differentiating (17) and rearranging, we obtain:

$$\frac{\partial G^u(\bar{c})}{\partial \gamma} = \left\{ \left[ \frac{\partial G(\bar{c})}{\partial \gamma} - \frac{\partial G(\bar{c})}{\partial \gamma} G_u(\bar{c}) \right] B \right\} / E$$

A sufficient condition for the derivative to be negative is that $[\frac{\partial G(\bar{c})}{\partial \gamma} - \frac{\partial G(\bar{c})}{\partial \gamma} G^u(\bar{c})] < 0$. Thus, we assume that $|g(\bar{c})\frac{\partial \bar{c}}{\partial \gamma}| > |g(\tilde{c})\frac{\partial \tilde{c}}{\partial \gamma}G^u(\bar{c})|$.

**Lemma A9: $G^u(c)$ is increasing in $A$**.

**Proof:**
Implicitly differentiating (17) and rearranging, we can also write

$$ \frac{\partial G^u(\bar{c})}{\partial A} = \left\{ \left[ \frac{\partial G(\bar{c})}{\partial A} - \frac{\partial G(\bar{c})}{\partial A} G^u(\bar{c}) \right] B \right\} / E $$

A sufficient condition for the derivative to be positive is that $\left[ \frac{\partial G(\bar{c})}{\partial A} - \frac{\partial G(\bar{c})}{\partial A} G^u(\bar{c}) \right] > 0$. Thus, we assume that $g(\bar{c}) \frac{\partial \bar{c}}{\partial A} > g(\bar{c}) \frac{\partial \bar{c}}{\partial A} G^u(\bar{c})$.

## Derivation of State Dependence

We have that

$$ \begin{aligned} P(Y_t = 1 | Y_{t-1} = 0) &= \frac{x(v_H + v_L)}{M^u}, \\ P(Y_t = 1 | Y_{t-1} = 1, c \le \bar{c}) &= 1 - s, \\ P(Y_t = 1 | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) &= P(Y_t = 1 \ \& \ H | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) \\ & \quad + P(Y_t = 1 \ \& \ L | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) \\ &= P(Y_t = 1 | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}, H) P(H | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) \\ & \quad + P(Y_t = 1 | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}, L) P(L | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}), \end{aligned} $$

and that

$$ \begin{aligned} P(Y_t = 1 | Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c}, H) &= 1 - s, \\ P(Y_t = 1 | Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c}, L) &= 1 - (s + (1-s)(1-\lambda)), \\ P(H | Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c}) &= \frac{P(c, \bar{c} \le c \le \tilde{c} | Y_{t-1} = 1, H) P(H | Y_{t-1} = 1)}{P(c, \bar{c} \le c \le \tilde{c} | Y_{t-1} = 1)}, \\ P(c, \bar{c} \le c \le \tilde{c} | Y_{t-1} = 1, H) &= g^u(c), \\ P(H | Y_{t-1} = 1) &= \frac{1 - \theta_0 - v_H}{1 - v_L - v_H}, \\ P(c, \bar{c} \le c \le \tilde{c} | Y_{t-1} = 1) &= \frac{\theta_0 - v_L}{1 - v_L - v_H} g^L(c) + \frac{1 - \theta_0 - v_H}{1 - v_L - v_H} g^u(c). \end{aligned} $$

Hence,

$$ P(H|Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c}) = \frac{g^u(c)(1 - \theta_0 - v_H)}{g^L(c)(\theta_0 - v_L) + g^u(c)(1 - \theta_0 - v_H)}, $$

and similarly,

$$ P(L|Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c}) = \frac{g^L(c)(\theta_0 - v_L)}{g^L(c)(\theta_0 - v_L) + g^u(c)(1 - \theta_0 - v_H)}. $$
Thus,

$$P(Y_t = 1 | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) = (1-s) \frac{g^u(c)(1-\theta_0 - v_H)}{g^L(c)(\theta_0 - v_L) + g^u(c)(1-\theta_0 - v_H)} + [1 - (s + (1-s)(1-\lambda))] \frac{g^L(c)(\theta_0 - v_L)}{g^L(c)(\theta_0 - v_L) + g^u(c)(1-\theta_0 - v_H)}.$$

Simplifying, we obtain

$$P(Y_t = 1 | Y_{t-1} = 1, \bar{c} \le c \le \tilde{c}) = \frac{(1-s)[1 + \lambda L]}{1 + L},$$

where $L \equiv \frac{(\theta_0 - v_L)}{(1-\theta_0 - v_H)} \frac{g^L(c)}{g^u(c)}$. Since for $c \ge \bar{c}$:

$$G^L(c) = sG^u(c) + (1-s)G^L(\bar{c}) + (1-s)(1-G^L(\bar{c}))(1-\lambda)G^u(c) + (1-s)\lambda(G^L(c) - G^L(\bar{c})),$$

we obtain for $c \ge \bar{c}$

$$g^L(c) = s g^u(c) + (1-s)(1-G^L(\bar{c}))(1-\lambda)g^u(c) + (1-s)\lambda g^L(c).$$

Hence:

$$\frac{g^L(c)}{g^u(c)} = \frac{s + (1-s)(1-\lambda)(1-G^L(\bar{c}))}{1 - (1-s)\lambda}$$

**Proposition 2: State dependence is increasing in the market size of the export destination.**

**Proof:**

We have shown in Lemmas A.1 and A.4 that $\bar{c}$ and $\tilde{c}$ are increasing in market size (A). Let us compare two destinations, $k$ and $k'$, with $A_k > A_{k'}$. Without loss of generality, assume that the following ordering holds: $\bar{c}_{k'} < \bar{c}_k < \tilde{c}_{k'} < \tilde{c}_k$. Then we can compare state dependence across intervals.

Firms with $c \in (0, \bar{c}_{k'}]$ face only exogenous separations in both countries, thus:

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (0, \bar{c}_{k'}]) - P(Y_t = 1 | Y_{t-1} = 0, c, c \in (0, \bar{c}_{k'}]) = 1 - s - \frac{x(v_H + v_L)}{M^u} \quad \text{for } k, k'$$

Firms with $c \in (\bar{c}_{k'}, \bar{c}_k]$ experience both endogenous and exogenous separations in the small country $k'$, while they face only exogenous separations in the large country $k$:

$$P(Y_t = 1 | Y_{t-1} = 1, c, c \in (\bar{c}_{k'}, \bar{c}_k]) - P(Y_t = 1 | Y_{t-1} = 0, c, c(\bar{c}_{k'}, \bar{c}_k]) = 1 - s - \frac{x(v_H + v_L)}{M^u} \quad \text{for } k, \\ P(Y_t = 1 | Y_{t-1} = 1, c, c \in (\bar{c}_{k'}, \bar{c}_k]) - P(Y_t = 1 | Y_{t-1} = 0, c, c(\bar{c}_{k'}, \bar{c}_k]) = \frac{(1-s)[1+\lambda L]}{1+L} - \frac{x(v_H + v_L)}{M^u} \quad \text{for } k'$$
Firms with $c \in (\bar{c}_k, \tilde{c}_{k'}]$ have endogenous and exogenous separations in both countries:

$P(Y_t = 1|Y_{t-1} = 1, c, c \in (\bar{c}_k, \tilde{c}_{k'}]) - P(Y_t = 1|Y_{t-1} = 0, c, c(\bar{c}_k, \tilde{c}_{k'})) = \frac{(1-s)[1+\lambda L]}{1+L} - \frac{x(v_H+v_L)}{M^u}$ for $k, k'$.

Firms with $c \in (\tilde{c}_{k'}, \tilde{c}_k]$ only export to the large country and thus state dependence is not defined in the small country for $c > \tilde{c}_{k'}$ because $P(Y_t = 1|Y_{t-1} = 1, c, c > \tilde{c}_{k'}) = \frac{P(Y_t=1\&Y_{t-1}=1, c, c>\tilde{c}_{k'})}{P((Y_{t-1}=1|c, c>\tilde{c}_{k'}))} = \frac{0}{0}$. Thus, state dependence cannot be compared for those firms that do not export to both destinations.

As we can see from the above expressions, for any firm $c$ state dependence is either similar in both markets or discretely larger in the bigger market.

While we do not think that general equilibrium effects that impact on state dependence indirectly through changes in $G(\tilde{c})$, $G^u(\bar{c})$ and $v_L$ are particularly relevant, we also show that the model is consistent with state dependence to be increasing in market size within a given interval.

Note that

$$ \frac{\partial P(Y_t = 1|Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c})}{\partial A} = \frac{(\lambda - 1)(1 - s) \partial L}{[1 + L]^2 \partial A} $$

The sign of this derivative is ambiguous. First, $(\lambda - 1) < 0$ and since $L \equiv \frac{(\theta_0 - v_L)}{(1 - \theta_0 - v_H)} \frac{g^L(c)}{g^u(c)}$, we have that $\frac{\partial L}{\partial A} = \frac{\partial(\frac{\theta_0 - v_L}{1 - \theta_0 - v_H})}{\partial A} \frac{g^L(c)}{g^u(c)} + \frac{\partial(\frac{g^L(c)}{g^u(c)})}{\partial A} \frac{(\theta_0 - v_L)}{(1 - \theta_0 - v_H)} > 0$. This is because $\frac{(\theta_0 - v_L)}{(1 - \theta_0 - v_H)}$ is increasing in $A$ (since $v_L$ decreases in $A$) and $\frac{g^L(c)}{g^u(c)}$ is decreasing in $A$, since $G^L(\bar{c}) = \frac{[s+(1-s)(1-\lambda)]}{[s/G^u(\bar{c})+(1-s)(1-\lambda)]}$ increases in $A$ (because $G^u(\bar{c})$ is increasing in $A$) and thus $1 - G^L(\bar{c})$ decreases in $A$. The total effect depends on which of the two effects is stronger. Moreover, we have that

$$ \frac{\partial P(Y_t = 1|Y_{t-1} = 0, c, \bar{c} \le c \le \tilde{c})}{\partial A} = \frac{\partial \left( \frac{x(v_H+v_L)}{MG(\bar{c})-1+v_H+v_L} \right)}{\partial A} $$

is decreasing in $A$, since $v_L$ is decreasing in $A$ and $G(\tilde{c})$ is increasing in $A$.

**Proposition 3:** *State dependence is increasing in the quality of the export destinations' legal institutions. Moreover, the impact of legal institutions on state dependence is larger for exporters with higher marginal costs.*

**Proof:**
We compare two destinations $k$ and $k'$ with $\lambda_k < \lambda_{k'}$. We have already shown that $\bar{c}$ and $\tilde{c}$ increase in $\lambda$. Thus, without loss of generality, assume that $\bar{c}_{k'} < \bar{c}_k < \tilde{c}_{k'} < \tilde{c}_k$.

Firms with $c \in (0, \bar{c}_{k'}]$ face only exogenous separations in both destinations. Thus,

$P(Y_t = 1|Y_{t-1} = 1, c, c \in (0, \bar{c}_{k'}]) - P(Y_t = 1|Y_{t-1} = 0, c, c \in (0, \bar{c}_{k'}]) = 1 - s - \frac{x(v_H+v_L)}{M^u}$ for $k, k'$

Firms with $c \in (\bar{c}_{k'}, \tilde{c}_{k'}]$ face both endogenous and exogenous separations in the country with low $\lambda$, while they only face exogenous separations in the destination with high $\lambda$.

$P(Y_t = 1|Y_{t-1} = 1, c, c \in (\bar{c}_{k'}, \tilde{c}_{k'}]) - P(Y_t = 1|Y_{t-1} = 0, c, c \in (\bar{c}_{k'}, \tilde{c}_{k'}]) = \frac{(1-s)[1+\lambda L]}{1+L} - \frac{x(v_H+v_L)}{M^u}$ for $k'$,

$P(Y_t = 1|Y_{t-1} = 1, c, c \in (\bar{c}_{k'}, \bar{c}_k]) - P(Y_t = 1|Y_{t-1} = 0, c, c \in (\bar{c}_{k'}, \bar{c}_k]) = 1 - s - \frac{x(v_H+v_L)}{M^u}$ for $k$.

Firms with $c \in (\bar{c}_k, \tilde{c}_{k'}]$ experience endogenous and exogenous separations in both countries.

$P(Y_t = 1|Y_{t-1} = 1, c, c \in (\bar{c}_k, \tilde{c}_{k'}]) - P(Y_t = 1|Y_{t-1} = 0, c, c \in (\bar{c}_k, \tilde{c}_{k'}]) = \frac{(1-s)[1+\lambda L]}{1+L} - \frac{x(v_H+v_L)}{M^u}$ for $k, k'$.

Firms with $c \in (\tilde{c}_{k'}, \tilde{c}_k]$ export only to country $k$. Thus, state dependence cannot be compared across destinations for firms with $c > \tilde{c}_{k'}$ because state dependence is not defined for those firms in country $k'$ (see Proposition 2).

For the impact of $\lambda$ on state dependence within a given interval, note that

$$ \frac{\partial P(Y_t = 1|Y_{t-1} = 1, c, \bar{c} \le c \le \tilde{c})}{\partial \lambda} = \frac{(1-s)[(\lambda-1)\frac{\partial L}{\partial \lambda} + L(1+L)]}{[1+L]^2} > 0. $$

Thus, there is a direct effect of higher $\lambda$: a given relation is more likely not to be destroyed.

There is also a composition effect: $\frac{\partial L}{\partial \lambda} = \frac{\partial \left( \frac{\theta_0 - v_L}{1 - \theta_0 - v_H} \right)}{\partial \lambda} \frac{g^L(c)}{g^u(c)} + \frac{\partial \left( \frac{g^L(c)}{g^u(c)} \right)}{\partial \lambda} \frac{(\theta_0 - v_L)}{(1 - \theta_0 - v_H)}$. This effect is ambiguous since $\frac{(\theta_0 - v_L)}{(1 - \theta_0 - v_H)}$ is increasing in $\lambda$ because $v_L$ is decreasing in $\lambda$ and the sign of $\frac{\partial g^L(c)}{\partial \lambda} = \frac{(1-s)[sG^L(\bar{c}) - (1-(1-s)\lambda)(1-\lambda)g^L(\bar{c})]}{[1-(1-s)\lambda]^2}$ is ambiguous. This is because, on the one hand, more relations survive and this increases the mass of exporters matched to impatient importers.

On the other hand, $\bar{c}$ shifts up and this decreases the probability of contract violations. We assume that the overall effect is positive.

Proof of claim that $\frac{\partial v_L}{\partial \lambda} < 0$:

$v_L$ can be written as $\frac{\theta_0 s^2 + \theta_0(1-s)(1-\lambda)s}{x[s+(1-s)(1-\lambda)G^u(\bar{c})]+s^2+(1-\lambda)(1-s)s}$. Thus, we have that

$$ \frac{\partial v_L}{\partial \lambda} = \frac{[G^u(\bar{c}) - 1]\theta_0 x s(1-s)[s - (1-s)(1-\lambda)] - \frac{\partial G^u(\bar{c})}{\partial \lambda}\theta_0 s(1-s)(1-\lambda)[s + (1-s)(1-\lambda)]}{\{x[s + (1-s)(1-\lambda)G^u] + s^2 + (1-\lambda)(1-s)s\}^2}. $$

Therefore, a sufficient condition for the expression to be negative is $s > (1-s)(1-\lambda)$. Since
$\frac{\partial G^u(\bar{c})}{\partial \lambda} > 0$ we have that $\frac{\partial v_L}{\partial \lambda} < 0$. Moreover,

$$ \frac{\partial P(Y_t = 1 | Y_{t-1} = 0)}{\partial \lambda} = \frac{\partial \frac{x(v_H + v_L)}{M^u}}{\partial \lambda} < 0, $$

since

$$ \frac{\partial \frac{x(v_H+v_L)}{M^u}}{\partial \lambda} = \frac{\partial \left( \frac{x(v_H+v_L)}{G(\tilde{c})M-1+v_H+v_L} \right)}{\partial \lambda} = \frac{\frac{\partial v_L}{\partial \lambda} x[G(\tilde{c})M-1] - x(v_H+v_L)M \frac{\partial G(\tilde{c})}{\partial \lambda}}{[G(\tilde{c})M-1+v_H+v_L]^2} < 0. $$

These observations imply that state dependence is also increasing in $\lambda$ within a given interval.

This proves that for any firm state dependence is larger in countries with higher $\lambda$.

For the second part of the proposition, note that $\lambda$ only matters for state dependence via its impact on the probability of surviving as long as $c > \bar{c}_{k'}$, else $\lambda$ only affects the probability of finding a partner. Thus, $\lambda$ has a larger impact on state dependence for less productive firms.

**Proposition 4: The positive impact of legal institutions on state dependence is larger in sectors with larger contracting frictions (sectors with higher levels of $\gamma$).**

**Proof:**

We compare the impact of a small improvement in legal institutions (from $\lambda_{k'}$ to $\lambda_k$) for two sectors that differ in the extent of their contracting frictions. Suppose that we compare state dependence for two sectors: sector $j'$ with large contracting frictions (high $\gamma$) and sector $j$ with low contracting frictions (low $\gamma$). We have shown that $\bar{c}$ and $\tilde{c}$ are both increasing functions of $\lambda$ and decreasing functions of $\gamma$. Hence, we have that $\bar{c}_{k'} < \bar{c}_k$ and $\tilde{c}_{k'} < \tilde{c}_k$. We also have that $\bar{c}_{j'} < \bar{c}_j$ and $\tilde{c}_{j'} < \tilde{c}_j$. Suppose that the ordering of cutoffs is such that $\bar{c}_{j'k'} < \bar{c}_{j'k} < \tilde{c}_{j'k'}$$^{36}$

Firms with $c$ below $\bar{c}_{j'k'}$ face only exogenous separations before and after the change in $\lambda$. Thus, the impact of a change in $\lambda$ works only through a reduction in the probability of finding a partner and thus increases state dependence in both sectors $j$ and $j'$.

Firms in $[\bar{c}_{j'k'}, \bar{c}_{j'k}]$: In sector $j'$ firms move from endogenous to exogenous separations, while in sector $j$ they face only exogenous separations before and after the change in $\lambda$.

Firms in $(\bar{c}_{j'k}, \tilde{c}_{j'k'}]:$ In sector $j'$ firms face endogenous separations both before and after the change in $\lambda$, while in sector $j$ the only impact of changing $\lambda$ works through changing the probability of finding a partner.

<footnote>$^{36}$Other orderings of the cutoffs that give less clearcut predictions are also possible. We focus on this ordering because it is consistent with the results from our empirical test.</footnote>
Firms with $c > \tilde{c}_{j'k'}$ do not export in sector $j'$ before the increase in $\lambda$. Thus state dependence is not defined for those firms and changes in state dependence cannot be compared across sectors for $c > \tilde{c}_{j'k'}$.

**Proposition 5: The hazard is decreasing in the age of the relationship.**

**Proof:**

For $c > \bar{c} H(c, c > \bar{c}) = s + \frac{v_L(1-\lambda)(1-s)}{v_L + \frac{v_H}{\lambda^{i-1}}}$, Since $\lambda^{i-1}$ is decreasing in $i$, $H(c, c > \bar{c})$ is decreasing in $i$.

**Proposition 7: The conditional hazard is decreasing in the destination country's market size.**

**Proof:**

Since $\bar{c}$ and $\tilde{c}$ is increasing in $A$, for a given $c$ compare two destinations with $A_k > A_{k'}$. Thus, without loss of generality assume that $\bar{c}_{k'} < \bar{c}_k < \tilde{c}_{k'} < \tilde{c}_k$.

Then for $c < \bar{c}_{k'}$: $H(c) = s$ for $k, k'$.

For $c \in (\bar{c}_{k'}, \bar{c}_k]: H(c) = s + \frac{v_L(1-\lambda)(1-s)\lambda^{i-1}}{v_L\lambda^{i-1}+v_H}$ for $k'$; $H(c) = s$ for $k$.

For $c \in (\bar{c}_k, \tilde{c}_k]: H(c) = s + \frac{v_L(1-\lambda)(1-s)\lambda^{i-1}}{v_L\lambda^{i-1}+v_H}$ for $k, k'$.

Finally, the hazard is not defined in destination $k'$ for $c > \tilde{c}_k$.

Moreover, within an interval note that $v_L$ is decreasing in $A$ and thus $\frac{\partial H(c,c>\bar{c})}{\partial A} < 0$.

**Proposition 8: The conditional hazard is decreasing in the quality of the legal system for sufficiently young relationships. Moreover, for those relationships an increase in the quality of the legal system leads to a larger decrease in the conditional hazard in sectors with larger contracting problems.**

**Proof:**

Proof of part 1: Since $\bar{c}$ and $\tilde{c}$ are increasing in $\lambda$, for a given $c$ compare two destinations with $\lambda_k > \lambda_{k'}$. Without loss of generality, assume that $\bar{c}_{k'} < \bar{c}_k < \tilde{c}_{k'} < \tilde{c}_k$.

Then for $c < \bar{c}_{k'}$: $H(c) = s$ for $k, k'$.

For $c \in (\bar{c}_{k'}, \bar{c}_k]: H(c) = s + \frac{v_L(1-\lambda)(1-s)\lambda^{i-1}}{v_L\lambda^{i-1}+v_H}$ for $k'$; $H(c) = s$ for $k$.

For $c \in (\bar{c}_k, \tilde{c}_{k'}]: H(c) = s + \frac{v_L(1-\lambda)(1-s)\lambda^{i-1}}{v_L\lambda^{i-1}+v_H}$ for $k, k'$.

Finally, the hazard rate is not defined for $c > c_{\tilde{k}'}$ and thus cannot be compared.
Moreover, within an interval note that $H(c, c > \bar{c})$ is decreasing in $\lambda$ for age $i$ sufficiently small.
For $i = 1$, $H(c) = s + \frac{v_L(1-s)(1-\lambda)}{v_L+v_H}$, and $\frac{\partial H}{\partial \lambda} = -(1-s)\frac{v_L}{v_L+v_H} < 0$.

**Proof of part 2:** We compare the impact of a small improvement in legal institutions (from $\lambda_{k'}$ to $\lambda_k$) for two sectors that differ in the extent of their contracting frictions. Suppose that we compare state dependence for two sectors: sector $j'$ with large contracting frictions (high $\gamma$) and sector $j$ with low contracting frictions (low $\gamma$). We have shown that $\bar{c}$ and $\tilde{c}$ are both decreasing functions of $\gamma$. Hence, we have that $\bar{c}_{j'} < \bar{c}_j$ and $\tilde{c}_{j'} < \tilde{c}_j$. Moreover, $\bar{c}$ and $\tilde{c}$ are increasing in $\lambda$. Suppose that the ordering of cutoffs is such that $\bar{c}_{j'k'} < \bar{c}_{j'k} < \tilde{c}_{j'k'} < \tilde{c}_{jk'} < \bar{c}_{jk}$.<fnref n="37" />

For $c \le \bar{c}_{j'k'}$: there is no effect of a change in $\lambda$ in sectors $j$ and $j'$, since $H(c, c < \bar{c}_{j'k'}) = s$.

For $c \in (\bar{c}_{j'k'}, \bar{c}_{j'k}]$: in sector $j'$ $H$ changes from $H(c) = s + \frac{v_L(1-\lambda)(1-s)\lambda^{i-1}}{v_L\lambda^{i-1}+v_H}$ to $H(c) = s$. In sector $j$ there is no effect on the hazard.

For $c \in (\bar{c}_{j'k}, \tilde{c}_{j'k}]$: in sector $j'$, and for $i$ sufficiently small ($i = 1$), $H$ changes by $\frac{\partial H}{\partial \lambda} = -\frac{(1-s)v_L}{v_L+v_H} < 0$. In sector $j$ the hazard does not change.

For $c > \tilde{c}_{j'k'}$ the hazard is not defined in sector $j'$ for $\lambda_{k'}$ and thus changes in hazard rates cannot be compared.

# B Robustness Checks

## B.1 Robustness Checks State Dependence

Here, we present several robustness checks of the state dependence results. We first add EU destinations to our sample, then we implement an Arellano-Bond dynamic panel estimator, which allows us also to control for firm-country fixed effects and finally, we present results from using a random effects dynamic Probit model instead of a linear probability model.

### B.1.1 Including EU-destinations

In Table 8 we add EU destinations to the sample. In columns (1)-(4) we present results for specification (9). All results continue to hold and the interactions of past export status

<footnote n="37">³⁷Other orderings of the cutoffs that give less clearcut predictions are also possible, in particular, we require $\bar{c}_{j'k} < \bar{c}_{jk'}$ and $\tilde{c}_{j'k'} < \bar{c}_{jk'}$ for our prediction to hold unambiguously. We focus on this ordering because it is consistent with the results from our empirical test.</footnote>
with legal institutions, market size and productivity remain positive and highly significant. In columns (5)-(8) we add sector interactions and present results for specification (10). Again, the triple interactions between past export, legal institutions and relationship dependence remain positive and highly significant. Thus, our results are robust to including EU destinations.

### B.1.2 Arellano Bond Dynamic Panel Estimator

One could argue that the residuals might still be auto-correlated even after controlling for firm-time and country-time fixed effects because of firm-destination (relationship-specific) specific unobserved heterogeneity. In order to control for firm-destination fixed effects, we employ the Arellano-Bond panel IV estimator (Arellano and Bond, 2001).

The specification is

$$ Pr(Y_{fkt} = 1|Y_{fkt-1}, X_{fkt}) = \beta_0 + \beta_1 Y_{fkt-1} + \beta_2 Y_{fkt-1} * Prod_{ft} + \beta_3 Y_{fkt-1} * A_k + \beta_4 Y_{fkt-1} * IQ_k + \delta_{ft} + \delta_{kt} + \delta_{fk}. \quad (18) $$

Using again the double-within transformation and taking time differences, we eliminate all unobserved heterogeneity. Since the lagged export status is correlated with the lagged residuals, lagged changes in export status need to be instrumented. We use as instruments the three-period lag of export status in order to account for even the possibility of an MA(1) auto-correlation of the residuals in addition to the firm-country fixed effects which are taken into account through first differentiation.

We perform the estimation year by year but unfortunately, this method proves a lot less powerful in terms of identification than the one without firm-country fixed effects, which is a common issue with the Arellano-Bond method due to the weakness of the instruments. The coefficients of the variables of interest usually have the right sign but they are often non significant. As an example, we provide the results obtained with the data for changes between 1999 and 2000 in Table 9, for which most of the coefficients exhibit some statistical significance. In columns (1) to (4) we present results for our baseline specification (9). Note that the interactions with legal and rule of law have the correct signs and are significant, while number of procedures and cost are insignificantly different from zero. The interactions with market size and productivity are mostly insignificant and sometimes exhibit the wrong sign. In columns (5)-(8) we add triple interactions between past export status, institutions and productivity.
This improves the results by increasing the magnitude and the significance of the legal quality interactions. Moreover, as expected, the triple interactions with productivity are negative and significant.

### B.1.3 Dynamic Random Effect Probit

As a final robustness check, we estimate a dynamic random effect probit model. We specify

$$ Pr(Y_{fkt} = 1|Y_{fkt-1}, X_{fkt}) = \Phi(\beta_0 + \beta_1 Y_{fkt-1} + \beta_2 Y_{fkt-1} * IQ_k + \beta_3 Y_{fkt-1} * X_{fkt} + \beta_4 X_{fkt} + \delta_{fk}), \quad (19) $$

where $X_{fkt}$ are observables and $\delta_{fk}$ is unobserved heterogeneity. Since any non-linear estimator needs to integrate out the unobserved heterogeneity, the question is how to treat the observations in the initial period. We follow Wooldridge (2005) and estimate the joint distribution of $(Y_{fk1}, ..., Y_{fkT})$, conditional on the initial conditions $Y_{fk0}$ and observables $X_{fk} = (X_{fk1}, ..., X_{fkT})$ with conditional maximum likelihood methods. We thus need to specify a density $h$ for $\delta_{fk}$ given $Y_{fk0}$ and $X_{fk}$, to obtain the density

$$ f(Y_1, Y_2, ..., Y_T|Y_0, X, \beta) = \int_{-\infty}^{\infty} f(Y_1, ..., Y_T|Y_0, X, \delta, \beta, )h(\delta|Y_0, X, \beta)d\delta. \quad (20) $$

We assume that the unobserved heterogeneity follows a Normal distribution with expectation $\delta_{fk} = \delta_0 + \delta_1 Y_{fk0} + \delta_2 Y_{fk0} * IQ_k + \delta_3 Y_{fk0} * X_{fk0} + \delta_4 IQ_k + \delta_5 \bar{X}_f + \delta_6 \bar{X}_k$ and variance $\sigma^2$. Here $X_{fkt}$ contains value added per worker, the bilateral real exchange rate and market size proxies, $\bar{X}_f$ is the time average of firm productivity and $\bar{X}_k$ are time averages of our market size proxies. This implies that $Y_{fkt}$ given $(Y_{fkt-1}, ..., Y_{fk0}, X_{fk})$ follows a Probit model.

$$ Pr(Y_{fkt} = 1|Y_{fkt-1}, Y_{fk0}, X_{fkt}) = \Phi(\dot{\beta}_0 + \dot{\beta}_1 Y_{fkt-1} + \dot{\beta}_2 Y_{fkt-1} * IQ_k + \dot{\beta}_3 Y_{fkt-1} * X_{fkt} + \dot{\beta}_4 X_{fkt} + \dot{\delta}_{fk}), \quad (21) $$

where the superscripts denote multiplication by $(1 + \hat{\sigma}^2)^{-1/2}$. Results for this specification are presented in Table 12. Note that the sign of the interaction term between past export status and institutional quality is given by the sign of $\dot{\beta}_2$.<fnref n="38" /> From Table 10 we find that the interaction with all our proxies for legal institutions are positive and highly significant.

<footnote n="38">³⁸Note that the part of $IQ_k$ that is part of unobserved heterogeneity must be held constant when computing partial effects. Thus $\frac{\partial Pr(Y_{fkt}=1|Y_{fkt-1}=1, Y_{fk0}, X_{fkt})}{\partial IQ_k} - \frac{\partial Pr(Y_{fkt}=1|Y_{fkt-1}=0, Y_{fk0}, X_{fkt})}{\partial IQ_k} = \phi(Y_{fkt-1} = 1, Y_{fk0}, X_{fkt})\dot{\beta}_2$.</footnote>
Similarly, interactions with firm productivity and GDP are positive and significant. Only the interaction with transport costs, which is also positive and significant, does not have the expected sign. We conclude that, overall, there is very strong support for state dependence being larger in countries with better legal institutions.

## B.2 Robustness Checks Survival Analysis

Here, we present robustness checks for the survival analysis results.

### B.2.1 Including EU destinations

In Table 12 we provide results for the sample including EU destinations. Columns (1)-(4) present results for the baseline specification (11). All variables have the expected signs and are strongly significant. In columns (5)-(8), we add interactions with relationship-dependence. Again, all interactions between institutional variables and relationship-dependence exhibit the correct sign and are significant.

### B.2.2 Multiple Spells

Around 60% of export relationships in our data involve multiple spells. As a final robustness check we confirm that the assumption of spell-independence is not biasing our previous results. Thus, we replicate our analysis using only relationships which involve single spells. The total number of single spells in our data set is of 49,479 and their length distribution, as well as all other descriptive statistics, are very similar to the total sample. Results for specifications (11) (columns (1)-(4)) and (12) (columns (5)-(8)) using only single spells are reported in Table 13. It is apparent that they are indeed very similar to those using the full sample, thus confirming that multiple spells are not a problem in our framework.
<table><caption>Table 1: Summary statistics II: country variables</caption><caption>Sample without EU countries ( 75 countries)</caption><thead><tr><th></th><th>Mean</th><th>SD</th><th>Min</th><th>25th Pct.</th><th>75th Pct.</th><th>Max</th></tr></thead><tbody><tr><td>rule of law</td><td>0.5</td><td>0.2</td><td>0.2</td><td>0.4</td><td>0.6</td><td>0.9</td></tr><tr><td>number procedures</td><td>28.4</td><td>11.9</td><td>2</td><td>19</td><td>37</td><td>49</td></tr><tr><td>cost</td><td>2.9</td><td>0.7</td><td>1.1</td><td>2.4</td><td>3.4</td><td>4.6</td></tr><tr><td>legal</td><td>5.3</td><td>1.5</td><td>2.4</td><td>4.5</td><td>5.8</td><td>9.2</td></tr><tr><td>GDP (log)</td><td>8.2</td><td>1.1</td><td>6.5</td><td>7.2</td><td>8.8</td><td>10.3</td></tr><tr><td>GDP p.c. (log)</td><td>-1.6</td><td>1.8</td><td>-6.1</td><td>-2.6</td><td>-0.4</td><td>4.4</td></tr><tr><td>distance (log)</td><td>8.2</td><td>0.6</td><td>6.8</td><td>7.9</td><td>8.7</td><td>9.4</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>Figure 1: State dependence to be explained by legal institutions.</figcaption></figure>

The figure shows the correlation between the estimated marginal effect of past export status on current export decisions with *rule of law* from Kaufmann et al. (2006).

<figure><img src="image_3.png" /></figure>

Source: authors' calculation on INSEE data

<caption>Figure 2: Hazard rate by institutional quality quartile</caption>

The legal quality variable is from Gwartney and Lawson (2003). This index, which ranges from 1 to 10, measures the legal structure and the security of property rights in each country in 1995.
<figure><img src="image_4.png" /><figcaption>Figure 3: Nominal export values by age of the relationship</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: Hazard rate: Nonparametric estimate</figcaption></figure>
<table><caption>Table 2: State dependence: linear probability model. Dependent variable is export status. Explanatory variables are past export status and interactions of past export status with different measures of legal institutions, GDP, per capita GDP, distance and VA per worker.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th></tr></thead><tbody><tr><td>Y<sub>ikt-1</sub></td><td>0.641***<br>(0.0009)</td><td>0.096***<br>(0.014)</td><td>0.031***<br>(0.013)</td><td>0.005<br>(0.013)</td><td>0.050***<br>(0.013)</td><td>0.007<br>(0.027)</td><td>-0.050***<br>(0.019)</td><td>-0.105***<br>(0.030)</td><td>-0.068**<br>(0.022)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law</td><td></td><td>0.118***<br>(0.006)</td><td></td><td></td><td></td><td>0.269***<br>(0.025)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × number procedures</td><td></td><td></td><td>0.0009***<br>(0.00007)</td><td></td><td></td><td></td><td>0.0034***<br>(0.0004)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × cost</td><td></td><td></td><td></td><td>0.014***<br>(0.001)</td><td></td><td></td><td></td><td>0.048***<br>(0.008)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal</td><td></td><td></td><td></td><td></td><td>0.009***<br>(0.0006)</td><td></td><td></td><td></td><td>0.028***<br>(0.002)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(VA/worker)</td><td></td><td>0.051***<br>(0.002)</td><td>0.051***<br>(0.002)</td><td>0.051***<br>(0.002)</td><td>0.051***<br>(0.002)</td><td>0.073***<br>(0.004)</td><td>0.071***<br>(0.004)</td><td>0.078***<br>(0.007)</td><td>0.081***<br>(0.005)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP)</td><td></td><td>0.017***<br>(0.0005)</td><td>0.014***<br>(0.0004)</td><td>0.015***<br>(0.0005)</td><td>0.016***<br>(0.0005)</td><td>0.017***<br>(0.0005)</td><td>0.014***<br>(0.0004)</td><td>0.015***<br>(0.0004)</td><td>0.015***<br>(0.0004)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.)</td><td></td><td>0.014***<br>(0.001)</td><td>0.031***<br>(0.0009)</td><td>0.030***<br>(0.001)</td><td>0.024***<br>(0.001)</td><td>0.014***<br>(0.001)</td><td>0.031***<br>(0.001)</td><td>0.030***<br>(0.001)</td><td>0.024***<br>(0.001)</td></tr><tr><td>Y<sub>ikt-1</sub> × logensistance)</td><td></td><td>-0.022***<br>(0.001)</td><td>-0.020***<br>(0.001)</td><td>-0.019***<br>(0.001)</td><td>-0.021***<br>(0.001)</td><td>-0.022***<br>(0.004)</td><td>-0.020***<br>(0.001)</td><td>-0.018***<br>(0.001)</td><td>-0.021***<br>(0.001)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td>-0.037***<br>(0.005)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × number procedures × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.0006***<br>(9e-5)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × cost × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.008***<br>(0.001)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.005***<br>(0.0006)</td></tr><tr><td>Observations</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td></tr><tr><td>Country-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Firm-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Cluster</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td></tr><tr><td>R<sup>2</sup></td><td>0.52</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.53</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 3: State dependence: linear probability model, sector regressions. Dependent variable is export status. Explanatory variables are past export status and interactions of past export status with different measures of legal institutions, GDP, per capita GDP, distance, VA per worker and sectoral measures of contracting frictions.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Y<sub>ikt-1</sub></td><td>0.653***<br>(0.008)</td><td>0.608***<br>(0.006)</td><td>0.459***<br>(0.031)</td><td>0.43***<br>(0.022)</td><td>0.640***<br>(0.009)</td><td>0.596***<br>(0.007)</td><td>0.495***<br>(0.026)</td><td>0.421***<br>(0.019)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law</td><td>0.091***<br>(0.011)</td><td>0.143***<br>(0.008)</td><td>-0.036*<br>(0.021)</td><td>0.023***<br>(0.015)</td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal</td><td></td><td></td><td></td><td></td><td>0.011***<br>(0.001)</td><td>0.016***<br>(0.001)</td><td>0.001<sup>1</sup><br>(0.002)</td><td>0.002<br>(0.001)</td></tr><tr><td>Y<sub>ikt-1</sub> × Nunn</td><td>-0.222***<br>(0.013)</td><td></td><td>-0.28***<br>(0.047)</td><td></td><td>-0.228***<br>(0.014)</td><td></td><td>-0.375***<br>(0.041)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × Rauch</td><td></td><td>-0.138***<br>(0.008)</td><td></td><td>-0.223***<br>(0.031)</td><td></td><td>-0.147***<br>(0.009)</td><td></td><td>0.242***<br>(0.027)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × Nunn</td><td>0.196***<br>(0.018)</td><td></td><td>0.149***<br>(0.033)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × Rauch</td><td></td><td>0.105***<br>(0.011)</td><td></td><td>0.05**<br>(0.021)</td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × Nunn</td><td></td><td></td><td></td><td></td><td>0.102***<br>(0.002)</td><td></td><td>0.076***<br>(0.003)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>0.012***<br>(0.001)</td><td></td><td>0.005**<br>(0.002)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.)</td><td></td><td>0.031***<br>(0.005)</td><td>0.028***<br>(0.003)</td><td></td><td></td><td></td><td>0.024***<br>(0.004)</td><td>0.029***<br>(0.003)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.) × Nunn</td><td></td><td>0.01<br>(0.007)</td><td></td><td></td><td></td><td></td><td>0.026***<br>(0.006)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.) × Rauch</td><td></td><td></td><td>0.013***<br>(0.005)</td><td></td><td></td><td></td><td>0.016***<br>(0.004)</td><td></td></tr><tr><td>Observations</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td></tr><tr><td>Country-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Firm-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Cluster</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td></tr><tr><td>R<sup>2</sup></td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 4: Duration: Cox regressions. Explanatory variables are different measures of legal institutions, GDP, per capita GDP, distance and VA per worker.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>log(rule of law)</td><td>-0.04<br>(0.027)</td><td></td><td></td><td></td></tr><tr><td>log(number procedures)</td><td></td><td>-0.03***<br>(0.005)</td><td></td><td></td></tr><tr><td>log(legal)</td><td></td><td></td><td>-0.05***<br>(0.014)</td><td></td></tr><tr><td>log(cost)</td><td></td><td></td><td></td><td>-0.05***<br>(0.006)</td></tr><tr><td>log(VA/worker)</td><td>-0.10***<br>(0.007)</td><td>-0.10***<br>(0.007)</td><td>-0.10***<br>(0.007)</td><td>-0.10***<br>(0.007)</td></tr><tr><td>log(GDP)</td><td>-0.05***<br>(0.002)</td><td>-0.04***<br>(0.002)</td><td>-0.05***<br>(0.002)</td><td>-0.05***<br>(0.002)</td></tr><tr><td>log(GDP p.c.)</td><td>-0.05***<br>(0.006)</td><td>-0.05***<br>(0.004)</td><td>-0.05***<br>(0.005)</td><td>-0.03***<br>(0.005)</td></tr><tr><td>logensistance)</td><td>0.06***<br>(0.005)</td><td>0.06***<br>(0.005)</td><td>0.06***<br>(0.005)</td><td>0.05***<br>(0.005)</td></tr><tr><td>Observations</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td></tr><tr><td>Robust</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Start</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Sector FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 5: Duration: sectoral Cox regressions. Explanatory variables are different measures of legal institutions, GDP, per capita GDP, distance, VA per worker and interactions with sectoral measures of contracting frictions.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>log(rule of law)</td><td>-0.12***<br>(0.04)</td><td>-0.15***<br>(0.03)</td><td>0.03<br>0.04</td><td>0.01<br>0.03</td><td></td><td></td><td></td><td></td></tr><tr><td>log rule of law) × Numn</td><td>-0.15**<br>(0.06)</td><td></td><td>-0.13**<br>(0.06)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>log rule of law) × Rauch</td><td></td><td>-0.09*<br>(0.047)</td><td></td><td>-0.09**<br>(0.03)</td><td></td><td></td><td></td><td></td></tr><tr><td>log(legal)</td><td></td><td></td><td></td><td></td><td>-0.14***<br>(0.05)</td><td>-0.17***<br>(0.04)</td><td>0.02<br>(0.05)</td><td>0.02<br>(0.04)</td></tr><tr><td>log(legal) × Numn</td><td></td><td></td><td></td><td></td><td>-0.14*<br>(0.08)</td><td></td><td>-0.12<br>(0.07)</td><td></td></tr><tr><td>log(legal) × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>-0.10<br>(0.07)</td><td></td><td>-0.10**<br>(0.04)</td></tr><tr><td>log(VA/worker)</td><td></td><td>-0.10***<br>(0.007)</td><td>-0.10***<br>(0.008)</td><td></td><td></td><td></td><td>-0.10***<br>(0.007)</td><td>-0.10***<br>(0.008)</td></tr><tr><td>log(GDP)</td><td></td><td>-0.05***<br>(0.003)</td><td>-0.05***<br>(0.003)</td><td></td><td></td><td></td><td>-0.05***<br>(0.003)</td><td>-0.05***<br>(0.003)</td></tr><tr><td>log(GDP p.c.)</td><td></td><td>-0.04***<br>(0.008)</td><td>-0.04***<br>(0.009)</td><td></td><td></td><td></td><td>-0.05***<br>(0.006)</td><td>-0.05***<br>(0.007)</td></tr><tr><td>logensistance)</td><td></td><td>0.06***<br>(0.006)</td><td>0.06***<br>(0.007)</td><td></td><td></td><td></td><td>0.06***<br>(0.007)</td><td>0.06***<br>(0.007)</td></tr><tr><td>Observations</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td><td>79,549</td></tr><tr><td>Cluster</td><td>country-sector</td><td>country-sector</td><td>country-sector</td><td>country-sector</td><td>country-sector</td><td>country-sector</td><td>country-sector</td><td>country-sector</td></tr><tr><td>Start</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Sector FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 6: Summary statistics I: firm variables</caption><thead><tr><th></th><th>Level</th><th>N</th><th>Mean</th><th>SD</th><th>Min</th><th>25th Pct.</th><th>Med.</th><th>75th Pct.</th><th>Max</th></tr></thead><tbody><tr><td>export value (log)</td><td>firm - year - country</td><td>503,336</td><td>10.6</td><td>2.2</td><td>0</td><td>8.9</td><td>10.4</td><td>12.0</td><td>21.1</td></tr><tr><td>export value (log)</td><td>firm - year</td><td>63,040</td><td>12.2</td><td>2.6</td><td>1.9</td><td>10.3</td><td>12.2</td><td>14.1</td><td>21.4</td></tr><tr><td>export value (log)</td><td>firm</td><td>6,594</td><td>13.9</td><td>3.1</td><td>4.8</td><td>11.8</td><td>14.1</td><td>16.1</td><td>23.5</td></tr><tr><td>number of countries</td><td>firm - year</td><td>63,040</td><td>8.0</td><td>9.7</td><td>0</td><td>2</td><td>4</td><td>10</td><td>75</td></tr><tr><td>number of countries</td><td>firm</td><td>6,594</td><td>14.6</td><td>14.7</td><td>1</td><td>3</td><td>9</td><td>21</td><td>75</td></tr><tr><td>productivity (log)</td><td>firm - year</td><td>63,040</td><td>3.9</td><td>0.5</td><td>-3.2</td><td>3.6</td><td>3.9</td><td>4.2</td><td>11.7</td></tr></tbody></table>
<table><caption>Table 7: Sector characteristics.</caption><thead><tr><th>NES sector name</th><th>Rauch</th><th>Nunn</th></tr></thead><tbody><tr><td>Production, processing and preserving of meat and meat products</td><td>0.00</td><td>0.36</td></tr><tr><td>Man. of dairy products</td><td>0.00</td><td>0.36</td></tr><tr><td>Man. of beverages</td><td>0.33</td><td>0.73</td></tr><tr><td>Man. of grain mill products, starch products, prepared animal feeds</td><td>0.50</td><td>0.33</td></tr><tr><td>Man. of other food products</td><td>0.33</td><td>0.35</td></tr><tr><td>Man. of tobacco products</td><td>0.00</td><td>0.32</td></tr><tr><td>Man. of wearing apparel; dressing and dyeing of fur</td><td>0.90</td><td>0.73</td></tr><tr><td>Man. of leather and leather products and footwear</td><td>0.63</td><td>0.57</td></tr><tr><td>Publishing, printing and reproduction of recorded media</td><td>0.56</td><td>0.73</td></tr><tr><td>Man. of pharmaceuticals, medicinal chemicals and botanical products</td><td>0.50</td><td>0.69</td></tr><tr><td>Man. of soap and detergents, perfumes and toilet preparations</td><td>0.50</td><td>0.52</td></tr><tr><td>Man. of furniture</td><td>1.00</td><td>0.52</td></tr><tr><td>Man. of jewelry and musical instruments</td><td>1.00</td><td>0.60</td></tr><tr><td>Man. of sports goods, games, toys and others n.e.c</td><td>0.73</td><td>0.56</td></tr><tr><td>Man. of domestic appliances</td><td>0.75</td><td>0.68</td></tr><tr><td>Man. of television and radio receivers, sound or video recording</td><td>1.00</td><td>0.82</td></tr><tr><td>Man. of optical instruments, photographic equipment, watches and clocks</td><td>0.89</td><td>0.83</td></tr><tr><td>Man. of motor vehicles, bodies and trailers</td><td>1.00</td><td>0.79</td></tr><tr><td>Man. of parts and accessories for motor vehicles</td><td>0.50</td><td>0.67</td></tr><tr><td>Building and repairing of ships and boats</td><td>0.57</td><td>0.75</td></tr><tr><td>Man. of railway and tramway locomotives and rolling stock</td><td>0.67</td><td>0.68</td></tr><tr><td>Man. of aircraft and spacecraft</td><td>1.00</td><td>0.89</td></tr><tr><td>Man. of motorcycles, bicycles and other transport equipment n.e.c</td><td>0.57</td><td>0.84</td></tr><tr><td>Man. of structural metal products</td><td>1.00</td><td>0.53</td></tr><tr><td>Man. of tanks, containers of metal, central heating radiators, boilers, steam generators</td><td>1.00</td><td>0.61</td></tr><tr><td>Man. of machinery for the production and use of mechanical power</td><td>0.44</td><td>0.82</td></tr><tr><td>Man. of other general purpose machinery</td><td>0.71</td><td>0.78</td></tr><tr><td>Man. of agricultural and forestry machinery</td><td>1.00</td><td>0.63</td></tr><tr><td>Man. of machine tools</td><td>0.89</td><td>0.84</td></tr><tr><td>Man. of other special purpose machinery</td><td>0.85</td><td>0.80</td></tr><tr><td>Man. of weapons and ammunition</td><td>1.00</td><td>0.68</td></tr><tr><td>Man. of office machinery and computers</td><td>1.00</td><td>0.85</td></tr><tr><td>Man. of electric motors, generators and transformers</td><td>1.00</td><td>0.82</td></tr><tr><td>Man. of television and radio transmitters and apparatus for line telephony and line telegraphy</td><td>1.00</td><td>0.82</td></tr><tr><td>Man. of medical and surgical equipment and orthopaedic appliances</td><td>1.00</td><td>0.78</td></tr><tr><td>Man. of industrial process control equipment, instruments for measuring, navigating</td><td>1.00</td><td>0.84</td></tr><tr><td>Man. of glass and glass products</td><td>0.85</td><td>0.58</td></tr><tr><td>Man. of other non-metallic mineral products</td><td>0.57</td><td>0.43</td></tr><tr><td>Preparation and spinning of textile fibers, weaving and finishing of textiles</td><td>0.50</td><td>0.38</td></tr><tr><td>Man. of textile articles, except apparel</td><td>0.86</td><td>0.48</td></tr><tr><td>Man. of knitted and crocheted fabrics and articles</td><td>1.00</td><td>0.38</td></tr><tr><td>Man. of wood and wood products</td><td>0.57</td><td>0.52</td></tr><tr><td>Man. of pulp, paper and paperboard</td><td>0.25</td><td>0.38</td></tr><tr><td>Man. of articles of paper and paperboard</td><td>0.17</td><td>0.46</td></tr><tr><td>Man. of basic inorganic chemicals</td><td>0.00</td><td>0.27</td></tr><tr><td>Man. of basic organic chemicals</td><td>0.15</td><td>0.27</td></tr><tr><td>Man. of agro-chemical products, paints and other chemical products</td><td>0.89</td><td>0.50</td></tr><tr><td>Man. of man-made fibers</td><td>0.00</td><td>0.33</td></tr><tr><td>Man. of rubber products</td><td>0.60</td><td>0.58</td></tr><tr><td>Man. of plastic products</td><td>0.67</td><td>0.37</td></tr><tr><td>First processing of iron and steel</td><td>0.00</td><td>0.44</td></tr><tr><td>Man. of basic precious and non-ferrous metals</td><td>0.06</td><td>0.23</td></tr><tr><td>Casting of metals</td><td>0.00</td><td>0.27</td></tr><tr><td>Industrial services for treatment of metals</td><td>0.43</td><td>0.38</td></tr><tr><td>Man. of fabricated metal products</td><td>0.90</td><td>0.62</td></tr><tr><td>Recycling</td><td>0.80</td><td>0.39</td></tr><tr><td>Man. of electrical equipments and apparatus n.e.c.</td><td>0.86</td><td>0.76</td></tr><tr><td>Man. of electronic valves, tubes and other electronic components</td><td>1.00</td><td>0.82</td></tr></tbody></table>

Fraction of final goods (Rauch)/ intermediate inputs (Nunn) not sold in organized exchanges and not reference priced by NES sector.
<table><caption>Table 8: State dependence robustness I: Sample including EU-destinations. Dependent variable is export status. Explanatory variables are past export status and interactions of past export status with different measures of legal institutions, GDP, per capita GDP, distance, VA per worker and sectoral measures of contracting frictions</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Y<sub>ikt-1</sub></td><td>0.417***<br>(0.002)</td><td>0.431***<br>(0.002)</td><td>0.413***<br>(0.002)</td><td>0.409***<br>(0.002)</td><td>0.632***<br>(0.007)</td><td>0.595***<br>(0.005)</td><td>0.614***<br>(0.008)</td><td>0.579***<br>(0.006)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law</td><td>0.169***<br>(0.002)</td><td></td><td></td><td></td><td>0.150***<br>(0.009)</td><td>0.175***<br>(0.007)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × number procedures</td><td></td><td>0.001***<br>(0.00002)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × cost</td><td></td><td></td><td>0.011***<br>(0.0005)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal</td><td></td><td></td><td></td><td>0.011***<br>(0.0002)</td><td></td><td></td><td>0.017***<br>(0.001)</td><td>0.019***<br>(0.001)</td></tr><tr><td>Y<sub>ikt-1</sub> × Nunn</td><td></td><td></td><td></td><td></td><td>-0.208***<br>(0.011)</td><td></td><td>-0.252***<br>(0.043)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>-0.138***<br>(0.007)</td><td></td><td>-0.223***<br>(0.031)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × Nunn</td><td></td><td></td><td></td><td></td><td>0.157***<br>(0.014)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>0.112***<br>(0.009)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × Nunn</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.016***<br>(0.002)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × Rauch</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.012***<br>(0.001)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(VA/worker)</td><td>0.039***<br>(0.0004)</td><td>0.039***<br>(0.0004)</td><td>0.039***<br>(0.0004)</td><td>0.039***<br>(0.0004)</td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP)</td><td>0.012***<br>(0.0001)</td><td>0.007***<br>(0.0001)</td><td>0.008***<br>(0.0001)</td><td>0.009***<br>(0.0001)</td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.)</td><td>-0.001***<br>(0.0005)</td><td>0.023***<br>(0.0003)</td><td>0.024***<br>(0.0003)</td><td>0.011***<br>(0.0004)</td><td></td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × logensistance)</td><td>-0.031***<br>(0.0002)</td><td>-0.036***<br>(0.0002)</td><td>-0.038***<br>(0.0002)</td><td>-0.033***<br>(0.0002)</td><td></td><td></td><td></td><td></td></tr><tr><td>Observations</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td><td>7,659,696</td></tr><tr><td>Country – time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Firm – time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Cluster</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td><td>firm-time</td></tr><tr><td>R<sup>2</sup></td><td>0.45</td><td>0.45</td><td>0.45</td><td>0.45</td><td>0.468</td><td>0.468</td><td>0.468</td><td>0.468</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 9: State dependence Robustness II: Arellano Bond estimator for the year 2000. Dependent variable is export status.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th></tr></thead><tbody><tr><td>Y<sub>ikt-1</sub></td><td>0.631***<br>(0.053)</td><td>2.171***<br>(0.987)</td><td>1.729*<br>(0.998)</td><td>1.795*<br>(0.999)</td><td>1.883*<br>(1.001)</td><td>0.065<br>(1.375)</td><td>-0.604<br>(1.426)</td><td>-1.574<br>(2.872)</td><td>-0.053<br>(1.491)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(VA/worker)</td><td></td><td>0.072<br>(0.094)</td><td>0.046<br>(0.094)</td><td>0.026<br>(0.092)</td><td>0.081<br>(0.095)</td><td>0.666**<br>(0.294)</td><td>0.682**<br>(0.316)</td><td>0.94<br>(0.736)</td><td>0.644*<br>(0.337)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP p.c.)</td><td></td><td>-0.15744<br>(0.109)</td><td>0.113<br>(0.084)</td><td>0.171<br>(0.116)</td><td>-0.081<br>(0.101)</td><td>-0.174<br>(0.109)</td><td>0.095<br>(0.083)</td><td>0.157<br>(0.110)</td><td>-0.103<br>(0.101)</td></tr><tr><td>Y<sub>ikt-1</sub> × log(GDP)</td><td></td><td>-0.081*<br>(0.042)</td><td>-0.131***<br>(0.043)</td><td>-0.113***<br>(0.043)</td><td>-0.095**<br>(0.043)</td><td>-0.079*<br>(0.042)</td><td>-0.129***<br>(0.042)</td><td>-0.114***<br>(0.042)</td><td>-0.093**<br>(0.042)</td></tr><tr><td>Y<sub>ikt-1</sub> × logens)</td><td></td><td>0.023<br>(0.092)</td><td>0.004<br>(0.095)</td><td>-0.028<br>(0.100)</td><td>0.008<br>(0.093)</td><td>0.016<br>(0.091)</td><td>0.002<br>(0.095)</td><td>-0.03<br>(0.099)</td><td>-0.003<br>(0.092)</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law</td><td></td><td>1.545***<br>(0.401)</td><td></td><td></td><td></td><td>6.103***<br>(2.07)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × number procedures</td><td></td><td></td><td>0.005<br>(0.005)</td><td></td><td></td><td></td><td>0.091**<br>(0.039)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × cost</td><td></td><td></td><td></td><td>-0.123<br>(0.208)</td><td></td><td></td><td></td><td>1.114<br>(0.907)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal</td><td></td><td></td><td></td><td></td><td>0.144***<br>(0.037)</td><td></td><td></td><td></td><td>0.555**<br>-0.231</td></tr><tr><td>Y<sub>ikt-1</sub> × rule of law × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td>-1.206**<br>(0.537)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × number procedures × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.022**<br>(0.010)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × cost × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.324<br>(0.242)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub> × legal × log(VA/worker)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.107*<br>(0.059)</td></tr><tr><td>Observations</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td><td>491,775</td></tr><tr><td>Country-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Firm-time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Firm-country FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>

Explanatory variables are past export status and interactions of past export status with different measures of legal institutions, GDP, per capita GDP, distance, VA per worker

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 10: State dependence Robustness III: Dynamic Random Effect Probit estimator. Individual dimension: country-firm; time dimension: time. Dependent variable is export status. Explanatory variables are past export status and interactions of past export status with different measures of legal institutions, GDP, distance, VA per worker. Additional controls: time dummies and real exchange rate. Country-Firm heterogeneity modeled à la Mundlak (1978), i.e., including time averages of the country and firm-specific variables; Initial conditions modeled à la Wooldridge (2005) i.e., including interactions of the initial export status with the other explanatory variables.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>Y<sub>ikt-1</sub></td><td>0.163***<br>(0.053)</td><td>0.178***<br>(0.053)</td><td>0.045<br>(0.054)</td><td>0.165***<br>(0.053)</td></tr><tr><td>Y<sub>ikt-1</sub>×log(VA/worker)</td><td>0.059***<br>(0.006)</td><td>0.059***<br>(0.006)</td><td>0.060***<br>(0.006)</td><td>0.059***<br>(0.006)</td></tr><tr><td>Y<sub>ikt-1</sub>×log(GDP)</td><td>0.017***<br>(0.002)</td><td>0.014***<br>(0.002)</td><td>0.012***<br>(0.002)</td><td>0.017***<br>(0.002)</td></tr><tr><td>Y<sub>ikt-1</sub>×logensistance)</td><td>0.048***<br>(0.005)</td><td>0.050***<br>(0.005)</td><td>0.057***<br>(0.005)</td><td>0.047***<br>(0.005)</td></tr><tr><td>Y<sub>ikt-1</sub>×rule of law</td><td>0.073***<br>(0.018)</td><td></td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub>×number procedures</td><td></td><td>0.002***<br>(0.0003)</td><td></td><td></td></tr><tr><td>Y<sub>ikt-1</sub>×cost</td><td></td><td></td><td>0.060***<br>(0.006)</td><td></td></tr><tr><td>Y<sub>ikt-1</sub>×legal</td><td></td><td></td><td></td><td>0.009***<br>(0.002)</td></tr><tr><td>Observations</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td><td>5,901,300</td></tr><tr><td>Time FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Real exchange rate</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Productivity</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Market size proxies</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Country-Firm unobserved heterogeneity à la Mundlak</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Initial conditions à la Wooldridge</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>

Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.
<table><caption>Table 11: Frequency of spells</caption><thead><tr><td>length of the spell</td><td>percentage</td></tr></thead><tbody><tr><td>1</td><td>55.9</td></tr><tr><td>2</td><td>16.7</td></tr><tr><td>3</td><td>8.0</td></tr><tr><td>4</td><td>5.0</td></tr><tr><td>5</td><td>3.6</td></tr><tr><td>6</td><td>2.6</td></tr><tr><td>7</td><td>2.1</td></tr><tr><td>8</td><td>1.6</td></tr><tr><td>9</td><td>1.4</td></tr><tr><td>10</td><td>1.2</td></tr><tr><td>11</td><td>1.0</td></tr><tr><td>12</td><td>0.9</td></tr></tbody></table>
<table><caption>Table 12: Duration robustness I: Cox regressions: Sample including EU-destinations. Explanatory variables are different measures of legal institutions and their interactions with sectoral measures of contracting frictions, as well as GDP, per capita GDP, distance and VA per worker
Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>log rule of law</td><td>-0.06***<br>(0.013)</td><td></td><td></td><td></td><td>-0.01<br>(0.039)</td><td>-0.01<br>(0.028)</td><td></td><td></td></tr><tr><td>log (number procedures)</td><td></td><td>-0.03***<br>(0.004)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>log (legal)</td><td></td><td></td><td>-0.08***<br>(0.013)</td><td></td><td></td><td></td><td>-0.03<br>(0.069)</td><td>-0.03<br>(0.049)</td></tr><tr><td>log (cost)</td><td></td><td></td><td></td><td>-0.04***<br>(0.005)</td><td></td><td></td><td></td><td></td></tr><tr><td>log (rule of law) × Nunn</td><td></td><td></td><td></td><td></td><td>-0.09*<br>(0.05)</td><td></td><td></td><td></td></tr><tr><td>log (rule of law) × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>-0.08**<br>(0.033)</td><td></td><td></td></tr><tr><td>log (legal) × Nunn</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.18*<br>(0.099)</td><td></td></tr><tr><td>log (legal) × Rauch</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.176***<br>(0.065)</td></tr><tr><td>log (VA/worker)</td><td>-0.10***<br>(0.005)</td><td>-0.10***<br>(0.005)</td><td>-0.10***<br>(0.005)</td><td>-0.10***<br>(0.005)</td><td>-0.10***<br>(0.006)</td><td>-0.10***<br>(0.006)</td><td>-0.159***<br>(0.009)</td><td>-0.159***<br>(0.009)</td></tr><tr><td>log (GDP)</td><td>-0.04***<br>(0.001)</td><td>-0.04***<br>(0.001)</td><td>-0.04***<br>(0.001)</td><td>-0.04***<br>(0.001)</td><td>-0.05***<br>(0.002)</td><td>-0.05***<br>(0.002)</td><td>-0.075***<br>(0.004)</td><td>-0.075***<br>(0.004)</td></tr><tr><td>log (GDP p.c.)</td><td>-0.05***<br>(0.005)</td><td>-0.06***<br>(0.003)</td><td>-0.05***<br>(0.004)</td><td>-0.05***<br>(0.004)</td><td>-0.05***<br>(0.007)</td><td>-0.05***<br>(0.009)</td><td>-0.087***<br>(0.010)</td><td>-0.087***<br>(0.011)</td></tr><tr><td>log (distance)</td><td>0.11***<br>(0.003)</td><td>0.11***<br>(0.003)</td><td>0.10***<br>(0.003)</td><td>0.11***<br>(0.003)</td><td>0.11***<br>(0.004)</td><td>0.11***<br>(0.004)</td><td>0.162***<br>(0.006)</td><td>0.162***<br>(0.006)</td></tr><tr><td>Observations</td><td>117,982</td><td>117,982</td><td>117,982</td><td>117,982</td><td>117,982</td><td>117,982</td><td>117,982</td><td>117,982</td></tr><tr><td>Robust</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Start Dummies</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Sector FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>
<table><caption>Table 13: Duration robustness II: Cox regressions, only single spells. Explanatory variables are different measures of legal institutions, GDP, per capita GDP, distance and VA per worker.
Notes: Robust standard errors are in parentheses denoting *** 1%, **5%, and *10% significance.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>log(rule of law)</td><td>-0.16***<br>(0.04)</td><td></td><td></td><td></td><td>0.06<br>(0.06)</td><td>0.03<br>(0.05)</td><td></td><td></td></tr><tr><td>log(number procedures)</td><td></td><td>-0.05***<br>(0.007)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>log(legal)</td><td></td><td></td><td>-0.12***<br>(0.02)</td><td></td><td></td><td></td><td>0.05<br>(0.07)</td><td>-0.03<br>(0.06)</td></tr><tr><td>log(cost)</td><td></td><td></td><td></td><td>-0.08***<br>(0.009)</td><td></td><td></td><td></td><td></td></tr><tr><td>log rule of law × Nunn</td><td></td><td></td><td></td><td></td><td>-0.27***<br>(0.09)</td><td></td><td></td><td></td></tr><tr><td>log rule of law × Rauch</td><td></td><td></td><td></td><td></td><td></td><td>-0.11*<br>(0.06)</td><td></td><td></td></tr><tr><td>log(legal) × Nunn</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.28***<br>(0.11)</td><td></td></tr><tr><td>log(legal) × Rauch</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.14*<br>(0.07)</td></tr><tr><td>log(VA/worker)</td><td>-0.16***<br>(0.009)</td><td>-0.16***<br>(0.009)</td><td>-0.16***<br>(0.009)</td><td>-0.16***<br>(0.009)</td><td>0.16***<br>(0.01)</td><td>-0.16***<br>(0.01)</td><td>-0.16***<br>(0.01)</td><td>-0.16***<br>(0.01)</td></tr><tr><td>log(GDP)</td><td>-0.03***<br>(0.003)</td><td>-0.08***<br>(0.003)</td><td>-0.08***<br>(0.003)</td><td>-0.08***<br>(0.009)</td><td>-0.08***<br>(0.004)</td><td>-0.08***<br>(0.004)</td><td>-0.08***<br>(0.004)</td><td>-0.08***<br>(0.004)</td></tr><tr><td>log(GDP p.c.)</td><td>-0.05***<br>(0.009)</td><td>-0.07***<br>(0.005)</td><td>-0.05***<br>(0.007)</td><td>-0.04***<br>(0.006)</td><td>-0.04***<br>(0.01)</td><td>-0.04***<br>(0.01)</td><td>-0.05***<br>(0.004)</td><td>-0.05***<br>(0.01)</td></tr><tr><td>logensistance)</td><td>0.12***<br>(0.007)</td><td>0.12***<br>(0.007)</td><td>0.12***<br>(0.007)</td><td>0.11***<br>(0.007)</td><td>0.12***<br>(0.01)</td><td>0.12***<br>(0.01)</td><td>0.12***<br>(0.01)</td><td>0.12***<br>(0.01)</td></tr><tr><td>Observations</td><td>49,479</td><td>49,479</td><td>49,479</td><td>49,479</td><td>49,479</td><td>49,479</td><td>49,479</td><td>49,479</td></tr><tr><td>Robust</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Start</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Sector FE</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr></tbody></table>