metadata: authors: 0: author: Neri--Lainé,Matteo
1: author: Orefice,Gianluca
2: author: Ruta,Michele
count: World
docna: 0: docna: Deep Trade Agreements and Heterogeneous
            Firms Exports
docty: Policy Research Working Paper
abstracts: cdata!: This paper studies the effect of
            regional trade agreements on firms&#x2019; exports.
            Using detailed information on the content of trade
            agreements and firm-level exports for 31 developing
            countries between 2000 and 2020, the analysis shows that the
            depth of trade agreements matters for the export performance
            of firms. Moving from shallow to deep trade agreements
            boosts firms&#x2019; exports, on average, by 3.6
            percent. In line with models of trade with heterogeneous
            firms, the trade impact of deep trade agreements depends on
            firm&#x2019;s characteristics. The impact is stronger
            for large firms and firms involved in global value chains
            and is negative for small firms. Robustness tests and an
            Instrumental Variable strategy confirm the causal
            interpretation of the results. These heterogeneous impacts
            on firms&#x2019; exports imply a selection effect of
            deep trade agreements with significant welfare consequences.
display_title: Deep Trade Agreements and
            Heterogeneous Firms Exports
listing_relative_url: /research/2023/01/33980908/deep-trade-agreements-heterogeneous-firms-exports
topicv3: Trade m1326924 698,Trade Policy m1327640 776
publishtoextweb_dt: 2023-01-17T00:00:00Z
dois: 10.1596/1813-9450-10277
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: NA
1: author_key: 1999773
2: author_key: 1245806
model_extractions: Policy Research Working Paper 10277 Deep Trade Agreements and Heterogeneous Firms Exports _Matteo Neri--Lainé Gianluca Orefice Michele Ruta_ Macroeconomics, Trade and Investment Global Practice January 2023
Policy Research Working Paper 10277

# **Abstract**

This paper studies the effect of regional trade agreements on firms’ exports. Using detailed information on the content of trade agreements and firm-level exports for 31 developing countries between 2000 and 2020, the analysis shows that the depth of trade agreements matters for the export performance of firms. Moving from shallow to deep trade agreements boosts firms’ exports, on average, by 3.6 percent. In line with models of trade with heterogeneous firms, the trade impact of deep trade agreements depends on firm’s characteristics. The impact is stronger for large firms and firms involved in global value chains and is negative for small firms. Robustness tests and an Instrumental Variable strategy confirm the causal interpretation of the results. These heterogeneous impacts on firms’ exports imply a selection effect of deep trade agreements with significant welfare consequences.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at mruta@imf.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Deep Trade Agreements and Heterogeneous Firms Exports<sup>∗</sup> Matteo Neri--Lainé<sup>†</sup> Gianluca Orefice<sup>‡</sup> Michele Ruta<sup>§</sup>

**Keywords:** Deep Trade Agreements, Export Performance, Firm Heterogeneity, Developing Countries

**JEL-Classification:** F13, F14, F15

> ∗We would like to thank seminar participants at the World Bank, Indiana University, University of Mainz and the European Trade Study Group for helpful comments and suggestions and to Ana Fernandes for help with the data. The views expressed in this paper are the authors’ and do not necessarily reflect those of the institutions they belong to.

> †University Paris-Dauphine PSL, Place du Maréchal de Lattre de Tassigny 75016 Paris, France.

> ‡University Paris-Dauphine PSL and Cesifo, Place du Maréchal de Lattre de Tassigny 75016 Paris, France.

> §International Monetary Fund, 700 19th Street N.W., Washington, D.C. 20431, USA.
# **1 Introduction**

During the last two decades, many developing countries have signed Regional Trade Agreements (RTAs) in the attempt to better integrate their economies into regional and global markets and improve the export performance of their firms – see Freund and Ornelas (2010); Limão (2016). In particular, out of the 190 RTAs signed during the period 2000-2020, 175 involved at least one developing country as a member. Over the same period, the content of RTAs has widely changed (Hofmann et al., 2017; Mattoo et al., 2020). The average RTA signed by a developing country at the end of the period covered roughly 30 percent more policy areas than at the beginning of the period, with issues like technical and sanitary standards, investment, and intellectual property rights protection being added to the more traditional areas covered by RTAs (such as tariff liberalization and the reduction of other border barriers). We refer to these more complex trade agreements as “deep RTAs” or simply “Deep Trade Agreements” (DTAs hereafter).

The effects of regional trade agreements on trade have been largely studied, but there remain some important gaps in the literature. In part motivated by the changing depth of RTAs, a number of studies have empirically investigated the trade effects of different types of trade agreements. A key finding of this literature is that the heterogeneity of trade agreements matters (Baier et al., 2018, 2019), and that the depth of RTAs can help explain different trade outcomes (Orefice and Rocha, 2014; Mattoo et al., 2017). At the same time, theoretical models have emphasized a different type of heterogeneity, namely that the reduction of trade costs affects different types of firms differently. Larger and more productive firms can more easily take advantage of the change in trade costs than smaller and less productive firms (Melitz, 2003; Melitz and Redding, 2015). As deep trade agreements can reduce trade costs among members by eliminating tariffs and by reducing other frictions due to regulatory differences and/or policy uncertainty, a natural extension of this literature is that DTAs should affect firms differently based on their characteristics, promoting the export performance of larger firms and leading to a selection effect.

This paper empirically investigates the effect of RTAs’ depth on the export performance of heterogeneous firms. The analysis combines firm-level export data for 31 developing countries from the World Bank Exporter Dynamics Database (Fernandes et al., 2016) and information on the detailed content of more than 300 RTAs from the World Bank Deep Trade Agreements database (Hofmann et al., 2017). The richness of the data allows to precisely take into account the heterogeneous consequences of deep RTAs on the exports of different firms. We use a decomposition à la Berman et al. (2012) to study the extent to which the effects of deep RTAs 1
on trade come from the intensive and the extensive margins of trade. Importantly, we carefully investigate the endogeneity of trade and deep RTAs through different methods. We use an Instrumental Variable approach based on the domino effect of RTAs (Baldwin and Jaimovich, 2012), a plausible exogeneity test à la Conley et al. (2012), and we employ an event study approach to check the parallel trend assumption and confirm the validity of the key results.

To assess the impact of deep RTAs on the export performances of firms, we adapt the standard gravity model for trade (Head and Mayer, 2014) to firm-level analysis and include a variable capturing the depth of RTAs. Using information from the Deep Trade Agreements database, we construct different measures of RTA depth based on the policy areas covered by the agreements and their legal enforceability. Our specification allows to identify the impact on firms’ exports of a _change_ in the depth of RTAs (i.e. newly signed RTAs or amendment of preexisting ones) between two countries, controlling for any firm-year and country-specific factor that may affect the export performance of firms. The baseline results show that one additional legally enforceable policy area in RTAs boosts the exports of firms by 0.3%; corresponding to a 3.6% increase in firms’ exports when moving from _shallow_ to _deep_ RTAs.<sup>1</sup> This effect is larger for policy areas in RTAs that are not regulated by the agreements of the World Trade Organization (WTO-extra), such as investment or competition. One additional legally enforceable WTOextra provision increases the firm’s exports by 0.7%. The instrumental variable approach and the plausible exogeneity test both suggest the causal interpretation of our results.

This average effect of deep RTAs on the export performance of firms may hide substantial heterogeneity across firms with different characteristics. In New New Trade Theory models à la Melitz (2003) firms are heterogeneous and a reduction in fixed and/or variable export cost is expected to favor exports of large and highly productive firms at the expenses of low-productivity firms, leading to a selection effect. This selection effect is magnified in presence of heterogeneous demand elasticity: if large and more productive firms face smaller demand elasticity and higher mark-ups, the pro-competitive effect induced by deep RTAs exacerbates the reduction in foreign sales of less productive firms (in line with Atkeson and Burstein 2008 and Crowley et al. 2022). Our second set of estimations tests the effect of deep RTAs on heterogeneous exporters.<sup>2</sup> In line with the findings of the New New Trade Theory, we uncover strong heterogeneous effects of deep RTAs on firms with different characteristics. While large and high-productivity firms benefit from deep RTAs, small and less productive firms suffer the increased competition

> 1We consider _shallow_ those RTAs including only the two tariff related provisions that are always included in RTAs (i.e. tariff cut on agriculture and industrial sectors), and _deep_ those RTAs including 14 provisions (i.e. the 75 percentile in the depth of RTAs).

> 2For our large sample of developing countries, we do not have data on the balance sheet of firms to compute direct measures of productivity, so we resort to several proxies discussed in detail in section 5.2.

2
at destination and export less – a selection effect of deep trade agreements. On average, the inclusion of an additional legally enforceable provision in RTAs stimulates the exports of large firms by 0.4%-0.6%, while it reduces the exports of small firms by 0.5%-0.6%.<sup>3</sup> Interestingly, high-productivity firms participating in Global Value Chains (GVC), i.e. firms that export and import to/from the same country, benefit the most from the signature of deep RTAs. For these firms, an additional legally enforceable provision in RTAs stimulates exports by 0.8%. The selection effect of deep trade agreements shows that using firm-level data is key to understand the welfare implications of RTAs. Specifically, by favoring exports of large and high-productivity firms and reducing exports of small and less productive firms, deep RTAs promote a reallocation of resources from the latter to the first which entails adjustment costs but also leads to an overall increase in the average productivity of firms.

We next investigate how deep trade agreements affect the margin of trade at the firm level. Deep RTAs could reduce both the variable and the fixed trade costs between member countries. This in turn impacts on the margin of trade that is affected. Previous work by Baier et al. (2014) uses aggregate trade data to study how different types of RTAs affect the intensive and the extensive margin of trade. Here, we use a decomposition approach à la Berman et al. (2012), to disentangle the average export sales effect of deep RTAs into intensive _versus_ extensive (firm-based) margin component. Namely, we use the firm-specific export behavior to impute the extensive _versus_ intensive margin effect of deep RTAs. We show that the extensive margin channel has only a slightly larger contribution (60%) than the intensive margin channel (40%). This evidence, in light of the theoretical predictions in Chaney (2008), suggests that indeed deep RTAs represent a reduction in both the fixed and the variable export cost components. This is the second contribution of this paper which provides novel firm-level evidence on the channel through which deep RTAs boost aggregate exports.

Finally, we study the dynamic effects of deep trade agreements on firms’ exports. The positive effect of _bilateral_ deep RTAs may vanish over time because of the worldwide increase in RTAs and their depth and the inclusion in RTAs of non-discriminatory provisions that _de facto_ can reduce trade costs for exporters in third countries (Lee et al., 2019). By adopting an event study approach in the vein of Fajgelbaum et al. (2020), we show that a _change_ in the depth of RTAs makes firms export more during the two years after the shock. The effect of the change in depth of RTAs vanishes afterwards. The event study approach also shows the validity of the

> 3This finding is the average effect of deep trade agreements on firms’ exports. It is still possible that individual provisions in DTAs have effects that are more favorable to small firms. For instance, Fernades et al. (2021) find that for a sample of Latin American countries firms’ exports increase significantly in destination markets with RTAs that promote regulatory cooperation and that the effect is stronger for smaller firms. They find that this effect is driven by entry into new product markets and increases in export quality of smaller firms.

3
parallel trend assumption and hence reinforces the causal interpretation of our baseline results.

The rest of the paper is organized as follows. Section 2 discusses the possible theoretical channels underlying the firm-specific effect of deep trade agreements. Section 3 presents the data used in the analysis and proposes some descriptive evidence. Section 4 discusses the empirical strategy. Section 5 shows the baseline results and the heterogeneity tests. In section 6 we address the potential endogneneity problem. Section 7 tests the dynamic effect of deep RTAs. Concluding remarks follow.

# **2 Theoretical framework**

Deep trade agreements are wider in scope and more complex than shallow trade agreements as they go beyond a standard improvement in market access via reductions in bilateral import tariffs. Specifically, by filling regulatory gaps among member countries, DTAs may among other things reduce fixed export costs and uncertainty in bilateral trade relationships. These features make any attempt of setting a general theoretical framework extremely complicated (and likely unsatisfactory). However, some general predictions can be drawn. The reduction in fixed or variable export costs and the reduction in uncertainty associated to DTAs unambiguously increase market access at destination, thus make it easier for firms of a given origin to export to destination. In a world with homogeneous firms, this simply implies larger export values for firms at destination. But firms are heterogeneous (Bernard et al. 2007) and the expected trade effect of DTAs is not as simple.

In a standard model of trade with heterogeneous firms à la Melitz (2003), where all firms face the same demand elasticity, an improved market access at destination makes large and more productive firms export relatively more than less productive firms. But firms differ also along other relevant dimensions. First, firms that participate into global value chains (i.e. GVC firms) can be more affected by DTAs either because they tend to be high-productivity firms (Goldberg et al., 2010; Feng et al., 2016) and/or because they import and export from the destination market, so that the reduction of trade costs and uncertainty associated to DTAs affects them both on the import and export side. A second way firms differ is in the demand elasticity they face. Large and high-productivity firms face lower demand elasticity (Spearot, 2013) and have larger mark-ups than small and less productive firms (Atkeson and Burstein, 2008). This implies that, after the entry into force of a DTA, large and high-productivity firms at origin may reduce their export price at destination to a larger extent to gain market share, exerting a tougher “within origin” competition on small and less productive firms. Such a strong heterogeneous impact of DTAs on firms with different characteristics is even starker in a framework in which 4
the degree of substitutability across varieties of a given origin country is stronger than that between origin countries—see Crowley et al. (2022). In these settings, DTAs may have very different consequences on the export performance of large and small firms at destination, with large firms unambiguously benefiting the most from the trade agreement.

The impact of DTAs on small and less productive exporters also depends on whether the new agreement has an impact on the market structure of the origin country. If the number of exporters is unaffected by the entry into force of a deep trade agreement, small incumbent exporters may benefit through an increase in exports even if these gains are milder relative to large exporters. Conversely, if the DTA has an impact on the market structure in the origin country by increasing the number of exporters, small exporters may also experience a reduction in their exports (and market share) at destination, and eventually may be induced to exit from the export market due to enhanced competition.

All in all, while DTAs are expected to have an unambiguous positive effect on the export value of large and high-productivity firms, the effect on small and less productive firms is an empirical question. The within-origin competition effect of DTAs can be so strong to offset the reduction of fixed and variable costs and induce the exit of small firms from the destination market. This effect has relevant welfare implications. If small and less productive firms exit from a specific destination market and large and high-productivity firms survive and thrive, resources are reallocated from low- to high-productivity firms. This selection effect implies adjustment costs, but also an increase in the average productivity of firms. The heterogeneous trade effects of DTAs on low- _versus_ high-productivity firms, and the consequent selection effect, is at the core of the empirical investigation in the rest of this paper.

# **3 Data and descriptive evidence**

Our empirical analysis is based on two main World Bank data sources: (i) the Exporter Dynamics Database (Fernandes et al., 2016) providing firm-level exports for 55 developing countries in the period 1996-2020, and (ii) the Content of Deep Trade Agreements (Hofmann et al., 2017) on the content of RTAs in force and notified to the WTO for the period 2000-2020. Moreover, we complete our dataset by including gravity-related variables (such as distance, common border, language, etc.) from the CEPII gravity database, and data on the effectively applied tariffs faced by each exporter at the destination from the MacMap (CEPII) database.

We build our final dataset in several steps. First, we reorganize the original DTA database into a country-pair-year-specific dataset. Indeed, since a given pair of countries (origin and destination) may have two (or more) RTAs contemporaneously in force, we collapse trade agreement 5
provision dummies indicating the presence of each policy area in RTAs by country-pair-year, and take the maximum value of each provision dummy across multiple RTAs (if any) within each country-pair-year combination.

As a second step, we construct several measures of RTAs’ depth based on the provisions included in the trade agreement that each country pair shares in a given year. Specifically, we consider different count variables, differentiating by type of provision: (i) number of provisions (independently of their legal enforceability), (ii) number of legally enforceable provisions (i.e. whose implementation is supported by strong legal language and by the availability of a dispute settlement mechanism), (iii) number of WTO-plus provisions (WTO+) – i.e. provisions covered by the current mandate of the WTO, (iv) the number of WTO-extra provisions (WTO-X) – i.e. provisions not covered by the current mandate of the WTO, and (iv) number of core provisions – i.e. provisions directly related to trade enhancing factors.<sup>4</sup> While in our empirical exercise, we use all these proxies for the depth of RTAs, our baseline measure of RTA depth is the count of legally enforceable provisions in each RTA.<sup>5</sup> The simple count of provisions in RTAs gives equal weight to each clause included in the agreement, and one may want to give more weight to “rare” provisions (i.e. provisions included less frequently in RTAs and likely to signal stronger market integration). To address this concern, as a robustness check, we also use alternative measures of RTA depth based on the weighted sum of provisions (using one minus the frequency to which each provision appears in the 300 RTAs covered by the DTA database).<sup>6</sup> One drawback of the DTA database is that it does not cover RTAs that are no longer in force.<sup>7</sup> So, when controlling for the presence of an RTA between two countries (see section 4), we complement the DTA database with the CEPII data covering active and inactive RTAs. The _RTA adjusted_ dummy is equal to one if a RTA is observed (from CEPII and/or DTA dataset) and zero otherwise. As for the depth of RTAs not mapped in the DTA database, we construct two proxies of depth. First, we (arbitrarily) set the depth measures for these RTAs as equal to

> 4See Horn et al. (2010) for definition of WTO+ and WTO-X provisions. Core provisions are defined in Hofmann et al. (2017) and include all WTO+ provisions plus clauses that regulate competition policy, bilateral investment, movement of capital and intellectual property rights.

> 5It should be noted that in this paper we aim to capture the impact of the _overall_ depth of RTAs on firms with different characteristics. Different provisions in trade agreements, however, have different effects on aggregate trade outcomes (Fernandes et al., 2021) and are likely to have heterogeneous effects on firms’ exports. For example, provisions that lower fixed entry costs on the destination market, such as provisions aimed at improving trade facilitation or reducing regulatory divergence, can make it easier for small firms to export. Fernades et al. (2021) finds some preliminary evidence of this focusing on provisions on technical and sanitary standards in trade agreements involving a sample of Latin American countries. Other provisions may have just the opposite effect. For instance, requirements in DTAs to meet higher environmental or labor standards could make it easier for larger exporters relative to smaller firms to export in the destination market, reinforcing the competition effect that we stress in this paper.

> 6In Figure A1 we show how frequently each provision is included in Regional Trade Agreements.

> 7The World Bank provides information on the content of RTAs active in the year of the creation of the DTA database. RTAs that were active in the past, but inactive at the time of the creation of the database are not covered.

6
one. Second, we set the depth of non-mapped RTAs as the value of the closest-in-time (positive) RTA depth observed for the considered country-pair.

The Exporter Dynamics Database (EDD) takes the form of multiple databases: one per country.<sup>8</sup> So, as a last step in the construction of the final data set, each country-specific EDD is merged with the CEPII gravity database. Finally, we merge the tariffs data from MacMap (CEPII), and pool all the 55 country-specific databases to get a single proper and complete firm level base. This dataset initially contains 29,009,865 observations (firm-destination-productyear specific) spanning from the late 1990s to 2020. However, the DTA database covers only the period 2000-2020; so we keep only firm export data over that period. It must be noted that the coverage of the EDD varies by country: for some countries we have data for the entire 2000-2020 period, for some other countries we have a more limited time period (cf. table A1 in appendices). Although original firm-level exports data are (also) product (HS6) specific, our main variable of interest is not, so we aggregate (sum) export data by firm-destination-year across HS6 products.

As described in Table 1, the majority of exporters included in the EDD have at least one active RTA in force (i.e. 48 out of 55). However, only a sub-sample of countries (and countrypairs) have changed the depth of their RTAs in the period 2000-2020 (i.e. a newly signed RTA or amendment of pre-existing RTAs). Namely, 31 exporting countries signed new RTAs or amended a pre-existing one, giving _within_ variation to our measures of RTAs depth. This translates into 701 country-pairs having time variation in the depth of RTAs in the period 2000-2020. This time variation comes mainly from the entry into force of new trade agreements.<sup>9</sup> Since in the empirical strategy we rely on the within country-pair variation in RTAs’ depth, the final estimation sample considers only such 31 exporting countries and contains 4,659,362 observations with non-missing information on export value and content of RTAs. The estimation sample shrinks to 2,924,126 observations because of missing values in the tariff data.

Among the 31 exporting countries having _within_ variation in the RTA depth values, 15 countries account for 87% of the overall variation in the RTA depth. These are: Croatia, Georgia, Colombia, Chile, South Africa, Serbia, Slovenia, Peru, Mauritius, Guatemala, Madagascar, Nicaragua, Tanzania, Ecuador, Malawi. In Figure 1 we show the empirical distribution of country-pairs exports (panel a and b) and firm-destination specific exports (panel c and d) for the sub-sample of the 15 countries that provide much of the variation in RTA depth.<sup>10</sup> In panel (a) of Figure 1 we show the empirical distribution of bilateral exports for country-pairs with and

> 8In case of breaks in the firms’ identifiers over the time period covered, the Exporter Dynamics Database contains two separate data sets per country (before _versus_ after the break in the firms’ identifier). In case of breaks in the firms’ identifiers, we keep the most recent period (i.e. after-break period).

> 9In our final sample, 72 RTAs involve more than two members, while 2 are bilateral for a total of 74 agreements contributing to the within variation of our RTA depth variable.

> 10In Figure A2 we provide the same evidence for the full set of 31 countries with time variation in RTA depth.

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without RTA in force (respectively dash and continuous line in the figure), while in panel (b) of Figure 1 we show the empirical distribution of bilateral exports for pairs having deep _versus_ shallow RTA in force. It clearly emerges that the presence of a RTA and its depth matters for the aggregate country-pair exports. In panel (c) of Figure 1 we show the empirical distribution of firm-destination export sales in 2020 depending on whether the exporting country has (or not) an active RTA with the destination market. In panel (d) of Figure 1 we consider only RTA partners (i.e. pairs with RTA in force), and distinguish between destinations at the top- and bottom-quartile of the RTA depth. There is only small evidence that RTA depth matters for the export of firms. The positive effect of RTAs and their depth is less stark at firm level than at aggregate country-pair level, suggesting a strong heterogeneous effect of DTAs on firm level export. While some firms largely benefit from deep RTAs (boosting the aggregate exports of the country), other firms are hindered by the presence of deep RTAs. The empirical distribution of firms’ exports is thus only marginally affected by the presence of deep trade agreements. In what follows we carefully test such a heterogeneous effect of deep RTAs.

Finally, in Table 2 we report the in-sample descriptive statistics for the variables included in our econometric exercise (overall RTA depth, WTO-plus, WTO-extra and core provisions). It clearly emerges the large variation in the depth of RTAs across country-pairs. Regardless of the type of provisions considered to define the RTAs’ depth (i.e. count of provisions), the standard deviation is almost equal to the average value. We exploit the variability in the depth of RTAs in the econometric exercise reported in the next section.

# **4 Identification strategy**

This section discusses the empirical strategy adopted to test the effect of deep RTAs on the exports of firms in developing countries. Our baseline specification is as follows: where the subscripts _f_ , _i_ , _j_ , and _t_ stand respectively for firm, origin country (i.e. the country where the exporting firm is located), destination country and year. The explanatory variable of interest – _DTAijt_ – is the depth of the RTA (if any) that country _i_ has with destination _j_ at time _t_ . As a first, coarse measure of RTA depth we use the count of any type of provisions included in the RTA. However, our preferred measure of RTA depth is the count of legally enforceable provisions. This measure is then refined and we use the count of WTO+, WTO-X and “core” legally enforceable provisions in RTAs. The firm-year fixed effects ( _θft_ ) control for 8
any unobserved time-variant firm specific characteristics, such as productivity shocks, size and workforce composition (i.e. quality of the management, etc.). Since each firm is unambiguously located in a country _i_ , the firm-year fixed effects subsume origin-year fixed effects and capture any origin country-year specific shock affecting the export performances of all firms in country _i_ (i.e. multilateral resistance term on the exporter side). Any country specific technological or productivity shock, as well as the distribution of firms productivity in the exporting country, are implicitly captured by firm-year fixed effects. In equation (1) we also control for the multilateral resistance term in the importer side by including destination-year fixed effects _θjt_ capturing also any demand shock that affects the import demand at destination. Finally, any country-pair (time-invariant) factor, such as geographical distance and any other gravity-type covariate is captured by country-pair fixed effects _θij_ .

Given the set of fixed effects included in equation (1) our variable of interest _DTAijt_ is identified on the _change_ in the depth of RTAs (i.e. newly signed RTAs or amendment of preexisting ones) between country _i_ and _j_ , controlling for any firm- and country-specific factor that may affect the export performances of firms. Specifically, we compare a given firm’s exports towards destinations with _versus_ without changes in RTA’s depth (conditional on any firmand destination-specific shock). The omitted variable concern is therefore very reduced here. Moreover, the concern that a specific firm in country _i_ may affect the signature and the content of a trade agreement between country _i_ and _j_ is in general remote, and the reverse causality argument is unlikely to bias our baseline estimations. In Table A2 we perform a pre-trend test correlating the (average) firms’ export growth before a change in RTA depth and extent of the change in the depth of RTAs. Table A2 shows the absence of correlation between firms’ export growth and the change in RTAs’ depth supporting qualitatively the absence of reverse causality issue. Nevertheless, in section 6 we propose an Instrumental Variable (IV) approach aimed to reduce further any residual endogeneity concern. This could come, for instance, from large exporters lobbying for deep trade agreements. A plausible exogeneity test à la Conley et al. (2012), discussed in section 6.1, supports the robustness of our 2SLS results to deviations from the perfect validity of the exclusion restriction hypotheses and reinforces the causal interpretation of our results. The parallel trend assumption in the pre-treatment period is tested in section 7.

The main empirical challenge here is the high-collinearity between the mere presence of an active RTA (abstracting from its content, _RTAijt_ ) and the depth of the agreement ( _DTAijt_ ). This problem is exacerbated when country-pair fixed effects ( _θij_ ) are included in the estimation and absorb any cross country-pair variability in the presence of RTAs and depth. For this reason in our baseline estimations we do not control for the presence of an RTA; this is _de facto_ 9
subsumed by the _DTAijt_ variable when larger than zero. However, since the main and everpresent objective of any RTA is to reduce bilateral tariffs, we control for the presence of an RTA by including in all the estimations the weighted average applied tariffs faced by a given firm _f_ into a given destination _j_ across exported products, _ln_ (1 + _τfijt_ ). We use the product share of firm’s exports in the initial year as a weight in averaging the applied tariffs faced by each firm at destination across exported products. As an alternative test, we disregard the collinearity problem and propose a robustness check explicitly controlling for the _RTAijt_ dummy (namely the _RTA adjusted_ dummy discussed in section 3).

In order to test the heterogeneous effect of deep RTAs on firms with different characteristics, we extend eq. (1) by interacting the _DTAijt_ variable with a firm characteristic indicator _I_ ( _kf > k_ ̄) as follows: The indicator _I_ ( _kf > k_<sup> ̄</sup> ) is equal to one if a given firm’s characteristics _kf_ is above a threshold _k_<sup> ̄</sup> . Four firm specific characteristics are used to define the indicator _I_ ( _kf > k_<sup> ̄</sup> ). First, as a proxy for the firm’s size, we use the total exports of the firm (across destinations and years),<sup>11</sup> and define dummy variables equal to one if the size of the firm is in turn above the 75<sup>_th_</sup> and 90<sup>_th_</sup> percentile of the distribution. This is an intuitive but coarse proxy of firm size. It can be endogenously affected by the presence of deep trade agreements among firm’s destinations. To address this problem, we use the total exports of the firm in the initial year _t_ 0 (i.e. the first year in which the firm is observed in the data). Firm’s total export at time _t_ 0 is used to define our second indicator variable _I_ ( _kf > k_<sup> ̄</sup> ). Percentiles 75<sup>_th_</sup> and 90<sup>_th_</sup> of the initial firms’ exports distribution are used as threshold _k_<sup> ̄</sup> . Third, we capture the GVC status of the firm by a dummy equal to one if the exporting firm is also an importer, indicating that the firm is likely to use imported inputs in production for exports. Finally, we refine the GVC nature of the firm by using a dummy equal to one if the firm exports and imports to/from the same country _j_ – _GVC bilateral_ . This last firm characteristics is meat to capture the importance of deep RTAs for firms in developing countries having _bilateral_ (import-export) relations with destination _j_ .

We adopt a PPML estimator to address the heteroskedasticity problem in structural gravity model for trade (Santos-Silva and Tenreyro, 2006), and cluster standard errors by origin-

> 11 High-productive firms export more. So the total exports of the firm (across all products and destinations) is a plausible proxy for its productivity. See Fontagné et al. (2015).

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destination-year (i.e. the source variation of our main variable of interest). As a benchmark, in Appendix Table A3 we show OLS estimations.<sup>12</sup>

# **5 Results**

This section discusses our main results on the effect of deep RTAs. We start by showing the results obtained by estimating our baseline specification, equation (1), on the full sample of firms in developing countries facing changes in their RTAs’ depth - section 5.1. In the same section we propose a robustness check using the weighted count of provisions as an alternative measures of RTA depth. In section 5.2, we estimate equation (2) and show the heterogeneous effect of deep RTAs on firms with different characteristics. Finally, in section 5.3, we disentangle the effect of deep RTAs into extensive _versus_ intensive margins of exports.

## **5.1 Baseline results**

Table 3 shows our baseline results. The depth of RTAs has a positive and significant effect on the export performance of firms in developing countries no matter the type of provisions considered to approximate the depth of the RTA (all, legally enforceable, WTO+, WTO-X or core). In particular, one additional legally enforceable provision in the agreement boosts the exports of firms by 0.3%. This means that, by moving from a _shallow_ agreement (here defined as an RTA including only legally enforceable provisions related to tariff cuts in manufacturing and agriculture sectors) to a _deep_ RTA containing legally enforceable provisions at the 75<sup>_th_</sup> percentile of the distribution of the RTAs depth implies a 3.6% increase in firm exports.<sup>13</sup> If we consider the count of WTO+ provisions, moving from shallow to deep RTAs implies a 2.7% increase of firm exports (i.e. one additional legally enforceable WTO+ provision boosts the exports of firms by 0.3%).<sup>14</sup> The effect _per-provision_ is larger for legally enforceable WTO-X provisions: one additional WTO-X provision boosts the export of firms by 0.7% (moving from shallow to deep RTAs in WTO-X provision implies a 2.1% increase in firm exports).<sup>15</sup> As expected, the applied tariffs at destination have a negative and significant effect on the exports of firms. The point estimates on applied tariffs are lower than commonly obtained in the previous literature. This is due to the aggregation bias. Indeed, we disregard the product dimension of both export

> 12In the log-linear OLS estimations we set to zero the log of zero firms’ exports.

> 13RTAs at the 75 _th_ percentile of legally enforceable provisions contain 14 provisions.

> 14WTO+ provisions contain standard tariff cut provisions on agriculture and manufacturing sectors, so we consider RTAs with two WTO+ provisions as shallow. The 75<sup>_th_</sup> percentile in the count of WTO+ provisions is equal to 11.

> 15WTO-X provisions do not contain standard tariff cut provision, so we consider RTAs with zero WTO-X provision as shallow. The 75<sup>_th_</sup> percentile in the count of WTO-X provision is equal to 3.

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and tariffs, and the consequent aggregation bias produces tariff elasticity that are smaller in magnitude (Redding and Weinstein, 2019).<sup>16</sup> Using the simple count of provisions to approximate the RTAs’ depth implicitly gives the same importance to any type of provision. One may want to assign relatively higher value of depth to those RTAs including rare provisions. So, as a robustness check, in Table 4 we show results by using weighted count to approximate the depth of RTAs (the weight is equal to one minus each provision’s frequency in the matrix of the RTAs mapped by the World Bank Deep Trade Agreements database). The resulting index weights relatively more RTAs containing rare provisions. Results, reported in Table 4, support the robustness of our baseline results. Interestingly, the estimations coefficients in Table 4 point to a stronger impact of deep RTAs on exports when approximated by a weighted sum. This suggests that the inclusion of rare provisions in RTAs is a good signal of the extent of trade costs reductions associated to deep RTAs between member countries.

The effect of RTA depth is robust to the inclusion of dummies for the presence of a RTA between country _i_ and _j_ at time _t_ . See results reported in Table A6. To take into account the presence of non-mapped active RTAs (i.e. those RTAs not included in the World Bank database), in Table A6 we take the list of RTAs from CEPII and assign a value of depth respectively equal to one (see columns 1-2), or equal to the closest (in time) country-pair’s RTA depth to nonmapped active RTAs (see columns 3-4). As expected, the presence of an empty (active) RTA – i.e. a RTA with zero depth – has null effect on the export of firms (see coefficient on RTA _adjusted_ in table A6 columns 1-3). The presence of a RTA has positive effects on export only if the agreement has some depth (i.e. positive number of provisions) - see columns (1),(2) and (3). While reassuring, results in Table A6 must be taken _cum grano salis_ because of the high collinearity between the RTA dummy and the measure of depth in regional trade agreements. As a last robustness check, we estimate equation (1) on the sub-sample of country-pairs that change RTA status during the period 2000-2020. Results, reported in Table A7 support the robustness of our baseline results.

The baseline and the robustness check regressions discussed so far suggest that deep RTAs have a statistically significant positive effect on the exports of firms in developing countries. However such a positive effect may hide strong heterogeneity across firms of different types, and dynamic effect after the change in depth of a RTA. We dig more into the heterogeneous effects

> 16The negative and significant coefficients on applied tariffs reassure us on the accuracy of our estimations. This accuracy is also supported by point estimates on standard gravity controls reported in appendix Tables A4 and A5. In these appendix tables we remove country-pair fixed effects and include standard gravity model controls (such as distance, colony, common language and border) to have a benchmark with previous literature on gravity controls’ coefficients (Head and Mayer, 2014). These variables have the expected sign and magnitude in line with previous studies.

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of deep RTAs in the next section.

# **5.2 Firm heterogeneity**

In line with the theoretical discussion in section 2, deep RTAs may have a different effect on low- _versus_ high-productivity firms and/or on firms with different involvement in GVCs. This section explores the heterogeneous effects of deep RTA across different types of firms based on size and GVC participation. Namely, we interact the _DTAijt_ variable with four firm specific indicators: (i) large firm dummy variables equal to one if the total exports of the firm (across destination and years) is in turn above the 75<sup>_th_</sup> and 90<sup>_th_</sup> percentile of the distribution, (ii) large firm dummy if the exports of the firm at _t_ 0 is in turn above the 75<sup>_th_</sup> and 90<sup>_th_</sup> percentile of the distribution, (iii) a dummy equal to one if the exporting firm imports some products (i.e. GVC firm indicator), and (iv) a dummy variable equal to one if the firm exports and imports to/from the same destination _j_ ( _GVC bilateral_ ).

Results reported in Table 5 show an interesting and robust pattern: large and GVC firms benefit from deep RTA.<sup>17</sup> For small firms, and firms that do not participate in GVCs, the depth of RTAs has a negative effect on exports. Specifically, for large high-productivity firms, one additional legally enforceable provision implies a 0.3% - 0.6% increase in exports (see columns 1 - 4). This means that, moving from _shallow_ to _deep_ RTAs implies a 3.6% - 7.2% increase in exports. For GVC firms exporting/importing to/from the same country _j_ , moving from _shallow_ to _deep_ RTAs implies a 9.6% increase in exports (see columns 6). These results uncover an interesting selection effect à la Melitz (2003). Deep RTAs reduce variable and fixed trade costs between members, and more productive firms are more likely to take advantage of this policy change. In addition to this size/productivity channel, GVC firms benefit as they see a reduction in trade costs on imports of intermediate products used in production for exports. The heterogeneous effect of deep RTAs is confirmed also by using the weighted sum of provision as a proxy for the depth of RTAs (see Table A9).

The negative effect on small firms is in line with trade models with heterogeneous elasticity of demand (Atkeson and Burstein, 2008; Crowley et al., 2022) that predict a strong within-country competition effect hurting less productive firms, and implying an increase in the concentration of foreign market shares among high-productivity firms. So, deeper RTAs favor the export sales of firms with certain characteristics (large, more productive and GVC firms) at the expense of small and less productive firms. Such a selection effect of deeper RTAs is shown in Table 6

> 17The same conclusion holds by using a non-parametric binned model where the _DTA_ variable is interacted by three firm size bins based on whether the total exports of the firm (across destination and years) are below the 25<sup>_th_</sup> percentile (small firms), above the 75<sup>_th_</sup> percentile (big firms), or in between (medium size firms). See appendix table A8.

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where we estimate the effect of deep RTAs on: (i) the number of firms in _i_ that keep exporting at destination _j_ at time _t_ (i.e. surviving exporters), and (ii) the average export _per_ firm.<sup>18</sup> Deep RTAs reduce the number of firms surviving in the export market (columns 1-2) but increase the average export (value) _per_ firm (columns 3-4). This further confirms the selection effect of DTAs in developing countries, and points to welfare effects associated to adjustment costs and improved productivity deriving from the re-allocation of resources from less- to more-productive firms.

# **5.3 The extensive and intensive margin channels**

The export sales effect of deep RTAs may come from the intensive and/or the extensive margin of trade. Indeed, the reduction in trade costs associated to deep trade agreements may lead incumbent firms to boost their exports in destinations with deep RTAs (i.e. _intensive_ margin channel), or may allow new firms to start exporting in such destination (i.e. _extensive_ margin channel). In order to disentangle the overall export sales effect into the extensive and intensive margin channel, we calculate the change in _aggregate_ country-pair specific exports from: (i) incumbent firms – i.e. firms always exporting toward a given destination (intensive margin channel); and (ii) entry-exit firms to/from a specific market (extensive margin channel). Then, we adopt the decomposition approach as in Berman et al. (2012). Namely, we regress the aggregate exports by origin-destination-year for respectively incumbent and entry-exit firms on RTAs’ depth, and country-year fixed effects. The coefficients on RTA depth are respectively ˆ ˆ _βincumbent_ and _βentry_ . We then calculate the share of total exports from respectively incumbent and entry-exit firms ( _Vincumbent/Vtot_ and _Ventry/Vtot_ ), and multiply such shares for the respective elasticity _β_<sup>ˆ</sup> _incumbent_ and _β_<sup>ˆ</sup> _entry_ .

The results of this calculation are reported in Table 7. As expected, the elasticity to deep RTAs for both incumbent and entry firms are positive and significant, with a larger effect for incumbent firms. But since the share of total exports is larger for entry-exit firms than for incumbent firms, we obtain a lower contribution from the intensive margin channel to the aggregate effect. Namely, the intensive (extensive) channel accounts for 40% (60%) of the total impact of deep RTAs. The not too different contribution of the intensive and extensive margin channel suggests that deep RTAs represent at the same time a reduction in both the fixed and the variable export cost component. This is consistent with the view that several deep provisions in RTAs, such as the ones on technical standards, sanitary measures or services, allow to reduce fixed entry costs associated to divergent regulations and policy uncertainty.

> 18PPML estimator is used in Table 6.

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In a trade model with Pareto distributed firm productivity as in Chaney (2008), the aggregate exports of country _i_ to country _j_ , and hence the extensive and the intensive margin of trade, depend on the firm productivity dispersion parameter. When low- and medium-productivity firms represent a large fraction of firms in the country (i.e. skewed productivity distribution), a change in the productivity threshold induced by higher market access is expected to have large aggregate export consequences because many firms enter the export market (large extensive margin effect). Conversely, when the distribution of firm productivity is more dispersed, and large and high-productive firms represent a larger fraction of firms in the country, a change in the productivity threshold has only a marginal effect on the extensive margin, and the aggregate exports of the country increases only through the intensive margin channel. Thus, no matter the specific type of export costs impacted by deep RTAs, the aggregate effect of deep RTAs depends on productivity distribution of firms in the exporting country.

In Table 8, we interact the RTA depth variable with two proxies of country-specific Pareto distribution parameter (falling with increase in the share of high-productive firms). One obtained by following the QQ approach in Head et al. (2014),<sup>19</sup> the other by following Gabaix and Ibragimov (2011).<sup>20</sup> To facilitate the interpretation of the results, we use a dummy variable for countries having above-the-median Pareto shape parameter. In line with the intuition, deep RTAs have a strong positive effect on the extensive margin of countries having very skewed productivity distribution (i.e. high Pareto shape parameter) – see columns (1)-(2). Interestingly, in countries with a larger share of highly productive firms (i.e. Pareto shape parameter below the median) the extensive margin of export is negatively affected. This is likely due to the selection effect of deep RTAs discussed above. When the exporting country is populated by a large share of high-productivity firms (low Pareto shape parameter), the within-origin procompetitive effect of DTAs makes less-productive firms exiting the market. Results for the intensive margin channel are showed in columns (3)-(4). Deep RTAs have a strong positive effect on the intensive margin of countries having large share of highly productive firms (i.e. Pareto parameter below the median) and tiny negative effect on countries having very skewed firm productivity distribution (i.e. large Pareto shape parameter).<sup>21</sup> Results on total aggregate exports are reported in columns (5)-(6) and reflect results on the extensive and intensive margin channels discussed above.

> 19As in Head et al. (2014), we retrieve the Pareto-shape parameter of firm size distribution by using the QQ estimator. We regress the empirical quantiles of the sorted log exports on the theoretical quantiles (i.e. _−ln_ (1 _−_ (( _k −_ 0 _._ 3) _/_ ( _n_ +0 _._ 4)), where _k_ is the firm’s ascending order of exports and _n_ the rank of the firm having the highest export value). The coefficient of such regression, 1 _/θ_<sup> ̃</sup> , gives us the inverse of the Pareto shape parameter, that we recover as _θ_ = ( _σ −_ 1) _θ_<sup> ̃</sup> . We use elasticity of substitution _σ_ = 5.

> 20To reduce any endogeneity concern, we use beginning of the sample data to calculate Pareto share parameters.

> 21In the regressions reported in table 8 we include origin-year, destination-year and origin-destination fixed effects.

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# **6 Endogeneity**

The inclusion of the set of fixed effects discussed above strongly reduces any omitted variable concern. Namely, any firm specific productivity shock, as well as any import demand shock and country-pair specific transaction cost are captured by fixed effect. In this setting, the only endogeneity concern may come from the presence of unobserved factors affecting contemporaneously a _change_ in the RTA depth and in the exports of firm _f_ in country _i_ . To further reduce any endogeneity concern, we propose an Instrumental Variable (IV) approach based on the idea that each country ( _i_ or _j_ ) sets the depth of _new_ RTAs based on the depth of existing ones (in the vein of the domino effect of RTA formation by Baldwin and Jaimovich 2012). Our instrumental variable is therefore the following: where the two terms in brackets represent: (i) the average depth of RTAs signed by country _i_ with trade partners _k_ = _j_ within the _j_ ’s macro region, and (ii) the average depth of RTAs signed by country _j_ with trade partners _z_ = _i_ within the _i_ ’s macro region.<sup>22</sup> We use the leave-one-out means to construct the average depth in brackets to address the finite sample bias coming from using own-observation information. The exclusion restriction is based on: (i) the absence of a direct effect of firms’ exports toward destination _j_ on the average depth of RTAs signed by country _i_ and _j_ with third-countries, and (ii) on the absence of a direct effect of average RTA depth signed with third countries on firms’ exports toward _j_ . While condition (i) is likely to hold, condition (ii) deserves careful discussion. Indeed, the presence of a trade diversion effect of deep RTAs threatens the validity of our IV: if country _i_ signs a deep RTA with third country _k_ ( _k_ = _j_ ) and this diverts firm’s exports from _j_ to _k_ , the validity of the IV is challenged. Notice, however, that the average reduction in trade costs of country _i_ and country _j_ with third countries is captured here by respectively firm-year and destination-year fixed effects. We are therefore confident of the exclusion restriction validity in our empirical setting. Still, in the next section we present a plausible exogeneity test aimed at supporting the validity of our results even in presence of weak deviation for the perfect validity of exclusion restriction assumption.

Our baseline results are confirmed by the 2SLS estimations addressing any residual endogeneity concerns - see Table 9 column 1. The (instrumented) measure of RTA depth has a positive and significant effect on the exports of the average firm. Also our results on the hetero-

> 22 Macro-regions are: East Asia and Pacific, Europe and Central Asia, Latin America and Caribbean, Middle East and North Africa, North America, South Asia, Sub-Saharan Africa.

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geneous impact of DTAs on firms with different characteristics is confirmed by 2SLS estimations - see Table 9 columns 2-7.<sup>23</sup> The interaction terms are instrumented by simply interacting the firm indicators _I_ ( _kf > k_<sup> ̄</sup> ) with the IV discussed above. The bottom part of Table 9 shows the first stage results of the 2SLS approach. Our IVs (one for the RTA depth and the other for its interaction with the firm type dummy) are good predictors of the endogenous variables (i.e. significant first stage coefficients). Also, the joint F-stat statistics well above 10 support the absence of a weak instrument problem.

## **6.1 IV validity**

As discussed above, the validity of our instrumental variable is based on the absence of a direct effect of the depth of RTAs signed with third-country on _fij_ -specific exports. In this section we test the robustness of our baseline results to a deviation from the perfect validity of the exclusion restriction (Conley et al., 2012). A degree of deviation from the exclusion restriction can be obtained by regressing the exports of firms _Xfijt_ on our main _DTAijt_ and IV variable. The coefficient associated to the IV represents an approximation of the direct effect of the IV on the outcome variable (i.e. degree of deviation from the exclusion restriction) – van Kippersluis and Rietveld (2018). We obtain a small and not statistically significant direct effect of IV on firm exports - see parameter _ν_ in Table 10. We therefore plug such a degree of deviation from exclusion restriction in the plausible exogeneity test à la Conley et al. (2012), and obtain a lowerand upper-bound coefficients that do not cross the zero. Thus, we can safely argue that the depth of RTAs has an unambiguous positive causal effect on the export of firms in developing countries.<sup>24</sup>

# **7 The dynamic effect of deep RTAs: An event study approach**

We relied so far on a fixed effects approach delivering the average effect of deep RTAs on the exports of firms (i.e. pre- _versus_ post- change in RTA depth). However, deep RTAs may stimulate firms’ exports dynamically and for a limited amount of time. In this section we adopt an event-study approach to visualize the dynamic effect of deep RTAs. Namely, we follow Fajgelbaum et al. (2019), and compare the targeted varieties (i.e. firm-destination combinations

> 23Point estimates from _linear_ 2SLS estimations in Table 9 cannot directly compared with our baseline _non-linear_ PPML estimations.

> 24For computational reasons (i.e. maximum number of covariates allowed by `plausexog` STATA command) we had to reduce the number dummies (fixed effects) included in the estimations. First, we replaced destination-year fixed effects by destination-period fixed effects, with periods containing 6-year each. Second, we restricted the number of destinations by: (i) using top-50 destinations for the all the 31 exporting countries of our sample (panel a in Table 10), (ii) keep only destinations representing at least the 0.5% of total exports of all the 31 exporting countries of our sample.

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that face a change in RTA depth) to non-targeted varieties, using the following specification: .

The event-study specification includes firm ( _θf_ ), destination-year ( _θjt_ ) and origin-destination ( _θij_ ) fixed effects. The indicator variable **I** ( _eventijt_ = _z_ ) captures the event time coefficient before ( _z_ = _−_ 2 _, −_ 1) and after ( _z_ = 1 _,_ 2 _,_ 3) the change in the RTA depth ( _z_ = 0).<sup>25</sup> The target variable, _targetfjt_ , is a dummy for varieties (i.e. firm-destination) that experience a change in the RTA depth during the period. The presence of firm fixed effects implies that _β_ 1 _z_ coefficients are identified using the variation between targeted and non-targeted destinations in each point in time _z_ . For targeted varieties, the event date is the year of the first change in the RTA depth between country _i_ and _j_ . For non-targeted varieties we assign the event date to be the earliest year in which the destination market _j_ experiences a change in RTA’s depth with at least one of its trade partners. As in the baseline specification we adopt a PPML estimator and cluster standard errors by origin-destination-year.

Figure 2 reports the impact of RTA depth on targeted varieties. On impact, we find a positive but imprecisely estimated effect of RTA depth on the export value of firms. The effect becomes statistically significant one and two years after the change in RTAs’ content. The positive effect vanishes after two years from the change in RTA depth. Interestingly, the event study approach also addresses concerns on the anticipation of changes in RTA depth (and/or RTA signature). During the pre-treatment period targeted and non-targeted varieties show a parallel trend. The absence of pre-trend reassures on the causal interpretation of our baseline results.

# **7.1 Two-way (robust) fixed effects estimations**

As recently argued by De Chaisemartin and d’Haultfoeuille (2020), two-way fixed effects estimations with heterogeneous treatment across groups and over time may be biased by negative weights. Indeed, comparing the outcomes of _treated_ country-pairs with those of _non-treated_ pairs that may (or may not) be treated afterwards may cause negative weights in the difference-indifference estimator. Moreover, RTAs’ depth is a continuous treatment that can change over

> 25We adopt asymmetric time period before _versus_ after change in RTA depth because in our data the pretreatment period is limited.

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time and may have a dynamic effect (i.e. the initial variation in RTA depth may affect future variations in depth and the outcome variable), implying a second possible source of bias.<sup>26</sup> Therefore, we follow De Chaisemartin and d’Haultfoeuille (2020) and perform a robust two-way fixed effects estimation of the trade effect of the number of legally enforceable provisions in RTAs. Since we are interested in the dynamic effect, we specifically adopt the estimator proposed by De Chaisemartin and D’Haultfoeuille (2020). The intuition behind this estimation is that, to avoid negative weights that may bias standard two-way fixed effects estimators, one should compare the outcome change from _t −_ 1 to _t_ + _l_ for only the first time switchers’ (i.e. firm-destination pairs at first change in RTA depth occurred at _t_ ), to the outcome change of firm-destination pairs whose treatment has remained stable until _t_ .<sup>27</sup> We present the results of the estimation with _l ∈_ [0 _,_ 3] in Table 11.<sup>28</sup> In line with the event study approach reported in Figure 2, the depth of RTAs has a weak positive effect on the export of firms in the year of the first variation in RTA depth (i.e. _t_ ). The effect of RTA depth becomes strongly significant the year after _t_ + 1, increases in magnitude at time _t_ + 2 and vanishes at _t_ + 3. While the pattern is the same as in the standard event study approach reported in the previous section, the point estimates in Table 11 differ with respect to those reported in Figure 2. However, such a difference is small if standard errors are considered; suggesting the presence of a (very) small negative bias in the standard two-way fixed effects event study approach.

# **Conclusion**

This paper studies the effect of deep trade agreements on the export performance of firms in 31 developing countries. We show a moderate but statistically significant effect of RTA depth on the exports of the _average_ firm. Namely, one additional legally enforceable provision boosts the export of firms by 0.3%. This implies that moving from _shallow_ to _deep_ RTAs leads to a 3.6% increase in firms’ exports. This average effect is however strongly heterogeneous across firms with different characteristics. Large and GVC firms are more positively affected by deep RTAs. For firms belonging to the top-quartile of size distribution, moving from _shallow_ to _deep_ RTAs implies 4.8% increase in their exports. For GVC firms importing and exporting from/to the same country, moving from _shallow_ to _deep_ RTAs implies a 9.6% increase in their exports. Conversely, small and less productive firms are negatively affected by deep RTAs as they suffer the higher degree of competition induced by deep RTA at destination. These results

> 26Notice that this second source of bias is already taken into account in the event study exercise where we focus exclusively on the first variation in RTAs depth.

> 27See De Chaisemartin and D’Haultfoeuille (2020) for more details on the robust two-way fixed effects estimator.

> 28In Table A10 we show the same estimations including firm’s tariffs as a controls and results hold.

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are robust to a number of extensions and robustness checks that confirm the causal impact of deep RTAs on firms’ exports. These findings have relevant welfare and policy implications for developing countries. While the selection effect, through the reallocation of resources toward more productive firms, is expected to improve welfare in countries joining deep trade agreements, the negative export performance of small firms signals that the adjustment process in developing countries can be significant.

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