Comparing Apples to Apples: Estimating Consistent Partial Effects of Preferential Economic Integration Agreements

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1 Comparing Apples to Apples: Estimating Consistent Partial Effects of Preferential Economic Integration Agreements Peter Egger and Filip Tarlea Abstract The estimation of causal effects of the partial effect of preferential economic integration agreements (such as customs unions or free-trade areas) on trade costs or trade flows typically relies on selection-on-observables methods. The leading paradigm of such methods is that one can find a vector of joint determinants of agreements and trade flows and condition on it in some way so that a comparison of similar country-pairs in terms of observables is informative about the causal effect of agreements on trade-cost or trade-flow outcome. Since conditioning on a flexible function of all individual covariates is inefficient and eventually even infeasible, researchers typically employ scalar-valued compact metrics which are based on all observables to identify comparable country pairs. This paper is concerned with the problem that a prerequisite for this approach to obtain consistent estimates is that the score used for comparison actually reflects comparability in all covariates at the same time. Keywords: Preferential economic integration agreements; Causal effects; Propensity score estimation; Weighted regression; Balancing property JEL codes: F10; F12; F17 ETH Zurich, LEE G101, Leonhardstrasse 21, 8092 Zurich, Switzerland. Co-affiliations: CEPR, CESifo, GEP, and WIFO. ETH Zurich, LEE G101, Leonhardstrasse 21, 8092 Zurich, Switzerland. Acknowldgements: To be added. 1

2 1 Introduction Obtaining valid estimates of the partial (or direct) effects of the membership in preferential economic integration agreements (PEIAs) of which there is a host of types on bilateral trade flows is the primary object of interest of a cottage literature in international economics (see, e.g., Ghosh and Yamarik, 2004; Carrére, 2006; Baier and Bergstrand, 2007, 2009; Egger, Egger, and Greenaway, 2008; Chang and Lee, 2011). The econometric problem with this task is that PEIAs are foremost meant to stimulate trade, and, according to economic theory, concluding PEIAs has greater benefits for natural trading partners than otherwise (see Frankel, Stein, and Wei, 1996; Baier and Bergstrand, 2004). Hence, the recent empirical literature on this issue recognizes that the assignment into PEIA membership is not random, which is confirmed by a glance on the frequency of such agreements across types of countries and country-pairs in terms of observable characteristics capturing country size, per-capita income, geography, and remoteness. An influential paper by Baier and Bergstrand (2004) illustrated that the fundamental drivers of trade flows alone explain a lion s share in the variation of a binary variable capturing preferential trade-agreement (PTA) membership as one form of PEIAs. Egger and Wamser (2013) demonstrate that this is the case also for other forms of PEIAs such as bilateral investment treaties (BITs) or double-tax treaties (DTTs), all of which aim at regulating preferential market access in some dimension. The theoretical arguments put forward in earlier work suggest that it will be hard if not impossible to find fundamentals which directly determine PEIAs while influencing trade flows exclusively through PEIA membership. Econometrically speaking, this means that it will be virtually impossible to find fundamental drivers of PEIAs for which exclusion restrictions are met 2

3 in trade-flow regressions. Consequently, the leading assumption in empirical work geared towards estimating PEIA effects is one of the so-called selection on observables. According to this framework, it should be possible guided by economic theory as in Baier and Bergstrand (2004) to (i) identify all joint determinants of PEIA membership and trade flows, and (ii) to condition in some way on them so that the remainder (conditional) variation in PEIA membership and trade flows reveals the causal relationship between agreement membership and trade flows. While earlier work used a log-linear regression approach for identification conditional on observables (see Aitken, 1973; Soloaga and Winters, 2001), more recent work parted with the related strong assumption about functional form and resorted to nonparametric estimation techniques. The latter with the most prominent example in related applied work being propensity-core matching (see Rosenbaum and Rubin, 1983) relies on the idea of obtaining a compact metric which captures the joint fundamentals behind PEIA membership and trade flows, and which permits determining similar country pairs which more or less solely differ in terms of PEIA membership for identification of the treatment effect (see, e.g., Egger, Egger, and Greenaway, 2008; Baier and Bergstrand, 2009). A prerequisite for this approach is that similarity in terms of the compact, scalar-valued score metric (the propensity of PEIA membership) is not an artifact which could flow from largely different individual observable fundamentals whose differences between PEIA members and non-members are eliminated through aggregation into the score. The latter would mean comparing PEIA-member apples to -non-member oranges. Econometrically, this problem is referred to as a lack of balancing of the observables, whereby members and non-members of PEIAs with similar-valued propensity scores of being a PEIA member would have very different moments in the distri- 3

4 bution of at least some of the observables the score is based on. The results might be a bias in the estimates of partial PEIA effects on outcomes such as bilateral trade flows. The goal of this paper is to provide a first comparison of (partial) treatment effects of PEIAs on bilateral exports with enforced versus unenforced balancing of the covariates in a selection-on-observables approach. In a large panel of 1,801,930 observations for all years and 3 types of PEIAs (PTA-, BIT-, DTT-membership, and all combinations thereof distinguishing between PTAs of different depth in some of the analysis) the paper demonstrates that not enforcing balancing of the covariates in a nonparametric selection-on-observables approach leads to upward-biased PEIA effects. For instance, the partial impact of a membership in an average PTA only is estimated to be almost 7 percentage points lower with enforced covariate balancing than without it. The partial effect of a membership in an average BIT only is estimated to be almost 15 percentage points lower with enforced covariate balancing than without it, and the bias in the estimated partial impact of a membership in an average DTT only is estimated at a similar magnitude. We illustrate that the quantitative importance of proper conditioning on the covariates in nonparametric selection-on-observables approaches relative to not doing so is of a similar magnitude as the difference between simple (biased) ordinary-least-squares estimates and simple (and also biased) selection-on-observables estimates of partial PEIA treatment effects as relied upon in earlier work. The remainder of the paper is organized as follows. The subsequent section briefly portrays nonparametric selection-on-observables estimates of PEIA treatment effects as weighting estimators and distinguishes between covariate-balancing-unenforcing and -enforcing approaches. Section 3 in- 4

5 troduces the specification of the vector of observables and the underlying data considered. Section 4 summarizes estimates of the comparison (propensity) score and illustrates the degree of lack of balancing of the covariates. Moreover, this section demonstrates the difference between the scores of a covariate-balancing-enforcing approach and an -unenforcing one. This section also provides a comparison of the estimates of partial effects of PEIA treatment effects on bilateral exports. The last section concludes with a brief summary. 2 Causal partial PEIA-effects estimation as weighting regression The customary condition-on-observables approaches towards estimating causal partial PEIA effects can all be portrayed as variants of weighting regressions (see Wooldridge, 2007). With this in mind, the simple linear conditioning approach in the form of ordinary least squares of log bilateral exports on one or more PEIA indicator variables and a linear function of observable control variables conforms to an approach with identical weights for each observation. Also matching on the propensity score (of PEIA membership) can be represented as a weighting regression. However, neither linear regression nor matching on the propensity score ensure that PEIA members and nonmembers are fully comparable after conditioning on the observables by the associated linear or nonparametric functions. The reason is that the linear index with OLS or the propensity score with matching may take on similar values when the individual covariates are quite different in a few or many dimensions of the observables. However, there are weighting approaches which are capable of ensuring comparability (not even in only the average value as 5

6 the first moment of the distribution of an observable) in all of the dimensions of the observables. One such weighting approach is entropy balancing, which is based on optimally-chosen weights as a function of the distributions of observables for the treated and the untreated (see Hainmüller, 2012; Imai and Ratkovic, 2014; Zubizarreta, 2015). 2.1 Notation Let us use P θ0 ijs to denote the propensity score of exporter i and importer j to be members of a PEIA of generic type θ rather than being a member in no PEIA whatsoever at time s. Denoting the binary indicator for specific PEIA memberships by T θ0 ijs and the specific realization of θ for ijs by Θ ijs. T θ0 ijs is unity in case that i and j have a PEIA of type θ at time s and zero else, and denoting the vector of observables determining membership by H θ0 ijs, the propensity score is defined as the conditional probability P θ0 ijs = P (T θ0 = 1 H θ0 ijs). (1) With three types of binary PEIA indicators, there are 2 3 = 8 possible combinations of agreement types, one being no PEIA agreement of any kind in place which will serve as the general control or comparison state in this 6

7 paper. 1 The remaining seven combinations are P T A if P T A ijs = 1, BIT ijs = 0, DT T ijs = 0 BIT if P T A ijs = 0, BIT ijs = 1, DT T ijs = 0 DT T if P T A ijs = 0, BIT ijs = 0, DT T ijs = 1 Θ ijs = θ P T A&BIT if P T A ijs = 1, BIT ijs = 1, DT T ijs = 0 (2) P T A&DT T if P T A ijs = 1, BIT ijs = 0, DT T ijs = 1 BIT &DT T if P T A ijs = 0, BIT ijs = 1, DT T ijs = 1 P T A&BIT &DT T if P T A ijs = 1, BIT ijs = 1, DT T ijs = 1 each of which we will refer to as one form (or status) of treatment. We use N θ and N 0 for the number of treatment-θ and control observations and N θ0 = N θ + N 0, and we refer to the sets of observations corresponding to these numbers by N θ, N 0, and N θ0 = N θ N 0, respectively. Finally, we use H θ0 to refer to the matrix of observables for the units with treatment θ and the control units. 2.2 Assumptions behind consistent estimates of partial TTs The goal of selection-on-observables approaches upon choice of untreated units (here, indicated by super-script 0) being the single reference group is to estimate the average treatment effect of PEIA membership from a comparison of outcome Y θ of the units {ijs} N θ with observable characteristics 1 In theory, any other state than complete PEIA nonmembership could serve as a comparison. However, for the sake of simplicity, and given the extent amount of control units in that state, we choose it as a natural reference point in this paper. It should be borne in mind that what we do in the comparison state is to switch off all PEIAs at the same time. 7

8 H θ0 ijs to outcome Y 0 of the units {ijs} N 0. In order to not misattribute that average difference in Y θ and Y 0 to differences in H θ0, the vector of propensity-scores P θ0 for weighting in some way (depending on the required similarity between treated and control units specified by the researcher). 2 However, this approach only leads to consistent estimates of the average treatment effect under the following assumptions. Balancing of the observables H θ0 ijs with regard to P θ0 ijs: A second key condition is the aforementioned balancing of the covariates. Informally, balancing makes sure that the propensity score is a meaningful metric of comparison. Notice that this is the case only if, for units {ijs} and {i j s }, P θ0 ijs and P θ0 i j s means pairwise similarity for all columns in Hθ0 ijs and Hi θ0 θ0 j s, respectively. Otherwise, similarity of Pijs and Pi θ0 j s would be an artifact, and estimating the average treatment effect from comparison groups of treated and untreated units with similar propensity score will eventually not be consistent. However, the assumption about balancing of the covariates is testable, and remedies against a lack of balancing are available. For instance, tests about the equality of moments of the distribution of the elements in H θ0 for the treated and the control units are available. Moreover, balancing can be enforced for several moments by entropy-balancing weighting regression (see Hainmüller, 2012; Imai and Ratkovic, 2014; Zubizarreta, 2015). Unconfoundedness or conditional mean independence of treatment: Unconfoundedness means that, for the same unit {ijs} and conditional on the observable determinants of its treatment status, H θ0 ijs, the hypothetical outcomes Y θ ijs and Y 0 ijs for that unit are independent of the treatment θ. 2 With matching, this similarity is specified by way of k-nearest neighbor matching, radius matching, or kernel matching. The matching-function type determines the nature of the weights based on the propensity scores. 8

9 Formally, using Y θ0 ijs for all units with either treatment θ or control units (i.e., an element of the vector Y θ0 = (Y θ, Y 0 ) ) Y θ0 ijs T ijs H θ0 ijs. (3) The latter assumption means that H θ0 ijs needs to include all joint determinants of outcome Y θ0 ijs and treatment T θ ijs (and, hence, P θ0 ijs). Consistency of the functional form of P θ0 ijs: An inconsistency of the propensity-score estimates could flow from an erroneous assumption about the functional form of the distribution for the mapping of H θ0 ijs into P θ0 ijs. Then, maximum-likelihood estimates of the scores P θ0 ijs would be biased and inconsistent. 3 However, this would not necessarily be a problem for comparison estimators as long as the ranking of units {ijs} would be consistent, and the degree of similarity if two comparison units would be only marginally affected (i.e., similarity in similarity of all columns in H θ0 ijs). P θ0 ijs would still mean 2.3 Treatment-effect estimation through weighting regression In this subsection, we present two alternative types of weighting regression for a framework of selection on observables, each of which involves a specific first stage to determine the weights and an outcome which corresponds to weighted least squares. In each case, the second stage is run on a subset of 3 Leading estimators and functional forms in applied work are probit (normality) and logit. In estimating the propensity of PEIA membership, probit is used in most applications (e.g., see Baier and Bergstrand, 2004, 2009; Egger, Egger, and Greenaway, 2008; Egger and Wamser, 2013). 9

10 the data where either Θ ijs = θ or Θ ijs = 0, namely N θ0. For convenience, let us also introduce a subvector of the joint determinants of PEIA membership and bilateral trade, H ijs, which we refer to as Z ijs Inverse-probability weighting (IPW) regression With inverse probability weighting, the first stage of the approach is concerned with estimating the response (or PEIA membership) probabilities P θ0 ijs. Since response probabilities are typically estimated by a maximumlikelihood estimator for nonlinear probability models, one concern may arise with respect to the repeated occurrence of the index tuple ij over s and an associated cluster structure of the variance-covariance matrix of the disturbances. 4 We address this problem by generally estimating P θ0 ijs year by year (see also Wooldridge, 1995, for a recommendation along those lines) and for each treatment θ separately (ensuring that the propensities add up properly). One prominent example of a first-stage model along those lines is the probit model, which we employ here. The (inverse) propensities obtained in this first stage are the weights used in the second stage of the IPW regression framework. Formally, the (conditional) propensity score is obtained by conditioning on H θ ijs from eq. (??). In the second stage, we may condition on the covariates, Z ijs, exerting an impact on bilateral exports, X ijs, or not. If we do, we obtain parameters from two weighting expressions for the treated as ijsβθ )2 min (4) α θ,β θ P ijs θ0 4 Note that the country-pair dimension indexed by ij accounts for the lion s share of the variance in bilateral exports, even in a long panel of data as the one used here. ijs N θ (X ijs αθ Z 10

11 and for the controls as (X ijs min α0 Z α 0,β 0 θ0 1 P ijs N 0 ijs ijsβ0 )2. (5) Using the notation Z θ0 and Z θ to denote row vectors containing the average values of Z ijs in the subsets of the observations in N θ0 and N θ, respectively, the average treatment effect (ATE) and the average treatment effect of the actually treated (ATT) of a type-θ PEIA membership in comparison to no treatment at all with inverse probability weighting are then defined as ÂT E θ0 ipwra = ( α θ α 0 ) + Z θ0 ( β θ β 0 ) (6) and ÂT T θ0 ipwra = ( α θ α 0 ) + Z θ ( β θ β 0 ), (7) respectively. One major advantage of this framework is its simplicity. However, a fundamental drawback is that it assumes covariate balancing, which in reality is often rejected by the data. As argued before, a lack of covariate balancing may lead to a bias of the second-stage weighting-regression estimates and, hence of ÂT E θ0 ipwra and ÂT T θ0 ipwra Covariate balance-enforcing (CBE) weighting regression The second approach to PEIA-treatment-effect estimation by weighting regression differs from the one in the previous subsection only with respect to the first stage. In contrast to a propensity-score model, the weights here are obtained as follows. 11

12 Let us define an unknown weight for unit {ijs} N 0, e ijs, a base weight, q ijs, and a distance metric f(e ijs ) = e ijs log(e ijs /q ijs ) (8) Then, the weights e ijs are chosen so as to minimize the loss function subject to the set of balance constraints min F (e) = e f(e ijs ) (9) ijs {ijs N 0 } {ijs N 0 } e ijs c r,ijs (H ijs ) = m θ r (10) where c r,ijs (H ijs ) is the moment function for the covariates H ijs among the control observations {ijs} N 0 up to moment r and the r-th moment of the (base-unweighted) treated observations {ijs} N θ, m θ r, and subject to the normalization constraints e ijs 0, and {ijs N 0 } e ijs = 1. (11) Let us denote the solution for e ijs by this procedure by ê θ0 ijs. Using this estimate, we may formulate the entropy-balancing counterparts to equations (??) and (??) for the treated and control observations as min α θ,β θ (X ijs αθ Z ê θ0 ijs N θ ijs ijsβθ )2 (12) 12

13 and (X ijs min α0 Z α 0,β 0 ê θ0 ijs N 0 ijs ijsβ0 )2 (13) respectively, and the corresponding treatment effects are defined as AT E θ0 balance = AT T θ0 balance = α θ α 0. (14) There are two notable and desirable differences between eq. (??) and eqs. (??) and (??), apart from their being based on different parameter estimates. First, any difference in the moments of Z ijs is eliminated by the minimization in eq. (??) subject to the aforementioned constraints, differences in Z ijs between the treated and control units do not influence average treatment effects. Second, for the same reason, the average treatment effect (ATE) is identical to the average treatment effect of the treated (ATT). 3 Data We cover the time interval of We restrict our sample to country pairs within this time frame where stricly positive trade flow is observed. Our main regressor of interest is the country pair s membership status in one of the preferential economic integration agreements: PTA, BIT, DTT. Information on PTA membership is collected from WTO s website. The variable PTA takes the value of 1 if the two countries in the country pair have at least one trade agreement signed amongst themselves. Information on DTT and BIT membership is collected from UNCTAD s website. There is only one double taxation treaty possible between two countries, which if existent will assign the value of 1 to the DTT binary variable. The same 13

14 applies for BIT. The entire dataset is described in Table?? and individual and joint frequency of PEIA memberships in our data is apparent in Table?? below. 14

15 Table 1: Determinants of PEIAs and trade (description and source) Variables Description Source 1st-stage covariates only RGDP the sum of log of real GDPs WDI DRGDP the difference of log of real GDPs WDI DKL the difference in the two countries WDI relative factor endowments DROWKL the average difference in relative factor endow- WDI ments between the pair and the rest of the world 1st- and 2nd-stage covariates PTA Prefferential Trade Agreement WTO BIT Bilateral Investment Treaty UNCTAD DTT Double-Taxation Treaty UNCTAD BIT&DTT PTA&BIT PTA&DTT PTA&BIT&DTT log(dist) log distance between two countries economic centers CEPII BORDER 1 if the two countries share a common border CEPII LANG1 1 for common official primary language CEPII LANG2 1 if a language is spoken by at least 9% CEPII of the population COLONY1 1 for pair ever in colonial relationship CEPII COLONY2 1 for common colonizer post 1945 CEPII COLONY3 1 for pair currently in colonial relationship CEPII COLONY4 1 for pair in colonial relationship post 1945 CEPII SMCTRY 1 if countries were or are the same country CEPII 15

16 Table 2: Descriptive Statistics Variable Obs Mean Std. Dev. Min Max log(exports) 434, YEAR 434, st-stage covariates only RGDP 434, DRGDP 434, DKL 434, DROWKL 434, st- and 2nd-stage covariates PTA 346, BIT 329, DTT 344, BIT&DTT 328, PTA&BIT 318, PTA&DTT 317, PTA&BIT&DTT 321, log(dist) 434, BORDER 434, LANG1 434, LANG2 434, COLONY1 434, COLONY2 434, COLONY3 434, COLONY4 434, SMCTRY 434, One-year-lagged complemetary treatments are included as regressors in the first stage, weighted by distance in the following categories: [0km, 500km], (500km, 1000km], (1000km, 2000km], (2000km, 5000km], (5000km, km]. Table 3: Presence of PEIAs PTA DTT BIT %

17 4 Results and discussion thereof Four important results are revealed by our analyses. First, Tables??,?? and?? are meant for illustrative purpose, particularly to visualize how well the the balancing of covariates condition is met. For brevity we only show the snapshot for the year 2000 cross-section, however the same results for all years of the period are available upon request. Indeed the tables indicate that there is significant difference in the comparability of the treated and non-treated samples across the log-linear, inverse-propensity weighted and covariate balance-enforcing estimators. As expected, CBE transforms the data such that the means are identical in the treated and non-treated group, while variance and skewness are very similar. However, weighting the two groups by the propensity of each unit to receive the treatment expands the difference in the first, second and third moment of the distribution across the two groups, even further than simply splitting the sample into two based on treatment status, as our least-square estimator does. Second, ignoring the covariate balancing assumption when trying to estimate the marginal impact of PEIAs on bilateral trade flows will consistently lead to overestimated coefficients. For example, looking at Model 2 results in Table?? we see that log-linear estimation of PTA s effect on the natural logarithm of bilateral exports is more than 50% larger than the result estimated by our covariate-balancing technique. While this discrepancy might be the largest of all PEIAs and their combinations, the overestimation pattern is consistent throughout all seven treatments. The economic meaning of this result can be quantified (on average) for any country pair, implying that for the same country pair trade will increase 1.5 times in the years after the PTA was signed compared to the years before. The third important result reveals that the joint effect of multiple PEIAs 17

18 signed between two countries exceeds the effect of any individual one in part. The same country pair will trade 2.2 times more if in addition to a PTA the two also sign a BIT. Given that for some countries net exports make up for over a third of total contributions to GDP, having bilateral trade and investment agreements would consequently boost GDP by one third. Signing a DTT in addition to a PTA increases exports by a factor of 2.3. The economic intuition behind these results is that BITs and DTTs have a positive impact on FDI (as documented by Egger and Pfaffermayr, 2004; Egger et. al, 2006; Egger and Merlo, 2007) and often trade is complemented but also enhanced by foreign investment, either in the form of green field investment or acquisition. Ensuring protection from expropriation, security and fair treatment towards foreign investors is reasonble to have some effect on exporters also. Slightly surprising is that having all three PEIAs (considered in our analysis) has on average a slightly smaller effect on exports than the joint effect of PTA and DTT. The other possible explanation is the composition effect. The way our treatment variables were coded distinguishes between country pairs with say PTA and DTT and country pair with PTA, DTT and BIT, ensuring there is no overlap. Lastly, we distinguish between country pairs with one PTA, two, three or more than three. As expected, results confirm that trade increases at the extensive margin of PTAs. When combined with other PEIAs however, having two PTAs seems to increase exports the most. One very large magnitude stands out, with our covariate balance-enforcing estimator suggesting an increase of a 8.3 factor when the country pair signs a DTT and more than three PTAs. 18

19 5 Conclusions New covariate balance enforcing technique for non-parametric estimation of trade determinants. The new technique generates identical to the first moment and very similar to the second and third moment output variables conditional on covariates. Failure to reach covariate balance generates on average an upward bias in estimated coefficients of PEIAs. Despite a significant difference in magnitude of the second-stage coefficients, probit estimation is far from satisfying CIA. Any combination of two or three PEIAs has a stronger effect on exports than any individual PEIA has. Our results are robust to accounting for the number of PTAs that two countries have. In general, one PTA generates less trade than two, but not always than three or more. 19

20 Table 4: Model 1: ATE of PEIAs on Log Exports OLS IPW CBE PTA SE BIT SE DTT SE PTA & BIT SE PTA & DTT SE BIT & DTT SE PTA & BIT & DTT SE OLS: coefficient estimates of one stage least-squares regression of dependent variable log(exports) on covariates shown in Table??. IPW: second-stage coefficient estimates of inverse probit-based weights-weighted regression. CBE: second-stage coefficient estimates of covariate-balanceenforcing weights-weighted regression. Exporter*year fixed effects and importer*year fixed effects included in the second stage only. Standard errors are obtained through bootstrapping, by drawing 100 times with replacement. Table 5: Model 2: ATE of PEIAs on Log Exports OLS IPW CBE PTA SE BIT SE DTT SE PTA & BIT SE PTA & DTT SE BIT & DTT SE PTA & BIT & DTT SE OLS: coefficient estimates of one stage least-squares regression of dependent variable log(exports) on covariates shown in Table??. IPW: second-stage coefficient estimates of inverse probitbased weights-weighted regression. CBE: second-stage coefficient estimates of covariate-balance-enforcing weights-weighted regression. Exporter*year fixed effects and importer*year fixed effects included in both stages. Standard errors are obtained through bootstrapping, by drawing 100 times with replacement.

21 Table 6: Model 3: ATE of PEIAs on Log Exports OLS IPW CBE BIT SE PTA SE PTA SE PTA SE PTA SE DTT SE BIT & DTT SE BIT & PTA SE BIT & PTA SE BIT & PTA SE BIT & PTA SE DTT & PTA SE DTT & PTA SE DTT & PTA SE DTT & PTA SE BIT & DTT & PTA SE BIT & DTT & PTA SE BIT & DTT & PTA SE BIT & DTT & PTA SE OLS: coefficient estimates of one stage least-squares regression of dependent variable log(exports) on covariates shown in Table 21??. IPW: second-stage coefficient estimates of inverse probitbased weights-weighted regression. CBE: second-stage coefficient estimates of covariate-balance-enforcing weights-weighted regression. Exporter*year fixed effects and importer*year fixed effects included in both first and second stage. Standard errors are obtained through bootstrapping, by drawing 10 times with replacement. PTA 1 is a dummy indicating a country pair with one PTA, PTA 2 - two, PTA 3 - three, and PTA 4 - four or more.

22 Table 7: PTA extensity Number of PTAs per country pair-year Frequency Percent Cummulative 0 1,700, , , , , Total 1,801, Table 8: PTA extensity - collapsed to categories used in this paper Number of PTAs per country pair-year Frequency Percent Cummulative 0 1,700, , , , >3 10, Total 1,801,930 22

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26 7 Appendix Table 9: Covariate balancedness of PTA and non-pta members before weighting, year 2000 Treated Control Variable Mean Variance Skewness Mean Variance Skewness log(dist) RGDP DRGDP DKL DROWKL BORDER LANG LANG COLONY COLONY COLONY COLONY SMCTRY

27 Table 10: Covariate balancedness of PTA and non-pta members after IPW weighting, year 2000 Treated Control - IPW Variable Mean Variance Skewness Mean Variance Skewness log(dist) RGDP DRGDP DKL DROWKL BORDER LANG LANG COLONY COLONY COLONY COLONY SMCTRY Table 11: Covariate balancedness of PTA and non-pta members after CBE weighting, year 2000 Treated Control - CBE Variable Mean Variance Skewness Mean Variance Skewness log(dist) RGDP DRGDP DKL DROWKL BORDER LANG LANG COLONY COLONY COLONY COLONY SMCTRY