The effect of free trade agreements revisited: Does residual trade cost bias matter?

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1 Received: 12 October 2017 Revised: 14 July 2018 DOI: /roie Accepted: 22 August 2018 ORIGINAL ARTICLE The effect of free trade agreements revisited: Does residual trade cost bias matter? Paras Kharel South Asia Watch on Trade, Economics and Environment (SAWTEE), Kathmandu, Nepal Correspondence Paras Kharel, South Asia Watch on Trade, Economics and Environment (SAWTEE), Baluwatar, Kathmandu, Nepal. JEL Classification C23, F13, F14, F15 Abstract This paper revisits a prominent gravity model based empirical literature on the effects of free trade agreements by accounting for a potential bias caused by unobservable trade costs that operate through general equilibrium constraints. It embeds state of the art panel estimation techniques in a recently proposed two step remedy that features a constrained ANOVA type estimation. Using a dataset on manufacturing trade flows in eight sectors in 40 countries and a rest of the world aggregate for the period , it finds evidence of significant residual trade cost bias. The direction and magnitude of bias vary across sectors, with the standard one step approach used in the literature overestimating or underestimating the partial effect of free trade agreements by up to 110 percent. Overall, coefficients on trade costs variables are jointly significantly different between the standard method and the twostep method. The biases in partial effect estimates translate into biases in general equilibrium effects. 1 INTRODUCTION There has long been an interest among economists and policymakers alike in the effect of regional trade agreements, or free trade agreements (FTAs), on trade. The proliferation of such agreements since the early 1990s gave an impetus to empirical investigations. 1 As trade agreements continue to be negotiated, interest in the subject is likely to sustain. The gravity model is the go to method for ex post quantification of FTAs. FTA membership is one of the very few available observable proxies for trade costs in a gravity equation that is naturally at the bilateral level, varies across bilateral pairs, exhibits some variation over time and, importantly, is reflective of trade policy. Rev Int Ecom. 2019;27: wileyonlinelibrary.com/journal/roie 2018 John Wiley & Sons Ltd 367

2 368 KHAREL A key concern in estimating the trade effects of FTAs is endogeneity. A traditional source of endogeneity is selection: the existence of unobservables that influence both the signing of FTAs and trade flows, and the possibility of reverse causality (e.g., country pairs that have a high level of trade may be entering into FTAs). The literature on the determinants of FTA formation provides robust evidence of the endogeneity of FTAs to trade flows for example, Baier and Bergstrand (2004), Magee (2003), Baier, Bergstrand, and Mariutto (2014b) and Bergstrand, Egger, and Larch (2016). A number of methods have been employed in the literature to deal with such endogeneity concerns. One approach is to use instrumental variables (IVs). A challenge this approach faces is to find a valid instrument, that is, a variable that is not only strongly related to the FTA variable but affects the outcome of interest only through the FTA variable. To avoid relying solely on functional form for identification in their non linear model, Egger, Larch, Staub, and Winkelmann (2011), for example, use as instruments three dummies denoting whether a country pair has ever had a common colonizer, has ever been in a colonial relationship and has ever been part of the same country. Another route is to use matching econometrics, as used by, among others, Baier and Bergstrand (2009a) and Egger, Egger, and Greenaway (2008). Matching methods assume selection on observables. A third approach is the use of panel data econometrics. Exploiting panel data on trade flows and FTA formation, papers in this mold use country pair fixed effects to account for pair level selection into FTAs, assuming that time varying bilateral unobserved heterogeneity is orthogonal to the FTA variable. Since Baier and Bergstrand (2007), there has been a wave of empirical studies on the trade effects of FTAs using the panel estimation approach for example, Eicher and Henn (2011), Behar and Cirera i Crivillé (2013), Dahi and Demir (2013), Baier, Bergstrand, and Feng (2014a), Bergstrand, Larch, and Yotov (2015) and Anderson and Yotov (2016) making it the most established method in this line of literature. A common finding is that FTAs do increase trade substantially, albeit with heterogeneous effects. Although a variety of methods have been brought to bear on the selection issues around the age old topic of FTA trade relationship, an additional source of endogeneity remains ignored. It arises from the general equilibrium structure of the gravity model, as demonstrated in Egger and Nigai (2015). In this paper, I show that ignoring this endogeneity substantially biases the effect of FTAs on trade. To understand the source of this bias, first note that the error term in a panel gravity equation can be decomposed as a sum of (i) bilateral country pair fixed effects, which capture pair specific timeinvariant heterogeneity, including time invariant bilateral trade costs; (ii) importer year fixed effects; (iii) exporter year fixed effects; and (iv) residual or unobserved trade costs. The inclusion of pair fixed effects speaks to the traditional endogeneity of FTAs discussed earlier, while the use of exporter year and importer year fixed effects controls for multilateral resistance and other country time specific factors. 2 As Egger and Nigai (2015) show, the country time specific factors are themselves endogenous to residual trade costs. In a general gravity context, this endogeneity arises from the market clearing general equilibrium structure underlying a gravity equation. Just as general equilibrium linkages yield the now well appreciated importance of multilateral resistance, the same linkages also imply that the country time specific factors are a function of, inter alia, residual trade costs. Egger and Nigai (2015) demonstrate that this leads to biased estimates of total bilateral trade costs, country specific effects and the partial effects of observable trade cost measures, while also biasing general equilibrium consistent comparative statics. They suggest a two step remedy to this problem: first obtain unbiased measures of total trade costs from a constrained ANOVA type (CANOVA) estimation of the gravity model 3 and then decompose them into their individual observable components. To what extent residual trade cost bias is reflected in estimates of FTA effects arguably the most prominent policy effect analyzed with a gravity model is the primary empirical question that I attempt to answer. In their empirical illustration, Egger and Nigai (2015) take a balanced sample of manufacturing trade flows in 31 OECD countries for the year 2005 and compare the estimates from

3 KHAREL 369 a standard, single step gravity equation with those from the proposed two step method. They find differences between the two sets of point estimates but do not formally test for statistical significance. Crucially, they do not tackle the usual endogeneity concern associated with estimating FTA impacts, as it is not their focus. Therefore, the empirical relevance of residual trade cost bias emphasized in Egger and Nigai (2015) merits further investigation in the context of FTAs. To do so, I estimate the partial effects of FTAs using panel data techniques, as in Bergstrand et al. (2015), but embed them in the two step CANOVA approach of Egger and Nigai (2015). The dataset, from Bergstrand et al. (2015), covers manufactures trade in eight sectors in 40 countries (OECD and some developing countries) and a rest of the world (RoW) aggregate for the years 1990, 1994, 1998, and The CANOVA method of obtaining unbiased total trade costs in the first step can be readily applied as the data include intranational trade flows. The panel structure of the data, coupled with the availability of intranational trade flows, enabled Bergstrand et al. (2015) to additionally assess the effects of international borders (the border effect ) and bilateral distance (the distance elasticity puzzle ) over time. I assess these also using the CANOVA approach. Additionally, I quantify how differences in partial equilibrium effects of trade costs (including but not limited to FTA formation) between the two methods translate into differences in general equilibrium (GE) effects. Comparing the results of the two step CANOVA approach with the standard panel technique based approach as in Bergstrand et al. (2015), which I dub the one step approach, I find evidence that the one step approach overestimates the partial effects of FTAs that entered into force during in overall manufactures by 31.6 percentage points (or 57 percent). At the sectoral level, I uncover heterogeneity across sectors in terms of the importance of residual trade cost bias when estimating the total, partial effects of FTAs. 4 More broadly, coefficients on trade cost variables FTA dummies (current and lagged), time interacted standard gravity covariates, time interacted international border dummies and time invariant bilateral trade costs captured by pair fixed effects are jointly significantly different between the two methods. Correlations between unobservable trade costs and country specific fixed effects provide additional evidence of residual trade cost bias. The two step method also confirms Bergstrand et al. s (2015) finding, based on the one step method, of the decline in the effect of the international border and of distance. While the GE effects of changes in trade costs, which account for changes in multilateral resistance and endogenous changes in incomes, being muted relative to partial effects is well recognized in the literature (see, e.g., Head & Meyer, 2014), it is not a priori clear how the differences in the partial estimates obtained from the one step standard method and the two step CANOVA approach play out when fed into the system of non linear equations representing structural gravity. I find that differences in partial effect estimates translate into non trivial differences in GE effects. In a globalization experiment, the difference in magnitude is on the order of a third for the entire world. Interestingly, the sign of the difference depends on the type of globalization considered. CANOVA estimates deliver lower GE effects than one step estimates when only the effect of FTA formation during is considered, and higher GE effects when broader globalization, inclusive of the declining effect of the international border and standard gravity covariates, is considered. This paper contributes to the empirical literature on the quantification of the trade effects of FTAs by accounting for a recently highlighted endogeneity in structural gravity estimation. 5 In a focused policy relevant empirical application of the CANOVA method developed in Egger and Nigai (2015), my results indicate that residual trade cost bias may be important for particular sectors in quantifying the trade effects of FTAs. Methodologically, to my knowledge this is the first paper that combines well established panel estimation techniques with the two step CANOVA method. 6 Baier and Bergstrand (2007) made it de rigueur to use pair fixed effects to account for the endogeneity of FTAs in a panel setting. Bergstrand et al. (2015), using panel data inclusive of intranational trade flows,

4 370 KHAREL emphasize the importance of including (time interacted) international border dummies in addition to pair fixed effects to get more reliable estimates of FTA effects. My findings are supportive of a case for embedding state of the art panel gravity estimation techniques that include international border dummies and pair fixed effects in a two step CANOVA approach to improve the reliability of the estimates. Additionally, this paper shows that the residual trade cost bias in partial effect estimates extends to general equilibrium effects based on those partial estimates. The rest of the paper is organized as follows. Section 2 discusses the methodology and the data. Section 3 presents the results. Section 4 concludes. 2 ESTIMATION TECHNIQUES AND ISSUES I embed the panel data gravity techniques used in Bergstrand et al. (2015) in the two step CANOVA approach of Egger and Nigai (2015). I first describe the panel techniques, and briefly discuss the data. I then explain residual trade cost bias, followed by an explanation of the CANOVA approach and a combination of the techniques. 2.1 Panel estimation techniques Bergstrand et al. (2015) estimate the following gravity equation: [ ] X = exp β 0 +FTA β 1 +INTER β 2 +GRAV β 3 +μ i,t +ζ j,t +φ ij +u (1) with i, j = 1, , t = 1990, 1994, 1998, where X is exports from country j to country i in year t; FTA is a vector of dummy variables capturing the current and lagged presence of an economic integration agreement between i and j in year t 7 ; INTER is a vector of the product of a year dummy (for 1994, 1998 or 2002, with 1990 as base year) and a time invariant binary variable, INTERNATIONAL ij, which takes the value 1 if i = j and 0 otherwise; GRAV is a vector of standard gravity variables (log of distance, contiguity, colonial relationship and common language) interacted with year dummies; μ i,t is an importer year fixed effect; ζ j,t is an exporter year fixed effect; φ ij is a bilateral (country pair) fixed effect 8 ; and u is an error. 9 Bergstrand et al. (2015) also interact the bilateral fixed effect, φ ij, with a time trend but find that the results are unaffected and hence focus their analysis on Equation (1). 10 Adding up the coefficients on all FTA dummies gives an estimate of the total partial effect of FTAs that came into effect during ,12 All data are from Bergstrand et al. (2015). 13 There are 40 countries and one RoW aggregate. Years span from 1990 through 2002, in four year intervals. Trade flows (international and intranational) are available for total manufactures and eight 2 digit ISIC sectors: food, textiles, wood, paper, chemicals, minerals, metals, and machinery. Table 1 provides some summary statistics of variables used in the estimation of Equation (1). A key reason for using this dataset is that it contains intranational trade flows in a sample that also includes non OECD countries. Data on intranational trade flows are a prerequisite to CANOVA estimation, while the presence of non OECD countries adds to the cross sectional and time variation in FTA, otherwise limited when using only an OECD sample. The sectoral disaggregation, albeit limited, is another attractive feature. In short, to my knowledge, this is the best available data for the research question at hand. 14

5 KHAREL 371 Equation (1) is estimated by Poisson Pseudo Maximum Likelihood (PPML) with standard errors clustered by country pair. Variants of the equation are also estimated with different combinations of regressors. Bergstrand et al. (2015) also estimate the model with OLS, but they prefer PPML estimation as it accounts for heteroskedasticity bias (Santos Silva & Tenreyro, 2006, 2011). 15 Bergstrand et al. (2015) summarize the key features of their preferred specification thus: exporterand importer year fixed effects that account for multilateral resistance and other time varying importer and exporter unobservables; country pair fixed effects or country pair fixed effects interacted with a time trend to account for unobserved time invariant or time varying bilateral effects, including pair specific initial border effect levels; international border dummies that account for possible average declining international relative to intranational bilateral trade costs; and PPML estimation to account for heteroskedasticity bias and zero flows. 2.2 Residual trade cost bias Notice that in Equation (1), where the trade costs are parameterized, the unobservable trade costs are partly captured by the pair fixed effects (φ ij ) and international border dummies (INTER ij, t ), but other time varying unobserved trade costs remain unmeasured, residual trade costs, absorbed into the error term. The latter cannot be avoided even by interacting the pair fixed effect with a trend. The pair fixed effect does not capture year specific asymmetric bilateral trade costs, for example. Even if the time varying unobserved trade costs were uncorrelated with the observed trade cost proxies, the total TABLE 1 Summary statistics Mean SD Min Max Trade flows, in billion US$ Total manufactures , Food Textiles Wood Paper Chemicals Minerals Metals Machinery , FTA t FTA t FTA t FTA t FTA t DIST*Year CNTG*Year LANG*Year CLNY*Year INTER*Year Notes. No. of observations = 6724.

6 372 KHAREL trade cost estimates as well as the partial effect estimates would still be biased since the unmeasured trade costs would still be correlated with the exporter and importer specific variables (fixed effects) through general equilibrium constraints. 16 This is the key insight from Egger and Nigai (2015). Let s clarify it further, drawing on Egger and Nigai (2015). In a typical gravity framework, on which Equation (1) is based, bilateral imports of country i from j at time t can be expressed as: X = exp(ζ j,t +δ +μ it ), (2) where δ represents country pair time specific trade costs and ζ j,t and μ i,t are, respectively, exportertime and importer time specific variables. δ can be interpreted as δ σ ln τ where τ is ad valorem trade costs, and σ<0 is the partial effect of bilateral trade costs or trade elasticity. ζ j,t and μ i,t are implicit functions of bilateral trade costs through the resource constraint (with deficit parameter D j,t ): J J X = X ji,t +D j,t. i=1 i=1 (3) The structural country time parameters can be expressed as: exp ( ζ j,t ) = J i=1 exp ( ζ i,t +δ ji,t +μ j,t ) +Dj,t J i=1 exp(δ +μ i,t ), exp ( J ) j=1 μ exp ( ) ζi,t +δ ji,t +μ j,t Di,t i,t = J j=1 exp(δ +ζ j,t ). (4) Empirical specifications, such as Equation (1), typically decompose δ as: K δ = o +u = β k o k, +u, k=1 (5) where o is a parameterized observable component, u is an unobservable component, and K denotes the number of observables behind o. To illustrate, in Equation (1), o = FTA β 1 +INTER β 2 +GRAV β 3 +φ ij.17 Equation (2) is then expressed as: X = exp ( ζ j,t +o +μ i,t +u ). (6) This can be rewritten as: X = exp ( ζ j,t +o +μ i,t ) exp(u ), (7) and country specific terms are either solved iteratively as implicit functions of o or estimated as fixed effects. PPML estimation of Equation (6) is based on the assumption: E [ exp ( u ) ζj,t,o k,,μ i,t ] = 1, or E [ exp ( u ) 1 ζj,t,o k,,μ i,t ] = 0 As Egger and Nigai (2015) point out, it is clear from the GE constraints in (4) that the country specific terms are not independent of residual trade costs. Hence, E [ exp ( u ) 1 ζj,t ] 0 and

7 KHAREL 373 E[exp(u ) 1 μ i,t ] 0, thereby biasing the estimates of ζ j,t, μ i,t and δ. As a result, comparative static exercises are also biased (e.g., gauging the contribution of trade costs to changes in trade flows). They further show that estimates of the partial effects, β k, are biased. The independence of an observable trade cost measure from unobservable trade costs is not sufficient for estimating the partial effect of the measure without bias: it has to be independent also of the bias in the estimated country specific effects. The latter is not the case, due to the GE constraints in (4) (Egger and Nigai, 2015). 2.3 CANOVA approach I apply a remedy to the residual trade cost bias proposed by Egger and Nigai (2015) to the estimation of specification (1). The two step approach first involves obtaining unbiased estimates of trade costs δ through the CANOVA method. This method uses, for each period, J 2 observations on aggregate bilateral sales underlying Equation (2), of which 2J degrees of freedom are used by the constraints in Equation (4). As a result, J(J 2) values of δ ij are identifiable for each year. Intranational trade costs are normalized to zero (δ jj = 0) for each year. The δ ij s thus obtained are unbiased since all trade costs parameterized as well as residual are always treated jointly and properly accounted for (Egger and Nigai, 2015). 18 I obtain δ, separately for each t (1990, 1994, 1998, 2002), for aggregate manufacturing trade as well as for disaggregated manufacturing trade for eight 2 digit ISIC sectors. 19 The CANOVA method does not deliver finite values for δ when trade is zero. So I estimate a lower bound of trade costs for zero trade observations as the maximum (relative) level of trade costs obtained for country pairs with non zero trade flows. 20 Zero trade flows are not highly prevalent in the dataset: in total manufactures, the share of zero trade flows in the total number of observations is 1.3 percent, and at the sectoral level it is 5.8 percent (food), 4.5 percent (textile), 13 percent (wood), 12.4 percent (paper), 5.3 percent (chemicals), 11.5 percent (minerals), 13.4 percent (metals) and 3.2 percent (machinery). Reassuringly, excluding zero flows does not materially change the results of the paper, either at the aggregate level or the sectoral level. The second step decomposes δ into their individual components. In my application, I use exp(δ ) following Egger and Nigai (2015) in their empirical illustration as a dependent variable in Equation (1) and its variants, and estimate it by PPML. 21 The estimating equation in the CANOVA second step is thus: [ ] exp(δ ) = exp β 0 +FTA β 1 +INTER β 2 +GRAV β 3 +μ i,t +ζ j,t +φ ij +u. (8) I call direct estimation of (1) as done by Bergstrand et al. (2015) and which I also reproduce the one step approach, to contrast it with the CANOVA approach that involves two steps. Notice that while the use of the CANOVA based unbiased estimates of δ in the second step avoids the bias stemming from the correlation between observable trade costs and the bias in country specific structural parameters due to residual trade cost bias, the use of panel estimation techniques in the second step helps mitigate the usual endogeneity concerns applicable to FTAs; for example, selection of country pairs into FTAs. Table 2 provides summary statistics of the dependent variables used in the two approaches. Although the absolute levels of δ are not identified from the CANOVA approach, their relative level or variation is (Egger & Nigai, 2015). In a regression, it is the variation in δ that is exploited. If there were no residual trade cost bias, the two methods would yield similar estimates of the partial effects of observable trade costs. Estimation is done for total manufactures trade as well as for manufactures trade disaggregated into eight sectors. The difference between the coefficients from the two

8 374 KHAREL approaches is tested statistically in a seemingly unrelated estimation framework. This ensures that the test statistics have the correct size, by accounting for the possible dependence between the two sets of coefficients. 22 To understand why the coefficients from the second step in the CANOVA approach and from the one step approach can be compared although the dependent variables are different (exp ( ) δ vs X ), recall that δ σ ln τ, where τ is ad valorem trade costs. This implies that the dependent variable in the CANOVA second step is exp(δ ) = τ σ. For expositional purposes, let s consider a cross sectional setting and assume τ ij = d ρ ij bfta ij exp(uij ), where d ij is distance, u ij is unobserved trade costs, and ρ and b are parameters. It is standard to express a theory consistent multiplicative gravity equation as X ij = exp(σρln d ij +σ ln b FTA ij +μ i +ζ j +u ij ), (9) TABLE 2 Summary statistics of dependent variables Mean SD Min Max Total manufactures Trade , exp(δ) < Food Trade exp(δ) < Textiles Trade exp(δ) < Wood Trade exp(δ) < Paper Trade exp(δ) < Chemicals Trade exp(δ) < Minerals Trade exp(δ) < Metals Trade exp(δ) < Machinery Trade , exp(δ) < Notes. No. of observations = 6724; trade is in US$ billion. See section 2.3 for details about computation of δ.

9 KHAREL 375 to be estimated with PPML, where μ i and ζ j are importer and exporter specific fixed effects, measuring country specific factors influencing trade, including multilateral resistance. This is the estimating equation in the one step approach. To get the estimating equation for the CANOVA second step, first use the definition of the ad valorem trade cost: τ ij = d ρ ( ) ( ) ij bfta ij exp uij = exp [ln d ρ ij bfta ij exp ( ) ] u ij = exp(ρ ln d ij +ln b FTA ij +u ij ). τ σ = exp(σρln d ij +σ ln b FTA ij +u ij ), where, with a slight abuse of notation, u ij also absorbs the multiplicative elasticity parameter. We can decompose the unmeasured trade cost, u ij, as u ij = ũ i +ũ j +ũ ij, where ũ i and ũ j can be captured by importer and exporter specific fixed effects. We now have the estimating equation for the CANOVA second step: exp(δ ij ) τ σ = exp(σρln d ij +σ ln b FTA ij +ũ i +ũ j +ũ ij ), (10) Clearly, the coefficients on log of distance and FTA are measuring the same object in the two approaches (Equations (9) and (10)). Under both methods, they represent the elasticity of ad valorem trade costs with respect to observable trade costs multiplied by the elasticity of trade flows with respect to ad valorem trade costs. 3 RESULTS 3.1 Partial equilibrium Focusing on the partial estimates, I first present broad similarities between the findings from the single step method as used in Bergstrand et al. (2015) and the two step CANOVA method. Including time varying international border variables reduces the total partial effect of FTA by over a half. There is a declining effect of the international border between 1990 and In specifications that include interactions of year dummies with the log of distance, a common language dummy, a contiguity dummy and a colonial relationship dummy, in addition to the time varying international border variables, these standard gravity covariates have mostly no significant effect on trade flows. There is a decline in the trade reducing effect of distance over time in general mirroring a fall in bilateral fixed and variable costs. 23 Online Appendix Tables A1 A14 present detailed results from the two approaches. Now let s focus on the total, partial effects of FTA obtained from the two methods. Table 3 provides a summary by comparing the total, partial effects of FTA obtained from the two approaches across different specifications, along with statistical tests of difference. 24 In specifications that have neither the border variable nor standard gravity covariates (panel 1), the differences in the estimates from the two methods are statistically significant for total manufactures, textiles, wood, paper, minerals, and metals. The one step method overestimates in total manufactures (by 41 percentage points or 35 percent), textiles (226 percentage points or 119 percent), minerals (23 percentage points or 80 percent) and metals (65 percentage points or 61 percent), and underestimates in wood (36 percentage points or 65 percent) and paper (53 percentage points or 56 percent). When one throws in the border

10 376 KHAREL variables (panel 2), the statistical significance of the difference between the two sets of estimates of FTA effects disappears for all but two sectors: textiles and paper, with the direction of bias as before. Theoretically, the differences between the estimates from the one step approach and the CANOVA approach arise from the failure of the one step approach to account for all trade costs, a problem avoided by the CANOVA approach in the first stage estimation of trade costs where all trade costs are fully and jointly accounted for. The inclusion of the border variables, by capturing changes in international relative to intranational trade costs that are otherwise unobserved, seems to mitigate this problem for total manufactures and all sectors except textiles and paper. This suggests that the inclusion of border variables is not sufficient enough to address residual trade cost bias in the latter two sectors. In specifications that include both the border variables and standard gravity covariates (panel 3) that is, the full specification as used in Bergstrand et al. (2015) the total, partial FTA estimates from the two approaches are statistically different for in addition to textiles and paper total manufactures (overestimation), chemicals (overestimation) and machinery (overestimation). In specifications that exclude the border variables but include standard gravity covariates (panel 4), the differences are statistically significant for total manufactures and chemicals, besides textiles and paper. The estimates of the coefficient on INTER 2002 (see Appendix Tables A5 A12), which captures the changes in the effect of the international border between 1990 and 2002, are not robustly statistically different between the two methods across different specifications, suggesting residual trade cost bias may not be affecting estimates of the declining effect of the international border. 25 While both sets of results show a declining effect of distance (see Appendix Tables A13 A14), they are not statistically different for total manufactures and most sectors barring wood, minerals and metals. 26 In the wood sector, the one step method shows no decline in the negative distance effect whereas the two step method delivers a decline in the negative distance effect of 10.6 percent over 12 years, or 0.93 percent per year. In minerals, the two step method shows no decline, whereas the one step method indicates a decline of 5.2 percent over 12 years, or 0.44 percent per year. In metals, the two step method shows no decline, whereas the one step method delivers a decline of 11.4 percent over 12 years, or 1 percent per year. What do the residual trade costs represent? They capture, for example, bilateral asymmetric trade costs that vary over time, ranging from non tariff measures to transport costs, some of which may differ across sectors and also result from agreement specific features. Because residual trade cost bias arises from non linear general equilibrium constraints, which make exporter( time) and importer( time) specific factors functions of residual trade costs, it is not straightforward to pin down the direction of bias a priori. Investigating the exact forces that drive these biases, which differ in direction and magnitude across sectors, is left for future work. 3.2 Testing differences in multiple trade cost variables I also test whether the coefficient estimates on different trade cost measures are jointly significantly different between the two approaches. The rationale for the joint tests is that statistical (in)significance in the difference between the effects of individual trade cost measures need not imply statistical (in) significance in the difference between their joint effects. The idea, therefore, is to gauge whether various trade cost variables jointly exert statistically different effects on trade flows across the two methods. To illustrate, the null hypothesis for the joint tests is H o :TC One-step = TC CANOVA, where TC is a vector of estimated coefficients on trade cost measures considered. I consider the full specification that includes border variables as well as standard gravity covariates. The p values of the tests are presented in Table 4. The first panel refers to the joint test of FTA dummies. 27 The p values indicate that the FTA dummies are jointly significantly different between the

11 KHAREL 377 TABLE 3 Comparison of estimates of total, partial FTA effects from one step and CANOVA approaches Total Food Textiles Wood Paper Chem. Minerals Metals Machin. No border, no gravity vars One step CANOVA p val < Difference in % points Difference in percentage With border, no gravity vars One step CANOVA p val Difference in % points Difference in percentage With border, gravity vars One step CANOVA p val Difference in % points Difference in percentage (Continues)

12 378 KHAREL TABLE 3 (Continued) Total Food Textiles Wood Paper Chem. Minerals Metals Machin. With gravity vars, no border One step CANOVA p val Difference in % points Difference in percentage a Notes: One step and CANOVA are the sum of coefficients on current and lagged FTA dummies from respective estimations: Equations (1) and (8). Full estimation results are in the Appendix: Panel 1 is based on Tables A1 A4; Panel 2 on Tables A5 A8; Panel 3 on Tables A9 A12; Panel 4 on Tables A13 A14. b+ p value of test of difference of one step and CANOVA total, partial effect estimates. c++ [exp(one step) 1] 100 [exp(canova) 1] 100. d *[{[exp(one step) 1]/ [exp(canova) 1]} 1].

13 KHAREL 379 two approaches for total manufactures, wood, paper, chemicals, minerals, and machinery. The second panel indicates that the FTA dummies, border variables and all standard gravity covariates are jointly significantly different between the two methods for total manufactures as well as all sectors. The third panel refers to the joint test of total FTA effect (instead of individual FTA dummies), border variables and all standard gravity covariates. The differences are jointly statistically significant for all sectors but paper. The fourth panel tells us that the bilateral pair fixed effects, which capture time invariant bilateral trade costs, are jointly significantly different for total manufactures and all sectors between the two methods. The fifth panel indicates that, for total manufactures and all sectors, the pair fixed effects, FTA dummies, border variables and all standard gravity covariates are jointly significantly different between the two methods. The last panel suggests that, for total manufactures and all sectors, the pair fixed effects, total FTA effect, border variables, and all standard gravity covariates are jointly significantly different between the two methods. 3.3 Another test of importance of residual trade cost bias The analysis above operated on the logic that significant differences between the partial estimates obtained from the two methods indicate residual trade cost bias. Since, theoretically, residual trade cost bias in the usual one step method arises from the linkages between residual trade costs and countryspecific effects, another way to gauge this endogeneity is to look at the associations between residual trade costs and exporter year and importer year fixed effects. Recall the estimating equation from the one step method (Equation (7): X = exp ( ζ j,t +o +μ i,t ) exp(u ). In our sample, we test the following conditions: [ ( ) COV exp [ ( COV exp û CANOVA û CANOVA ] 1, ζ One-step = 0 and j,t ) ] 1,û One-step = 0. i,t (11) TABLE 4 P values of joint test of significance of differences between one step and CANOVA estimates Total Food Text. Wood Paper Chem. Minerals Metals Machin. FTA dummies < < FTA dummies, border variables, and all other gravity variables < <0.001 <0.001 < < <0.001 Total FTA effect, border variables, and all other gravity variables < <0.001 < <0.001 Pair fixed effects <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Pair fixed effects, FTA dummies, border variables, and all other gravity variables <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 Pair fixed effects, total FTA effect, border variables, and all other gravity variables <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

14 380 KHAREL A violation of any of these conditions implies that exp ( u ) 1 is not independent of ζj,t and μ i,t, which is the population moment condition discussed in Section 2.2. The conditions in (11) can be tested as we can obtain estimates of residual trade costs, u, from the CANOVA approach. More precisely, one can obtain estimates of residual trade costs using Equation (5): û CANOVA = δ CANOVA ô CANOVA, where ô CANOVA = FTA β CANOVA +INTER 1 β CANOVA +GRAV 2 β CANOVA + φ CANOVA 3 ij Note that δ CANOVA is obtained from CANOVA first stage and ô CANOVA from CANOVA second stage. Notice that φ CANOVA, the estimated pair fixed effects, are part and parcel of the observed trade ij costs in our model since they capture all time invariant symmetric bilateral trade costs, including initial border [ effects. ( ) ] [ ( ) ] COV exp û CANOVA 1, ζ One-step 0 and/or COV exp û CANOVA 1,û One-step 0 would imply j,t i,t that the fixed effects are endogenous to residual trade costs. Table 5 shows the coefficients of these correlations, as well as between û CANOVA and ζ One-step and between û CANOVA and μ One-step. Focusing on ( ) j,t i,t the correlation between exp û CANOVA 1 and the fixed effects, we see that it is highly statistically significant with respect to the exporter fixed effect ( ζ One-step ), with coefficients ranging from 0.12 for j,t wood to 0.26 for total manufacturing to 0.32 for food. The correlation with respect to the importer fixed effect ( μ One-step ) is negative and statistically significant for total manufacturing and all sectors, i,t but weaker compared to the correlation with respect to the exporter fixed effect. Overall, these correlations provide further evidence of residual trade cost bias in total manufacturing as well as in almost every sector. 3.4 General equilibrium Given that the coefficients on all trade cost variables are jointly significantly different between the two methods for total manufactures, it is interesting to investigate the implications of these differences in partial effect estimates for the general equilibrium (GE) effects of globalization. Partial estimates of trade cost effects do not incorporate the changes in multilateral resistance and endogenous changes in income triggered by a change in trade cost. The need to do so is increasingly recognized in the gravity literature (see Head & Mayer, 2014). The GE consistent counterfactual analysis in Egger and Nigai (2015) seeks to gauge the contribution of changes in total trade costs to changes in observed trade flows between two periods (t 1 and t 2 ), whereby the change in total trade costs is given by Δδ ij = δ 1 δ 2. In contrast, the aim here is to quantify the effect of a change in an observable trade cost variable (e.g., FTA formation) on trade flows, which necessitates the use of a parameterized trade cost function for counterfactual analysis. 28 The idea is to ascertain to what extent differences in the partial estimates obtained from the onestep standard method and the two step CANOVA method yield different GE effects when these estimates are fed into the system of non linear equations representing structural gravity. Consequently, I follow a standard approach based on an endowment economy trade model (as described in Head and Mayer, 2014) 29 in computing two measures of GE effects using one step and CANOVA estimates separately: the modular trade impact (MTI) that accounts for changes in multilateral resistance (MR) but ignores changes in incomes; and the general equilibrium trade impact (GETI) that accounts for changes in both MR and incomes. 30 While the details of MTI and GETI computation are described

15 KHAREL 381 TABLE 5 Correlations between residual trade costs and exporter, importer fixed effects Total Food Textiles ζ One-step j,t μ One-step i,t ζ One-step j,t μ One-step i,t û CANOVA exp(û CANOVA ) 1 û CANOVA exp(û CANOVA ) 1 û CANOVA Wood Paper Chemicals û CANOVA exp(û CANOVA ) 1 û CANOVA exp(û CANOVA ) 1 û CANOVA Minerals Metals Machinery exp(û CANOVA ) 1 exp(û CANOVA ) 1 ζ One-step j,t μ One-step i,t û CANOVA exp(û CANOVA ) 1 û CANOVA exp(û CANOVA ) 1 û CANOVA Notes. All correlations are significant at 1% level. See text for details. exp(û CANOVA ) 1 in Head and Mayer (2014), an intuitive way to understand these measures is that they are the partial effect estimate multiplied by a factor representing changes in, respectively, MR and MR cum incomes induced by changes in trade costs. For a comparison with the analysis in Bergstrand et al. (2015), I also compute the so called partial trade impact (PTI) that potentially varies across countries but ignores changes in MR and incomes. 31 Globalization is defined in two ways, in the spirit of Bergstrand et al. (2015). First, the formation of FTAs between 1990 and Second, as in Bergstrand et al. (2015), the formation of FTAs between 1990 and 2002 and the changes in the effects of international borders and standard gravity covariates (distance, colonial relationship, language, and contiguity) observed during the same period. Under both definitions, observed trade costs are those prevailing in Under the first definition, the FTA variables are switched off in the counterfactual equilibrium, while bilateral pair fixed effects and time interacted international borders and standard gravity covariates are common to both observed and counterfactual equilibria. Under the second definition, the FTA variables and time interacted international borders and standard gravity covariates are switched off in the counterfactual equilibrium, while bilateral pair fixed effects are common to both observed and counterfactual equilibria. Tables 6 and 7 show the PTI, MTI and GETI for individual countries and RoW as well as (weighted) averages for three groups: the world, country pairs that have entered into an FTA and country pairs that have never entered into an FTA. The MTI and GETI are substantially lower than the PTI with both CANOVA and one step estimates under both counterfactual exercises (Tables 6 and 7). This is not surprising. We know since Anderson and van Wincoop (2003) and, more recently, from Behar and Nelson (2014) that multilateral resistance serves to mute the effects of trade liberalization when carried out on a global scale. Of more relevance to our context, there are differences in the MTI and GETI resulting from the two sets of estimates. Interestingly, the sign of the differences depends on the definition of globalization employed. When only the effects of the formation of FTAs are considered, the PTI, MTI, and GETI all are lower when CANOVA partial estimates are used instead of one step partial estimates (Table 6). For example, the PTI, MTI, and GETI of FTA formation are lower in magnitude by a quarter to a third in the aggregate, whether considering the world as a whole,

16 382 KHAREL or country pairs that entered into FTAs, or country pairs that did not enter into FTAs. At the country level, all three measures are lower for most countries when based on CANOVA estimates. In contrast, when the broader definition of globalization is used (Table 7), all three measures are higher, for almost all countries, when computed with CANOVA estimates. When using CANOVA estimates, the MTI and GETI are higher by a third for the world as a whole, and higher by 50 percent for country pairs that did not enter into FTAs, although higher by barely 7 percent for country pairs that formed FTAs. An explanation for the difference in the results between the two types of globalization experiments is as follows: In the broader globalization experiment, both (i) FTA formations and (ii) changes in the effects of international borders and gravity covariates are happening, such that CANOVA partial estimates of the latter set of effects appear to be more than offsetting the lower CANOVA partial estimates of FTA formations alone. 33 The method of GETI computation yields as a by product, for each country i, the change in its share of expenditure on domestically produced goods, π ii, resulting from the change in trade costs. This and the trade elasticity parameter, σ, have been shown to be sufficient statistics for the calculation of gains from trade in a fairly broad class of quantitative trade models utilizing the gravity equation (Arkolakis et al., 2012; Costinot & Rodríguez Clare, 2014). Welfare associated with the formation of FTAs or globalization (inclusive of FTAs) in a one sector model, such as ours when we consider only 1 σ total manufactures, is given by a simple formula: π. Unlike trade effects, stark differences are not ii found between the welfare numbers computed using one step and CANOVA estimates, under either definition of globalization. For example, when only the effect of FTA formation is considered, the median welfare change for the world is percent and percent, respectively, with CANOVA and one step estimates. 34 When broader globalization is considered, the median welfare change for the world is percent with CANOVA estimates and percent with one step estimates. 35 An explanation for the modest differences in welfare change despite non trivial differences in the change in cross border trade could be the presence of an offsetting difference in the change in internal trade flows. Note that although internal trade costs are assumed zero, international trade cost changes affect not just cross border trade but also internal trade by changing relative trade costs. One must not, however, read too much into these welfare numbers. Simple as the welfare formula is, it assumes trade costs to be exclusively of the non revenue generating iceberg type, whereby welfare change is a function of terms of trade alone and changes in tariff revenue are not accounted for. An adjusted formula incorporates changes in tariff revenue (Costinot & Rodríguez Clare, 2014, p. 227), but data limitations preclude its use here CONCLUSION This paper revisits a prominent gravity model based empirical literature on the effects of FTAs by accounting for residual trade cost bias that standard gravity equations with parameterized trade cost functions ignore, as shown in Egger and Nigai (2015). I estimate the partial effects of FTAs using panel estimation techniques, as in Bergstrand et al. (2015), but embed them in the two step CANOVA approach proposed by Egger and Nigai (2015) to address a bias that would otherwise arise from the correlation of observable trade cost measures with the bias in country specific structural parameters. I find that the conventional one step approach overestimates or underestimates the total, partial effects of FTAs during by up to 110 percent. The importance of such residual trade cost bias varies across sectors. There is also evidence that coefficients on trade costs variables are jointly significantly different between the two methods. Correlations between unobservable trade costs and country specific fixed effects provide additional evidence of residual trade cost bias.

17 KHAREL 383 TABLE 6 GE effects of FTA formation (% change) One step CANOVA PTI MTI GETI Welfare PTI MTI GETI Welfare World a FTA b No FTA c Asia AUS CHN ISR JPN KOR TUR Europe AUT Latin America BGR BLX CHE DEU DNK ESP FIN FRA GBR GRC HUN IRL ISL ITA NLD NOR POL PRT ROM SWE ARG BOL BRA CHL COL CRI ECU MEX URY (Continues)