On the widely differing effects of free trade agreements: Lessons from twenty years of trade integration

2.1. Structural gravity

Our starting point is a simple, generalized version of the “structural gravity” equation, as originally derived by Anderson (1979) and as popularized by Eaton & Kortum (2002) and Anderson & van Wincoop (2003) and subsequently extended to the panel dimension by Baier & Bergstrand (2007).⁷ Let X_ij denote the value of exports from an origin country i to a destination country j. The gravity equation for these trade flows is

In (1), E_j is the total expenditure by purchasers in j on goods across all different origins (including goods produced domestically in j). The share of j’s expenditure allocated specifically to products from any one origin i is then directly dependent on the following three factors: A_i, the overall quality of the production technologies available in i; w_i, the wage in i; and τ_ij, the “iceberg” trade cost required to send goods from i to j. Goods from different origins are assumed to be imperfectly substitutable; therefore, the effects of production costsand trade costs on trade are subject to a constant trade elasticity θ > 1. Importantly, all cost factors only weigh on trade relative to the overall degree of competition in j’s import market, which is accounted for via the summation term in the denominator of (1). Noting that this summation term is specific to the importing country (because it sums across all origins), a more compact way of writing (1) is

where P_j^−θ = ∑_iA_iw_i^−θτ_ij^−θ. As noted by Anderson & van Wincoop (2003), P_j^−θ serves as a useful aggregate of all bilateral trade costs faced by consumers in importer j.⁸ Writing the structural gravity equation as in (2) – with distinct i, j, and i-by-j components – lends itself naturally to deriving a “fixed effects” estimation equation for trade flows, as we demonstrate below.

2.2. Panel econometric implementation

From an empirical perspective, our primary object of interest is the combined trade frictions parameter τ_ij^−θ. We are not, however, interested in the general determinants of trade frictions -e.g., geographical distance, historical affinities, etc. – which have been widely explored in the broader gravity literature.⁹ Rather, we wish to focus on how FTAs have shaped changes in τ_ij^−θ over time. More specifically, we aim to shed light on how different agreements have had very different effects on τ_ij^−θ and, furthermore, how changes in τ_ij^−θ may vary widely even within the same agreement.

Our first step in this direction is to follow Baier & Bergstrand (2007) in deriving a panel implementation of (2) that permits identification of an average FTA effect across all the agreements in our sample. To ease this derivation, we first add a time subscript, t, as well as an error term, ε_ij, t, and re-write (2) in exponential form:

Next, use the following generic functional form for the trade costs term lnτ_ij, t^−θ

where Z_ij can be thought of a set of time-invariant controls for the general level of trade costs between i and j with coefficient vector δ. For more traditional gravity applications, the contents of Z_ij would normally be specified to include geographical and/or historical ties between countries, as discussed above. For our purposes, however, the main variables of interest are FTA_ij, t, a 0/1 indicator for if i and j belong to a common free trade agreement at time t, and FTA_ij, t−5, a 5 year lag of FTA_ij, t. The inclusion of this lagged term accounts for the possibility that FTA effects may “phase-in” over time, as has been previously shown by such papers as Baier &Bergstrand (2007) and Anderson & Yotov (2016).¹⁰

A concern that arises is that there are components of Z_ij that are unobserved and correlated with FTAs, and not accounting for these factors will result in biased coefficient estimates. A key insight from Baier & Bergstrand (2007) is that specific knowledge of δ is neither necessary nor sufficient in order to obtain consistent estimates of the effects of FTAs. Instead, drawing on standard panel estimation techniques described in Wooldridge (2002), Baier & Bergstrand (2007) recommend using pair-specific fixed effects in place of Z_ijδ, such that the time dimension of the panel identifies the (average) causal effect of FTAs on trade. With this same strategy in mind, our baseline specification for estimating the average effect of FTAs on trade barriers becomes

Here, η_i, t and ψ_j, t are, respectively, time-varying exporter- and importer- fixed effects meant to absorb the lnA_i, tw_i, t^−θ and lnE_j, t/P_j, t^−θ terms in (3), which are endogenous and cannot be observed directly. In addition, η_i, t and ψ_j, t also effectively control for all country-level factors on the exporter and on the importer side, respectively. γij¯ is a (symmetric) pair-wise fixed effect that strips out all time-invariant determinants of trade barriers between i and j.¹¹ Lastly, we treat the additive residual term ε_ij, t as both reflecting measurement error in trade values as well as now also absorbing the error term in lnτ_ij, t^−θ above. Following the recommendations of Santos Silva and Tenreyro, 2006, Santos Silva and Tenreyro, 2011, we estimate (4) – as well as all subsequent specifications described in this section – using Poisson Pseudo-maximum Likelihood (“PPML”).¹²

We obtain our final baseline specification for estimating the effects of FTAs by incorporating the methods of Bergstrand et al. (2015), who argue that FTA estimates based on specification (4) may be biased upward because they may be capturing the effects of globalization. Adapting a related idea from Yotov (2012), the simple adjustment proposed by Bergstrand et al. (2015) is to explicitly control for the effects of globalization in the gravity model by introducing a set of globalization dummies.

Applied to our setting, this adjustment results in the following econometric model:

where the added term ∑_tb_t is a set of dummies that equal 1 for international tradeobservations (as opposed to internal trade, X_ii) at each time t. The coefficients on these time-varying border dummies, the b_t’s, capture the process of globalization over time, as all countries trade more with each other and less with their own internal markets.

The average “total” (or “cumulative”) effect of FTAs on trade after accounting for phasing-in can be constructed as β ≡ β₁ + β₂. The specific interpretation of β can be described in one of two ways. From a strictly econometric point of view, β is the total average partial effect of an FTA on bilateral trade flows, noting that FTAs also influence trade through the country-specific terms η_i, t and ψ_j, t. A second, more structural interpretation is that β gives the average treatment effect of an FTA specifically on “trade costs” -i.e., its effect on the lnτ_ij, t^−θterm in (3). To ease this latter interpretation, note that the combined term expγij¯+bt+β1FTAij,t+β2FTAij,t−5 describes the predicted level of τ_ij, t^−θ in place between countries i and j at time t. To comment more thoroughly on the identification of β, note that increases in trade between i and j do not translate directly to implied reductions in the trade cost term lnτ_ij, t^−θ. Instead, due to the presence of the time-varying exporter and importer fixed effects, the impact of FTAs is only identifiable when trade increases between iand j relative to each country’s trade with all other partners. Importantly, and consistent with theory, the set of outside partners for each country includes the value for X_ii, the value of sales to one’s own market, or “internal trade”. We regard accounting for internal trade as a key feature of our empirical approach. As documented empirically in Dai et al. (2014), including internal trade in the estimation should lead to larger, more precise estimates of FTA effects.¹³

2.3. Allowing for FTA heterogeneity

With the wide adoption of Baier & Bergstrand’s methods, most estimates of the effects of FTAs in the prior literature generally find positive and significant “average” results.¹⁴However, for the purposes of policy analysis, an obvious weakness of estimating an “average” FTA effect is that the effects of a given agreement may be substantially different from the average; thus, it may not be appropriate to apply an average estimate of the effects of all existing FTAs for making ex ante predictions about the effects of specific FTAs. To capture and analyze this potential heterogeneity in FTA effects, we expand on the initial specification shown in (5) in three successive steps:

First, we consider a specification where FTA effects are allowed to vary at the level of the underlying agreement, similar to the approach taken in Kohl (2014)¹⁵:

where we allow for a distinct average partial effect –β_A ≡ β_1, A + β_2, A– for each individual agreement, using superscript A to index by agreement and also allowing for agreement-specific lags. This initial refinement allows us to make useful statements about which FTAs in our sample have been more successful than others about promoting trade. However, it is silent about the possibility that the same agreement may not affect all countries involved in exactly the same way.

Second, we allow for further heterogeneity at the level of each trading pair within an agreement. For example, we allow Sweden’s accession to the E.U. in 1995 to have different effects on its trade barriers with Germany vs. its trade barriers with the U.K. The resulting specification is

where each p ∈ A is a pair of countries (i, j) belonging to agreement A, counting (i, j) and (j, i) as the same pair. β_A:p ≡ β_1, A:p + β_2, A:p then gives us a corresponding set of agreement-pair-specificFTA estimates.

Third, we consider the possibility that, even within a given pair, an FTA may not affect trade in both directions symmetrically. For this last refinement, let d ∈ A denote a unique “directional pair” of countries i,j→ belonging to agreement A, where the notation i,j→refers specifically to the effect on trade flows where i is the exporter and j is the importer. We thus estimate two effects for each agreement-pair, one for each direction of trade. In addition, since FTAs no longer affect each partner symmetrically within a given pair, we now also introduce an asymmetric pair fixed effect “γij→”, which varies by direction as well. We then have the following econometric model:

β_A:d ≡ β_1, A:d + β_2, A:d then gives us a unique set of direction-specific estimates which we will soon use for our “second stage” analysis of the empirical determinants of trade integration.

Before proceeding further, we pause to clarify two important details. First, the heterogeneous FTA estimates that will be obtained from specifications (6), (7), and (8) should be interpreted with care. While Baier & Bergstrand (2007) has emerged as the standard method for consistently estimating the average treatment effect of FTAs, the same cannot be said when we pull apart our average “β” to obtain increasingly more finely-grained coefficients, which we should regard as being estimated with at least some unobserved error. Instead, our preferred method draws on the suggested approach of Lewis & Linzer (2005): even if the individual β_A:d’s we estimate from our empirical specifications contain some unobserved noise, we can still investigate heterogeneity in the causal effects of FTAs by using a “second stage” regression analysis to extract some useful signals from that noise.¹⁶

Second, our desire to allow for individual lagged effects creates an additional complication because it is not possible to estimate 5 year lagged effects for the agreements that form within the last 5 years. While we could drop these later agreements from the sample, doing so effectively discards the useful information in the contemporaneous FTA effects β_1, A, β_1,A:p, and β_1, A:d. Instead, our preferred way of addressing this issue is to use the direction-specific estimates (the β_A:d’s) from the first 15 years of data to estimate the following auxiliary regression

such that we may then infer the needed remaining lags using β_2, A:d = π₀ + π₁β_1, A:d. We use the same coefficients to infer missing values for β_2, A’s and β_2, A:p’s where needed.¹⁷

3.1. Trade and FTA data for first stage analysis

3.2. Key covariates for second stage analysis

4.1. Average FTA estimate

We start by briefly discussing the average (across all agreements and pairs) total FTA effect that we obtain based on (5). This specification corresponds to the standard approach in the literature and is the easiest to describe: we estimate an average total FTA effect of β = 0.293, with a standard error of 0.105 (p = 0.005). This estimate yields the interpretation that, on average, FTAs have a partial effect of (e^0.293 − 1) ∗ 100 = 34.0% on trade flows. Alternatively, using a typical value for the trade elasticity of θ = 4 in combination with gravity theory, our average estimate implies a 1−e−0.2934∗100=7.1% average decline in bilateral trade frictions.³⁰

4.2. Inferring lags for later agreements

As noted, we would like to extract as much information as possible from our first stage estimates of later agreements while still acknowledging that “phasing-in” is an important component of FTA-related trade growth. After first obtaining estimates of β_1, A:d and β_1, A:dfrom (8), we subsequently estimate (using (9))

With “robust” standard errors, both of the estimates in (13) are highly statistically significant (p < 0.001 in both cases.) Importantly, in addition to allowing us to include later agreements in our analysis, this method also generates results that contribute to the literature on the timing of FTA effects (c.f., Magee, 2008; Baier et al., 2014). In particular, our finding that π₀ > 0 implies that lagged effects of FTAs are more likely to be positive than their corresponding initial effects. Likewise, π₁ > 0 suggests that agreements with larger initial effects should also be expected to have larger lagged effects.

4.3. Agreement-specific estimates

Our estimates of agreement-specific effects obtained by estimating (6) are shown in Table 1, grouped by sign and significance and listed in descending order. As an alternative means of conveying the heterogeneity in these effects, we also offer a graphical depiction in Fig. 1, which presents the distribution of our estimates with their associated 95% confidence bounds.³¹ Several features of these results stand out. First, not all the agreement-specific effects that we estimate are positive and statistically significant. We find that 38.5% of our estimates (25/65) are statistically insignificant at the p = 0.05 significance level, and 7.6% of our point estimates (5/65) are negative and significant. Nonetheless, the fact that we find positive, statistically significant partial effects for the majority (53.9%) of the agreements in our sample is re-assuring given the more mixed results found in the prior literature. Kohl (2014), for example, only obtains positive and significant effects for 27% of the agreements in his study. We attribute the more “optimistic” findings from our analysis to the inclusion of internal trade values in our estimation. As shown in Dai et al. (2014), internal trade is an important component of the overall reference group for estimating theoretically consistent effects of trade policies; thus, estimations that include internal trade generally obtain larger, more precisely estimated FTA effects.³²

Table 1. Estimates of agreement-specific FTA effects.

Agreement	βA	s. e.	Agreement	βA	s. e.	Agreement	βA	s. e.
Positive effects:			(cont’d)			(cont’d)
Bulgaria-Turkey†	1.485	0.342	Israel-Mexico	0.553	0.136	Israel-Romania	0.174	0.195
EU-Romania†	1.463	0.142	EU-Turkey†	0.535	0.083	Pan Arab FTA	0.171	0.192
Romania-Turkey†	1.403	0.165	Canada-Costa Rica	0.492	0.189	EU-Egypt	0.149	0.125
Andean Community†	1.331	0.170	Canada-Israel†	0.481	0.091	Australia-Singapore	0.139	0.282
Israel-Turkey†	1.269	0.434	Egypt-Turkey	0.463	0.232	EU-Morocco	0.117	0.090
EU-Bulgaria†	1.248	0.225	Chile-China	0.462	0.167	Morocco-US	0.096	0.106
CEFTA†	1.240	0.242	Tunisia-Turkey	0.389	0.109	EU-Chile†	0.045	0.111
EU-Poland†	1.162	0.195	EU-Mexico	0.313	0.095	EU†	−0.016	0.066
Costa Rica-Mexico	1.087	0.461	Chile-US	0.283	0.128	Mercosur-Bolivia	0.007	0.260
Mercosur†	1.024	0.205	EU-Tunisia	0.283	0.086	EFTA-Singapore	−0.018	0.248
EU-Hungary†	0.996	0.170	Chile-South Korea	0.275	0.103	ASEAN†	−0.107	0.145
Poland-Turkey†	0.976	0.152				EFTA-Mexico†	−0.140	0.142
Bulgaria-Israel†	0.948	0.212	Insignificant effects (p > .05):			EFTA-Israel†	−0.213	0.129
EFTA-Hungary†	0.939	0.244	Jordan-US	0.954	0.684	Singapore-US	−0.279	0.312
Hungary-Turkey†	0.932	0.132	Canada-Chile	0.851	0.447
EFTA-Poland†	0.921	0.193	Hungary-Israel	0.757	0.400	Negative effects:
EFTA-Romania†	0.890	0.230	Mexico-Uruguay	0.463	0.377	Australia-US†	−0.170	0.064
Colombia-Mexico†	0.762	0.226	Chile-Costa Rica	0.419	0.313	EU-Cyprus†	−0.194	0.096
EFTA-Bulgaria	0.740	0.353	EFTA-Morocco	0.384	0.234	EU-Israel†	−0.256	0.080
Japan-Mexico†	0.701	0.115	Mercosur-Chile	0.353	0.244	Canada-US†	−0.375	0.126
NAFTA†	0.662	0.152	EFTA-Turkey	0.299	0.154	Chile-Singapore†	−1.099	0.174
Australia-Thailand†	0.623	0.093	EU-EFTA	0.294	0.184
Mercosur-Andean†	0.622	0.125	Chile-Mexico	0.266	0.486
Israel-Poland	0.566	0.202	Agadir Agreement	0.188	0.123
Summary statistics
Simple				Weighted Averages
Median βA estimate::			0.0.463	by inverse variance			0.293
Mean βA estimate:			0.491	by number of country-pairs			0.382
Variance of estimates:			0.261	by (#pairs×inv. var):			0.200

This table reports estimates of the partial FTA effects for all agreements in our sample. Standard errors are “three-way” clustered by exporter, importer, and year. † denotes estimates that are statistically different from the overall average estimate of β = 0.293. There are 33 such estimates, or 50.8%. See text for further details.

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Fig. 1. Distribution of agreement-level FTA partial effects, with 95% CIs.

Second, we notice that some countries in our sample generally seem to have had consistently larger (partial equilibrium) impacts from trade agreements. Central and Eastern European countries in particular (e.g., Bulgaria, Hungary, Romania, Poland) are well-represented in the first column of Table 1. We also note generally strong effects for agreements signed by Israel, Turkey, Mexico, Mercosur, and the Andean Community. On the other hand, with the exception of Israel and Turkey, other Mediterranean nations – such as Egypt, Tunisia, and Morocco- have generally experienced more modest effects. We will return to this issue of whether some countries consistently experience larger FTA effects than others in our second stage analysis in Section 5.

Overall, the estimates from Table 1 and Fig. 1 confirm that FTAs have had very heterogeneous effects on trade. The degree of heterogeneity we document echoes some earlier findings in the literature, although we generally observe a more optimistic picture of the efficacy of FTAs on an agreement-by-agreement basis. While these factual considerations are useful to note, there remain three important avenues along which we would like to deepen the analysis. First, many agreements involve three or more countries; thus, we wish to examine how the same agreement will affect different pairs of member countries. Second, policymakers generally want to know how trade policies will affect their countries specifically; thus, it is important to allow for direction-specificFTA effects. Third, as noted in Baier et al. (2018), even the most finely-tuned appraisals of past FTAs do not by themselves tell us anything about what the effects of future FTAs will look like. These considerations motivate our more detailed pair- and direction-specificFTA estimates.

4.4. Pair-specific and direction-specific estimates

Given the number of estimates we can potentially obtain from specifications (7) and (8) – 455 and 910, respectively – it is not practical to present a full listing of the many pair- and direction-specific effects we estimate. Instead, we summarize the heterogeneity we observe in our pair- and direction-specific estimates in two complementary ways. First, in Table 2, we offer a snapshot of the substantial variation in partial effects that can be observed within a single agreement, using the E.U. as our example. Second, in Fig. 2 and Fig. 3, we add graphical depictions of how the distribution of partial effects changes when we allow for more specificity, i.e. for variation at the agreement-pair level and for directional effects at the agreement-pair level, respectively. The distributions shown in Fig. 2 can be compared directly with the distribution of agreement-specific effects shown in Fig. 1. The two plots shown in Fig. 3 then more specifically highlight, respectively, the degree of pair-wise heterogeneity within each agreement and the degree of asymmetry within each pair.

Table 2. Heterogeneity in EU accession effects.

Pair	βEU:p	s. e.	Pair	βEU:p	s. e.	Pair	βEU:p	s. e.
Largest EU accession effects (by pair):
Hungary-Poland*†	2.186	0.487	Cyprus-Hungary*	0.503	0.251	Spain-Poland	0.412	0.228
Cyprus-Finland*†	1.711	0.399	BLX-Cyprus*	0.493	0.176	U.K.-Hungary	0.400	0.218
Hungary-Malta*†	1.600	0.571	Finland-Hungary	0.470	0.418	Austria-BLX*	0.394	0.086
Austria-Malta*	1.101	0.514	U.K.-Poland*	0.469	0.225	Austria-Spain*	0.375	0.191
Cyprus-Netherlands*†	0.716	0.135	Cyprus-Greece*	0.457	0.196	Italy-Poland*	0.370	0.168
Cyprus-U.K.	0.703	0.370	Cyprus-Germany*	0.456	0.153	BLX-Finland*	0.352	0.100
Cyprus-Italy*	0.555	0.139	Denmark-Hungary*	0.437	0.149	Austria-Poland*	0.352	0.105
France-Poland*	0.517	0.147	BLX-Sweden*	0.431	0.129	Germany-Poland*	0.334	0.110
Small and negative EU accession effects (by pair):
Austria-Sweden†	−0.202	0.107	Cyprus-Malta	−0.307	0.371	Denmark-Finland*†	−0.443	0.150
Germany-Malta†	−0.205	0.112	Finland-Sweden*†	−0.312	0.102	Cyprus-Denmark*†	−0.455	0.213
Greece-Sweden†	−0.210	0.255	Denmark-Malta†	−0.327	0.193	Italy-Malta†	−0.584	0.403
U.K.-Sweden†	−0.213	0.143	Finland-U.K.*†	−0.331	0.133	Finland-Portugal†	−0.630	0.441
Germany-Sweden*†	−0.220	0.107	Cyprus-Ireland*†	−0.334	0.159	Portugal-Sweden*†	−0.694	0.353
Finland-Italy†	−0.256	0.136	Finland-Ireland*†	−0.356	0.125	Ireland-Malta*†	−1.069	0.232
Hungary-Ireland†	−0.269	0.264	Italy-Sweden*†	−0.360	0.087	Cyprus-Poland*†	−1.220	0.247
Ireland-Sweden*†	−0.291	0.144	BLX-Hungary†	−0.399	0.210	Greece-Malta*†	−1.819	0.308

Pair	βEU:d	s. e.	Pair	βEU:d	s. e.	Pair	βEU:d	s. e.
Examples of asymmetric EU accession effects (arrows indicate direction of trade):
Netherlands →Austria*	0.418	0.158	Spain →Austria*†	0.734	0.212	Poland →Austria*	0.575	0.186
Austria →Netherlands*†	−0.486	0.162	Austria →Spain	0.110	0.187	Austria →Poland	0.157	0.152
Poland →Spain*	0.795	0.258	Poland →Sweden*	0.549	0.223	Poland →Netherlands	0.364	0.193
Spain →Poland	0.057	0.183	Sweden →Poland	0.040	0.156	Netherlands →Poland	0.157	0.158
Poland →U.K.*†	0.825	0.266	U.K. →Sweden	0.048	0.197	Sweden →Austria	−0.105	0.224
U.K. →Poland	0.100	0.184	Sweden →U.K.*†	−0.431	0.182	Austria →Sweden†	−0.293	0.239
Netherlands →Sweden	0.317	0.199	Spain →Sweden	0.285	0.209	U.K. →Austria*	0.342	0.141
Sweden →Netherlands†	−0.353	0.200	Sweden →Spain†	−0.152	0.207	Austria →U.K.	0.197	0.147
Summary of within-EU estimates
Pairwise estimates (βEU:p)				Directional estimates (βEU:d)
Mean: 0.047	Median: 0.046		s.d.: 0.514	Mean: 0.085		Median: 0.048	s.d.: 0574
# positive and significant:			27/98 (27.6%)	# positive and significant:			37/196 (18.9%)
# negative and significant:			13/98 (13.3%)	# negative and significant:			26/196 (13.3%)
# statistically different from β = 0.293:			41/98 (41.8%)	# statistically different from β = 0.293:			82/196 (41.8%)

This table reports examples of pair-specific and asymmetric estimated partial effects for the EU accessions in our sample. * denotes estimates that are statistically different from 0. † denotes estimates that are statistically different from the overall average estimate of β = 0.293. See text for further details.

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Fig. 2. Distributions of agreement-pair-specific (left) and direction-specific (right) FTA effects, with 95% CIs.

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Fig. 3. Pair-wise heterogeneity within agreements (left); directional heterogeneity within Pairs (right).

We focus on the E.U. in Table 2 because it is by far the largest agreement in our sample. There are 98 distinct pair-specific effects -and 196 direction-specific effects – that can be estimated within the E.U. alone. Rather than show all these estimates, Table 2 presents (roughly) the upper and lower quartiles from the pair-specific effects, as well as some representative examples of asymmetries within pairs. Both panels of Fig. 3 also place these EU-specific estimates in the context of the heterogeneity we observe within other agreements, such as NAFTA and the E.U.’s agreements with Poland and Chile.

From the top panel of Table 2, we can clearly see a very wide variance in the effects of recent E.U. accessions across different E.U. pairs. Consistent with our expectation that more finely-grained estimates should exhibit relatively more noise, the ranking of the various estimates seems somewhat more random than the ordering seen in Table 1. Smaller countries, such as Malta and Cyprus, appear regularly at the extremes of both lists. Other, more economically large countries – such as the U.K., Hungary, and Portugal- also appear multiple times on both lists.

The lower panel of Table 2 shows some representative examples of E.U. pairs with strongly asymmetric E.U. pairs. For brevity, we only show these effects for three acceding countries (Poland, Austria, and Sweden) and three existing E.U. members (Netherlands, Spain, and the U.K.), though these examples are generally representative. Here, we do see strong, country-specific patterns, confirming again the general pattern suggested by Table 1. Poland’s accession has led more so to increases in exports from Poland to existing E.U. members than to increases in trade in the other direction. This dynamic does not appear to be a regular function of E.U. accession, however: asymmetries in the Spain-Austria and Netherlands-Austria pairs both favor trade flows to the acceding country (in these cases, Austria) rather than the other way around. We also see a similar pattern for Sweden, another acceding country, in its pairings with these countries. Overall, these examples suggest that, even within agreements, there can be large, country-specific patterns of effects that are worth investigating further.

The graphical depictions of the distributions of our various estimates from Fig. 2, Fig. 3 echo these same messages and provide a broader overview.³³ The wider confidence intervalsseen in each panel of Fig. 2 confirm that, as we move to increasingly more detailed estimates, it becomes increasingly more difficult to obtain statistical precision. Indeed, only 40.4% of our agreement-pair-specific estimates (shown in the left panel of Fig. 2) are positive and statistically significant, with this same percentage narrowing to 32.0% for our direction-specific estimates (shown in the right panel of Fig. 2). Fig. 3 then uses different colors to separate out these effects by the different agreements they belong to. The left panel of Fig. 3, which plots agreement-specific estimates against pair-specific estimates, confirms there is generally substantial heterogeneity within the same agreement whenever multiple pairs are involved. Finally, the right panel of Fig. 3, which plots directional effects within the same pair against one another, then shows that asymmetries within pairs are also very prevalent, but – at the same time – directional FTAeffects within the same pair tend to be highly correlated with one another.

Admittedly, as we focus on increasingly specific estimates of changes in trade costs associated with FTAs, we also increase the likelihood that our estimates reflect omitted factors that may enter specifications (6)–(8) via the error term. Causal interpretation of these more specific FTA effects would require that these effects are directly reflected in changes in trade that occur around the time of the agreement. While this assumption may not strictly hold in all (or even most) cases, presenting these results still allows for a broad description of the vast heterogeneity we observe in the ex post partial effects of FTAs in our sample, especially within agreements. In addition, while we acknowledge that individual FTA effects may be measured with unobservable error, taken collectively, these effects can still be analyzed to determine what factors may be expected to be associated with stronger or weaker effects ex ante. This is the focus of our second stage analysis.

5.1. Econometric approach

Before turning to the full-blown second stage analysis, we pause to consider two preliminary matters of interest. First, because our first stage estimates of FTA partial effects have been potentially estimated with unobservable error, it is important to discuss how this this error enters the second stage and how our analysis may be structured to account for it. An exceptionally useful reference in this regard is Lewis & Linzer (2005), who carefully examine the consequences of various different ways of weighting a “second stage” dependent variable to account for residual error variance from a prior stage. As Lewis & Linzer (2005)demonstrate, so long as a White (1980) correction for heteroskedasticity-robust standard errors is used, simply using (unweighted) OLS to estimate the second stage will enable us to obtain conservative, if inefficient, inferences of our second stage parameters. That is, while other weighting methods might lead to more efficient estimates, the White (1980) correction should still generate reliable consistent estimates of our second stage standard errors and confidence intervals, such that we should not be worried about “over-confidence” in our inferences. Lewis & Linzer (2005) also demonstrate that other popular weighting methods for dealing with first stage error can actually perform far worse in terms of efficiency and generally conclude that OLS with heteroskedasticity-robust standard errors is “probably the best approach” in most cases. With these recommendations in mind, we adhere strictly to OLS with robust standard errors for all of our main second stage regressions.³⁴

Second, as a direct lead-in for the second stage, we perform a standard “analysis of variance” exercise, sequentially adding agreement-specific followed by (symmetric) pair-agreement-specific dummy variables as regressors in order to absorb all variance that is associated with heterogeneity “across agreements” and (respectively) “across pairs within agreements”. The remaining variance, that is not specific to either an agreement or a pair within agreement, then strictly reflects residual asymmetries in estimated FTA effects within pairs of countries. The main results from this initial decomposition exercise are as follows. First, the agreement-level dummies we use to absorb differences across agreements collectively only explain 35.5% of the overall variation in our estimated directional FTA effects (measured by R²). When we parse the estimates further by next adding pair-agreement-level dummies, the share of explained variation increases to 70.4%, suggesting that 70.4 %  − 35.5 %  = 34.9% can be explained by heterogeneity across different pairs within the same agreement. The remaining unexplained variation, 29.6%, specifically reflects asymmetries within the same pair. Notably, this last term is of comparable magnitude to the other two components.

Usefully, this exercise also serves to preview some of the techniques we will use in the analysis that follows to isolate how different variables may explain different aspects of the overall heterogeneity in our estimates. For example, regressing our FTA estimates on a set of observables in the presence of agreement-level fixed effects will allow us to narrowly focus on potential sources of “within agreement” heterogeneity. Similarly, the introduction of agreement-by-pair fixed effects will, much as in our initial decomposition exercise, allow us to narrow the focus further to sources of “asymmetries within pairs”. Generally speaking, heterogeneity in FTA partial effects within agreements is a topic which has not received much attention in the literature, despite its intuitive appeal. The opportunity to selectively vary our focus in this way – made significantly easier by approaching the problem in two stages – will thus be a key aspect of our overall methodology.

5.2. Decomposing the sources of FTA heterogeneity

The preceding discussion highlighted broad patterns of heterogeneity in our first stage FTA estimates. In earlier sections, we have also described at length some attractive, theoretically-guided indices for potentially accounting for some of this variance. The stage is set for a more detailed investigation: What can we say about the empirical determinants of FTA effects? In short order, we will introduce a wide variety of covariates that may hold sway in this context, including “economic geography” variables, institutional factors, as well as neoclassical determinants of trade. For now, however, we start with only a basic specification, drawing solely on a few key hypotheses:

As we have established in Section 3.2, each of the key variables in (14) has an intuitive expected sign. The first stage pair fixed effect term, for example, provides a novel and comprehensive (inverse) measure of the level of trade frictions between i and j just before the signing of their agreement. Intuitively, country-pairs with a lower first stage pair fixed effect suffer from higher ex ante bilateral trade frictions and, therefore, have more potential for larger trade creation effects from FTAs ex post.³⁵ We therefore expect the sign of α₁ to be negative. lnToT^A:j, meanwhile, measures the sensitivity of the importer’s terms of tradebased on the simulation procedure described in Section 3.2. A smaller lnToT^A:j indicates that the importing country has relatively more influence over the terms of trade over its partners. Thus, we expect that α₂ < 0, in accordance with the influential arguments of Bagwell & Staiger (1999). We also expect that α₃, the coefficient on the ex ante extensive margin, to be < 0, incorporating the arguments of Kehoe & Ruhl (2013).

Column 2 adds several other, more standard variables that specifically draw on the “gravity” literature. These include bilateral relationships – such as log distance, contiguity, the sharing of a common language, or the presence of a prior free trade agreement – and also the GDPs and GDP per capitas of each partner.³⁶ For the most part, we do not impose strong priors on these added variables. We do, however, generally expect log distance (“  ln  DIST ”) to be negative, either because more distant countries are more sensitive to changes in trade policies (as emphasized in Baier et al. 2018) or perhaps because they simply sign weaker agreements due to weaker cultural affinities.³⁷ Likewise, countries that already have a prior trade agreement (“ Prior Agreement ”) should experience weaker trade creation, because the earlier agreements have likely already picked much of the “low hanging fruit” in terms of easily addressed barriers to trade.

The signs on   ln  DIST  and  Prior Agreement  are indeed negative as expected. We also find larger FTA effects for contiguous countries (“CONTIG”) and for countries with common legal system (“LEGAL”). The positive and significant result we observe for CONTIG may be due to the same reasons we have already cited for the negative sign we observe on log distance. The positive and significant sign for LEGAL, however, merits further discussion, as we would ordinarily expect countries with dissimilar legal systems to have higher ex antebarriers to trade. The key remark to make here is that, because we already have in place an “inclusive” measure of trade costs – in the form of our first stage pair fixed effect – we may interpret these latter variables as affecting the efficacy of the FTAindependently of how they affect initial trade costs. Conditional on the level of ex ante trade frictions, sharing a common legal system (for example) could conceivably make it easier for countries to coordinate on stronger trade creation measures.

Three of the added country-level gravity variables— the log GDPs of both countries and the log per capita GDP of the importer— also enter the analysis significantly. Interestingly, we find that FTA effects are generally stronger for larger countries (measured in real GDP), both on the export-side as well as on the import-side, with the exporter’s GDP having more overall influence. While agreements between larger countries are associated with more trade, the combined impact is less than proportionate; that is, a 1% increase in export and importer GDP increases trade by less than 1%. The positive sign on the importer’s per capita GDP implies an asymmetry in how FTAs affect trade between countries with differing levels of development, a result we will query in more detail below.

Another important aspect of including a direct measure of country “size” in our analysis is that, all else equal, we would expect size/GDP to be a reasonable proxy for a country’s market power over world prices. However, while the magnitude of the coefficient for lnToT^A:j does weaken when we add these controls, it remains robustly significant. Furthermore, the relative magnitudes of the coefficients for GDPs are not consistent with a story based on market power: if anything, they suggest FTAs promote trade from larger countries to smaller ones. We also note that, while our estimate of the coefficient on the extensive margin variable is still positive and significant, its magnitude falls by roughly half when these other controls are added.

5.3. Robustness

Having established our main specifications in columns 1–4 of Table 3, we now move on to several key sensitivity analyses encompassing some natural lines of inquiry as well as some deeper concerns about causal interpretation. Our first task is to introduce more detailed information on trade policies in place and/or the “depth” of the agreement being signed. To this end, columns 5 to 8 of Table 3 repeat the same specifications as before, only now adding the pre-FTA tariff level (“ln 1 + AppliedTariff”, which uses weighted-average applied tariffs taken from TRAINS), a 0/1 dummy variable for if the agreement entails the formation of a customs union and/or common market, and two other, more specific measures of FTA depth (the “Count of Enforceable Provisions” and the “Institutional Quality” of the agreement, which we take from Kohl et al., 2016).³⁸

The inclusion of these trade policy variables at first appears meaningful. In particular, the estimate on the ex ante tariff level in column 5, where we are repeating the same specification as column 1, is positive and highly significant as expected (p < .01). In addition, while the coefficient for Customs Union is basically zero, the other depth measures also enter positively, albeit with marginal (p < .10) significance.³⁹ Interestingly, the statistical significance of ln Appliedtariff disappears in the presence of gravity controls (column 6), agreement fixed effects (column 7), or agreement-pair fixed effects (column 8). Our original main variables and controls, meanwhile, remain largely unaffected. We conclude, based on these results, that our approach allows us to capture important sources of variation in the ex post effects of FTAs that go beyond what we can infer based on tariffs alone.⁴⁰

The results of these experiments offer mixed support for the notion that FTAs specifically promote the exports of countries with weak institutions. When we look at broad results without any agreement-level or agreement-pair fixed effects (columns 1 and 2 of Table 4), we generally find that FTAs have stronger effects for countries with strong legal institutions (i.e., high “Rule of Law”) and/or weak bureaucratic institutions (i.e., low “Bureaucracy Quality”). While there is indeed an implied asymmetry potentially favoring exporters with weaker institutions in these initial specifications, all of these variables lose their significance when we introduce agreement fixed effects (in column 3) as well as when we add agreement-pair fixed effects (in column 4). For democracy and checks and balances, we see a similar story: in columns 1 and 2, we overwhelmingly find that these variables are positively associated with signing stronger agreements. However, they play no role in explaining heterogeneity within agreements. Other key results remain unchanged.

Motivated by the Neoclassical “Heckscher-Ohlin” trade theory, the remaining columns of Table 4 control for factor endowment differences across countries (e.g., physical and human capital-to-labor ratios, skill-to-labor ratios). We also include the absolute difference in these relative endowments, as well as the absolute difference in (log) per capita GDPs, in order to get at various potential dimensions of comparative advantage. Data for each of these endowment measures are constructed using information from the Penn World Table. Echoing what we have seen in previous results, while we do find some significant results of note – in particular for physical capital-ratios and the difference therein – these results only appear to be meaningful for describing variations in FTA effects across different agreements. When we examine these variables in the presence of agreement fixed effects (column 7) or agreement-pair fixed effects (column 8), none are robustly significant. Our main results still retain the same sign and significance.

The estimates from Table 5 show that such a line clearly exists between the 3rd and 4th year leading up to an FTA: when we include residuals from years t₀ − 6 to t₀ − 4 directly in our second stage, we observe no statistical relationship with our first stage estimates across all of our key specifications, whereas residuals from the two-to-three year period immediately preceding FTAs tend to be significantly correlated. Importantly, all our earlier results maintain the same signs and significance as in columns 2, 3, and 4 of Table 3 and their magnitudes are only modestly affected. Since we are now allowing actual changes in trade from just before an FTA to explain our estimates, this last set of results confirms that our second stage coefficients are primarily being identified by the trade growth that occurs after each FTA goes into effect.⁴¹

6.1. Developing a prediction model

Our out-of-sample analysis proceeds by dropping one agreement at a time and then trying to predict its effects based on a model fitted using the other agreements in the sample. For our criteria, we aimed for a set of predictors which: (i) performs well against other alternatives in terms of R²; (ii) can be naturally motivated based on our empirical results from Section 5; (iii) contains variables that were shown to be important for “within-agreement” and (if applicable) “within-pair” heterogeneity. We also focus only on the 5th through 95th percentiles of our estimates.⁴²

Based on these criteria, our preferred model is the following simple prediction specification:

All the predictors used in (15) were shown to be consistently significant throughout the preceding section, especially when we zeroed in on heterogeneity within agreements and (if applicable) within pairs. FTA effects should be smaller for countries that have a higher first stage pair fixed effect (indicating lower ex ante trade frictions) and/or are further apart geographically, and/or if they already have an existing agreement in place. In addition, we also allow for asymmetries in FTA effects within pairs by including the GDPs of both partners and our (inverse) measure of the importing country’s market power, lnToT^A:j. Fig. 4 offers a visualization of the resulting predictive fit. Each data point in Fig. 4 represents a predicted FTA effect (indexed by the horizontal axis), which we compare with the actual estimate obtained from the first stage (indexed by the vertical axis). The coefficient on our fitted regression line, ρ₁ = 0.773, is positive and highly significant. The constant from the fitted regression line, ρ₀ = 0.091, is also positive and highly significant.

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Fig. 4. Out-of-sample validation results.

Before turning to TTIP, we acknowledge two limitations of this approach. First, the predictive fit of our preferred model (R² = 0.178) indicates that we are able to predict a significant but modest amount of the overall heterogeneity in the effects of FTAs with our simple model. Obviously, if the R² were our sole criterion, we could easily inflate the fit of our predictive model by adding many more variables on the righthand-side. However, this runs the risk of “overfitting” the model and, furthermore, leads us away from being able to provide an intuitive understanding of what factors are driving our predictions.⁴³A second caveat is that, because not all the directional FTA effects we computed in our first stage are positive, our methodology can and will predict negative partial effects for at least some TTIP pairs. We do not take a stand on why we observe negative FTA effects in our estimates. Our prior would ordinarily be that TTIP should generally lead to trade creation between all pairs. Where negative values are encountered, we take this to mean that trade creation is likely to be small. Despite these limitations, we believe that our approach is able to shed light on some novel and meaningful sources of predictive power.

6.2. Predicting the effects of TTIP

Our task in this section is to predict the effects of a U.S./E.U. FTA, given different assumptions about how it will affect trade barriers between the U.S. and its prospective partners in the E.U. In particular, we will explore two main scenarios. Under the “average” scenario, we base the change in trade barriers for all U.S./E.U. pairs on our estimate of the overall average partial effect using (5). In other words, τ^ij−θ=eβavg=e0.293, for all U.S./E.U. pairs. Under our second, “heterogeneous” scenario, we predict direction-pair-specific partial effects for TTIP using the insights from our prior analysis. In particular, we let τ^ij−θ=eβij,where β_ij is computed using both the coefficients estimated from our preferred second stage model as well as the ρ’s shown in Fig. 4. In other words,

where β˜TTIP:d is the fitted value for each directional pair d within TTIP computed from our second stage estimates. Essentially, we are using the predictive fit from our out-of-sample validation analysis to determine how much weight we should place on our ability to predict heterogeneity in partial effects (ρ₁ = 0.773), versus using a common average component (ρ₀ = 0.091). We use this information in the interest of providing additional conservatism. The underlying regression coefficients used to compute β˜TTIP:d are:

which are computed using all agreements in the sample, instead of excluding one at a time. All estimates shown in (17) are statistically different from zero at the p < 0.01 significance level.

What explains the diversity in predictions across the various pairs? It cannot be variation in bilateral distance, for instance, since all European countries are collectively separated from the U.S. by the Atlantic. Actually, the major source of heterogeneity across pairs is the first stage pair fixed effect, recovered from (10), representing ex ante trade frictions between the different potential TTIP pairings. Ireland, for example, is already very tightly integrated with the U.S. in trade: for Ireland-U.S. trade, we obtain an ex ante level of trade integration (i.e., iceberg frictions raised to the minus θ) between the U.S. and Ireland of dUS,IR¯−θ=0.027. While this may not, on the surface, seem like a large number, it is actually the largest of any U.S.-E.U. pair.⁴⁴ The smallest trade cost index (0.001) is for the U.S.’s trade with Cyprus, along with, unsurprisingly, its trade with Bulgaria and Romania, followed closely by its trade with Poland (0.002).⁴⁵

Turning to asymmetries, one might expect that, as the largest participant, the U.S. should have more “market power” ex ante with respect to its potential E.U. partners. Actually, because the E.U. countries are very tightly integrated with one another, their terms of tradeare significantly less sensitive to liberalizing with the U.S. than this logic would indicate. When we simulate the agreement using a common average effect, thelnToT^A:j we obtain for the U.S. is 0.0036, whereas the mean value we obtain for this index for the E.U. countries (0.0023) is actually lower, indicating a symmetric liberalization between the U.S. and E.U. actually tends to benefit the U.S. more than the E.U. As such, we infer that an “efficient agreement” would involve the E.U. countries granting relatively more concessions in this scenario. In addition, the fact that our coefficient on exporter GDP is slightly larger than that of importer GDP would also tend to favor the exports of the U.S., since it is the larger country in each pair.

For our general equilibrium predictions, we will stick with the simple trade model implied by (1) and (2). In particular, we will maintain that labor is the only factor of production and that trade takes place in final goods only. As shown in Head & Mayer (2014), imposing market clearing on a model of this type then delivers a standard general equilibrium system that generalizes across a wide range of different models. While this simple framework omits several factors that have been shown to be important for delivering larger gains from trade (e.g., multiple industries, trade in intermediates, dynamic effects, etc.), it is widely accepted in the literature as a benchmark for computing the general equilibrium effects of trade policies. Furthermore, it will allow us to capture the basic point that, even when an agreement has the same partial effect on all trade flows, general equilibrium outcomes can still be quite heterogeneous. The competitive equilibrium in such a model can be described by the following system of equations,

where π_ij ≡ A_iw_i^−θτ_ij^−θ/P_j^−θ is the share of j’s total expenditure on goods produced in origin country i. Note that we allow trade to be unbalanced. Total expenditure in j is therefore comprised of an (endogenous) labor income term, w_jL_j, and an (exogenous) trade balanceterm D_j. According to (18), the total amount of output produced in origin i, w_iL_i, must be equal to the sum of expenditure on goods produced in i across all destinations j.

Eq.(18) can be solved (in changes) to predict general equilibrium effects of an FTA on both welfare and trade as a result of an FTA. To see this, first let x^=x′/x denote the equilibrium change in a variable from an initial level x to a new equilibrium level x^′ (i.e., the now-standard “hat algebra” notation of Dekle et al., 2007). The equilibrium in changes version of (18) is therefore:

where P^j−θ can be computed as:

Given initial trade shares {π_ij}, output levels {Y_i}, expenditure levels {E_j}, and a set of changes in trade barrier levels, {τ^ij−θ}, one can solve the system defined by (19) and (20) for the resulting changes in wages w^i. With wages in hand, we then obtain the following expressions for the associated general equilibrium changes in both welfare levels and trade flows:

where the change in national expenditure, E^i, is computed as Yiw^i+Di/Ei.⁴⁶ We will use the year 2006, the last year in our data, to compute the initial trade levels and trade balances.⁴⁷ Finally, since (19) is non-linear in w^i, we require an assumption regarding the trade elasticity, θ. Following the recommendations of Simonovska & Waugh (2014), we assume θ = 4.

Table 7 reveals several key insights we wish to focus on. First, even in the “average” scenario, where all TTIP pairs enjoy a common partial effect, the general equilibrium implications of TTIP introduce their own layer of heterogeneity. Usefully, this heterogeneity can largely be related back to a key aspect of our analysis, the level of ex ante trade frictions between countries. For example, the largest welfare effect is for Ireland, who enjoys a 1.35% increase in its welfare thanks to closer trade ties with the U.S. Intuitively, since Ireland already has the lowest ex ante trade barriers with the U.S., using a common partial effect for TTIP would eliminate a relatively larger portion of Ireland’s remaining trade frictions with the U.S. than those of other E.U. members.⁴⁹ Similarly, the lowest welfare gainers under the average scenario include Cyprus, Bulgaria, Greece, Poland, and Romania— countries with which the U.S.’s ex ante trade relations are not as strong.

Of course, these same close relations between the U.S. and Ireland also led us to predict much smaller partial effects under the “heterogeneous” scenario. In turn, the subsequent welfare effect for Ireland is likewise predicted to be much smaller than that of the “average” scenario and is indistinguishable from zero based on the accompanying bootstrapped 95% confidence interval. The case of Ireland thus illustrates the following simple, powerful conclusion: low ex ante trade frictions are associated with both small partial effects ex postas well as larger welfare effects ex post. Therefore, using a common average partial effect will tend to systematically overestimate welfare gains for country-pairs who are already well-integrated in trade. A similar principle also applies in reverse. The Eastern European E.U. members Bulgaria, Hungary, Poland, and Romania are among those that see the largest improvements in welfare from introducing heterogeneous partial effects, reflecting the large partial effects we predicted for these countries in Table 6. For non-TTIP countries, general equilibrium effects are relatively similar across scenarios. As one would expect, these countries all experience mild trade diversion and most experience small welfare losses. The largest losers notably major regional trade partners on either side of the Atlantic not included in the agreement, such as the EFTA countries Norway, Iceland, and Switzerland, the U.S.’s NAFTA partners Canada and Mexico, as as well as the United Kingdom (owing to its presumed “Brexit” from the E.U.)