Terms of Trade and Global Efficiency Effects of Free Trade Agreements,

Transcription

1 Terms of Trade and Global Efficiency Effects of Free Trade Agreements, James E. Anderson Boston College NBER Yoto V. Yotov Drexel University September 6, 2013 Abstract This paper infers the terms of trade effects of Free Trade Agreements (FTAs) implemented in the 1990s. We estimate large FTA effects on bilateral trade volume in 2 digit manufacturing goods from , using panel data methods to resolve two way causality in the gravity model. The terms of trade changes implied by these volume effects are deduced for 40 countries plus a rest-of-the-world aggregate using an endowments general equilibrium model. Some countries gain over 10% of real manufacturing income, some lose less than 0.2%. Global efficiency of manufactures trade rises 0.62% based on a new distance function measure of iceberg melting. JEL Classification Codes: F13, F14, F16 Keywords: Free Trade Agreements, Gravity, Terms of Trade, Distance Function. We are grateful to Scott Baier, Jeff Bergstrand, Rick Bond, Yoosoon Chang, Carlos Cinquetti, Thibault Fally, Joseph François, Tomohiko Inui, Paul Jensen, Mario Larch, Nuno Limao, Vova Lugovskyy, Vibhas Madan, Thierry Mayer, Peter Neary, Maria Olivero, Joon Park, Javier Reyes, Robert Staiger, Costas Syropoulos and Daniel Trefler for helpful comments and discussions. We also thank participants at the Western Economic Association Meetings 2009, the Fall 2009 Midwest International Trade Conference, the 2011 Canadian Economic Association Meetings, the 2011 NBER Summer Institute, the 2011 Econometric Society European Meeting and the LACEA-TIGN III Annual Conference, as well as department seminar participants at Boston College, Drexel University, Fordham University, Indiana University, Oxford University, Paris School of Economics/Sciences Po, the University of Nottingham, the University of Toronto and the World Bank. All errors are ours only. Contact information: James E. Anderson, Department of Economics, Boston College, Chestnut Hill, MA 02467, USA. Yoto V. Yotov, Department of Economics, Drexel University, Philadelphia, PA 19104, USA.

2 Introduction The proliferation of Free Trade Agreements (FTAs) in the 1990 s alarmed many trade policy analysts and popular observers. Trade diverted from non-partners reduces their terms of trade. Losses to outsiders could even outweigh the terms of trade gains to partners, reducing the efficiency of the world trading system. This paper calculates the terms of trade and global efficiency effects on manufacturing income of trade agreements implemented in the 1990s. The results are reassuring: FTAs delivered benefits while negligibly harming outsiders. Some countries gain over 10%, a few lose less than 0.2% and global efficiency rises 0.62%. Theory gives great prominence to the terms of trade effects of trade agreements and simulation models provide numerical measures of terms of trade changes due to tariff changes induced by particular FTAs. In contrast, there is little empirical evidence on the effect of trade agreements on the terms of trade, because terms of trade are notoriously hard to measure and there are difficult inference problems with ascribing causation. 1 Our solution is to estimate the volume effects of the FTAs implemented in the 90s using the empirical gravity model, and then use the estimated volume effects to calculate the terms of trade implications of their hypothetical implementation in Compared to the simulation literature using tariff changes (e.g., Romalis, 2007, for NAFTA), our approach focuses on volume changes induced by FTA effects that include more than tariffs while treating the entire set of FTAs and countries simultaneously. 1 Feenstra (2004, pp ) reviews the literature. Studies using prices directly are quite limited in scope due to the difficulties in assembling comparable price data across a wide range of countries as well as inferring the effect of FTAs on prices. Chang and Winters (2002) address both problems using export unit values at the 6 digit Harmonized System level for Brazil. See their footnote 5, pp , for discussion of the severe limitations. They treat prices as set by a foreign and domestic firm in a duopoly pricing game that avoids general equilibrium considerations. Clausing (2001) uses a partial equilibrium model disaggregated by sector that links import volume changes to tariff changes for Canada, and does not go on to link them to price changes. Romalis (2007) simulates the equilibrium price changes induced by the Canada-US Free Trade Agreement (CUSFTA) and the North American Free Trade Agreement (NAFTA) tariff changes using detailed demand elasticities estimated with a difference in differences based estimation technique to identify demand elasticities that focuses on where each of the NAFTA partners sources its imports of almost 5,000 6-digit Harmonized System (HS-6) commodities and comparing this to the source of European Union (EU) imports of the same commodities. The technique enables identification of NAFTAs effects on trade volumes even when countries production costs shift. Caliendo and Parro (2011) calculate what proportion of NAFTA members trade changes can be accounted for by the tariff changes using the Eaton-Kortum (2002) version of the gravity model.

3 Our estimation methods extend an empirical gravity literature on the trade volume effects of FTAs. Notable studies include Frankel (1997), Magee (2003) and Baier and Bergstrand (2002, 2004, 2007). Early findings on the effects of FTAs and trading blocs on bilateral trade flows were mixed, 2 but recent developments deal effectively with two way causality and show that trading blocs and FTAs have large direct effects on aggregate bilateral trade between member countries relative to non-member countries. Baier and Bergstrand (2007) find that, on average, a FTA induces approximately a 100% increase in bilateral trade between member relative to non-member countries within ten years from their inception. Volume changes like these, larger than explicable by tariff changes, are plausible because FTAs typically induce unobservable trade cost reductions alongside the formal tariff reductions that are the direct object of the agreement. Non-tariff policy barriers typically fall between FTA partners 3 while the enhanced security of bilateral trade induces relationship-specific investment in trade with partner counter-parties. We infer the volume effects of FTAs implemented between 1990 and 2002 for 40 separate countries and an aggregate region consisting of 24 additional nations (none of which entered FTAs). The inference is drawn from estimated gravity equations at the 2 digit ISIC level in manufacturing, a disaggregation that contrast with much of the empirical gravity literature that uses aggregate trade data. We find large volume effects comparable to the aggregate estimates of Baier and Bergstrand (2007) but varying across sectors. We then calculate the terms of trade changes implied by hypothetically implementing all the FTAs of the 90s in the 1990 base year. General equilibrium sellers prices are calculated from market clearance equations for each national variety in each sector. Supply is fixed in each sector and country for simplicity. Intermediate input demand is given by a two level Cobb-Douglas/CES system. Sectoral CES demand systems are consistent with 2 For example, Bergstrand (1985) found insignificant European Community (EC) effects on bilateral member s trade and Frankel et al (1995) supported his findings. Frankel (1997) found significant Mercosur effects on trade flows but even negative EC effects on trade in certain years. Frankel (1997) also provides a summary of coefficient estimates of the FTA effects from different studies. Ghosh and Yamarik (2004) perform extreme-bounds analysis to support the claim that the FTA effects on trade flows are fragile and unstable. 3 Canadian support for the CUSFTA was based primarily on its provision for bi-national review of US antidumping procedures, a benefit not measurable by reduction of already low tariffs. 2

4 a gravity model for each sector. Manufacturing demand and supply nest inside national GDP functions. Inserting the equilibrium sellers prices across sectors into a fixed weight sellers price index in each country gives the numerator of the terms of trade. Buyers prices equal sellers prices times trade cost factors modeled as iceberg costs. The equilibrium buyers prices aggregate into Cobb-Douglas/CES buyers price indexes for each country, the denominator of the terms of trade. (Our definition of the terms of trade as the ratio of sellers price index to buyers price index differs slightly from the standard one because it includes internal trade in both numerator and denominator, but ours is the relevant concept in the gravity model.) The results show that the 1990 s FTAs significantly increased real manufacturing income of most economies in the world. 10 out of the 40 countries had terms of trade gains greater than 5% while gains of 10% or more were enjoyed by Bulgaria, Hungary and Poland. Losses were smaller than 0.2% and confined to countries that did not enter into FTAs: Australia, China, Korea and Japan (and the rest of the world aggregate). The global efficiency effect of FTAs is intuitively quantified as the change in how much of the iceberg melts due to FTAs, aggregated consistently across countries and sectors. The method is a novel application of the distance function (Deaton, 1979; itself an application of Debreu s coefficient of resource utilization, 1951) in the context of the gravity model. The global efficiency of trade rises in each manufacturing sector (ranging from 0.11% for Minerals to 2.1% for Textiles) with an overall efficiency gain of 0.62%. An important feature of our terms of trade results is their non-zero sum nature, in contrast to the usual zero-sum implication of simple trade policy theory. An alternative global efficiency measure highlights this feature. Sum the real income changes in the world by summing the product of the initial income shares times the national terms of trade changes, a weighted average of the national terms of trade changes. This yields 0.43%. The non-zero sum arises for two reasons. Directly, less of the iceberg melts in bilateral shipments between FTA partners due to a reduction in border frictions. Indirectly, inward and outward multilateral resistance for each country changes, further changing the global amount melted. In principle, the second effect could be negative and even outweigh the 3

5 first effect. For the 1990s implementations of FTAS the net effect is positive. A NAFTA counter-factual experiment reveals large benefit to Mexico. Most of Mexico s gains disappear if NAFTA is switched off, while without NAFTA the US and Canada would have lost a little from the FTA inceptions in the rest of the global economy. A limitation of the paper is that the calculated terms of trade effects of FTAs use an endowments model of supply for manufacturing only. This model choice avoids the onerous data, specification and parameter estimation requirements of a complete computable general equilibrium model, while non-manufacturing is suppressed because our methods require internationally comparable sales and expenditure data that is only available for manufacturing. An alternative model with substitution within manufacturing or for substitution between manufacturing and non-manufacturing could shift calculated terms of trade effects in either direction. On the one hand, standard implications of maximizing behavior with substitution imply that for given price changes, our estimates are lower bounds of the real income gains from FTAs due to terms of trade effects. On the other hand, substitution presumptively reduces the size of price changes. These opposing effects may even cancel out. Another limitation is that in the benchmark case all FTAs are equal in their volume effects. We test the sensitivity of the benchmark case to this surely oversimplified approach by splitting the FTAs of the 1990s into deep and shallow agreements, finding small effects for the most part. Nevertheless, this test and common sense suggest that all FTAs are not equal. Capturing their differences requires a simple model differences of FTA differences that does not absorb too many degrees of freedom. A less serious limitation is that when measuring national gains the benchmark case does not allow for rents in the trade costs. The no rents assumption avoids measuring and modeling many unobservable rents on inward and outward trade and their division between buyers and sellers. Our main conclusions are robust to the alternative extreme assumption that the only rents are tariffs and all tariff revenue is fully rebated locally. National gains on balance remain for almost all partners, 4 and while some big gains 4 We only find two cases, Morocco and Tunisia, where revenue losses can potentially outweigh terms of trade gains. Their manufacturing sectors are small and there are missing terms of trade gains that 4

6 remain (e.g. Poland), some other big gains are considerably reduced (e.g., Mexico). This robustness is because tariff revenue changes are a very small part of the income changes because tariffs are generally low. Global efficiency gains properly ignore rents, since these are transfers. Section 1 presents the theoretical foundation. Section 2 discusses the estimation of the gravity equation and the trade volume effect of FTAs. Section 3 presents the terms of trade and global efficiency effects of switching on the FTAs of the 1990 s in the base year Section 4 concludes with some suggestions for further research. 1 Theoretical Foundation Manufactures are intermediate goods produced and used in a convex technology. The maximum value GDP function is given by g(π, p, C, v) for a generic country, where π denotes the tradable goods price vector for non-manufactures, v denotes the primary factor vector, p denotes the marginal cost vector for producing another unit of each manufactured good and C denotes the input buyers price index of manufactured goods. National production of manufactures is frozen at the vector q. The GDP of the unconstrained part of the economy subject to the quantity constraint is g(π, q, C, v) min p g(π, p, C, v) pq. 5 Then GDP is equal to g (π, q, C, v; p ) = p q + g(π, q, C, v) (1) where the market sellers prices p are used to value manufacturing output, not equal to marginal cost p = g q. By construction, g p GDP by qdp. = q, hence changes in sellers prices alter g is specialized to yield 2 stage Cobb-Douglas/CES manufactures input demand, applying Shephard s Lemma. Within each sector the input demand for manufactures is spread across national varieties, derived (using Shephard s Lemma) from a Constant presumably accrue to agriculture and other natural resource industries. 5 Quantity constrained GDP and expenditure functions are analyzed in Anderson and Neary (1992). 5

7 Elasticity of Substitution (CES) cost function for sector k. The aggregate input quantity index is gc, aggregating across sectors with a Cobb-Douglas cost function. The change in buyers prices alters GDP by gc dc. The change in GDP due to FTA-induced price changes is given by qdp gc dc the local change in real manufacturing income. In percentage terms this is the initial manufacturing income times times the percentage change in terms of trade. Our application extends to discrete changes but the intuition is the same. A closure assumption relates aggregate manufactures input expenditure g C C to sales p q as a constant ratio that can differ by country. This assumption avoids a full general equilibrium treatment, and is valid if (i) manufactures inputs are a constant proportion of GDP, and (ii) the non-manufactures portion of GDP rises in proportion to the manufactures portion of GDP under FTA implementation. 6 Potential bias in our terms of trade measures due to the fixed supply assumption is ambiguous. On the one hand, the value of a marginal change in the quantity constraint is p + g q = p p, the market sellers price vector minus the marginal cost vector. The constant quantity assumption of our approach omits the value of quantity changes (p p)dq 0 where the sign follows from maximization. On the other hand, the implied changes in production will increase supply where p k i p k i > 0 and hence tend to lower the market equilibrium p k i. The net effect of suppressing substitution in supply between the manufacturing sectors and between manufacturing and non-manufacturing is ambiguous on this reasoning. The closure assumption suggests a further potential bias due to an omitted multiplier effect of intermediate goods linkages between manufacturing and non-manufacturing output. A fall in input prices could lower non-manufacturing prices that serve as inputs to manufactures. Caliendo and Parro s NAFTA exercise argues that intermediate linkages raise trade and welfare estimates by some 40%. 7 Our results do not appear to be sensitive 6 The second part of the assumption is that g π π rises proportionately to p q. The first part of the assumption is that gc C/g is constant. Since g is homogeneous of degree 1 in π, C, p, the ratio gc C/p q is constant. 7 The difficulties facing more elaborate CGE studies prominently include very inaccurate information on the actual end users of imported intermediate goods based on a distribution of imports in proportion to the distribution of domestic shipments across sectors. 6

8 to the closure assumption, as explained below. 1.1 Manufactures Trade with Structural Gravity Let p k ij denote the price of origin i goods in class k for region j buyers and let p k i denote the factory-gate price at i. The arbitrage condition implies p k ij = p k i t k ij, where t k ij 1 denotes the trade cost factor on shipment of goods in class k from i to j. Effectively it is as if goods melt away in distribution so that 1 unit shipped becomes 1/t k ij < 1 units on arrival. Cost minimizing buyers of inputs using the globally common CES technology have expenditure on goods of class k shipped from origin i to destination j given by: X k ij = (β k i p k i t k ij/p k j ) 1 σ k E k j. (2) Here E k j is country j s expenditure on goods of class k while in the CES share expression preceding it σ k is the elasticity of substitution for goods class k, 8 β k i is a CES share parameter, and P k j = [ i (βk i p k i t k ij) 1 σ k ] 1/(1 σ k ) is a CES price index. Now consider the supply side. An endowment q k i at the origin is valued at the factory gate price p k i. The value of shipments at end user prices for country i and goods class k is equal to p k i q k i = Y k i, where the iceberg trade cost metaphor implies that some of q k i melts en route to the buyers who must pay the full production plus distribution cost. Market clearance for goods in each class and origin implies Y k i = j (β k i p k i ) 1 σ k (t k ij/p k j ) 1 σ k E k j, i, k. (3) Define Y k i Y k i and divide (3) by Y k to obtain: (βi k p k i Π k i ) 1 σ k = Yi k /Y k, (4) 8 Recent developments in the empirical trade literature suggest that the elasticity of substitution varies across countries. See Broda et al (2006). In the empirical analysis however, we do not allow the elasticity to vary across countries. 7

9 where (Π k i ) 1 σ k j (tk ij/p k j ) 1 σ k E k j /Y k. The derivation of the structural gravity model is completed using (4) to substitute for β k i p k i in (2), the market clearance equation and the CES price index. Then: Xij k = Ek j Yi k Y k ( t k ij P k j Πk i ) 1 σk (5) (Π k i ) 1 σ k = j (P k j ) 1 σ k = i ( ) 1 σk t k ij Ej k (6) Pj k Y k ( ) 1 σk t k ij Yi k Y. (7) k Π k i (5)-(7) is the structural gravity model. Π k i denotes outward multilateral resistance (OMR), while P k j denotes inward multilateral resistance (IMR). For analyzing the effect of FTAs (and other comparative static shifts) on the terms of trade, multilateral resistance provides a useful peek inside the black box of the general equilibrium model. Outward multilateral resistance is the average sellers incidence. It is as if each country i shipped its product k to a single world market facing supply side incidence of trade costs of Π k i. (4) is interpreted as the market clearance condition for a hypothetical world market where a single representative buyer purchases variety i in class k at price p k i Π k i. 9 The equilibrium factory gate price p k i implied by (4) is negatively related to the equilibrium sellers incidence of trade costs and also negatively related to the sellers share of the world market. Solving (4) for p k i using Y k i = p k i q k i : p k i = (Y k /q k i ) 1/σ k (β k i Π k i ) (1 σ k)/σ k. (8) Leaving aside the influence of Y k, which is constant due to a normalization discussed in 1.2, each remaining term on the right hand side is intuitive because it boils down to effectively partial equilibrium with supply shifter q k i, demand shifter β k i Π k i. Of course, in full general equilibrium the sellers incidence Π k i and sellers incidence is a function of the 9 The CES cost index for this hypothetical user in the world market is equal to 1 because this is implied by summing (4) over i. 8

10 sellers price p k i through the seller s share Y k i /Y k. But Π k i carries the general equilibrium complexity into a separable partial equilibrium market module that determines the sellers price for each origin and sector. Inward multilateral resistance in (7) is a CES index of bilateral buyers incidences t k ij/π k i, using the interpretation of Π k i as the sellers incidence and recognizing that t k ij/π k i is the incidence falling on the buyer. It is as if each country j bought its vector of class k goods from a single world market facing buyers incidence of P k j. The structural gravity representation of the model provides a useful interpretation and decomposition of the global efficiency and terms of trade changes developed in Sections The global efficiency deflator is the product of theoretically consistent global indexes of buyers and sellers incidence of trade costs. As for national terms of trade changes, buyers price index changes in each sector are equal to buyers incidence changes while sellers price changes decrease in sellers incidence changes with elasticity 1/σ k 1 all else equal, due to (8). 1.2 Calculating the Effects of Free Trade Agreements The effects of FTAs of the 1990s are calculated by solving for the terms of trade in the initial 1990 equilibrium and then the hypothetical equilibrium with the FTAs imposed in The 1990 terms of trade are calculated with the set of estimated t k ijs at actual 1990 values with the FTAs switched off. The hypothetical FTA terms of trade are calculated based on factory gate prices that clear the markets with the 1990 supply data and the hypothetical t k ijs that include the estimated volume effects of all FTAs actually implemented in the 1990s. For the base year terms of trade the sellers price index is equal to 1 by choice of units. The buyers price indexes for each sector are solved from system (6)-(7) using the 1990 sales and expenditure data and the estimated no-fta trade costs t k ij. The aggregate buyers price index is calculated as the Cobb-Douglas index of sectoral price indexes, with the shares α k calibrated to the 1990 world production shares Y k / k Y k. The hypothetical FTA terms of trade require computing the general equilibrium so- 9

11 lution to market clearing factory gate prices. The specification includes the budget constraint requirements and a normalization. In addition, the computation requires a further calibration of the sectoral technology distribution parameters (βi k ) 1 σ k, i, k. These are calibrated from the base year market clearance equations (11) given below, subject to a normalization. The level of the multilateral resistance variables is affected by the normalization of the βi k s, but their proportional change is invariant to to the normalization. See Section 3.1 for details. It is convenient to solve the market clearance system in world share form. The world supply shares in the endowments economy are given by Y k i Y k = The world demand shares are given by p k i q k i i p k i q k i, i, k. (9) E k j Y k = φ j k p k j qj k k p k j qk j j φ j, j, k. (10) The demand share on the right hand side of (10) uses the assumption of identical Cobb- Douglas technology at the upper level to set country j s share of world spending on goods of class k as the ratio of j s spending on all goods to world spending on all goods, canceling the common parameter α k in numerator and denominator. φ j > 0 is the ratio of total expenditure to income for manufacturing as a whole in country j. φ j 1 allows for nationally varying manufacturing trade imbalance. 10 φ j is assumed to be constant, rationalized under the assumption that manufactured inputs are a constant share of GDP and that non-manufactured goods are affected by FTAs in proportion to their effect on manufactures. Variation in φ s is not an important concern in practice based on sensitivity experiments, because the results are almost completely insensitive to setting φ j = 1, j. There are NK p s that change from their initial value equal to 1 when the t s change. 10 If all goods were included in K and total trade was balanced, φ j = 1, j. 10

12 They are solved from the market clearance equations p k i q k i i p k i q k i = j (β k i p k i t k ij/pj k ) 1 σ k k φ jp k j qj k j,k φ, i, k (11) jp k j qk j where (P k j ) 1 σ k = i (β k i p k i t k ij) 1 σ k, j, k (12) and (10) is utilized to replace E k j /Y k on the right of the right hand side of (11). There are NK equations in (11) and another NK in (12), the latter being solved recursively with the solution {p k i } obtained by substituting the right hand side of (12) into (11). A normalization of prices is required to solve (11)-(12) because the system is homogeneous of degree zero in the vector of factory gate prices. A natural normalization holds world real resources constant: i,k p k i q k i = i,k p k0 i q k i = k Y k0. (13) By choice of units p k0 i = 1. In (11)-(12), due to separability and homotheticity, only 2NK-K equations are linearly independent, so (13) must apply in each sector in equilibrium: i qk i = i p k i qi k, k. To see this, let p 1k {p k i }, denote the vector of equilibrium factory gate prices in sector k in some particular equilibrium with the new t s. At this equilibrium p 1k, a scalar shift λ k in p k raises the P k j s equiproportionately. Then for the block of equations for sector k within (11), conditional on the initial equilibrium value of k p k j q k j / i,k p k i q k i = λ k k p1k i q k j / i,k qk i under the normalization (13), the equation block continues to hold. Consistency with normalization (13) requires λ k = 1, k. The change in the sellers equilibrium incidence due the trade cost changes is useful in decomposing the change in factory gate prices using (8). More importantly, sellers incidence is required for the world efficiency measure proposed below in Section 1.4. The equilibrium value of {Π k i } is implied by the multilateral resistance system (6)-(7) for the 11

13 initial and FTA equilibria. In practice, since the P s in the FTA equilibrium are solved recursively from (11)-(12), the Πs are solved recursively using the solution P s in (6) National Gains Measures Accounting for the effect of trade cost changes on manufacturing real income in this setup is simple. National manufacturing income with multiple goods is given by k p k i q k i. Buyers in i face price indexes P k i for goods class k. The user cost index for all goods is given by C i = exp( k α k ln P k i ). Then real manufacturing income R i = k p k i q k i /C i = T i k qk i, i s real product k qk i (under normalization (13)) times i s terms of trade T i given by T i = k p k i qi k / k qk i. (15) C i T i is the ratio of the exact price index of exportable goods to the true cost index of importable goods, a variation on the standard definition of the terms of trade because it includes goods produced and sold at home in both numerator and denominator. The preceding analysis is related to the full GDP structure as follows. Differentiating GDP given by (1) with respect to the manufacturing prices and using Hotelling s and Shephard s Lemmas, the proportional rate of change of GDP is ĝ = k Y k g [ k w k ˆp k k ω k ˆP k ] + k (Ek Y k ) g ω k ˆP k, k where w k = Y k / k Y k and ω k = E k / k Ek. The square bracket term on the right hand side is the percentage change in the terms of trade. It is multiplied by the importance of manufacturing in GDP, a scaling factor we disregard. The second term on the right is equal to zero under balanced trade. While this is not generally true for any subset 11 This solution is consistent with solving (6)-(7) for the supply and expenditure shares implied by the solution p s and normalizing the Πs by (βi k ) 1 σ k (p k i Π k i ) 1 σ k = 1, k. (14) i (14) arises from interpreting the global sales pattern {Yi k/y k } as arising from sales to a hypothetical world buyer with CES technology, resulting in Yi k/y k = (βi kp k i Π k i )1 σ k where the hypothetical CES global price index is equal to 1. 12

14 of sectors, the normal convention is to impose it when all sectors are included, so we suppress this term in our treatment. Equation (15) follows by integrating the square bracket under the restrictions of fixed q s and a Cobb-Douglas cost function C for input prices. The effect on real manufacturing income in country i from a switch from No FTA (denoted with superscript 0) to FTA (denoted with superscript F ) can be evaluated by computing the proportional real income change with the ratio R F i /R 0 i, equal to the proportionate change in the terms of trade T F i /T 0 i. Ti F /Ti 0 gives the terms of trade effects component of the standard decomposition of welfare changes (e.g., Anderson and Neary, 2005), not attempting to calculate the marginal deadweight loss effects that embody rent changes, many of which are invisible. All trade costs and their changes are treated as real in our benchmark treatment. To check on sensitivity to this treatment we also compute the change in tariff revenues induced by FTAs to compare it with the terms of trade effects. Other rents continue to be ignored due to lack of data on quota rents (which are large for some country pairs and product lines but notoriously hard to measure), monopoly rents associated with market structure and asymmetric information, extortion and so forth. 12 The Appendix develops a welfare accounting setup that would allow for a fuller evaluation as context for our sensitivity analysis, a special case being the treatment in Section World Efficiency Measures The effect of FTAs on world efficiency of trade is evaluated in terms of the change in iceberg melting. This natural measure is an application of Debreu s (1951) coefficient of resource utilization as specialized in Deaton s (1979) distance function. Global aggregate sellers incidence (outward multilateral resistance) is interpreted as global aggregate shrinkage factor on the original endowment due to melting prior to arrival on the world 12 Anderson and van Wincoop (2002) perform a gravity model based simulation of NAFTA s effects where tariff revenue changes combine with terms of trade changes. Terms of trade changes are far more important than revenue changes in the net welfare effects. That study points out that gravity does a far better job of predicting the actual bilateral trade flow changes than did any of the Computable General Equilibrium (CGE) models surveyed. 13

15 market. Global aggregate buyers incidence (inward multilateral resistance) is interpreted as the melting due to shipment from the world market to its various destinations. Our global efficiency measure reverts to ignoring rents, consistent with a focus on the efficiency of shipments and recognition that rents are a transfer. The endowment of world resources is the vector {q k i qk i }. In equilibrium, only a fraction of the endowment arrives at the hypothetical world market for sellers to exchange with buyers because some melts away in shipment to the world market. A further nationally varying fraction melts away as the buyers ship their world market purchases to their destinations. The aggregate sellers (across origins) and buyers (across destinations) shrinkage for each goods class k are derived utilizing market clearance and the CES demand system. Aggregation across goods classes uses the Cobb-Douglas demand structure for manufacturing inputs. Consistent aggregation of sellers incidence across sources follows from defining the global aggregate sellers incidence in each goods class k: Π k by: Π k ( i (βi k p k i ) 1 σ k ) 1/(1 σk ) = ( i (βi k p k i Π k i ) 1 σ k ) 1/(1 σk ) = 1. (16) Π k is a CES function of the Π k i s, the (variable) weights being the hypothetical frictionless equilibrium world shares wi k = (βi k p k i ) 1 σ k / i (βk i p k i ) 1 σ k. Re-writing (16), the CES aggregator in terms of power transforms is (Π k ) 1 σ k = i w k i (Π k i ) 1 σ k (17) Aggregate sellers incidence is interpreted as iceberg melting by exploiting the second equation in (16): global sales can be interpreted as the product of effective world use q k /Π k and the frictionless user price index ( i (βk i p k i ) 1 σ k) 1/(1 σk ). The second equation in (16) follows from summing (4): the user price index for class k goods for a hypothetical user located in the world market is equal to 1. In the initial situation (without FTAs for example) the factory gate prices in (16) are all equal to one, yielding aggregate sellers incidence Π k0. Bringing in the new trade costs 14

16 (the FTAs) induces new p s and new Π s, and hence new aggregate effective consumption. Let Π kf denote the value of Π k in the FTA equilibrium. For each goods class, the effect of the FTA on global efficiency via the sellers incidence is measured by Π k0 /Π kf. On the buyers side of the market, goods are in effect purchased on the world market in the total amount q k /Π k. For each destination j the goods are shipped home with further melting such that only E k j /P k j arrives at destination j. Effectively the buyers on average cover the full margin Π k P k j for each destination. The world average melting across destinations is based on the global average buyers incidence defined by 1 P k j E k j Y k 1 P k j. Then world use at destination of sector k goods is given by q k Π k P k. The world endowment of good k is deflated here by the product of the appropriate average buyers and sellers incidence. (1 1/Π k P k )q k is the iceberg melting due to trade costs. A scalar measure of the overall efficiency gain requires some sort of weighting across goods classes. Making use of the identical Cobb-Douglas technology across goods classes and the hypothetical world market, the world efficiency measure is defined by 1 ΠP = 1 exp[ k α k(ln Π k + ln P k )], (18) where α k is the cost share parameter for goods class k. Evaluating ΠP at initial and FTA trade costs and forming their ratio Π 0 P 0 /Π F P F gives a scalar measure of the global efficiency gain from the shift in trade costs due to the FTA, neatly decomposable into sellers efficiency change Π 0 /Π F times buyers efficiency change P 0 /P F. From the perspective of the compensation principle, world efficiency measure (18) makes hypothetical international transfers of shares of the endowment vector, a quantity alternative to international income transfers that compensate between the national effi- 15

17 ciency measures (15) given a positive aggregate. Real income for the world is given by i T i k qk i = T i,k qk i where the right hand side implicitly defines the average efficiency T. A conventional income measure of efficiency gains from FTAs can be constructed as T F / T 0. Generally T 1/ΠP, as in our application. We prefer the distance function measure developed here because it has a natural efficiency of trade interpretation whether transfers are made or not. Figure 1 in the Appendix illustrates (18) for two goods classes. It should be emphasized that the level of 1/ΠP that measures the total fraction of the iceberg that melts in any situation is in practice not measurable because gravity equations cannot measure the absolute level of trade costs, only relative trade costs inferred from the distortion of trade relative to its frictionless benchmark. In contrast, relative global efficiency is conceptually and practically useful. 2 Empirical Implementation and Analysis 2.1 Econometric Specification The standard procedure infers FTA effects on bilateral trade flows accounts with a fixed effect for the presence of free trade agreements, interpreted as part of the unobservable trade costs, t k ij, in the structural gravity equation (5). For a generic good, we define: t 1 σ ij = e β 1F T A ij +β 2 ln DIST ij +β 3 BRDR ij +β 4 LANG ij +β 5 CLNY ij + 46 i=6 β i SMCT RY ij. (19) Here, F T A ij is an indicator variable for a free trade agreement between trading partners i and j. ln DIST ij is the logarithm of bilateral distance. BRDR ij, LANG ij and CLNY ij capture the presence of contiguous borders, common language and colonial ties, respectively. Finally, we follow Anderson and Yotov (2010b) to define SMCT RY ij as a set of country-specific dummy variables equal to 1 when i = j and zero elsewhere, which capture the effect of crossing the international border by shifting up internal trade, all else equal It should be noted that while controlling for internal trade has been ignored in the vast majority of gravity estimates, the few studies that do include a variant of our SM CT RY covariate always estimate 16

18 The econometric specification of gravity is completed by substituting (19) for the power transform of t ij into (5) and then expanding the gravity equation with an error term. To obtain econometrically sound estimates of the parameters of interest we must meet the following challenges: presence of zero trade flows; heteroskedasticity in trade flows data; endogeneity of free trade agreements; and, unobservable multilateral resistance terms. To utilize the information carried by the zero trade flows and to account for heteroskedasticity in trade flows data, we resort to the Poisson pseudo-maximumlikelihood (PPML) estimator advocated by Santos-Silva and Tenreyro (2007) who argue that the truncation of trade flows at zero biases the standard log-linear OLS approach and results in inconsistent coefficient estimates. 14 Time-varying, directional (source and destination), country-specific dummies control for the multilateral resistances along with the sales (Y k i ) and expenditure (E k j ) variables in (5). 15 To account for FTA endogeneity, we use the panel data estimation techniques described in Wooldridge (2002) and first applied to a similar setting by Baier and Bergstrand (2007), who employ aggregate data to show that direct FTA effects on bilateral trade flows can be consistently isolated in a theoretically-founded gravity model by using countrypair fixed effects. As a robustness check, Baier and Bergstrand (2007) produce alternative large, positive and significant coefficient estimates on this dummy. For example, Wolf (2000) finds evidence of US state border effects using aggregate shipments data. In the case of Canadian commodity trade, Anderson and Yotov (2010a) find that internal provincial trade is higher than interprovincial and international trade for 19 non-service sectors during the period In a complementary study, Anderson et al (2011) obtain similar estimates for Canadian service trade. Jensen and Yotov (2011) estimate very large and significant SM CT RY impact for important agricultural commodities in the world in Finally, Anderson and Yotov (2010b) estimate significant, country-specific SMCTRY effects for 18 manufacturing sectors in the world (76 countries), Helpman, Melitz and Rubinstein (2008) (HMR) propose an alternative approach to zero trade flows. They develop a formal model of selection, where exporters must absorb some fixed costs to enter a market. They identify the model using religion as an exogenous variable that enters selection but is excluded from determination of the volume of trade. We choose not to use HMR, partly because of doubts about the exclusion restriction and partly because of doubts about the importance of fixed costs in light of evidence in Besedes and Prusa (2006a,b) that highly disaggregated bilateral US trade flickers on and off. Anderson and Yotov (2010b) show that HMR and PPML as well as OLS give essentially the same bilateral trade costs after normalization. 15 Anderson and van Wincoop (2003) use custom programming to account for the multilateral resistances in a static setting. Feenstra (2004) advocates the directional, country-specific fixed effects approach. To estimate the effects of the Canadian Agreement on Internal Trade (AIT), Anderson and Yotov (2010a) use panel data with time-varying, directional (source and destination), country-specific fixed effects. Olivero and Yotov (2012) formalize their econometric treatment of the MR terms in a dynamic gravity setting. 17

19 FTA estimates with first-differenced panel data, which eliminates the pair fixed effects. 16 Taking all of the above considerations into account, we use the PPML technique 17 to estimate the following econometric model across country pairs and time for each class of commodities: X ij,t = exp[β 0 +η i,t +θ j,t +γ ij +β 1 F T A ij,t +β 2 F T A ij,t 1 +β 3 F T A ij,t 2 ]+ɛ ij,t, k. (20) Here, X ij is bilateral trade (in levels) between partners i and j at time t. 18 F T A ij,t is an indicator variable that takes a value of one if at time t countries i and j are members of the same free trade agreement. η i,t denotes the time-varying source-country dummies, which control for the (log of) outward multilateral resistances and total shipments. θ j,t encompasses the time varying destination country dummy variables that account for the (log of) inward multilateral resistances and total expenditure. γ ij captures the countrypair fixed effects used to address FTA endogeneity. Following Baier and Bergstrand (2007), we specify the FTA volume effects,the β s, to be uniform (as opposed to varying by FTA) and we allow for gradual phasing-in of the free trade agreement effects by including FTA lags in specification (20). The reason for the former is that, due to the rich fixed effects structure of our econometric specification and 16 The issue of FTA endogeneity is not new to the trade literature (see Trefler 1993, for example). However, primarily due to the lack of reliable instruments, standard instrumental variable (IV) treatments of endogeneity in cross-sectional settings have not been successful in addressing the problem. See for example Magee (2003) and Baier and Bergstrand (2002, 2004b). Baier and Bergstrand (2007) summarize the findings from these studies as at best mixed evidence of isolating the effect of FTAs on trade flows. 17 Consistency of the PPML estimator arises from the large sample structure of the gravity model. If N is the number of regions and τ is the number of periods, the number of fixed effects grows at rate 2Nτ +N 2 while the number of observations grows at rate N 2 τ >> 2Nτ +N 2 as τ grows. As a robustness check, we also estimated with the first differences technique and obtain essentially the same results as with country fixed effects. (Since first differencing gave rise to some negative values of X ij,t that PPML cannot handle, our first difference estimator is log-linear, as in Baier and Bergstrand (2007).) 18 In a static setting, (5) implies that income and expenditure elasticities of bilateral trade flows are unitary and, therefore, size-adjusted trade is the natural dependent variable. Bringing output and expenditures on the left-hand side has the additional advantage of controlling for endogeneity of these variables. Using aggregate data however, Frankel (1997) shows that the bias due to GDP endogeneity is insignificant. In addition, Olivero and Yotov (2012) show that income and expenditure elasticities are not necessarily equal to one in a dynamic setting, such as the one that we employ here to account for FTA endogeneity. Thus, in addition to accounting for the unobserved multilateral resistances, the fixed effects in our estimations will also absorb country-specific output and expenditures. Using disaggregated manufacturing data, Anderson and Yotov (2010b) show that the multilateral resistance component explains about 32.3% of the variance of the fixed effects, while the size effect terms (output and expenditures) account for about 57.7% of the fixed effects variability. 18

20 the small variability in any individual FTA indicators, we cannot identify separately the effects of specific FTAs. 19 The reason for the latter is that private agents in the trading partners gradually adjust to the new economic conditions under a recently implemented FTA. From an econometric perspective, allowing for phasing-in adds a time dimension (in addition to the commodity, country, and seller and buyer dimensions) to the data sets of terms of trade (welfare) effects that we construct in the next section. Finally, as noted by Cheng and Wall (2005), Fixed-effects estimations are sometimes criticized when applied to data pooled over consecutive years on the grounds that dependent and independent variables cannot fully adjust in a single year s time. (p.8). To avoid this critique, we use only the years 1990, 1994, 1998, and This implies that F T A ij,t 1 and F T A ij,t 2 are four-year and eight-year lags, respectively; comparable to the 5 year lags in Baier and Bergstrand (2007). To calculate terms of trade effects, estimated t ij s with and without FTA effects are required. A two-step procedure allows estimation of all bilateral trade costs including internal trade costs. 20 First, we estimate the panel gravity model (20) using the PPML estimator with time-varying, source and destination fixed effects. Next, we re-estimate while imposing the first stage estimated coefficients { β i, η it, θ jt } and replacing the bilateral 19 In the sensitivity analysis, we split our sample into deep vs. shallow FTAs. 20 This procedure evades the problem with the obvious alternative to calculate the t ij s using the estimates of the bilateral fixed effects from specification (20) in combination with the FTA effects: ˆt 1 σ ij = e ˆβ ij+ ˆβ fta F T A ij+ ˆβ l.fta L.F T A ij+ ˆβ l2.fta L2.F T A ij, (21) where ˆβ ij is constructed by adding up horizontally the estimates of the country-pair fixed effects. ˆβfta, ˆβ l.fta, and ˆβ l2.fta are the estimates of the current, lagged, and two-period lagged FTA effects, respectively. This approach cannot obtain internal trade costs t ii s because perfect collinearity does not allow for separate identification of the fixed effect estimates ˆβ ii s for individual countries in model (20). Another approach that simultaneously obtains consistent gravity estimates (that can be used to construct bilateral trade costs) and unbiased FTA estimates, is to regress the estimates of the bilateral fixed effects from (20) on the set of standard gravity variables. In analysis available by request, we improve on Cheng and Wall (2005) by using variance weighted least squares to obtain unbiased gravity estimates from the bilateral fixed effects. However, the same critique (not being able to identify internal trade costs separately for each country) applies here as well. 19

21 fixed effects with a regression on the standard time-invariant gravity covariates: X ij = exp[ ˆβ 0 + ˆβ 1 F T A ij,t + ˆβ 2 F T A ij,t 1 + ˆβ 3 F T A ij,t 2 + γ 1 ln DIST ij + γ 2 BRDR ij + 45 γ 3 LANG ij + γ 4 CLNY ij + γ i SMCT RY ij + ˆη i,t + ˆθ j,t ] + ε ij,t. (22) i=5 The estimates from (22) and actual data on the gravity variables are used to construct a complete set of power transforms of bilateral trade costs in the absence of FTAs: ) ( t NOF ij T A 1 σ = eˆγ 1 ln DIST ij + ˆγ 2 BRDR ij + ˆγ 3 LANG ij + ˆγ 4 CLNY ij + 45 i=5 ˆγ i SMCT RY ij. (23) The set of bilateral trade costs including FTA effects is constructed from (20) and (23): ( t F T A ij ) 1 σ = ( t NOF T A ij ) 1 σ e ˆβfta F T A ij + ˆβ l.fta L.F T A ij + ˆβ l2.fta L2.F T A ij. (24) Our procedure to obtain the direct FTA effects on bilateral trade costs is valid provided: (i) that the FTA estimates are unbiased (assured by the panel data treatment), (ii) ) 1 σ that is a good proxy for the time-invariant trade costs (as accepted by ( t NOF T A ij the literature) and (iii) that the formation of FTAs does not influence the effects of the standard gravity covariates from (23) Data Description Our study covers the period for a total of 41 trading partners including 40 separate countries and a rest of the world (ROW) aggregate, consisting of 24 additional nations. 22 None of the countries included in ROW are part of any FTAs with countries 21 We confirm that by estimating the standard gravity equation (22) with and without FTAs. The estimates on the standard gravity variables with and without FTAs are virtually identical. Results are available by request. 22 The 40 countries are Argentina, Australia, Austria, Bulgaria, Belgium-Luxembourg, Bolivia, Brazil, Canada, Switzerland, Chile, China, Columbia, Costa Rica, Germany, Denmark, Ecuador, Spain, Finland, France, United Kingdom, Greece, Hungary, Ireland, Iceland, Israel, Italy, Japan, Korea, Rep., Mexico, Morocco, Netherlands, Norway, Poland, Portugal, Romania, Sweden, Tunisia, Turkey, Uruguay, United States. The rest of the world includes Cameroon, Cyprus, Egypt Arab Rep., Hong Kong, Indonesia, India, Iran Islamic Rep., Jordan, Kenya, Kuwait, Sri Lanka, Macao, Malta, Myanmar, Malawi, Malaysia, Niger, Nepal, Philippines, Senegal, Singapore, Trinidad and Tobago, Tanzania, South Africa. 20