Empirical trade analysis

Transcription

1 Empirical trade analysis Gravity theory and estimation Cosimo Beverelli World Trade Organization Cosimo Beverelli Gravity Bangkok, Dec / 80

2 Outline 1 Introduction and learning objectives 2 Structural gravity derivations 3 Structural gravity estimation: challenges and solutions 4 Structural gravity estimation: practical recommendations 5 A generic comprehensive structural gravity model 6 Interpretation of gravity estimates 7 Data sources Cosimo Beverelli Gravity Bangkok, Dec / 80

3 Introduction and learning objectives Introduction According to Newton's Law of Universal Gravitation, any particle in the universe attracts any other particle thanks to a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them Applied to international trade, Newton's Law of Gravity implies that, just as particles are mutually attracted in proportion to their sizes and proximity, countries trade in proportion to their respective market size (e.g. gross domestic products) and proximity This is the a-theoretical gravity model of international trade Today, we will derive a theoretical gravity model of international trade, based on the Armington-CES model of Anderson and van Wincoop (2003) We follow Chapter 1 of the Advanced Guide where you will also nd all references and extensions (e.g., derivations of Eaton-Kortum gravity and of gravity with taris in Appendices A and B to Chapter 1) Equation numbering is the same as in the Advanced Guide Cosimo Beverelli Gravity Bangkok, Dec / 80

4 Introduction and learning objectives All roads lead to gravity Cosimo Beverelli Gravity Bangkok, Dec / 80

5 Structural gravity derivations Assumptions Consider a world that consists of N countries, where each economy produces a variety of goods (i.e. goods are dierentiated by place of origin as in Armington, 1969) that is traded with the rest of the world The supply of each good is xed to Q i, and the factory-gate price for each variety is p i Thus, the value of domestic production in a representative economy is dened as Y i = p i Q i, where Y i is also the nominal income in country i Country i's aggregate expenditure is denoted by E i. Aggregate expenditure can also be expressed in terms of nominal income by E i = φ i Y i, where φ i > 1 shows that country i runs a trade decit, while 0 < φ i < 1 reects a trade surplus (treated as exogenous) For brevity's sake, the time dimension t is omitted in the derivations Cosimo Beverelli Gravity Bangkok, Dec / 80

6 Structural gravity derivations Consumer preferences On the demand side, consumer preferences are assumed to be homothetic, identical across countries, and given by a CES-utility function for country j: { i α 1 σ σ i c σ 1 σ ij } 1 σ σ (1) where σ > 1 is the elasticity of substitution among dierent varieties, i.e. goods from dierent countries, α i > 0 is an exogenous CES preference parameter, and c ij denotes consumption of varieties from country i in country j Cosimo Beverelli Gravity Bangkok, Dec / 80

7 Structural gravity derivations Budget constraint Consumers maximize equation (1) subject to the following standard budget constraint: p ij c ij = E j (2) i Equation (2) ensures that the total expenditure in country j, E j, is equal to the total spending on varieties from all countries, including j, at delivered prices p ij = p i t ij Prices are a function of factory-gate prices in the country of origin, p i, marked up by bilateral trade costs, t ij 1, between trading partners i and j These bilateral trade costs are dened as iceberg costs, as is standard in the trade literature (Samuelson, 1952) In order to deliver one unit of its variety to country j, country i must ship t ij 1 units, since 1/t ij of the initial shipment melts en route" Cosimo Beverelli Gravity Bangkok, Dec / 80

8 Structural gravity derivations Solution to consumer's optimization problem Solving the consumer's optimization problem (see Appendix 2.A in Baldwin et al., 2011) yields the expenditures on goods shipped from origin i to destination j as: ( ) (1 σ) αi p i t ij X ij = E j (3) where X ij denotes trade ows from exporter i to destination j and P j can be interpreted as a CES consumer price index: P j [ P j = (α i p i t ij ) i ] 1 1 σ (4) Cosimo Beverelli Gravity Bangkok, Dec / 80

9 Structural gravity derivations Observations From equation (4), expenditure in country j on goods from source i, X ij, is: 1 Proportional to total expenditure, E j, in destination j. The simple intuition is that, all else equal, larger/richer markets consume more of all varieties, including goods from i 2 Inversely related to the (delivered) prices of varieties from origin i to destination j, p ij = p i t ij. This is a direct reection of the law of demand, which depends not only on factory-gate price p i but also on bilateral trade cost t ij between partners i and j. The ideal combination that favours bilateral trade is an ecient producer, characterized by low factory-gate price, and low bilateral trade cost between countries i and j Cosimo Beverelli Gravity Bangkok, Dec / 80

10 Structural gravity derivations Observations (ct'd) From equation (4), expenditure in country j on goods from source i, X ij, is: 3 Directly related to the CES price aggregator P j. This relationship reects the substitution eects across varieties from dierent countries. All else equal, the relatively more expensive the rest of the varieties in the world are, the more consumers in country j will substitute away from them and toward the goods from country i 4 Contingent on the elasticity of substitution σ when factory-gate prices or the aggregate CES prices (or in the combination of those as a relative price) change. All else equal, a higher elasticity of substitution will magnify the trade diversion eects from the more expensive commodities to the cheaper ones Cosimo Beverelli Gravity Bangkok, Dec / 80

11 Structural gravity derivations Market clearance Impose market clearance for goods from each origin, Yi j X ij i. Using equation (3), this yields: ( ) (1 σ) αi p i t ij E j (5) Y i = j P j Cosimo Beverelli Gravity Bangkok, Dec / 80

12 Structural gravity derivations Further manipulations Dening Y i Yi and dividing equation (5) by Y, the terms can be rearranged to obtain: (α i p i ) (1 σ) = Y i Y ( ) tij (1 σ) Ej j P j Y Following Anderson and van Wincoop (2003), the term in the denominator of equation (6) can be dened as Π (1 σ) i, allowing to rewrite equation (6) as: (α i p i ) (1 σ) = Y i/y Π (1 σ) i (6) (7) Cosimo Beverelli Gravity Bangkok, Dec / 80

13 Structural gravity derivations The structural gravity system Combining equation (7) with equations (3) and (4) yields the structural gravity system: X ij = Y ( ) (1 σ) ie j tij (8) Y Π i P j Π (1 σ) i = j ( tij P j ) (1 σ) E j Y (9) P (1 σ) J = i ( tij Π i ) (1 σ) Y i Y (10) Equation (10) (1-8) is the theoretical gravity equation that governs bilateral trade ows. It can be conveniently decomposed into two terms: (i) a size term, Y i E j /Y ; and (ii) a trade cost term, [t ij / (Π i P j )] (1 σ) Cosimo Beverelli Gravity Bangkok, Dec / 80

14 Structural gravity derivations Size vs. trade cost decomposition: size term The intuitive interpretation of the size term, Y i E j /Y, is as the hypothetical level of frictionless trade between partners i and j if there were no trade costs Mechanically, this can be shown by eliminating bilateral trade frictions (i.e. setting t ij = 1), and re-deriving the gravity system Intuitively, a frictionless world implies that consumers will face the same price for a given variety regardless of their physical location and that their expenditure share on goods from a particular country will be equal to the share of production in the source country in the global economy (i.e. X ij /E j = Y i /Y ) Overall, the size term already carries some very useful information regarding the relationship between country size and bilateral trade ows: namely, large producers will export more to all destinations; big/rich markets will import more from all sources; and trade ows between countries i and j will be larger the more similar in size the trading partners are Cosimo Beverelli Gravity Bangkok, Dec / 80

15 Structural gravity derivations Size vs. trade cost decomposition: trade cost term The natural interpretation of the trade cost term, [t ij / (Π i P j )] (1 σ), is that it captures the total eects of trade costs that drive a wedge between realized and frictionless trade. The trade cost term consists of three components: 1 1. Bilateral trade cost between partners i and j, t ij, is typically approximated in the literature by various geographic and trade policy variables, such as bilateral distance, taris and the presence of regional trade agreements (RTAs) between partners i and j 2 The structural term P j, coined by Anderson and van Wincoop (2003) as inward multilateral resistance represents importer j's ease of market access 3 The structural term Π i, dened as outward multilateral resistances by Anderson and van Wincoop (2003), measures exporter i's ease of market access The multilateral resistances are general equilibrium trade costs that take into account the changes in prices, incomes and expenditures induced by bilateral trade cost changes Cosimo Beverelli Gravity Bangkok, Dec / 80

16 Structural gravity derivations Analogy between the Newtonian theory of gravitation and the gravity trade model Newton's Law of Universal Gravitation: F ij = G M im j D 2 ij where F ij is the gravitational force between objects i and j; G is a gravitational constant: M i and M j are object i and j's masses; and D ij is distance between objects i and j Gravity Trade Model: X ij = G Y ie j T θ ij where X ij are exports from i to j; G is the inverse of world production, G 1/Y ; Y i is country i's domestic production; E j is country j's aggregate expenditure; and T ij are total trade costs between countries i and j, Tij θ [t ij / (Π i P j )] (σ 1) Cosimo Beverelli Gravity Bangkok, Dec / 80

17 Structural gravity estimation: challenges and solutions The log-linear gravity equation Given the multiplicative nature of the structural gravity equation (8), and assuming that it holds in each period of time t, it is possible to log-linearize it and expand it with an additive error term, ε ij,t : ln X ij,t = ln E j,t + ln Y i,t ln Y t + + (1 σ) ln t ij,t (1 σ) ln P j,t (1 σ) ln Π i,t + ε ij,t (11) Specication (11) is the most popular version of the empirical gravity equation, and it has been used routinely in the trade literature to study the eects of various determinants of bilateral trade: Geography, demographics, RTAs, taris, exports subsidies, embargoes, trade sanctions, the World Trade Organization membership, currency unions, foreign aid, immigration, foreign direct investment, cultural ties, trust, reputation, mega sporting events (Olympic Games and World Cup), melting ice caps, etc. Cosimo Beverelli Gravity Bangkok, Dec / 80

18 Structural gravity estimation: challenges and solutions Eight challenges 1 Multilateral resistances 2 Zero trade ows 3 Heteroskedasticity of trade data 4 Bilateral trade costs 5 Endogeneity of trade policy 6 Non-discriminatory trade policy 7 Adjustment to trade policy changes 8 Gravity with disaggregated data Cosimo Beverelli Gravity Bangkok, Dec / 80

19 Structural gravity estimation: challenges and solutions Eight challenges 1 Multilateral resistances Cosimo Beverelli Gravity Bangkok, Dec / 80

20 Structural gravity estimation: challenges and solutions Challenge 1: Multilateral resistances The multilateral resistance terms P j,t and Π i,t are theoretical constructs and, as such, they are not directly observable If not appropriately controlled for, there will be an omitted variable bias (Baldwin and Taglioni's 2006 Gold Medal Mistake) Cosimo Beverelli Gravity Bangkok, Dec / 80

21 Structural gravity estimation: challenges and solutions Solutions to challenge 1 (i) Iterative NLLS procedure suggested by Anderson and van Wincoop (2003): rst estimate the trade cost parameters without controlling for the multilateral resistances. Then, use the estimated trade costs to construct an initial set of multilateral resistances. re-estimate the gravity model obtaining new set of trade costs...until convergence (ii) Approximation of the multilateral resistance terms by remoteness indexes constructed as functions of bilateral distance, and Gross Domestic Products (GDPs) (Wei, 1996; Baier and Bergstrand, 2009): ln REM_EXP i,t = ln DIST ( ) ij Ej,t j Y t ln REM_IMP j,t = ln i DIST ( ) ij Yi,t Y t Head and Mayer (2014) criticize such reduced-form approaches as they bear little resemblance to the theoretical counterpart of multilateral terms Cosimo Beverelli Gravity Bangkok, Dec / 80

22 Structural gravity estimation: challenges and solutions Solutions to challenge 1 (ct'd) (iii) Eliminate multilateral resistance terms by using appropriate ratios based on the structural gravity equation. Notable examples include Head and Ries (2001), Head et al. (2010), and Novy (2013) (iv) Hummels (2001) and Feenstra (2016) suggest using directional (exporter and importer) xed eects in cross-section estimations More recently, Olivero and Yotov (2012) demonstrate that the multilateral resistance terms should be accounted for by exporter-time and importer-time xed eects in a dynamic gravity estimation framework with panel data In addition to accounting for the unobservable multilateral resistance terms, the exporter-time and importer-time xed eects will also absorb the size variables (E j,t and Y i,t ) from the structural gravity model as well as all other observable and unobservable country-specic characteristics, which vary across these dimensions, including various national policies, institutions, and exchange rates Cosimo Beverelli Gravity Bangkok, Dec / 80

23 Structural gravity estimation: challenges and solutions Eight challenges 2 Zero trade ows Cosimo Beverelli Gravity Bangkok, Dec / 80

24 Structural gravity estimation: challenges and solutions Challenge 2: Zero trade ows The ordinary least-squares (OLS) estimator has been the most widely used technique to estimate various versions of the gravity equation (11) A clear drawback of the OLS approach, however, is that it cannot take into account the information contained in the zero trade ows, because these observations are simply dropped from the estimation sample when the value of trade is transformed into a logarithmic form The problem with the zeros becomes more pronounced the more disaggregated the trade data are It is especially severe for sectoral services trade due to the highly localized consumption and highly specialized production Cosimo Beverelli Gravity Bangkok, Dec / 80

25 Structural gravity estimation: challenges and solutions Solutions to challenge 2 (i) One frequently applied and very convenient but theoretically inconsistent method is to just add a very small, and in fact completely arbitrary, value to replace the zero trade ows As noted in Head and Mayer (2014) this approach should be avoided because the results depend on the units of measurement and the interpretation of the gravity coecients as elasticities is lost (ii) Eaton and Tamura (1995) and Martin and Pham (2008) propose the use of the Tobit estimator as an econometric solution to the presence of zeroes However, gravity theory is silent about the determination of the Tobit thresholds, causing a disconnect between estimation and theory In practice, the Tobit model would apply to a situation where small values of trade are rounded to zero or actual zero trade might reect desired negative trade Cosimo Beverelli Gravity Bangkok, Dec / 80

26 Structural gravity estimation: challenges and solutions Solutions to challenge 2 (ct'd) (iii) Helpman et al. (HMR, 2008) propose a theoretically-founded two-step selection process, where exporters must absorb some xed costs to enter a market. Thus, xed costs provide an intuitive economic explanation for the zero trade ows to bridge theory and empirics The HMR model is estimated in two stages: (i) a rst-stage Probit estimation, which determines the probability to export, and (ii) a second-stage OLS estimation based on the positive sample of trade ows that also accounts for selection into exporting due to xed costs of exporting Some challenges with the HMR estimation are that it is hard to nd good exclusion restrictions for the rst-stage Probit estimation and/or the need for custom programming when identication relies on functional form Additional diculties with the HMR approach arise for panel data estimations and when dynamic considerations are taken into account Cosimo Beverelli Gravity Bangkok, Dec / 80

27 Structural gravity estimation: challenges and solutions Solutions to challenge 2 (ct'd) (iv) Egger et al. (2011) suggest a two-part gravity model that enables to decompose the eects of the explanatory variables on exports into an eect on the extensive country margin, i.e. the decision to export to a country at all, and on the intensive margin, i.e. the value of exports conditional on positive exports Additionally, and contrary to Helpman et al. (2008), their approach also takes care of potential endogenous regressors such as RTAs in the estimating equation for the extensive and intensive margin (see challenge 5) (v) An easy and convenient solution to the presence of zero trade ows is to estimate the gravity model in multiplicative form instead of logarithmic form This approach, advocated by Santos Silva and Tenreyro (2006), consists in applying the Poisson Pseudo Maximum Likelihood (PPML) estimator to estimate the gravity model Monte Carlo simulations show that the PPML estimator performs very well even when the proportion of zeros is large Cosimo Beverelli Gravity Bangkok, Dec / 80

28 Structural gravity estimation: challenges and solutions Eight challenges 3 Heteroskedasticity of trade data Cosimo Beverelli Gravity Bangkok, Dec / 80

29 Structural gravity estimation: challenges and solutions Challenge 3: Heteroskedasticity of trade data Trade data are plagued by heteroskedasticity As pointed out by Santos Silva and Tenreyro (2006), in the presence of heteroskedasticity (and owing to Jensen's inequality), the estimates of the eects of trade costs and trade policy are not only biased but also inconsistent when the gravity model is estimated in log-linear form with the OLS estimator (or any other estimator that requires non-linear transformation) Cosimo Beverelli Gravity Bangkok, Dec / 80

30 Structural gravity estimation: challenges and solutions Solutions to challenge 3 (i) Equation (11) can be estimated after transforming the dependent variable into size-adjusted trade, which is dened as the ratio between trade and the product of the sizes of the two markets, X ij,t /(E j,t Y i,t ) (Anderson and van Wincoop, 2003) The intuition behind this adjustment is that, arguably, the variance of the error term ε ij,t is proportional to the product of the sizes of the two markets A potential drawback of this approach is that it accounts for (the product of) country size as the only source of heteroskedasticity Furthermore, using the proposed size-adjusted trade as dependent variable would not eliminate the issue of zero trade ows challenge (ii) A more comprehensive approach, proposed by Santos Silva and Tenreyro (2006), is to apply the PPML estimator In principle, the heteroskedasticity issue can be addressed with other estimators, such as the Gamma estimator As discussed above, the PPML estimator also eectively handles the presence of zero trade ows Cosimo Beverelli Gravity Bangkok, Dec / 80

31 Structural gravity estimation: challenges and solutions Eight challenges 4 Bilateral trade costs Cosimo Beverelli Gravity Bangkok, Dec / 80

32 Structural gravity estimation: challenges and solutions Challenge 4: Bilateral trade costs Proper specication of bilateral trade costs is crucial for partial equilibrium as well as for general equilibrium trade policy analysis Cosimo Beverelli Gravity Bangkok, Dec / 80

33 Structural gravity estimation: challenges and solutions Solutions to challenge 4 (i) The standard practice suggested in the literature is to proxy for the bilateral trade cost term appearing in the structural gravity specication (11), (1 σ) ln t ij,t, by using a series of observable variables most of which have become standard covariates in empirical gravity specications, namely: (1 σ) ln t ij,t =β 1lnDIST ij + β 2CNTG ij + β 3LANG ij + + β 4CLNY ij + β 5RTA ij,t + β 6 τ ij,t (12) ln DIST ij is the logarithm of bilateral distance between trading partners i and j CNTG ij is an indicator variable that captures the presence of contiguous borders between countries i and j LANG ij and CLNY ij are dummy variables that take the value of one for common ocial language and for the presence of colonial ties, respectively RTA ij,t is a dummy variable that takes value one if an RTA between trading partners i and j is in place at time t, and zero otherwise Cosimo Beverelli Gravity Bangkok, Dec / 80

34 Structural gravity estimation: challenges and solutions Solutions to challenge 4 (ct'd) The term τ ij,t accounts for bilateral taris and is dened as τ ij,t ln (1 + tari ij,t ), where tari ij,t is the ad-valorem tari that country j imposes on imports from country i at time t Importantly, since taris act as direct price shifters (See Appendix A.2 to Chapter 1 of the Advanced Guide for details), the coecient on τ ij,t can be expressed only in terms of the trade elasticity of substitution β 6 = σ This means that the trade elasticity itself can be recovered directly from the estimate on τ ij,t, as σ = β 6 Note that this interpretation depends on trade ow data being expressed at cost, insurance and freight (c.i.f) prices, not inclusive of taris (see Appendix A.2 to Chapter 1 of the Advanced Guide for details) Cosimo Beverelli Gravity Bangkok, Dec / 80

35 Structural gravity estimation: challenges and solutions Eight challenges 5 Endogeneity of trade policy Cosimo Beverelli Gravity Bangkok, Dec / 80

36 Structural gravity estimation: challenges and solutions Challenge 5: Endogeneity of trade policy The trade policy variables RTA ij,t and τ ij,t are endogenous For instance, trade policy variables may suer from reverse causality, because, all else equal, a given country is more likely to liberalize its trade with another country that is already a signicant trade partner Cosimo Beverelli Gravity Bangkok, Dec / 80

37 Structural gravity estimation: challenges and solutions Solutions to challenge 5 (i) The issue of endogeneity of trade policy is well-known in the trade literature (Treer, 1993) (ii) However, primarily due to the lack of reliable instruments, early attempts to account for endogeneity of trade policy (Treer, 1993) in particular with reference to RTAs, Baier and Bergstrand (2007) propose applying the average treatment eect (ATE) methods described in Wooldridge (2010) In panel trade data, they suggest rst-dierencing bilateral trade ows or using country-pair xed eects This eliminates or accounts for, respectively, the unobservable linkages between the endogenous trade policy covariate and the error term in gravity regressions Note that the set of pair xed eects will absorb all bilateral time-invariant covariates (e.g. bilateral distance), but will have the plus of accounting for any unobservable time invariant trade cost components Egger and Nigai (2015) and Agnosteva et al. (2014) show that the pair-xed eects are a better measure of bilateral trade costs than the standard set of gravity variables Cosimo Beverelli Gravity Bangkok, Dec / 80

38 Structural gravity estimation: challenges and solutions Eight challenges 6 Non-discriminatory trade policy Cosimo Beverelli Gravity Bangkok, Dec / 80

39 Structural gravity estimation: challenges and solutions Challenge 6: Non-discriminatory trade policy Researchers have struggled to estimate the eects of non-discriminatory trade policies, export subsidies or most-favoured-nation (MFN) taris, within the structural gravity model Non-discriminatory trade policy covariates are exporter- and/or importer-specic, and therefore they will be absorbed, respectively, by the exporter-time and by the importer-time xed eects that need to be used in order to control for the multilateral resistances More generally, in the presence of importer and exporter xed eects, the gravity model can no longer estimate the impact of any variable (i) aecting exporters' propensity to export to all destinations (e.g. being an island); (ii) aecting imports without regard to origin (e.g. country-level average applied tari); and (iii) representing sums, averages, and dierences of country-specic variables (Head and Mayer, 2014) Cosimo Beverelli Gravity Bangkok, Dec / 80

40 Structural gravity estimation: challenges and solutions Solutions to challenge 6 (i) Approximate the multilateral resistances with the remoteness indexes rather than including directional (exporter and importer) xed eects This approach is not recommended because it does not account properly for the multilateral resistance terms, and is therefore likely to produce biased gravity estimates (including the eects of trade policy) (ii) Employ a two-stage estimation, where the estimates of the multilateral resistances from the rst-stage gravity regression are explained in an auxiliary regression that includes the non-discriminatory covariate of interest (Anderson and Yotov, 2016; Head and Mayer, 2014) Cosimo Beverelli Gravity Bangkok, Dec / 80

41 Structural gravity estimation: challenges and solutions Solutions to challenge 6 (ct'd) (iii) As suggested by Heid et al. (2015), estimate the structural gravity model with international and intra-national trade ows by capitalizing on the fact that while non-discriminatory trade policies are country-specic, they do not apply to intra-national trade The estimates of non-discriminatory trade policies in the structural gravity model are less likely to be subject to endogeneity concerns as compared to their bilateral counterparts for two reasons: (a) It is unlikely that a non-discriminatory trade policy will be inuenced by any bilateral trade ow (b) The directional xed eects in the structural gravity model will absorb much of the unobserved correlation between the non-discriminatory trade policy covariates and the gravity error term Cosimo Beverelli Gravity Bangkok, Dec / 80

42 Structural gravity estimation: challenges and solutions Eight challenges 7 Adjustment to trade policy changes Cosimo Beverelli Gravity Bangkok, Dec / 80

43 Structural gravity estimation: challenges and solutions Challenge 7: Adjustment to trade policy changes The adjustment of trade ows in response to trade policy changes will not be instantaneous Treer (2004) criticizes trade estimations pooled over consecutive years. The challenge of adjustment is even more pronounced in econometric specications with xed eects such as the ones we described, which allow identication through changes over years As noted in Cheng and Wall (2005), xed-eects estimation applied to data pooled over consecutive years is sometimes criticized on the grounds that dependent and independent variables cannot fully adjust in a single year's time Cosimo Beverelli Gravity Bangkok, Dec / 80

44 Structural gravity estimation: challenges and solutions Solutions to challenge 7 (i) Researchers have used panel data with intervals instead of data pooled over consecutive years For example, Treer (2004) uses 3-year intervals, Anderson and Yotov (2016) use 4-year intervals, and Baier and Bergstrand (2007) use 5-year intervals Olivero and Yotov (2012) provide empirical evidence that gravity estimates obtained with 3-year and 5-year interval trade data are very similar, while estimations performed with panel samples pooled over consecutive years produce suspicious estimates of the trade cost elasticity parameters Cosimo Beverelli Gravity Bangkok, Dec / 80

45 Structural gravity estimation: challenges and solutions Eight challenges 8 Gravity with disaggregated data Cosimo Beverelli Gravity Bangkok, Dec / 80

46 Structural gravity estimation: challenges and solutions Challenge 8: Gravity with disaggregated data Many trade policies are negotiated and applied at the sectoral level, such as taris While it is in principle possible to aggregate trade policy and still use the aggregate gravity model, such aggregation practices should be avoided and, whenever possible, gravity should be estimated at the level of aggregation which is the target of the specic policy Furthermore, even for policies that are negotiated at the aggregate level (e.g. some RTAs), it may be desirable to also obtain sectoral eects because the eects of these non-discriminatory policies may actually be quite heterogeneous across sectors Cosimo Beverelli Gravity Bangkok, Dec / 80

47 Structural gravity estimation: challenges and solutions Solutions to challenge 8 (i) Structural gravity is separable: bilateral expenditures across countries both at the aggregate and at the sectoral level are separable from output and expenditure at the country level (Larch and Yotov, 2016b) As demonstrated by Anderson and van Wincoop (2004), for a given set of country-level output (Yi,t) k and expenditure (Ej,t), k where k denotes a class of goods/sector, theory delivers the familiar sectoral gravity equation: X k ij,t = Y k i,tej,t k Yt k ( t k ij,t Π k i,t Pk j,t ) (1 σk ) (13) Equation (13) can be estimated for each sector as if the data were aggregate Alternatively, the gravity model can be estimated with data pooled across sectors, in which case the proper treatment of the multilateral resistance requires exporter-product-time and importer-product-time xed eects Depending on the question of interest, the estimates of the trade policy variables in gravity estimations that are pooled across sectors can be sector-specic or constrained to be common across sectors Cosimo Beverelli Gravity Bangkok, Dec / 80

48 Structural gravity estimation: practical recommendations Six recommendations 1 Use panel data 2 Use year intervals 3 Add intra-national trade ows 4 Include importer-time and exporter-time xed eects 5 Include pair xed eects 6 Estimate the model with PPML Cosimo Beverelli Gravity Bangkok, Dec / 80

49 Structural gravity estimation: practical recommendations Six recommendations 1 Use panel data Cosimo Beverelli Gravity Bangkok, Dec / 80

50 Structural gravity estimation: practical recommendations Recommendation 1: Use panel data (i) Using panel data leads to improved estimation eciency (ii) The panel dimension enables to apply the pair-xed-eects methods to address the issue of endogeneity of trade policy variables (Baier and Bergstrand, 2007) (iii) The use of panel data allows for a exible and comprehensive treatment and estimation of the eects of time-invariant bilateral trade costs with pair xed eects What if panel data are not available? See next slide Cosimo Beverelli Gravity Bangkok, Dec / 80

51 Structural gravity estimation: practical recommendations In the absence of panel data In the absence of panel trade data, the gravity model can still be estimated with cross-section samples: ln X ij = ln X ij + ln Y i ln Y + (1 σ) ln t ij (1 σ) ln P j (1 σ) ln Π i + ε ij In a cross-section setting, recommendations 3, 4, and 6 continue to hold, namely gravity specication should include intra-national trade and directional (importer and exporter) xed eects, and be estimated applying the PPML estimator However, the recommendations 2 and 5 to allow for adjustment in trade ows by using interval data and to include pair xed eects are no longer applicable The gravity specication in cross-section should include the standard set of gravity variables (e.g., bilateral distance, contiguity...) instead of pair xed eects, in order to proxy for bilateral trade costs That being said, the error term may capture systematic eects of unobserved trade costs In order to address the endogeneity of bilateral trade policy, IV treatment is highly recommended (Baier and Bergstrand, 2004; Egger et al., 2011) Cosimo Beverelli Gravity Bangkok, Dec / 80

52 Structural gravity estimation: practical recommendations Six recommendations 2 Use year intervals Cosimo Beverelli Gravity Bangkok, Dec / 80

53 Structural gravity estimation: practical recommendations Recommendation 2: Use year intervals Interval panel data should be employed in order to allow for adjustment in bilateral trade ows in response to trade policy or other changes in trade costs Olivero and Yotov (2012) nd that gravity estimates obtained with 3-, 4-, and 5-year lags deliver similar results It is recommended to experiment with alternative intervals while keeping estimation eciency in mind Cosimo Beverelli Gravity Bangkok, Dec / 80

54 Structural gravity estimation: practical recommendations Six recommendations 3 Add intra-national trade ows Cosimo Beverelli Gravity Bangkok, Dec / 80

55 Structural gravity estimation: practical recommendations Recommendation 3: Add intra-national trade ows The inclusion of intra-national trade data in structural gravity estimations is desirable for several reasons: (i) It ensures consistency with gravity theory, where consumers choose among and consume domestic as well as foreign varieties (ii) It leads to the theoretically consistent identication of the eects of bilateral trade policies (Dai et al., 2014) (iii) It enables to identify and estimate the eects of non-discriminatory trade policies (Heid et al., 2015) (iv) It resolves the 'distance puzzle in trade, by measuring the eects of distance on international trade relative to the eects of distance on internal trade (Yotov, 2012) (v) It enables to capture the eects of globalization on international trade and to correct for biases in the estimation of the impact of RTAs on trade (Bergstrand et al., 2015) Intra-national trade data has to be constructed consistently as the dierence between gross production value data and total exports Cosimo Beverelli Gravity Bangkok, Dec / 80

56 Structural gravity estimation: practical recommendations Six recommendations 4 Include importer-time and exporter-time xed eects Cosimo Beverelli Gravity Bangkok, Dec / 80

57 Structural gravity estimation: practical recommendations Recommendation 4: Include importer-time and exporter-time xed eects The use of exporter-time and importer-time xed eects enables to control for the unobservable multilateral resistances, and potentially for any other observable and unobservable characteristics that vary over time for each exporter and importer, respectively (Anderson and van Wincoop, 2003) The estimates of the xed eects of the gravity model can be used directly to recover the estimates of the general equilibrium eects of trade policy changes as well as to construct a series of useful general equilibrium indexes summarizing and aggregating consistently the eects of trade policy and trade costs (Anderson et al., 2015b; Larch and Yotov, 2016b) (See Chapter 2 of the Advanced Guide) Cosimo Beverelli Gravity Bangkok, Dec / 80

58 Structural gravity estimation: practical recommendations Six recommendations 5 Include pair xed eects Cosimo Beverelli Gravity Bangkok, Dec / 80

59 Structural gravity estimation: practical recommendations Recommendation 5: Include pair xed eects Two major benets are associated with using pair xed eects in gravity estimations: (i) The pair xed eects are able to account for the endogeneity of trade policy variables (Baier and Bergstrand, 2007) (ii) The pair xed eects provide a exible and comprehensive account of the eects of all time-invariant bilateral trade costs, observable and unobservable (Egger and Nigai, 2015; Agnosteva et al., 2014). The downside is that one cannot identify the eects of any time-invariant bilateral determinants of trade ows, which will be absorbed by the pair xed eects One way to address this issue is to apply a two-stage procedure, where the estimates of the pair xed eects from the rst-stage structural gravity equation are regressed on standard gravity variables in a second-stage estimation (Agnosteva et al., 2014) This two-step approach also enables to recover estimates of the pair xed eects that cannot be identied directly in the rst stage, due to missing or zero trade ows, allowing to construct the full matrix of bilateral trade costs and to perform counterfactual experiments (Anderson and Yotov, 2016) Cosimo Beverelli Gravity Bangkok, Dec / 80

60 Structural gravity estimation: practical recommendations Six recommendations 6 Estimate the model with PPML Cosimo Beverelli Gravity Bangkok, Dec / 80

61 Structural gravity estimation: practical recommendations Recommendation 6: Estimate the model with PPML The use of the PPML estimator is justied on various grounds: (i) The PPML estimator, applied to the gravity model expressed in a multiplicative form, accounts for heteroskedasticity, which often plagues trade data (Santos Silva and Tenreyro, 2006) (ii) The PPML estimator is able to take advantage of the information contained in the zero trade ows (iii) The additive property of the PPML estimator ensures that the gravity xed eects are identical to their corresponding structural terms (Arvis and Shepherd, 2013; Fally, 2015) (iv) The PPML estimator can also be used to calculate theory-consistent general equilibrium eects of trade policies (Anderson et al., 2015b; Larch and Yotov, 2016b) As a robustness check, the gravity model can be estimated by applying the Gamma Pseudo Maximum Likelihood (GPML) and the OLS estimators (Head and Mayer, 2014) Cosimo Beverelli Gravity Bangkok, Dec / 80

62 A generic comprehensive structural gravity model Structural gravity estimating equation The best practices and recommendations proposed are reected in the following generic and comprehensive econometric version of the structural gravity model, which can be modied and adjusted by researchers and policy makers depending on their specic needs: where: X ij,t = exp[π i,t + χ j,t + µ ij + η 1BTP ij,t + η 2NES i,t INTL ij + η 3NIP j,t INTL ij ] ε ij,t (14) X ij,t denotes nominal trade ows, which include international and intra-national trade, at non-consecutive year t The terms π i,t, χ j,t and µ ij denote exporter-time, importer-time and pair xed eects Cosimo Beverelli Gravity Bangkok, Dec / 80

63 A generic comprehensive structural gravity model Structural gravity estimating equation (ct'd) X ij,t = exp[π i,t + χ j,t + µ ij + η 1 BTP ij,t + η 2 NES i,t INTL ij + η 3 NIP j,t INTL ij ] ε ij,t The term BTP ij,t represents the vector of any time-varying bilateral determinants of trade ows, such as RTAs, bilateral taris and currency unions In principle, the BTP ij,t vector may include any time-varying covariates Cosimo Beverelli Gravity Bangkok, Dec / 80

64 A generic comprehensive structural gravity model Structural gravity estimating equation (ct'd) X ij,t = exp[π i,t + χ j,t + µ ij + η 1 BTP ij,t + η 2 NES i,t INTL ij + η 3 NIP j,t INTL ij ] ε ij,t The expression NES i,t INTL ij is the product between NES i,t and INTL ij NES i,t denotes the vector of any Non-discriminatory Export Support (NES) policies, such as export subsidies INTL ij is an international trade" dummy variable. It takes a value of one for international trade between countries i and j i, and zero otherwise (i.e. when the exporer and the importer are the same country, therefore trade is intra-national) The interaction term NES i,t INTL ij varies along the ij, t dimension, allowing to identify the eects of any non-discriminatory export support policies, even in the presence of exporter-time xed eects as required by gravity theory (Heid et al., 2015) With appropriate data on export support measures that act as direct price-shifters, the estimate of the coecient(s) associated with the variable(s) NES i,t INTL ij can be used to recover an estimate of the export supply elasticity, which has attracted little attention in the empirical trade literature Cosimo Beverelli Gravity Bangkok, Dec / 80

65 A generic comprehensive structural gravity model Structural gravity estimating equation (ct'd) X ij,t = exp[π i,t + χ j,t + µ ij + η 1 BTP ij,t + η 2 NES i,t INTL ij + η 3 NIP j,t INTL ij ] ε ij,t The covariate NIP j,t INTL ij is constructed as the product between the term NIP j,t, which denotes the vector of any Non-discriminatory Import Protection (NIP) policies, such as MFN taris, and the dummy for bilateral international trade INTL ij Given its bilateral nature, the interaction NIP j,t INTL ij can be used to identify the eects of any non-discriminatory import protection policies Cosimo Beverelli Gravity Bangkok, Dec / 80

66 Interpretation of gravity estimates Interpretation of gravity estimates Two related methods are widely used to interpret the estimates from gravity regressions: 1 Use the gravity estimates to construct trade volume eects 2 Convert the estimates of various trade policies and other determinants of trade ows into tari equivalent eects Consider the following simplied version of the empirical gravity model (14): X ij,t = exp [π i,t + χ j,t + β DIST ln DIST ij + β RTA RTA ij,t + β TARIFF τ ij,t ] ε ij,t (15) where DIST ij and RTA ij,t were dened in slide 32 and τ ij,t was dened in slide 33 Cosimo Beverelli Gravity Bangkok, Dec / 80

67 Interpretation of gravity estimates Trade volume eects 1 Trade volume eect of continuous variables The interpretation of the estimate of the coecient on the logarithm of the continuous variable is simply the elasticity of (the value of trade ows) with respect to the continuous variable For example, the standard empirical value for the distance variable estimate in gravity regressions of β DIST = 1 implies that a 10 percent increase in distance should be accompanied by a 10 percent decrease in trade ows (Disdier and Head, 2008; Head and Mayer, 2014) Cosimo Beverelli Gravity Bangkok, Dec / 80

68 Interpretation of gravity estimates Trade volume eects (ct'd) 2 Trade volume eect of dummy variables The volume eects triggered by a change in a dummy variable, such as the presence of RTAs, can be calculated in percentage terms as follows: [ ] e β DUMMY (16) To derive the formula in (17), note that: ln X ij (1) is the predicted value of trade when the dummy = 1, while ln X ij (0) is the value of trade when dummy = 0 The dierence ln X ij (1) ln X ij (0) = β DUMMY Therefore, X ij (1)/X ij (0) = e β DUMMY This in turn implies that the percentage change in trade value due to the dummy switching from 0 to 1 is: [ ] 100 [X ij (1) X ij (0)] /X ij (0) = e β DUMMY { } e Alternatively, one can compute DUMMY e [ 1 var(β 2 DUMMY )] 1 100, which is consistent and (almost) unbiased Cosimo Beverelli Gravity Bangkok, Dec / 80

69 Interpretation of gravity estimates Trade volume eects (ct'd) [ ] e β DUMMY (17) For example, the benchmark estimate of the eects of RTAs in gravity regressions found in the empirical literature of β RTA = 0.76 implies that the RTAs that entered into force between 1960 and 2000 on average have increased trade by [ e ] 100 = 114 percent (Baier and Bergstrand, 2007) Cosimo Beverelli Gravity Bangkok, Dec / 80

70 Interpretation of gravity estimates A useful decomposition With the exception of the direct price shifters, such as taris, the estimates of the remaining gravity covariates consist of two components: (i) a structural component and (ii) a trade cost component For example, the structural interpretation of the estimate of the coecient of distance is β DIST = (1 σ) ρ, where ρ is the elasticity of trade costs with respect to distance This decomposition enables to recover the distance elasticity of trade costs as: ρ = β DIST / (1 σ) Cosimo Beverelli Gravity Bangkok, Dec / 80

71 Interpretation of gravity estimates Tari equivalent eects Tari equivalent eect of quota dummy (ad-valorem tari equivalent whose removal would have generated the same impact as the removal of the quota): [ ( βquota ) ] β e TARIFF Tari equivalent eect of RTAs (average tari equivalent fall of the introduction of RTAs): [ ( ) ] βrta e β TARIFF (18) (See pp of the Practical Guide) and slides on Tari Equivalents Cosimo Beverelli Gravity Bangkok, Dec / 80

72 Interpretation of gravity estimates Tari equivalent eects (ct'd) In principle, since β TARIFF = σ (see slide 33), no data on taris are needed in order to obtain tari equivalent eects of other gravity covariates as long as reliable estimates of the trade elasticity of substitution are available from outside studies Returning to the example of the eects of RTAs from Baier and Bergstrand (2007), and taking a representative value for the elasticity of substitution from the literature, σ = 5, the [ average tari-equivalent fall of the introduction of RTAs would amount to e ( ] 0.76 ) = 16.4 percent Cosimo Beverelli Gravity Bangkok, Dec / 80

73 Data sources Bilateral aggregate trade ows data IMF Direction of Trade Statistics (DOTS) The database covers 184 countries Annual data are available from 1947 Data are reported in US dollars Cosimo Beverelli Gravity Bangkok, Dec / 80

74 Data sources Merchandise trade ows data UN COMTRADE The database covers more than 160 countries Data are reported in US dollars HS (up to 6 digits) and SITC classications for disaggregate data CEPII's BACI Cleaned version of COMTRADE (mirror data used when informative, re-exports excluded) The database covers more than 200 countries Time lag of 1-2 years w.r.t. COMTRADE Feenstra and Romalis (2014) World Trade Flows database Omits observations with cif/fob ratio (0.1, 10) and when cif < 50'000 USD The database covers 185 countries for the period Cosimo Beverelli Gravity Bangkok, Dec / 80

75 Data sources Services trade ows data OECD Trade in Services database Bilateral services trade for 12 main services sectors and several sub-sectors according to the Extended Balance of Payments (EBOPS) 2010 classication The database covers 35 countries including 32 OECD member countries as well as the Russian Federation, Colombia and Latvia from 1999 onwards UN Service Trade Database Covers 46 economies from 2000 onwards and follows the EBOPS 2002 classication WTO-UNCTAD-ITC database Bilateral annual service ows data for 36 countries at the same level of disaggregation as the OECD data from 2005 onwards according to the EBOPS 2010 classication These bilateral data can be retrieved from the ITC TradeMap Database by Francois and Pindyuk (2013) Based on adjusted data from the OECD, Eurostat, UN and IMF Bilateral service ows data classied according to the EBOPS 2002 classication and covering 248 countries, on average, for the period Cosimo Beverelli Gravity Bangkok, Dec / 80

76 Data sources Agriculture and resource sectors data FAOSTAT database Information on an annual basis in more than 100 countries The Detailed Trade Matrix reports information on agricultural bilateral trade ows for over 600 food and commodities per year Data for both quantities (in tons) and values (in thousands of US dollars) of agricultural imports and exports Data are available for the period and are gathered from national sources Cosimo Beverelli Gravity Bangkok, Dec / 80

77 Data sources Intra-national trade ows data Big problem: one cannot use apparent consumption (dened as the dierence between production and total exports)...rather, gross production should be used This is because aggregate production data are usually measured and reported as value added (e.g. GDP), while total exports are reported as gross value Cosimo Beverelli Gravity Bangkok, Dec / 80

78 Data sources Intra-national trade ows data World Bank's Trade, Production and Protection (TPP) database Covers approximately 100 countries for the period Information according to the Industrial Standard Industrial Classication (ISIC) Rev. 3 classication at the 3-digit level CEPII's Trade, Production and Bilateral Protection (TradeProd) database Covers over 150 countries for the period 1980â 2006 Data in ISIC Rev. 2 at the 3-digit level CEPII's Trade, Production and Bilateral Protection (TradeProd) database Covers over 150 countries for the period 1980â 2006 Data in ISIC Rev. 2 at the 3-digit level UNIDO Industrial Statistics (INDSTAT) Covers 166 countries INDSTAT2: Data from 1962 onwards at the 2-digit level of ISIC Rev. 3 INDSTAT4: Data from 1990 onwards at the 4-digit level of ISIC Rev. 3 Cosimo Beverelli Gravity Bangkok, Dec / 80

79 Data sources Databases used in this structural gravity course 1 The database gravity_dataset_ag_tpa_applications.dta is a balanced panel covering the aggregate manufacturing sector of 69 countries over the period Sources: Consistently constructed international and intra-national trade ows data, which were assembled and provided by Thomas Zylkin The original sources for the international trade data are the UN COMTRADE database and the CEPII TradeProd database Intra-national trade for each country is constructed as the dierence between total manufacturing production and total manufacturing exports Both of these variables are reported on a gross basis, which ensures consistency between intra-national and international trade Three sources are used to construct the production data: the UN UNIDO INDSTAT database, the CEPII TradeProd database, and the World Bank's TPP database Cosimo Beverelli Gravity Bangkok, Dec / 80