The wise use of dummies in gravity models

The wise use of dummies in gravity models: Export potentials in the Euromed region Juan M. Ruiz and Josep M. Vilarrubia Simposio de Análisis Económico 11 -13 December 2008

Use of gravity equations in international trade q Gravity equation has been extensively used in empirical applications of international trade q Despite theoretical foundation by Anderson (1979), important theoretical considerations were largely overlooked: • Role of multilateral trade resistance of trading partners [Anderson & van Wincoop, 2003] § E. g. trade between Australia and New Zealand q Not properly accounting for multilateral trade resistance could lead to important estimation biases. • Omitted variable bias • Misspecification Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 1

What does this paper do? 1. Correct implementation of theoretical gravity equation q Given our use of panel instead of cross-sectional data, we need to correctly account for multilateral trade resistance. • Use of exporter-time and importer-time dummies. • Panel data equivalent of the procedure suggested by Feenstra (2002) for cross-section data. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 2

What does this paper do? 2. Application: Estimation of export potentials in the Euromed Region q Euromed Region: southern and eastern Mediterranean Countries q Policy Question: Do countries in this region export too little? q Quick answer: a correctly specified model cannot answer this! • Different from Egger’s (2002) critique to estimation of trade potentials q Long answer: a correctly specified model can tell whether these countries’ actual composition of trade gives each destination country the importance predicted by the gravity model. • Measured by share of that destination on total exports of that exporter • Estimations show: § EU: actual shares close to those predicted by gravity equation § US: actual shares below potential (room for export growth) Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 3

Outline of the talk 1. Introduction 2. Properly specified gravity equation 3. Data and estimation of the gravity equation 4. Computing export potentials 5. Concluding remarks Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 4

Theoretical derivation of gravity equation From Anderson and van Wincoop (2003) q Each country produces a fixed quantity of a unique bundle of goods. q Consumer in country i (importer country) maximizes: • subject to Where • xeit is exports from country e to country i in period t • bet(1 -s)/s can be interpreted as the number of goods within the bundle produced by country e, • s >1 is the elasticity of substitution between goods from different countries, • peit is the import price from country e to country i at time t, • yit is nominal income in country i at time t Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 5

Theoretical derivation of gravity equation q International trade subject to “iceberg” transportation costs • teit >1 units of the exported good from country e need to be shipped in order for one unit to reach country i. q Price of country e’s exported good in country i is, thus, peit=petteit • where pet is the producer’s export price. q Consumer’s optimization gives rise to an import demand equation: • where Pit is the price index of country i at time t, given by Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 6

Theoretical derivation of gravity equation q Imposing market clearance ( yet=Si xeit ) the import demand equation becomes: • ywt is world income • Pet , Pit: overall price indexes, approximate multilateral trade resistance q Log-linearize to get equation to be estimated: Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 7

Empirical implementation of gravity equation q Problem estimating this equation: • Pet , Pit are not available, omitting them introduces bias § Error term would be b 5 Pet + b 6 Pit + heit , correlated with teit. § Recall • Two sensible options: § Estimate it using a multi-step procedure proposed by Anderson and van Wincoop (2003) – Requires a custom nonlinear-least-squares procedure § Include exporter and importer dummies in the regression to take their effect into account as proposed by Feenstra (2002) – Equivalent results and simpler. Usually done in empirical research Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 8

Empirical implementation of gravity equation q In a cross section, we could include exporter and importer dummies (fixed effects) in the regression (Feenstra, 2002) q But, in a panel, to properly account for Pet and Pit, which may change every year, we should include exporter-yearly (det) and importer-yearly dummies (dit). • Usually, empirical estimations with panel data only include fixed exporter and importer dummies (de , di). This has some problems: § Part of the bias (from omitted multilateral resistance terms) may be eliminated, but there will be a time-varying residual in the error term. § Results will still be biased as long as multilateral trade resistance moves differentially over time for different countries. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 9

Empirical implementation of gravity equation q Based on the previous discussion, we estimate: • where the bilateral trade resistance term teit is modeled as: § det , dit: country-yearly dummies – absorb all country characteristics (even time varying)!! § Zei : vector of time-invariant country-pair (ei) characteristics: – distance between trading partners, – dummies for a common land border, a common language, a common colonizer, if they were ever in a colonial relationship. § Zeit : vector of time-varying country-pair explanatory variables. – 3 dummies for each free trade area considered – 3 dummies for each currency union Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 10

Outline of the talk 1. Introduction 2. Properly specified gravity equation 3. Data and estimation of the gravity equation 4. Computing export potentials 5. Concluding remarks Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 11

Data q Original dataset of bilateral trade for 205 countries from IMF-DOTS q Period 1948 -2005 • Many gaps and zeroes, not used in regression. q Use directional flows, instead of the usual average of bilateral flows • Problem of asymmetric trade flows and the use of log(average). § Underreporting of very asymmetric flows due to concavity of log • Allows estimation of different trade diversion effects on exporters and importers left outside a free trade area or currency union. q Potentially almost 2. 5 million observations! Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 12

Estimation q Unfortunately, use of country-year dummies makes it computationally unfeasible to use whole dataset • Would imply (205+205)*58=23, 780 dummies! q Restrict to period 1976 -2005 and 70 top exporters in 2004 (and make sure to include all Euromed countries) • 70 top countries represented around 96% of world trade in 2004 • Note that this still means using (70+70)*30 = 4200 dummies. q Alternatively, we consider top 100 countries (over 98% of world trade in 2004). How to fit them in the computer? • Use country-triennial dummies instead of country-yearly dummies (meaning we “only” use 2000 dummies). • Does not exactly capture the effect of exporter and importer time-varying price indexes (Pet and Pit) • But, the associated estimation bias will presumably be much smaller than that of considering time-invariant country dummies over 30 years of data. § This is confirmed by regressions with different types of dummies Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 13

Regression Results: OLS with country-time dummies det , dit, 1976 -2005. Benchmark q 2 nd & 3 rd columns show effect of change in sample of countries • Mainly in border effect and some FTAs q Take regression with 100 countries and country-triennial dummies (third column) as our benchmark regression. • Over 200, 000 observations q Similar qualitative parameters extending sample in country or time dimension • 1976 -2005, 205 countries • 1948 -2005, 70 countries q Comparing with regressions without country-year dummies show different coefficients in time-varying regressors (FTAs mainly). • Evidence that omitting multilateral trade resistance effects might lead to important bias. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 14

Outline of the talk 1. Introduction 2. Properly specified gravity equation 3. Data and estimation of the gravity equation 4. Computing export potentials 5. Concluding remarks Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 15

Estimating Trade Potentials q Define trade potentials as difference between actual trade and that predicted by gravity model (regression error) q The traditional definition of trade potential: Actual exports Predicted exports q Try constructing an analog measure for total trade for country e (i. e. with respect to the world, Xe. Wt. P): • Use of country-year exporter dummies (det) implies we should be able to perfectly predict total exports for each exporter country e and each year t • So Xe. Wt. P should ideally be = 1, but it’s not! Jensen’s inequality q Thus, makes no sense to talk about trade potentials referred to levels! Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 16

Alternative: Export share potentials q The use of exporter-country dummies only allows us to predict deviations from average trade. q Modify our index of trade potentials to show difference of actual to predicted shares of exports from country e to destination i : • Easy to show that now Xe. Wt. PS = 0, as expected q Negative values of the index Xe. Wt. PS: share of destination i on total exports from country e below that predicted by the gravity model. q Estimate “in-sample” trade potentials, in spite of Egger’s (2002) critique • Country-year dummies make out-of-sample estimation impossible. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 17

Euro. Med countries q Dark blue: Resource-rich countries • Algeria • Libya • Syria q Light-blue: Resource-poor countries • Morocco • Tunisia • Egypt • Jordan • Lebanon q Green: high income • Israel q Most of them have signed association agreements with the EU (red). Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 18

Trade Structure: Destination of Mediterranean countries’ exports in 2005: in 1975: Rest of the World 26% Rest of the World 31% EU-15 50% Med. Countries 3% Med. Countries 5% EU-15 50% United States 19% United States 16% Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 19

Export share potentials Xeit. PS: preferred regression with country-triennial dummies det , dit, 100 countries, 1976 -2005. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 20

Some countries export more than predicted to the US … Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 21

… but for most Euromed countries, the US represents a bigger export potential than the EU. q Defies “common wisdom” in policy circles, which focus on the EU for export growth in Euromed countries. q Export share of EU mostly in line with model, but note negative export share potential to some individual EU countries Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 22

Are these computed export potentials useful? q Estimate: q Export share potentials are negatively correlated with future export growth (d <0) • That is, destinations that have an actual export share below that predicted by the model tend to experience subsequent higher export growth to that destination. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 23

Outline of the talk 1. Introduction 2. Properly specified gravity equation 3. Data and estimation of the gravity equation 4. Computing export potentials 5. Concluding remarks Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 24

Summary: What do we do q The paper estimates gravity equation properly, accounting for timevarying multilateral trade resistance terms. • Important biases in estimating gravity equation when not using timevarying country dummies to account for multilateral trade resistance q Application to computing export share potentials of Euromed countries. • Euromed countries actual composition of trade gives EU (as destination market) the importance predicted by gravity model. • Less so for the US § May point to primary direction of export growth for these countries. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 25

JUAN RUIZ & JOSEP VILARRUBIA The wise use of dummies in gravity models: Export potentials in the Euromed region DEPARTAMENTO DE ECONOMÍA Y RELACIONES INTERNACIONALES

Regression results: with and without country-time dummies det , dit, 1976 -2005, 100 countries. q Comparing with regressions without country-year dummies show different coefficients in timevarying regressors (FTAs mainly). q Thus, omitting multilateral trade resistance effects might lead to important bias. Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 27

Euro. Med association agreements signed with EU q Palestinian Authority (1997) q Tunisia (1998) q Israel (2000) q Morocco (2000) q Jordan (2002) q Egypt (2004) q Algeria (2005) q Lebanon (2006) q Syria (in negotiations) Ruiz & Vilarrubia (2007) – Dummies in gravity models: Export potentials in the Euromed region INTERNATIONAL ECONOMICS AND INTERNATIONAL RELATIONS DEPARTMENT 28