A workhorse model for empirical analysis of international trade. The gravity model. P. Montalbano - Sapienza Università di Roma

Transcription

1 A workhorse model for empirical analysis of international trade The gravity model

2 Newton s law of gravity: M a M b F d Where: M = mass of the given object eg. planet F = force M am b D = distance between the objects r F G 2 r G = a constant Hence the force exerted by the sun on the earth (and vice versa) depends on the mass of the sun, the mass of the earth, and on the distance between them.

3 A gravity equation for trade flows Based on Newton s law of gravity: relative economic masses and trade frictions determine bilateral trade Distance Country A Country B Econometric model (ex-post analysis) From being a fact without a theory it accords well with basic intuition about the drivers of international trade its structure fits with some important stylized facts to being an avoidable element of most trade theories: most trade models require gravity to work!

4 WHO INVENTED THE GRAVITY MODEL? The concept of the gravity model is so natural that it is hard to appoint one single inventor [only international economists have considered it so unusual only because it overcomes the HO theory]; Indeed, the very forefather of the gravity model remains Isaac Newton ( ), the author of the gravitational theory; Newton s gravitational theory says that the attractive force F between two heavenly bodies is proportional to the product of their masses and inversely related to the squared distance between them [In formula: F = G(m 1 m 2 )/d 2 - where G is the universal gravitation constant]; The Gravity model holds the same intuition: It says that trade between country i and country j is proportional to the product of their respective GDPs and inversely related to their relative distance.

5 Why Should We Care? It can be used to say interesting and useful things about the interactions between economic mass, behind-theborder policies and trade flows. Numerous applications looking at different types of trade costs, and their impacts on trade flows: Regional integration agreements, currency unions, and the GATT/WTO. Tariffs and non-tariff barriers. Transport costs. Time delays at export/import and trade facilitation. Governance, corruption, and contract enforcement.

6 Why Should We Care? Increasingly popular tool in the literature

7 THE GRAVITY EQUATION GM consists of a single equation. It asserts that the bilateral trade flow from country i to country j is directly proportional to the product of their relative dimension (measured by the respective GDPs or total populations) and inversely proportional to their relative distance. In formula: X ij = 0 Y i 1 (Y i /L i ) 2 Y j 3 (Y j /L j ) 4 D ij - 5 Pij 6 Where: - Xij trade flows from ctr i to ctr j ; - Yi ed Yj are the total GDP in country i and country j, respectively; - Yi/Li ed Yj/Lj are the per-capita GDP in country i and country j, respectively; - Dij is the grographical distance btw country i and country j ; - P is a dummy (or qualitative) variable; - 0 is the constant term of the regression.

8 The linear version Basic specification: log-linear model of trade, GDP, trade frictions and a policy variable Usually estimated by means of OLS ln X ij ln G a { ln M i a2 ln M j a3 ij a Nij a5v ij ij { { Questions one should ask: a 0 constant economic attractors distance policy iid Does the model explain well trade (R-squared)? Do regressors have the expected coefficient? Is the underlying model relating dependent to independent variables well approximated by the OLS specification? Is the OLS really the Best Linear Unbiased Estimator (BLUE)? Key checks: R-squared Test for omitted variables and non-linearities Test for serial correlation

9 Data For Gravity The Minimum: Trade (imports or exports) time series GDP and/or other economic mass time series Distance, trade frictions Sources: Comtrade, WITS (Trade data) World Bank, WDI (Economic Mass data): Nominal GDP in a common numeraire Value added in manufacturing CEPII or other open data sources, WDI, Doing Business (trade frictions) The choices you make matter! Ask what data address best your question Combine best practices in theory and econometrics to find the answer Interpret the results keeping in mind the caveats of the data you are using Look at ways to complement the basic specification and minimize the caveats other data, other approaches to trade modeling

10 WHY GEOGRAPHY SHOULD BE PART OF THE STORY? Surprisingly, traditional theory does not consider distance and other geographical factors as determinants of trade; According to HO Model, partner countries are disembodied identities that lacked a physical location in geographical space; REASONS: The traditional theory did not try to explain the composition of bilateral trade but rather the composition of total trade regardless which trading partners accounted for it; Classic trade theory seeks to predict what products a country is supposed to add to the world s supply pool (e.g. what products China will export to the Row). It is silent on whether China will export its goods specifically to Japan or France (the HO theory simply does not care about it). The assumptions of imperfect competition and increasing returns to scale made by the NTT permit to address new questions such us where industries choose to locate and hence the role of geography and its effects on bilateral trade flows. P. Montalbano, 2011

11 WHY DISTANCE MATTERS? Linemann (1966) identified 3 categories of costs associated with doing business at a distance: Objective resistance: Shipping costs i.e. measured as the ratio of CIF (cost of insurance and freight) values of the imports to FOB (free on board) values of the exports of a bilateral trade flows; It is the easiest way to mesaure the cost of doing business at a distance. Time-related costs, i.e. interest charges, perishability and the loss of adaptability to changing conditions that comes from long delivery lags; additional measure of distance costs; Subjective resistance: Unfamiliarity costs, i.e. unfamiliarity with very distant cultures, habits, religions, languages, regulations and institutions. A way to measure this cost is to count the additional costs for human travel, courier services and telephone calls that incur to operate with particular foreign countries.

12 Uses and Pitfalls of Gravity Regressions It looks easy: all you need for a basic specification is data on bilateral trade, GDP and your favorite explanatory variable Also it seems practical: you can develop a new proxy for your preferred policy-related variable and use a really big dataset. Pitfalls: The problem of omitted variables bias (value chain trade, third country effect, relative costs, market demand or openness) Selection bias (heterogeneity, zeroes) Dynamics (persistence, sunk costs) Interdependence (third country effect and network, clustering) Plus, data issues

13 Step 1: The Left Hand Side Typology of goods: What data: Merchandise trade vs. services, FDI, etc. Unilateral flows: Average or sum of imports and exports lead to bias of the coefficient for the treatment effect, because trade is not balanced! Conversion: Nominal terms and common numeraire: Gravity is a modified expenditure equation not a demand equation (Baldwin and Taglioni, JEI 2007) Empirically, lack of appropriate deflators: no good price indices for trade data. Their use risks to be an additional source of biases and spurious estimations CIF vs. FOB: Be aware of what data you are using and interpret the results accordingly Firm heterogeneity : Not all firms export, and few export to every partner Zeroes are a source of information Inclusion of zeroes rules out the use of OLS estimations

14 Step 2: right end - Specification Matters! VARIABLES limport limport limport limport limport lgdp i 0.704*** 0.957*** 0.803*** lgdp j 0.777*** 1.051*** 1.003*** ldistance *** *** *** *** border 0.406*** 0.537*** 0.587*** 0.564*** FTA 0.146** *** *** *** 0.266*** Constant *** *** *** 28.56*** 13.02*** Observations R-squared time effects no yes yes no no exporter and importer time invariant fe no no yes no no exporter and importer time-varying fe no no no yes yes time invariant pair fe no no no no yes Note: (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level.

15 STEP 3: The Omitted Variables Bias Add a time dimension and move to panels Most typical source of omitted variables bias is country heterogeneity Include one or more proxies correlated with the omitted variable Trade costs Add other trade frictions to distance, including border, common history, language, doing business indicators, etc. Estimated trade frictions (Jacks, Meissner, Novy, AER 2008.) Attractors Income per capita: higher income countries trade more with each other GDP is not enough when trade is driven by value chains (Baldwin and Taglioni, NBER 2012) Problems of interdependence: not easy to fix The relative costs problem

16 Trade Costs: Empirical Evidence 1. Distance variable does not reduce over time. De Menil e Maurel (1994) calculated for the period in Europe a dist coeff. = 70, less than in many current estimations (it reinforces the idea that distance is not only shipping costs but something more e.g. cultural unfamiliarity and it keeps matter nowadays!); 2. The so-called border effect. Mc Callum (1995) and Helliwell (1996) find that, after controlling for market size and distance, trade among Canada provinces is 22 times larger than trade between Canada provinces and U.S. states. It is referred to as the Mc Callum Border Puzzle, one of the 6 main puzzles of open economy macroeconomics (Obstfeld e Rogoff, 2001) since the actual distance among the Canada provinces is much more than that before Canada and USA and about 85% of the Canadian population leave less than 100 miles from the USA border.; However, more recently Anderson and van Wincoop (2003) show a reduced border effect by controlling for the multilateral resistance term. P. Montalbano, 2011

17 The Relative Costs Problem Implications of a world with many countries 3 rd countries mass and distance matters 2-way effect Rest of the World Country B Country A

18 The Relative Costs Problem Theory helps: The gravity equation is an expenditure function (and not a demand equation) and as such it depends on relative and not absolute prices. On the side of the exporter, the price p i that will clear the market is a function of nation i s sales over all markets, including its own market Hence we end up with the relative costs problem: Multilateral resistance (MR) terms (Anderson and van Wincoop AER, 2003 and JEL, 2004) In a multi-period setting, with unbalanced trade better to look at the individual components of multilateral resistance (Baldwin and Taglioni, REI 2007): Price index of importing country Market potential of exporting country X ij M 1 j ij 1 Pj M i i

19 Theoretical underpinnings for Trade costs - Anderson (1979): importance of transport costs as well as national tariffs in each country, both of which are expected to increase with distance. - Bergstrand (1985): trade costs differ depending on location, hence GM must include price indices. - Anderson and van Wincoop (AVW) (2003): seek to identify trade costs that give rise to international differences in prices. P. Montalbano, 2011

20 Accounting For The Relative Costs Problem Empirically Standard price indices (CPI, PPI, etc.) are not aggregated in the way implied by theory: Poor proxy for the true (ideal) price indices (weighted averages of bilateral trade costs) Ignoring them is not an option: This would lead to omitted variables bias unless the MR terms have zero correlation with exports and trade costs (or GDP) Common empirical fixes Fixed effects model Random effects model

21 MRT and the «Border Effect» Hence, bilateral trade between country i and j depends on the specific bilateral trade barrier (tij ) divided by the product of their multilateral resistance terms (PiPj) This means that for a given bilateral trade barrier, higher trade barriers between j and all its other trade partners will reduce the relative price of country i s exports to j and thereby cause a raise of i s exports to j. High multilateral resistance of i and j with regard to the rest of the world raises bilateral trade between i and j. Example: Australia and New Zealand should experience relatively high bilateral trade, as both countries face relatively high multilateral resistance due to their geographical remoteness with respect to the rest of the world. ATT: It solves the McCullogh border puzzle between USA and Canada (being Canada relatively open overseas, USA and Canada face relatively low bilateral trade (There isn t any Border Effect!)

22 A GENERALISED GRAVITY MODEL AVW then derived a complicated technique for solving for these multilateral trade resistance indices Cross-section panel estimation In a panel context (data for your cross-section but also over time), multilateral resistance terms are estimated using country fixed effects (dummy variables) 3 sets of main effects in the «full model»: 1. Country effect (exporter-specific effects and importer-specific effects): unobserved factors such as geographical, political, cultural, institutional factors 2. Time specific effect 3. Interactions (exporter importer interactions, exporter time interactions and importer time interactions) Xij = a 0 + a 1 (Yi) + a 2 (Yj) + a 3 (yi) + a 4 (yj) + a 5 (TCij) + g i + w j +q t +gw ij + gq it + wq jt +e ijt P. Montalbano, 2011

23 Fixed Effects Estimators X ijt =j 1-s ijt FE jt FE it FE ij Fixed effects specification Constant and time-varying dummies for each exporter and importer and time invariant pair dummy. Pros: Very simple to estimate Proper account of the relative costs problem Produces unbiased estimates for the policy variable Cons: Dimensionality quickly becomes an issue with sectoral models: N+N can be in the hundreds, or thousands Because of collinearity constraints, we cannot identify separate effects due to factors that vary in the exporter or importer dimensions Only factors varying bilaterally can be identified, and even here avoidance of collinearity is not warranted

24 STEP 4: Selecting The Appropriate Functional Form Non-linearities Selection bias and zeroes Dynamics Interdependence and networks

25 Selection Bias And Zeroes Heckman 2-stages least squared estimation (Heckman, 1979) It introduces in the specification the inverse of the so-called Mills ratio Crucially, computation of Mills ratio requires variables that may explain the selection (zero or positive trade) but not the value of traded good, when this is positive. If the variable included in the selection equation also affects the outcome variable, it can lead to the researcher preferring simple OLS to the Heckman procedure (Puhani 2000). Non-linear estimators (Santos-Silva and Tenreyro, 2006) Poisson Pseudo Maximum-Likelihood (PPML) estimator, using a log-linear function instead of log-log one: easy-to-implement strategy to deal with heteroskedasticity and zero trade flows. Need to pay attention to the structure of the data, the level of overdispersion and the assumptions one is willing to impose on the data. No easy choices. Need to take seriously the exclusion restriction to make correct choice Need convincing answer to question: where are all those zeros coming from?

26 Dynamics Persistence and sunk costs call for attention to dynamics Literature at its infancy and still exploratory in nature Blundell-Bond system GMM estimator (De Benedictis and Vicarelli 2005; De Benedictis et al. 2005) Full set of panel cointegration estimators (i.e. the Fully Modified OLS estimator or the Dynamic OLS) that control for the endogeneity of dependent variables (Fidrmuc 2009).

27 Interdependence Relative costs problem is one aspect of a more general problem of interdependence If i and j are part of a group g, assumption of an i.i.d. stochastic error term e ij is violated (Lindgren 2010). Traditional robust standard errors procedure may lead to biased estimated errors and erroneous statistical inference. When a cluster g is identified, standard errors need to be clustered around g (Cameron et al. 2010). In the gravity equation, several choices for clustering, e.g.: By country: if we believe that countries have a memory of their past decisions and project it onto the future. By FTA: if two countries belong to the same preferential trade agreement. If a hierarchical structure exists, need to nest the level of clustering choosing the most aggregate level. Caveat: number of clusters should be large and balanced. Solution: two-way or multi-way clustering, clearly discussing the adopted clustering structure

28 STEP 5: Testing for Policy Dummies vs. continuous variables Francois et al, 2006, De Benedictis and Salvatici 2011 book Aggregate vs. disaggregated data Exogeneity of trade policy Baier and Bergstrand, 2007 Heckman-type approaches Propensity score matching techniques Millimet and Tchernis, 2009, B-B 2009, De Benedictis and Nenci, 2013 Models of interdependence and network Formation of an FTA given the existence of previous FTA (Egger and Larch,2008 and Chen and Joshi, 2012) The role played by third countries is fundamental in understanding the formation of FTA MR term not sufficient in explaining interdependences (De Benedictis et al, 2010)

29 A GENERALISED GRAVITY MODEL Normal trade with resistances (in ln) Xij = a 0 + a 1 (Yi) + a 2 (Yj) + a 3 (yi) + a 4 (yj) + a 5 (TCij) + a 6 (MRTi) + a 7 (MRTj) + uij Trade costs (TC) are usually proxied by: Distance Adjacency Common language Colonial links Common currency Island Trade policy Bilateral tariff barriers often missing! While Multilateral Resistance Terms (MRT) are not observable (function of transport / trade costs and consumer prices, not only pecuniary costs) P. Montalbano, 2011

30 How to address ex post the policy effect in the gravity model? 3 subsequent strategies : Dummy strategy: standard strategy in log linear gravity equations with panels time series dimension to estimate the causal ATE on trade volumes of FTAs; Continuous variables strategy: i.e., measuring the treatment more appropriately by quantifying the preferential margin guaranteed by the preferential agreements; Non parametric Matching econometrics: i.e., to estimate the treatment effects without imposing a functional relationship & addressing the non random selection bias.

31 Main drawbacks of each strategy Dummy strategy It implies that all countries in the treatment group are assumed to be subject to the same dose of treatment It cannot distinguish between the treatment and any other event specific to the country pair and contemporaneous to the treatment (OV bias) It is unable to catch gradualism in the implementation process (trade policy does not switch from 0 to 1) The more control for heterogeneity and trade costs, the less we are able to capture the policy effect of interest (i.e., trade off btw method s accuracy& policy relevance) Continuous variable strategy Aggregation problem (a proper aggregation would take into account that imports of some goods are more responsive to changes in prices than others) The risk of endogeneity btw trade flows and trade policy Omitted nonlinearities: if the relationships btw the FTA treatment and the other tradeflows determinants are non linear, the OLS ATE will differ from the ATT (Persson, 2001) Selection bias: country pairs that share preferences tend to share similar economic characteristics that gravity eq. uses to explain their trade flows (i.e., the fact that country pairs with FTA trade more does not imply FTA actually causes trade). Matching strategy X dimensionality Selection bias in observables; Selection bias in unobservables(selfselection); No- Overlap assumption No multiple versions of the treatment and non-interference assumption

32 EU MED Case study: preferential margins before AAs Magrini, Montalbano & Nenci, IRAE 2016

33 EU MED Case study: preferential margins After AAs Magrini, Montalbano & Nenci, IRAE 2016

34 Pre-matching: selection bias P. Montalbano, S. Nenci, AE 2014

35 Post-matching: successful Sum of the logs of GDPs for matched bilateral pairs with and without an EA P. Montalbano, S. Nenci, AE 2014

36 Abadie-Imbens (2006) matching estimator where J M (i) denotes the set of indices for the first M matches for unit i. P. Montalbano, S. Nenci, AE 2014

37 P. Montalbano, S. Nenci, AE 2014

38 Actual vs Potential exports Towards EU P. Montalbano, S. Nenci, AE 2014

39 The impact of EU-Trade Preferences Magrini, Montalbano & Nenci, IRAE 2016