L5_gravity_empirics File
Transcript
L5_gravity_empirics File
International Economic Policy 2014-15 The Gravity Model: Eempirical issues Prof. PIERLUIGI MONTALBANO [email protected] P. Montalbano - Sapienza Università di Roma S 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 … Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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 Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma Step 2: right end - Specification Matters! VARIABLES limport limport limport lgdp i 0.704*** 0.957*** 0.803*** lgdp j 0.777*** 1.051*** 1.003*** ldistance -0.897*** -1.014*** -1.067*** -1.089*** border 0.406*** 0.537*** 0.587*** 0.564*** FTA 0.146** -0.172*** -0.632*** -0.717*** 0.266*** Constant -16.64*** -25.54*** Observations -19.85*** limport 28.56*** limport 13.02*** 10831 10831 10831 10831 10831 0.55 0.732 0.785 0.815 0.928 R-squared time effects no yes no no no yes yes exporter and importer time invariant fe no no no exporter and importer time-varying fe no no no yes no no no no yes yes time invariant pair fe Note: (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level. Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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 Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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 - Sapienza Università di Roma Trade Costs: Empirical Evidence 1. 2. Distance variable does not reduce over time. De Menil e Maurel (1994) calculated for the period 1924-26 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!); 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” (MRT). © P. Montalbano, 2011 P. Montalbano - Sapienza Università di Roma MRT and the «Border Effect» • Bilateral trade between country i and j depends on the specific bilateral trade barrier as well as their multilateral resistance terms 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!) P. Montalbano - Sapienza Università di Roma The Relative Costs Problem Implications of a world with many countries • 3rd countries mass and distance matters • 2-way effect Rest of the World Country A Country B Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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 pi 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 = φij 1−σ M j Mi Pj1−σ Ω i Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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 Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma A GENERALISED GRAVITY MODEL Normal trade with resistances (in ln) Xij = a0 + a1 (Yi) + a2 (Yj) + a3 (yi) + a4(yj) + a5 (TCij) + a6 (MRTi) + a7 (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 - Sapienza Università di Roma Cross-section ⇒ panel Natural to extend the above from cross section to panel regressions In a panel regression you now have data for your cross-section but also over time. The standard panel regression typically involves “fixed” effects, where for each variable you take the difference for each year, from the mean for that variable. • Hence the interpretation of the panel estimation is quite different from the cross-section. – Cross section is a static comparison across countries – Panel typically has much more of dynamic interpretation ie. you are looking at the impact of changes in the explanatory variables on changes in trade flows What form should these fixed effects take: • Country pair fixed effects – standard • Country fixed effects à la Anderson & Wincoop. P. Montalbano - Sapienza Università di Roma A GENERALISED GRAVITY MODEL • 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 possible sets of fixed effects in the « full model »: 1. Country effects (exporter-specific effects and importer-specific effects): unobserved factors such as geographical, political, cultural, institutional factors 2. Time specific effects 3. Interactions (exporter–importer interactions, exporter–time interactions and importer–time interactions) • Hence you now have bilateral trade depending on income levels in importing and exporting countries + transport costs + country specific fixed effects. • However… if you are including country specific fixed effects these are then perfectly collinear with the GDP variables. • The solution is therefore to take the GDP variables over to the left hand side (but then what are we left with?) P. Montalbano - Sapienza Università di Roma Preferred Fixed Effects’ Specification Xijt = ϕ ijt1−σ FEjt FEit FEij • Fixed effects specification – Constant and time-varying dummies for each exporter and importer – 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 P. Montalbano - Sapienza Università di Roma STEP 4: Selecting The Appropriate Functional Form Non-linearities Selection bias and zeroes Dynamics Interdependence and networks P. Montalbano - Sapienza Università di Roma 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? Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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; Olivero & Yotov, 2012) • 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). P. Montalbano - Sapienza Università di Roma The Global trade network Fonte: De Benedictis et al., (GEJ, 2014) 19 P. Montalbano - Sapienza Università di Roma 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 eij 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 Source: De Benedictis & Taglioni (2011) P. Montalbano - Sapienza Università di Roma 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) P. Montalbano - Sapienza Università di Roma 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”. © P. Montalbano, S. Nenci, 2011 P. Montalbano - Sapienza Università di Roma Dummy strategy Main drawbacks of each strategy Source: Montalbano & Nenci, 2014 Continuous variable Matching strategy strategy It implies that all Aggregation problem X dimensionality countries in the (a proper aggregation Selection bias in treatment group are would take into observables; assumed to be subject account that imports Selection bias in to the same dose of of some goods are unobservables(selfmore responsive to treatment selection); changes in prices than It cannot distinguish No- Overlap between the others) assumption The risk of No multiple versions treatment and any of the treatment and other event specific to endogeneity btw trade the country pair and flows and trade policy “non-interference” contemporaneous to Omitted nonassumption the treatment (OV linearities: if the bias) relationships btw the It is unable to catch FTA “treatment” gradualism in the and the other tradeimplementation flows determinants process (trade policy are non linear , the does not switch from 0 OLS ATE will differ to 1) from the ATT The more control for (Persson, 2001) heterogeneity and Selection bias: trade costs, the less country pairs that we are able to capture share preferences the policy effect of tend to share similar interest (i.e., trade off economic btw method’s characteristics that accuracy& policy gravity eq. uses to relevance) explain their trade flows (i.e., the fact that country pairs with FTA trade more does not imply FTA actually causes trade). P. Montalbano - Sapienza Università di Roma