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The most important, misused, tool of international economics

The most important, misused, tool of international economics. Estimating the gravity model. The gravity model of trade. Estimate trade flows among countries as a function of country size and distance Effect of policy changes on trade Trade liberalisation Currency unions

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The most important, misused, tool of international economics

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  1. The most important, misused, tool of international economics Estimating the gravity model

  2. The gravity model of trade • Estimate trade flows among countries as a function of country size and distance • Effect of policy changes on trade • Trade liberalisation • Currency unions • Calculate countries’ trade potential • Estimate border effects and trade costs

  3. Estimating the gravity model without gravity Joakim Westerlund Lund University Fredrik Wilhelmsson Norwegian Institute of International Affairs

  4. Our contribution • Propose a way to estimate the gravity model avoiding biased results when some countries do not trade and the data is heteroskedastic • Monte Carlo simulations show that the proposed fixed effect Poisson ML estimator produces unbiased results • Estimate the trade effects of the 1995 EU-enlargement using Stata

  5. The basic gravity model We can control for country heterogeneity by adding a country-pair (fixed) effect Giving the following equation to be estimated Which can be written as

  6. Estimating the model • Cross-section or simple OLS on a pooled sample • Do not control for country heterogeneity • Heteroskedasticity will bias the estimates • Panel data (log-linearized model) • Discard country-pairs without trade • selection bias • Heteroskedasticity will bias the estimates

  7. Solving the problems • Sample selection type of model • Random effect Tobit • We propose using a fixed effect Poisson ML estimator • Includes zeros • Practically unbiased estimates even with heteroskedastic data • Easy to use in empirical applications

  8. Log-linearized estimation The base-line gravity equation In log-linearized form

  9. Log-linerazied estimation (2) ln(0) is usually solved by • Removing the zeros • Replacing ln(0) by ln(1)

  10. Sample selection type models • Advantage • Model both the decision to trade and the level of trade • Disadvantages • Difficult to find an identification restriction • Same variables affect the decision to trade and the trade volume • Rather complicated to estimate in practice

  11. Estimation of the nonlinear model E(Mijt) = exp(aij + γDijt + β1ln(Yjt) + β2ln(Yjt)) Poisson MLE can be used

  12. The ML estimator Problem: N-consistency and # parameters grows with N (incidental parameters) we estimate by maximizing log(f(Mij1,…, MijT|∑Mijt)) Advantages: • No incidental parameters • Conditioning on ∑Mijtis not restrictive • Almost as simple as OLS!

  13. Monte Carlo studyData generating process Mijt = exp(aij + γDijt + βYijt)vijt • Mijt~ U(0,1), • aij= γ =β = 1 and • Dijt = 1 if t > τijT and Dijt = 0 otherwise • vijt ~ LN(1,σ2ij), • where σ2ij = 1 in case 1 • σ2ij = 1/exp(aij + γDijt + βYijt) in case 2 • λ = proportion of “zeros” in the sample

  14. Simulation results • bias(Poisson MLE) ≈ 0 • bias(OLS) >> 0 in Case 2 • bias(OLS) increases with λ • size(Poisson MLE) ≈ 5% in Case 2 • size(Bootstrap Poisson MLE) ≈ 5% in both cases • Generally, size(OLS) >> 5%

  15. Empirical application • Developed countries imports from all partners except oil exporting countries and formerly planed economies in Europe • 1992-2002 • Nominal trade (DOTS), real-GDP (WDI) • Estimated with country-pair and time fixed effects

  16. Estimation results

  17. Summary of the results • Large differences between OLS(1), OLS(2) & Poisson(3) • Significant trade diversion • No significant export diversion in OLS(1) or Poisson • No trade creation

  18. Conclusions • Substantial difference between Poisson and traditional estimates • The estimates from the log-linear gravity model is not suitable for inference since they are likely to be severely biased • A feasible alternative is the fixed effect Poisson ML with bootstrapped standard errors • The EU enlargement caused trade diversion

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