The most important, misused, tool of international economics

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

16. 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%

17. 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

18. Estimation results

19. 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

20. 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