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Semi-mixed effects gravity models for bilateral trade

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Abstract

In recent years, different alternatives have been suggested to specify and estimate gravity models for bilateral trade. Presently, the so-called Poisson pseudomaximum likelihood (PPML) with log-linear index is probably the most commonly used method. A method is proposed for panel data that targets to reconcile the pros and cons of fixed and random effects models, respectively. It applies equally to two- and three-way panel models and those with country-specific time-varying effects. It allows to filter out potential correlation between observed and unobserved heterogeneity and to identify the effects of time-invariant factors. It can also be used when panels are short in time, and to other specifications than the PPML-like gamma PML, zero-inflated, or Tobit-like models. We introduce and illustrate the proposed estimator with a study of bilateral trade flows across the European Union before the recent economic crisis.

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Notes

  1. Note that like for the log-linear OLS, the consistency of PPML depends on the assumptions made about the error structure.

  2. Except if the time-invariant covariate exhibits variation in a different dimension than the fixed effects, for example when we have covariates \(X_{ij}\) and FEs \((\eta _{i},\eta _{j})\).

  3. Exceptions are, for example, Logit or Poisson-distributed responses where conditioning on their mean eliminates the country-pair fixed effects.

  4. They actually do it in the context of small-area statistics.

  5. When including temporal means of covariates, one has to be careful for the coefficients’ comparison: for example, including \(\beta \ln x_{ijt} \) and \(\xi \cdot \frac{1}{n}_t \sum _t \ln x_{ijt}\), the total impact of \(\ln x_{ijt}\) is \(\beta +\frac{1}{n_t}\xi \). One can therefore find both, studies looking only at \(\hat{\beta }\) and those looking at \(\hat{\beta }+\frac{1}{n_t}\hat{\xi }\).

  6. The notation is not unique in the literature, while many use it as a synonym for penalized splines in general, others refer exclusively to its implementation with B-spline basis.

  7. Santos Silva and Tenreyro (2006) use the notation of pseudo referring to McCullagh and Nelder (1989) who speak of quasi- likelihood. Nelder (2000) differentiates between them. Along his classification, one might be more interested in the quasi-maximum likelihood methods, but in abuse of notation, we keep the abbreviation PPML.

  8. For the implementation, see Venables and Ripley (2002) concerning GLMM and the modifications of Wood (2011) for the particular case of P-splines for GAMMs.

  9. Henderson and Millimet (2008) state that the added value of nonparametric gravity models is poor. However, they start out from the more restrictive model of Anderson and van Wincoop (2003). Their conclusions do not necessarily hold for the more flexible gravity models considered here.

  10. See Racine and Parmeter (2014) for a method of model selection based on in-sample prediction that accommodates non- and semiparametric estimations and panel data.

  11. This selection is arbitrary and only to simplify the simulation study; it is neither a selection based on the findings from the previous sections nor a recommendation for empirical studies.

  12. Note that we conducted many more simulation studies, available from the authors, which were even more in favor of the SEM approach.

  13. We thank Enrique Martínez-Galán and Eliano Marques for their help in obtaining these data.

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Acknowledgments

Isabel Proença is grateful for the financial support received from FCT (Fundação para a Ciência e Tecnologia) through the PEst-OE/EGE/UI0491/2011 program and Stefan Sperlich for funding from the Swiss National Science Foundation 100018-140295. We thank helpful discussions with Jaya Krishnakumar, Inmaculada Martínez-Zarzoso, Marcelo Olarreaga, and Walter Zucchini, of participants of ESEM/EEA-2012, the seminars at ISEG and GSEM, an anonymous referee, and in particular the AE Christopher Parmeter who essentially contributed to the stepwise improvement of this article.

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Appendix: Addition information on used data

Appendix: Addition information on used data

Countries included in the data set: Austria (AU), Belgium (BE), Bulgaria (BU), the Czech Republic (CZ), Denmark (DK), Estonia (EE), Finland (FI), France (FR), Germany (DE), Greece (GR), Hungary (HU), Ireland (IR), Italy (IT), Latvia (LV), Lithuania (LH), Luxembourg (LU), the Netherlands (NE), Poland (PL), Portugal (PT), Romania (RO), Slovakia (SK), Slovenia (SV), Spain (SP), Sweden (SW), and the United Kingdom (UK).

Details about the used variables:Footnote 13

  • T: nominal import (cif) flows in \(10^{3}\) euros.

  • MGDP/XGDP: importer/exporter country’s nominal GDP at market prices in millions of euro, from Eurostat’s New Cronos Database.

  • MPOP/XPOP: importer/exporter country’s population, expressed in thousands of people at the end of the period, from Eurostat’s New Cronos Database.

  • DIST: absolute distance expressed in kilometers, the geodesic distance between capitals (in the case of the Netherlands, Amsterdam substitutes Den Haag), measured as the surface distance between two points of latitude and longitude (great circle distance) obtained from www.wcrl.ars.usda.gov/cec/java/lat-long.htm.

  • NEIGH: neighboring dummy variable is equal to one if two trading partners share a land or sea border, zero otherwise. From CIA’s World Factbook 2003 as published on www.cia.gov/cia/publications/factbook/index.html.

  • EU15: dummy equal to 1 if the exporting country belongs to the European 15.

  • MLOCK/XLOCK: landlockedness dummy for importer/exporter country; equals one if country has no direct connection to sea.

  • COMLANG: common language dummy variable is equal to one if two trading partners share the same official language, zero otherwise. From CIA’s Factbook 2003 on www.cia.gov/cia/publications/factbook/index.html.

  • ETHNIC: ethnic dummy, equal to one if there is an ethnic minority of the exporter country in the importer country that represents more than 5 % of total population of the latter. From CIA’s The World Factbook 2003.

  • MAREA/XAREA: importer/exporter country’s area.

  • PAT: the number of patents of importer country recorded as EPO (European patent office) patent applications (Direct EPO filings + EURO-PCT in regional phase); source OECD (Table 9).

Table 9 Pooled PPML

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Proença, I., Sperlich, S. & Savaşcı, D. Semi-mixed effects gravity models for bilateral trade. Empir Econ 48, 361–387 (2015). https://doi.org/10.1007/s00181-014-0891-x

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