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Empirical Economics

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01.02.2015

Semi-mixed effects gravity models for bilateral trade

verfasst von: Isabel Proença, Stefan Sperlich, Duygu Savaşcı

Erschienen in: Empirical Economics | Ausgabe 1/2015

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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.

Vorheriger Artikel A nonparametric analysis of firm size, leverage and labour productivity distribution dynamics

Nächster Artikel A new semiparametric test for superior predictive ability

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

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 \((\eta _{i},\eta _{j})\).

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

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

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 \(\hat{\beta }+\frac{1}{n_t}\hat{\xi }\).

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.

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.

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.

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.

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.

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.

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

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

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Titel: Semi-mixed effects gravity models for bilateral trade
verfasst von: Isabel Proença
Stefan Sperlich
Duygu Savaşcı
Publikationsdatum: 01.02.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2015
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-014-0891-x

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