Gravity model estimation: fixed effects vs. random intercept Poisson pseudo-maximum likelihood

ABSTRACT

The standard Anderson and van Wincoop gravity model has typically been estimated using a fixed-effects approach. However, a fixed-effects approach has a major drawback: it does not allow for the estimation of exporter- and importer-invariant variables. Thus, at least in a cross-sectional context, economically relevant variables such as exporter and importer gross domestic product are disregarded. We propose a random intercept model to address this gap. For large datasets, this approach not only provides identical estimates like a fixed-effects approach, but also allows for the estimation of exporter- and importer-invariant variables.

KEYWORDS:

• Gravity model
• Poisson pseudo-maximum likelihood
• fixed-effects model
• random intercept model

JEL CLASSIFICATION:

• F10
• C13
• C21

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ According to Staub and Winkelmann (2013), PPML also can deal with zero-inflated data. For zero-inflated data, the intercept consists of the standard intercept term and an additional zero-inflation term. All other estimators are still consistent.

² Our critic also applies for panel gravity models. According to Baldwin and Taglioni (2007) panel AvW models have to be estimated by time-varying fixed-effects approaches. Time-varying fixed effects, however, also capture the effects of exporter- and importer-invariant variables.

³ If one only focuses on positive trade flows, the approximation approach of trade cost effects by Baier and Bergstrand (2009) is an alternative. This approach, however, is not applicable to zero trade flows.

⁴ For the case with just one set of fixed effects, the result can be seen very clearly in Cameron and Trivedi (2013). We are extremely grateful to Prof Joao M. C. Santos Silva for making us aware of this explanation. We highly appreciate his help.

⁵ A mixed-effects approach is also recommended by Proença, Sperlich, and Savaşcı (2015). The authors, however, favour a semi-mixed-effects approach. Here, the assumption of identical preferences is skipped.

⁶ For details, see Feenstra (2002) and Anderson and van Wincoop (2003).

⁷ In principle, for large datasets the random intercept model also converges against a Bayesian fixed-effects model.