Estimating gravity equation models in the presence of sample selection and heteroscedasticity

Abstract

Gravity models are widely used to explain patterns of trade. However, two stylized features of trade data, sample selection and heteroscedasticity challenge the estimation of gravity models. We propose a two-step method of moments (TS-MM) estimator that deals with both issues. The Monte-Carlo experiments show that the TS-MM estimates are resistant to various combinations of sample selection and heteroscedasticity. Moreover, the TS-MM estimator performs reasonably well even when the data generating process deviates from the TS-MM assumptions. We revisit the world trade in 1990 to illustrate the usefulness of the proposed model, with emphasis on the identification of the extensive margin of trade.

Keywords:

• gravity equation
• heteroscedasticity
• zeros
• sample selection
• two-step method of moments
• extensive margin
• market access

JEL Classification:

• F10
• C10

Acknowledgements

The authors thank John Beghin and Joseph Herriges at the Iowa State University for discussions and the Westat editorial team for their assistance. The authors also appreciate the comments from an anonymous reviewer.

Notes

¹ See Anderson (2011) for a review of the developments of the gravity model.

² Baldwin and Taglioni (2006) extend the analysis by suggesting ways to control multi-lateral trade resistance terms when time series data are available.

³ Santos Silva and Tenreyro (2013) document that the HMR model might be mis-specified, but their investigation does not result in an alternative specification.

⁴ More specifically, the choice of the functional form depends on the distribution of firms’ productivity. Without prior knowledge of the distribution, HMR recommends a nonparametric method to correct for the selection bias.

⁵ Throughout the article, we refer to the extensive margin of trade as a new trade partnership at the country level. Alternatively, the extensive margin can refer to the newly entered firms (HMR) or the newly traded varieties (Hummels and Klenow, 2005) or the newly reached consumers (Arkolakis, 2010). We omit these dimensions because we deal with country-level data.

⁶ Westerlund and Wilhelmsson (2011) extend the cross-sectional analysis in SST to a panel setting and further confirm the robustness of the PPML estimator.

⁷ Santos Silva and Tenreyro (2011) reply that the PPML estimator can satisfactorily accommodate a high frequency of zeros. But the self-selection issue remains unaddressed.

⁸ More specifically, the estimates from the variants are sensitive to the unit of measurement of the dependent variable. For instance, measuring trade flows in thousands of dollars instead of dollars would result in different estimates. See the ‘log of gravity’ website for more discussions of the pitfalls of the variants of PPML. http://privatewww.essex.ac.uk/~jmcss/LGW.html

⁹ See Anderson and van Wincoop (2004) for more discussions on trade costs.

¹⁰ The concept of the notional trade is similar to the desired amount of trade as in Ranjan and Tobias (2007).

¹¹ For instance, HMR examines how institutional factors such as ‘days to start business’ affect firms’ decisions to trade.

¹² Nevertheless, Equation 8 maintains that the PPML specification only holds for the subsample of positive outcomes.

¹³ In other words, the exponential functional form facilitates the identification in the second stage of the TS-MM model.

¹⁴ Martin and Pham (2008) also report that the PPML estimates are severely biased when data contain frequent zero outcomes.

¹⁵ Due to the cross-sectional nature of the data, all country-specific characteristics, such as income, population and remoteness to the rest of the world are subsumed into the fixed effects.

¹⁶ Nevertheless, the distance effect is within the range reported by Disdier and Head (2008).

¹⁷ Baier and Bergstrand (2007) report an RTA effect of a similar magnitude.