Comparing alternative methods to estimate gravity models of bilateral trade
Summary (2 min read)
1. Introduction
- The gravity model of trade, which was originally inspired by Newton’s gravity equation, is based on the idea that trade volumes between two countries depend on their sizes in relation to the distance between them.
- After some additional discussions concerning its specification in the nineties, the debate has now turned to the performance of different estimation techniques.
- Helpman et al. (2008) propose a theoretical foundation based on a model with heterogeneity of firms à la Melitz (2003) and an adapted Heckman procedure to predict trade taking into account these features.
- The next section briefly reviews the different theoretical foundations of the gravity equation to justify the election of the empirical specification of the gravity equation chosen.
2. The gravity equation
- The theoretical foundation of the gravity equation appeared seventeen years after its empirical specification.
- Regarding the specification, Anderson and van Wincoop (2003) propose an augmented version of the Anderson (1979) model based on the assumption of differentiation of goods according to place of origin.
- Finally, the variables Pi and Pj are the multilateral resistance terms and are defined as a function of each country’s full set of bilateral trade resistance terms.
- Anderson and van Wincoop (2003) use the observed variables in their model (distances, borders, and income shares) to obtain the multilateral trade resistance terms.
- Their sample contains the same 30 US states and 10 Canadian provinces that McCallum (1995) includes.
3.1. Linear methods
- Since the logarithm of zero is not defined, truncation and censoring methods have been proposed in the literature to treat the problem of zero flows in data.
- In addition, a panel framework permits recognising how the relevant variables evolve through time and identifying the specific time or country effects.
- Two main techniques are employed to fit data depending on the a priori assumptions.
- By contrast, the random effects model imposes no correlation between the individual effects and the regressors, implicitly assuming that the unobserved heterogeneous 2 See Wei (1996), Wolf (1997), and Head and Mayer (2000) for further information.
3. 2. Nonlinear methods
- As Santos Silva and Tenreyro (2006) points out, the log-linearisation of the gravity equation changes the property of the error term, thus leading to inefficient estimations in the presence of heteroskedasticity.
- Among nonlinear estimation methods, the most frequently used are Nonlinear Least Squares (NLS), Feasible Generalised Least Squares (FGLS), Heckman sample selection model and Gamma and Poisson Pseudo Maximum Likelihood (GPML and PPML).
- The model allows for some positive correlation between both error terms to better reflect the real decision process.
- Not robust to heteroskedasticity - Sample selection bias Tenreyro (2006) FGLS (Feasible Generalised Least Squares) -.
- It provides a rationale for zero trade flows - Unbiased estimates - Difficult to estimate - Additional data is required (exclusion variables) Helpman et al. (2008); Santos Silva and Tenreyro (2008).
4. Comparing estimation methods for a baseline gravity
- The new workhorse in the estimation of the gravity equation is still unclear.
- Econometric estimation presents some challenges that remain unsolved as of yet.
- First, the exclusion of the multilateral trade resistance terms leads to biased estimates due to the omission of variables.
- Since the logarithm of zero is unfeasible, some information would be lost.
- This problem is becoming more important due to the use of disaggregated data, in which over 50% of values is zero.
4.1. Data and model
- The sample covers bilateral exports of 80 countries over the 1980-2008 period.
- All the countries of the EU15, the CEE new European members, and 6 Middle East and North African (MENA) countries (Morocco, Tunisia, Egypt, Turkey, Israel and Algeria) as well as most OECD countries are included.
- For the sake of comparison, a gravity equation based on Anderson and van Wincoop’s (2003) theoretical model will be used: ijtjtitijij ijijijjtitijt εγγγdα smctryαcomlaαcontigαyαyαX ln++++ln+ +++ln+ln=ln 6 54321 (3) The dependent variable is the logarithm of the volume of exports in current dollars from country j to i, obtained from the CHELEM-CEPII database.
- Dij is a variable representing the geodesic distance between i and j and is obtained from the CEPII database.
- Due to the inclusion of these dummies, GDP terms are dropped from the estimation.
4.2 Results
- Before estimating equation (3), some specification tests were conducted.
- As expected, both the exporter and importer GDP increases exports regardless of the estimation method used, while the distance reduces exports.
- The main differences among estimators are revealed in the magnitude of coefficients.
- PPML notably reduces the magnitude of the coefficients as well as the standard errors.
- While other methods treat zero flows as inexistent, Heckman considers them to be unobserved.
5. Concluding remarks
- The gravity model is considered one of the most successful empirical frameworks in international economics.
- Second, the logarithm of zero is unfeasible.
- After applying several criteria to test goodness of fit, it is argued that ad hoc methods are not appropriate for estimating the gravity equation since they provide biased and inefficient estimates.
- This paper suggests that the Heckman sample selection model is the preferred estimation method within nonlinear techniques when data are heteroskedasticity and contain a significant proportion of zero observations.
- The author is indebted to J. Milgram for her helpful comments.
7. References
- The gravity equation in international trade: some microeconomic foundations and empirical evidence.
- Some econometric considerations, also known as The gravity model.
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"Comparing alternative methods to es..." refers background or methods or result in this paper
...On the other hand, PPML shows the lowest coeffi ients; a result that is in line with Santos Silva and Tenreyro (2006) and Siliverstov and Schumacher (2009)....
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...As Santos Silva and Tenreyro (2006) points out, the log-linearisation of the gravity equation changes the property of the error term, thus leading to inefficient estimations in the presence of heteroskedasticity....
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...…A2 Articles related to the problem of zero-flows and heteroskedasticity Article Data Estimation methods Dependent variable Simulation studies Santos Silva and Tenreyro (2006) 136 countries; 1990 PPML, NLS, GPML, OLS, ET-tobit, OLS (y > 0.5) OLS (y+1) Trade - PPML, NLS, GPML OLS; OLS(y + 1);…...
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...Santos Silva and Tenreyro (2006) claim that this is the preferred estimation method in the presence of heteroskedasticity....
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...Santos Silva and Tenreyro (2006) point out that this is the most natural procedure without any further information on the pattern of heteroskedasticity....
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Frequently Asked Questions (2)
Q2. What future works have the authors mentioned in the paper "Comparing alternative methods to estimate gravity models of bilateral trade" ?
This paper has provided an in-depth review of recent developments in the literature on estimation methods for the gravity equation, finding that there are at least two problems related to the log linearisation of the gravity equation that require further research as there is no consensus about the optimal method to solve them. This paper suggests that the Heckman sample selection model is the preferred estimation method within nonlinear techniques when data are heteroskedasticity and contain a significant proportion of zero observations.