Abstract
Since Jan Tinberben’s original formulation (Tinbergen 1962, Shaping the World Economy, The Twentieth Century Fund, New York), the empirical analysis of bilateral trade flows through the estimation of a gravity equation has gone a long way. It has acquired a solid reputation of good fitting; it gained respected micro foundations that allowed it to move to a mature stage in which the “turn-over” gravity equation has been replaced by a gravity model; and it has dominated the literature on trade policy evaluation. In this chapter we show how some of the issues raised by Tinbergen have been the step stones of a 50-year long research agenda, and how the numerous empirical and theoretical contributions that followed dealt with old problems and highlighted new ones. Some future promising research issues are finally indicated.
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Notes
- 1.
- 2.
Leo Tornqvist, was a famous Finnish statistician teaching at the University of Helsinki and father of the Tornqvist Price Index.
- 3.
- 4.
Linnemann quotes Zipf’s work (Zipf 1946) and referring to Isard and Peck (see the impressive figure 1 on page 101 of Isard and Peck (1954)) surprisingly states that “Some authors emphasize the analogy with the gravitation law in physics … we fail to see any justification for this.” He was not prophetic, but he was basing this statement on the fact that the elasticity of trade flows to distance were never found equal to 2.
- 5.
All words and phrases in italics are Tinbergen’s. We will use them as milestones in our selective grand tour of the gravity model in international trade. This does not mean that all the main issues in this field of research were already pointed out by the author of the first path breaking contribution. However, many open questions were already intriguing researchers fifty years ago. A surprising persistence that we think is worth pointing out.
- 6.
For an early discussion of the zero trade flows see Linnemann (1966, p. 64).
- 7.
A dummy variable was also included for Benelux and, in a larger subsample to a broad variable identifying preferential agreements. The strategy of considering the effect of Preferential Trade Agreements (PTA) through the use of dummy variable has been prominent in the literature. Only recently the alternative strategy of explicitly including the preferential margin guaranteed by the agreement has been taken into account (see Chapter 3). We will come back to this issue in Section 4.4.2.4.
- 8.
The countries included in the first exercise were mainly developed countries: Brazil, Venezuela, South Africa, Japan, Canada, USA, Austria, Belgium-Luxembourg, Denmark, France, Germany (FR), Italy, Netherlands, Norway, Sweden, Switzerland, UK, and Australia. For a complete list of the 42 countries included in the second exercise see Tinbergen (1962, p. 274). The Benelux preference (between Belgium, Luxembourg and the Netherlands) was also represented by a dummy variable.
- 9.
The resulting estimation reproduces fairly well Tinbergen’s original one. We did not have data on Benelux and also the trade data for South Africa was largely missing. We used data for 1960 and replaced GNP with GDP.
- 10.
In his comments to the regression’s functional form, Tinbergen explained that in his view the economic size (GNP) of the importing country played a twofold role: it indicates its demand – external and internal – and its degree of diversity of production. In principle, the sign of the coefficient could have been positive (demand) or negative (self-sufficiency). For Tinbergen it was a surprise that the coefficient was positive. It was also a surprise to observe that countries “trading less than normally” (below the regression line) were the bigger and the richer countries. Though the second evidence – small countries trade more with the rest of the world – has been explored theoretically (Anderson and Yotov 2010) and empirically (Alesina et al. 2005; Rose 2006), the role played by self-sufficiency has been largely neglected by the literature.
- 11.
In this setting researchers are interested in the causal effect of a treatment that takes the form of binary trade policy intervention (when the treatment is a dummy variable) or an ordered or continuous trade policy intervention (when considering trade preferential margins). Units, in this case countries or specific sectors of a country, are either exposed or not exposed to the treatment. Even if the effect of the treatment can be potentially heterogeneous across units, usually researchers focus on the identification of an average treatment effect (see Angrist and Pischke 2008 for a discussion of quasi-experimental settings).
- 12.
The use of nominal GDP (instead of real GDP) is theoretically more sound. We will come back to this issue in Section 4.5.3.
- 13.
Another source of bias in the regression could come from self-selection, i.e. nations that choose to be in a given trade policy regime are not randomly chosen. Geographical proximity, common language, common border, former colonial status, size and wealth of a nation are likely to strongly influence the decision to enter or not in given policy regimes. This causes a selection problem. Matching methods have been used to control for self-selection (see Persson (2001) for an early application and Millimet and Tchernis (2009) for a discussion of the methodology). However, solving for self-selection needs to be done on a case by case basis.
- 14.
Fixed effects specifications require getting rid of RHS variables that are accounted for by the fixed effects. This explains why we have no entries for GDP, distance and border in columns (5) to (8).
- 15.
- 16.
The heterogeneity in firm behavior is due to fixed costs of entry which are market specific and higher for international markets than for the domestic market. Hence, only the most productive firms are able to cover them. Firm productivity is furthermore correlated with a large array of other observable firm characteristics. Hence firms that serve both domestic and foreign markets are not only more productive but also larger, more innovative and more intensive in human and physical capital. By contrast firms that only serve the domestic market are less productive, smaller, less innovative, and labor intensive.
- 17.
Anderson and van Wincoop (2003, p. 174) assume that this number is equal to 1 for all origin and destination markets.
- 18.
Obviously, some econometric fixes have been found. In particular, the practice introduced by Harrigan (2001) and popularized by Feenstra (2003), to control for Multilateral Resistance through the use of country fixed effects in the econometric estimation. Incidentally, the country fixed effect practice diverted the analysis from the causes of multilateral resistance to the effects of multilateral resistance. The latter remains a promising area of analysis, especially in the context of policy evaluation.
- 19.
From a practical point of view, it is not necessary to rely on firm-level data to consider the effect of firms heterogeneity. Given the productivity distribution of domestic firms, the aggregate volume of trade defines the volume of trade of the marginal exporting firm – the one with the productivity exactly equal to the cut-off point of the productivity distribution.
- 20.
Nevertheless, gravity models have also been employed for examining the determinants of trade in goods and services, other than merchandise. The gravity model offers a high probability of a good fit, but what we mentioned for trade in merchandise is also true for all other left-hand side variables: there is no reliable gravity equation without a supporting theoretical model. If one wants to explore a gravity model on Foreign Direct Investments (FDI), it is better to have a theory to refer to (as in Carr et al. 2001; or in Baltagi et al. 2007). The need for a theory is even more compelling if one wants to account for the many alternative strategies that heterogeneous firms have at their disposal to serve foreign markets, i.e. trade and FDI (and even differentiating further between offshoring or joint-ventures).
- 21.
It is true that reliability of the data varies significantly from country to country. But if this corresponds to a national characteristic that is considered to be constant along time, the country-specific quality of the data can be controlled for, as any other time-invariant country characteristic or country fixed effects.
- 22.
In constructing average trade, the researcher should make sure that the observations are statistically independent. Hence, if the two trade partners import and export from each other caution should be taken to cluster the four single observations in one single data point. We will come back to the issue of independence latter on.
- 23.
Most common sources of trade data include the following. International Monetary Fund (IMF) DOT statistics (http://www2.imfstatistics.org/DOT/) provides bilateral goods trade flows in US dollar values, at annual and monthly frequency. UN Comtrade (http://comtrade.un.org/) provides bilateral goods trade flows in US dollar value and quantity, at annual frequency and broken down by commodities according to various classifications (BEC, HS, SITC) and up to a relatively disaggregated level (up to 5 digit disaggregation). The CEPII offers two datasets CHELEM (http://www.cepii.fr/anglaisgraph/bdd/chelem.htm) and BACI (http://www.cepii.fr/anglaisgraph/bdd/baci.htm) which use UN Comtrade data but fill gaps. corrects for data incongruencies and CIF/FOB issues by means of mirror statistics. WITS by the World Bank provides joint access to UN Comtrade and data tariff lines collected by the WTO and ITC. The most timely annual, quarterly and monthly data are available from the WTO Statistics Portal. Similarly, the CPB provides data for a subset of world countries at the monthly, quarterly and annual frequency as indices. Series for values, volumes and prices are provided along with series for industrial production. Finally, regional or national datasets provide usually more detail. Notable examples are the US and EUROSTAT (EU27) bilateral trade data available in values and quantities up to the 10 digit and 8 digit level of disaggregation respectively. Australia, New Zealand and USA also collect consistent CIF and FOB values at disaggregate levels of bilateral trade. Interesting is also the case of China, It is interesting to note that China, besides providing SITC classifications also provides data series for processing trade.
- 24.
This is true not only for variables to be included but also for restrictions on coefficients. From (4.14) the coefficient of M i and M j must be constrained to be one (this is why Anderson and van Wincoop (2003) estimated the gravity equation using \( \frac{{{X_{ij}}}}{{{M_i} \cdot {M_j}}} \) as the left-hand side variable). With heterogeneous firm, as in (4.17), this is not required.
- 25.
It is difficult to give further details here, as the solutions should be devised case by case, based on the nature of the data at hand and on the research question. Nevertheless, options include introducing fixed effects at a different frequency than the attractors (Ruiz and Villarubia 2008; De Benedictis and Vicarelli 2009; Cardamone 2011) or to only look at entries and exits in a different (policy) regimes as we have done in Section 4.2.1.
- 26.
The great-circle, or orthodromic, formula is the formula used for calculating the distance between longitude-latitude coordinates of the polar city of two countries is based on the spherical law of cosines is: \( {\phi_{ij}} = { }a\cos { }(\sin (la{t_i}) \cdot \sin (la{t_j}) + \cos (la{t_i}) \cdot \cos (la{t_2}) \cdot \cos (lon{g_j} - lon{g_i})) \cdot R \); where R = 6,371 is the radius of the earth, in km.
- 27.
CEPII generated a positive externality for all researchers by making freely available their measures of distance (see http://www.cepii.fr/anglaisgraph/bdd/distances.htm). Jon Haveman, Vernon Henderson and Andrew Rose were pioneers in this matter. Haveman’s collection of International Trade Data and his “Useful Gravity Model Data” can be freely downloaded from, the FREIT. database http://www.freit.org/TradeResources/TradeData.html#Gravity.
- 28.
It is worth noting that in a multivariate regression we do not have such a clear and simple result, but the bias will also depend on the correlation between φ ij (measured with error) and other covariates. The problem is even more serious with estimates in first-differences, whose aim is to eliminate a possibly omitted fixed effect (Griliches and Hausman 1986). The traditional solution is to find an instrument correlated with distance but not with the error term.
- 29.
See also Novy (2010) for a distance measure derived from heterogeneous firms trade models.
- 30.
Blum and Goldfarb (2006) also show that Americans are more likely to visit websites from nearby countries, even controlling for language, income, and immigrant stock. For taste-dependent digital products, such as music, games, and pornography, a 1% increase in physical distance reduces website visits by 3.25%. On the contrary, for non-taste-dependent products, such as software, distance has no statistical effect.
- 31.
The WTO collects all Trade Agreements that have either been notified, or for which an early announcement has been made, to the WTO (http://rtais.wto.org/UI/PublicMaintainRTAHome.aspx). The World Bank – Dartmouth College Tuck Trade Agreements Database can also be consulted at http://www.dartmouth.edu/~tradedb/trade_database.html.
- 32.
Andrew Rose’s homepage (http://faculty.haas.berkeley.edu/arose/RecRes.htm) is a great example of data sharing. It has encouraged new research and promoted the good practice of replicability in empirical research.
- 33.
Francois et al. (2006) estimate of the trade policy elasticity has a huge variance and also include some negative cases. This result is by no means exclusive to this stream of literature. Also some dummy strategy papers find negative coefficients to preferential dummies (Martínez-Zarzoso et al. 2009).
- 34.
See Chapter 5 of this volume for a Meta Analysis of the literature on EU preferential trade policy.
- 35.
See Chapter 3 of this volume. Chapter 10 also shows that the different formula adopted to derive the preferential margins matter significantly for the assessment of the existence and extent of preference erosion for developing countries.
- 36.
It is difficult to argue that countries enter a preferential agreement at random. Whereas it is hard to observe the original motives that lead to the signing of the agreement, it is reasonable that those motives could be correlated with trade volumes. This gives rise to the selection bias. In particular, the estimated trade policy coefficient will be upward biased if the omitted variables guiding the selection and the trade policy variable are positively correlated.
- 37.
The inverse Mills ratio, named after the statistician John Mills, is the ratio of the probability density function over the cumulative distribution function of a distribution.
- 38.
Cameron and Trivedi (2005 p. 676) suggest using a likelihood ratio test on the dispersion parameter to test whether it is equivalent to use a NBPML or a PPML estimator.
- 39.
See De Benedictis and Vicarelli (2005) for a discussion of the issue in the context of the gravity model.
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Acknowledgments
This essay has been written while Luca De Benedictis was visiting ARE at the University of California, Berkeley and EIEF in Rome. He gratefully acknowledges UCB and EIEF for the great hospitality. Luca De Benedictis also acknowledges the financial support received by the Italian Ministry of Education, University and Research (Scientific Research Program of National Relevance 2007 on “European Union policies, economic and trade integration processes and WTO negotiations” – PUE & PIEC). We are grateful to Davide Castellani, Michele Di Maio, Lucia Tajoli, Claudio Vicarelli and especially Luca Salvatici for the comments and the many conversations on the topic. Any remaining errors are solely our responsibility.
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De Benedictis, L., Taglioni, D. (2011). The Gravity Model in International Trade. In: De Benedictis, L., Salvatici, L. (eds) The Trade Impact of European Union Preferential Policies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16564-1_4
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