Gravity equations: Workhorse or Trojan horse in explaining trade and FDI patterns across time and space?

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Abstract

Gravity equations are a widely used tool in the International Business (IB) literature to explain country-level trade and FDI flows. Against the background of its increased popularity and data availability, a range of commonly made econometric mistakes have recently been discussed in the literature, mostly pertaining to the (omitted) characteristics of countries or country pairs in gravity models. In this paper we complement this literature by focusing on the time-series aspects of gravity models, something that has become crucial with the increased use of panel data. Specifically, we concentrate on the possible non-stationarity of both the dependent variable (trade or FDI flows) and of one or more of the explanatory variables. In this paper we (i) show that there is indeed a problem with the non-stationarity of variables commonly used in gravity equations; (ii) show that not correcting for this yields overestimated results; and (iii) propose an effective solution.

Introduction

A central research question in International Business (IB) is why firms operate outside their own country and what determines the size and geographic distribution of these foreign activities. To explain these trade and foreign direct investment (FDI) flows, IB scholars have used gravity models. Since its inception in 1993 respectively 1970, 39 studies on the country-level determinants of FDI and exports published in this journal or the Journal of International Business Studies are implicitly or explicitly embedded in a gravity model (see Appendix A). Similarly, the economic geography literature makes use of gravity equations in order to explain the geographical dissemination of trade and FDI (see e.g., Bosker and Garretsen, 2009, Pantulu and Poon, 2003). This popularity is not without reason. Gravity models have been shown to have firm theoretical foundations (Anderson, 1979, Bergstrand, 1985) and have produced some of the clearest empirical results in international economics and business (Gerachi and Prewo, 1977, Leamer and Levinsohn, 1995; for an overview, see Frankel, 1997).

Gravity models postulate that the magnitude of merchandise trade and FDI flows between countries is conditional on several characteristics of these countries, notably their economic size and level of economic development, and on factors stimulating or discouraging the movement of merchandise or investment between countries (Bergstrand, 1985, Brainard, 1997). These factors include transportation costs, typically proxied by the presence or absence of a shared land border, by geographic distance, and formal trade barriers, often proxied by the presence or absence of free trade agreements. The increased availability of data on cultural and institutional characteristics of country pairs has triggered further research attempting to explain the size and geographic distribution of both trade and FDI by, for example, the role of host-country political risk and corruption (Cuervo-Cazurra, 2008, Globerman and Shapiro, 2003, Habib and Zurawicki, 2002, Sethi et al., 2003), institutions (Clougherty and Grajek, 2008, De Groot et al., 2004, Pajunen, 2008), culture and cultural distance (Dow and Karunaratna, 2006, Huang, 2007, Loree and Guisinger, 1995), and shared language and religion (Dow and Karunaratna, 2006, Frankel and Rose, 2002, Rose, 2004, Srivastava and Green, 1986).

Whereas early studies using gravity equations were typically based on a cross-section of countries, the increased data availability, improvements of econometric techniques and computing power have led authors to use panel data. The obvious big advantages are the possibilities to track developments over time, and the increased efficiency of estimates due to a considerably larger number of observations. Disadvantage, however, is that one also needs to take into account issues arising from time-series econometrics. As such, authors typically correct for autocorrelation in the residuals or use year dummies. However, there are more time-series related econometric issues that need to be dealt with for results to be both unbiased and efficient.

Among the larger issues in time-series analysis is the (non-) stationarity of variables (Engle and Granger, 1987, Hayashi, 2000). If the distribution of a certain variable is constant over time, it is said to be stationary. If not, it is considered non-stationary. Think in this respect for example of a variable with a clear positive trend; because of this trend, both the mean and the variance of this variable will increase over time. As such, its distribution is time-varying and the variable therefore non-stationary. If the variables on both the left- and the right-hand side of a regression equation have a certain positive trend, one will always find a significant statistical relation between the two when applying traditional techniques. The source of this statistical relation, however, might solely be the trend, and thus be spurious. This not only affects the variables having this trend, but may affect the results obtained for the other independent variables as well. If, on the other hand, the variables share a common trend because of underlying causal (economic) mechanisms, the estimation results are correct and the variables are said to be co-integrated. The estimates for the stationary variables in the model, however, remain biased.

This issue of non-stationarity and co-integrated variables is potentially harmful in the context of gravity equations (Fidrmuch, in press, Herwartz, 2003) because some of the independent variables typically found in gravity models potentially have an upward trend comparable to trade or FDI, like for example GDP. In this paper we investigate the time-series aspects of gravity equations and test whether FDI and trade are co-integrated with independent variables typically used in gravity equations. By doing so, we follow up on Baldwin and Taglioni (2006), who recently showed that gravity equations are very often mis-specified, a phenomenon observed by Dow and Karunaratna as well (2006: 587). Taking their guidelines into account, we complement their analyses and illustrate the importance of taking the time-series aspects of gravity models more seriously than has been done so far. As such, we contribute to the methodical aspects of our empirical understanding of the geographic distribution and determinants of trade and FDI. Given the increased use of gravity equations in IB, this is of great importance for the set-up of our empirical models to properly test our theoretical predictions on this distribution and its determinants and the subsequent policy implications.

Using data on US outward FDI and US exports for 1983–2003, we first estimate a traditional gravity equation. We subsequently show that GDP, political risk and FDI, respectively exports are both non-stationary and co-integrated. Correcting for this misspecification, we re-estimate the gravity equations on exports and FDI. We show that correcting for co-integration leads to (i) lower significance levels of many variables between the corrected and uncorrected model, and (ii) lower effect sizes of many of these variables. These findings are important because they suggest that not properly controlling for the time-series aspects of exports and FDI leads to overestimated coefficients and significance levels and hence to a biased picture of the determinants of trade and FDI and their relative importance. We conclude that not properly including the time-series aspects of panels will turn the workhorse that the gravity model currently is, into a Trojan horse.

Section snippets

Background

The gravity model used to explain trade and FDI patterns was inspired by Newton's gravity equation in physics, in which the gravitational forces exerted between two bodies depend on their mass and distance (Linders, 2006). The application of this mechanism in the field of international trade (and later FDI) was pioneered by Tinbergen (1962) and Linnemann (1966). Despite its intuitive attractiveness, initial criticism was that its theoretical foundations were weak resulting in attempts to

Exports

Our first dependent variable is the log of US merchandise exports (in millions of constant 2000 US dollars) between 1983 and 2003 from the IMF's Direction of Trade Statistics. In order to deal with Baldwin and Taglioni's (2006) comment regarding the proper deflation of trade flows, we used the export price index from the Bureau of Labor Statistics from the US department of Labor to convert export flows to 2000 prices.

FDI

The second dependent variable is the stock of outward US foreign direct

Conclusion

The gravity equation is generally considered to be the workhorse in IB in explaining international trade and FDI patterns. It is intuitively attractive, has a clear theoretical basis, and with the increased availability of data and computing power it seems a proper empirical model to shed light on the determinants of trade and FDI. Recently Herwartz (2003) and Baldwin and Taglioni (2006) question the econometrics of gravity equations.

In this paper we complement Baldwin and Taglioni's (2006)

Acknowledgements

We would like to express our gratitude to the editor, two anonymous referees, Roger Smeets, and Bart Frijns. The second author thanks the Netherlands Organization for Scientific Research (NWO) for their financial support.

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