Abstract
Purpose
This study proposes spatial origin-destination threshold Tobit to address spatial interdependence among bilateral trade flows while accounting for zero trade volumes.
Design/methodology/approach
This model is designed to capture multiple forms of spatial autocorrelation embedded in “directional” trade flows. The authors apply this improved model to export flows among 32 Asian countries in 1990.
Findings
The empirical results indicate the presence of all three types of spatial dependence: exporter-based, importer-based and exporter-to-importer-based. After further considering multifaceted spatial correlation in bilateral trade flows, the authors find that the effect of conventional trade variables changes in a noticeable way.
Research limitations/implications
This finding implies that the standard gravity model may produce biased estimates if it does not take spatial dependence into account.
Originality/value
This paper attempts to offer an improved model of the standard gravity model by taking spatial dependence into account.
Keywords
Citation
Luo, S. and Choi, S.-W. (2022), "Do trade flows interact in space? Spatial origin-destination modeling of gravity", International Trade, Politics and Development, Vol. 6 No. 2, pp. 46-60. https://doi.org/10.1108/ITPD-06-2022-0009
Publisher
:Emerald Publishing Limited
Copyright © 2022, Shali Luo and Seung-Whan Choi
License
Published in International Trade, Politics and Development. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY4.0) license. Anyone may reproduce, distribute, translate and create derivative works of this article (forboth commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this license may be seen at http://creativecommons.org/licences/by/4.0/ legalcode
Since Tinbergen (1962) introduced a gravity equation as an empirical specification of bilateral trade flows, his model “has dominated empirical research in international trade” (Helpman et al., 2008, p. 442). In its basic form, his gravity model explains trade volumes based on the economic size (often measured by real GDP) of two trading partners and the distance separating them through a functional form analogous to Newton’s Law of Gravity with stochastic features. During the past decades, subsequent research has extended his basic model by including other explanatory variables to help better understand the mechanism of trade (e.g. border effect, McCallum, 1995) and evaluate institutional or policy impacts on trade flows (e.g. preferential trade agreement and membership in WTO, Feenstra, 2004). As Anderson (2011, p. 106) succinctly summarized, “[A]pplied to a wide variety of goods and factors moving over regional and national borders under differing circumstances, [the gravity model] usually produces a good fit”. Given its strong explanatory power, simple formulation and easy interpretation in log-linear form, scholars view the gravity model as a successful empirical tool to examine trade flows (Anderson and van Wincoop, 2003).
Despite its wide popularity, several scholars have attempted to improve the gravity model over the years (e.g. Pfaffermayr, 2019; Weidner and Zylkin, 2021). In this study, we make an empirical contribution by modeling dependent variables with three nonstandard yet empirically relevant statistical features: censored, dyadic and spatially correlated data. By utilizing recent advances of spatial econometrics in modeling spatial autocorrelation for data featuring origin-destination (OD) flows (see LeSage and Pace, 2008, 2009; for a recent review of spatial econometric OD-flow models, see Thomas-Agnan and LeSage, 2021), we propose a spatial OD threshold Tobit model to allow for a censored and directed dyadic dependent variable, of which trade data represent a typical example. We apply this new method to a cross-section of bilateral export flows to address potential multiple sources of spatial dependence in trade flows and zero trade values. Since maximum likelihood estimation (MLE) becomes infeasible in this case, we develop a Bayesian procedure to estimate the model.
Our empirical results provide supporting evidence for exporter-based (origin-based), importer-based (destination-based) and exporter-to-importer-based (origin-to-destination-based) spatial correlation in export flows. Economic sizes and geographical distance are statistically meaningful determinants of trade flows, although magnitudes of their impacts are not close to unity after taking spatial dependence into account. Besides, sizable network effects are detected for GDP, the omission of which obscures the mechanism through which economic size affects trade flows.
Model specification
LeSage and Pace's (2008) spatial OD model represents a more tailored approach to dealing with spatial correlation in data featuring an origin-to-destination flow, such as bilateral trade flows. However, their model specification is not readily applicable to the gravity model of trade if the data contain zero trade values, as their spatial OD model is proposed for continuous dependent variables. When zero trade flows are present in a data set, the presence of a limited dependent variable normally requires a limited dependent variable approach, such as a Tobit-type (spatial) model. Moreover, zero trade values pose another technical challenge when employing the log-linear form of the gravity model. To handle zero trade observations and spatial autocorrelation concurrently, this study employs a spatial OD model in conjunction with the threshold gravity model first introduced by Eaton and Tamura (1994) [1].
According to the threshold gravity model, the volume of trade between a pair of countries records a positive value only if the potential trade exceeds a certain minimum amount (i.e. threshold). As Ranjan and Tobias (2007) point out, threshold Tobit allows us to “remain true to the mixed discrete-continuous nature of trade data” by “assign[ing] meaningful probabilities to the event of no trade” and also helps to “avoid the problem of taking the log of zero” (p. 818).
Following Eaton and Tamura (1994)’s framework, the trade flow from country j to country k is modeled as:
From an economic point of view, the threshold parameter
Also, technically, the log-linear formulation of the model may help alleviate possible heteroskedasticity, as it is known that homoskedasticity in logs allows a reasonable heteroskedasticity in levels (e.g. LeSage and Thomas-Agnan, 2012).
Using matrix notation, equation (1) can be rewritten as:
LeSage and Pace (2008)’s spatial OD model employs three spatial lag terms of the dependent variable defined through the weight matrices
For brevity, we use
Setting
Eaton and Tamura (1994) rely on maximum likelihood for the estimation of their threshold Tobit model. However, once spatial lags are introduced into the model, MLE becomes infeasible, as detailed in the first part of the Supplemental Material [3]. Due to space limit, the Supplemental Material shows how we develop a Bayesian estimation algorithm which accounts for the discrete-continuous feature of trade data while avoiding the computational difficulty associated with an ML estimator.
Data, construction of weight matrices and effects estimates
The data
To illustrate spatial effects among bilateral trade flows, this study employs the basic setup of the gravity equation and fits the spatial OD threshold Tobit to a sample of 32 Asian countries in 1990 (see Table A1). The explanatory variables,
When Santos Silva and Tenreyro’s dataset includes a contiguity variable, it is based only on land borders. This operationalization may be too restrictive because if two countries are separated by only a small body of water, they are de facto neighbors. For this reason, this study adopts a broader definition of contiguity which acknowledges not only land borders but also water borders. We retrieve the contiguity data from the Expected Utility Generation and Data Management Program (EUGene) <https://eugenesoftware.la.psu.edu/> Version 3.204, which allows the user to choose from several different distances over water under which two countries are to be considered contiguous. This study uses a conservative separation distance of less than 25 miles of water body as an alternative criterion for determining contiguity.
Handling weight matrices
Choice of the weight matrices
In spatial analysis, we use the weight matrices to capture inherent spatial correlation in the data. Therefore, we should construct these matrices considering the characteristics of data under study to make them more relevant to embedded spatial patterns.
Porojan (2001, p. 271) utilizes a contiguity weight matrix that codes countries that share a land border or are separated by a small body of water as contiguous. This choice is better than a predetermined capital distance as the cutoff for denoting neighbors, especially for trade participants with large territories, such as China and Russia, which might require quite large cutoff distances in order to capture possible spatial interactions. On the other hand, Porojan’s weight matrix does not reflect the dyadic and directional features of flow data by differentiating the sources of spatial correlation.
As pointed out by Behrens et al. (2012), the weight matrix may be defined in different ways. Behrens et al.’s weight matrix is called the “interaction matrix” to distinguish it from the more common, distance-based formulation, because it assigns weights based on the population ratio of the exporting country in a trading pair to the total population of countries in the sample. However, this way of defining the interdependence structure of trade flows rigidly sets the influence of one trade flow invariable with respect to all other relevant trade flows. For example, if two trading pairs share the same importing country and have a similar population size in the respective exporting country (i.e. same ratio to the total population of the sample) but are differentiated by the bilateral distance within each pair, then all other bilateral trade flows involving the same importing country are supposed to exert the exactly same effect on the trade volumes of the stated two pairs according to their interaction matrix. Further, though Behrens et al. acknowledge that trade data features an origin-to-destination flow, their model is incapable of handling the complex connectivity structure embodied in such directional flows.
Geographic distance matters to trade behavior in different ways. Admittedly, transportation cost is a factor when countries decide with whom to trade. Yet, physical proximity allows countries to benefit from the spread of technologies, ideas and policies, which are all conducive to the promotion of trade (e.g. technology spillover, LeSage et al., 2007). Therefore, we still rely on a first-order contiguity weight matrix
Elimination of self-directed pairs
In keeping with the structure of weight matrix
Behrens et al. (2012) include internal absorptions in their data; however, their construction of the “interaction matrix” assigns no weights to self-directed pairs (i.e. own trade flows), thus excluding the role of self-directed pairs from the interactive network. Santos Silva and Tenreyro (2006) consider only non-self-directed trade pairs in their investigation of the proper functional form for the gravity equation. Accordingly, it is difficult to assume that bilateral trade flows and internal flows operate under the same mechanism and should be estimated jointly, especially for the cross-section considered in this study’s application. In 1990, external trade volumes and internal trade flows were not on a comparable scale for many of the sample countries, either because they were not yet capable of participating in international trade or because they focused on an inward looking trade policy with international trade accounting for only a small part of national income. In this circumstance, it may not be necessary to include self-directed pairs in the model. However, to accommodate diverging perspectives, this study fits the spatial OD threshold Tobit model to data augmented with internal flows as an empirical exercise [7]. The latter case does not require the elimination process as described below, which removes the structural rigidity of the weight matrices associated with self-directed dyads.
To eliminate the role of self-directed pairs from the estimation, the
Weight matrices compliant with the restructured data
As explained earlier, we need to rearrange the data to stack zero-valued observations above non-zero ones in order to take advantage of the properties of a multivariate normal distribution and derive the conditional density of latent
Let
Given that
Marginal effects in spatial OD Tobit models
It is not straightforward to interpret the estimated coefficients of a Tobit model due to its inherent nonlinearity. The spatial autoregressive structure of the spatial OD threshold Tobit model further complicates interpretation. Using marginal effects, partial derivatives reflecting how changes in an explanatory variable affect the expected value of
Given that interpretation of coefficient estimates of a conventional regression model averages over impacts on all observations arising from changes in explanatory variables, LeSage and Thomas-Agnan (2012) propose using scalar summary measures providing interpretation of spatial autoregressive interaction models consistently. By averaging over the relevant marginal effects associated with changing a given characteristic for all regions,
In matrix notation, the partial derivatives measuring total effects on the latent variable (represented by the flow matrix
We calculate a scalar summary of the destination effects by averaging across the elements in the matrix TE corresponding to the partial derivatives for pairs in which the country with changed characteristic is the destination. Mathematically, we express this scalar measure as
Similarly, we construct a scalar summary of the origin effects by averaging across the elements in the matrix TE corresponding to the partial derivatives for pairs in which the country with changed characteristic is the origin, expressed as
Further, we create a scalar summary of the intraregional effects using
Consequently, we obtain a scalar summary for the network effects using:
In order to interpret the newly proposed spatial OD threshold Tobit model, this study adopts LeSage and Thomas-Agnan’s approach with a modification that sets intraregional effects to ‘zero’ when internal flows are not included in the model estimation. Not surprisingly, the nonlinear nature of Tobit means that the
Empirical results and interpretation
Following the algorithm described in section (b), this study runs 35,000 iterations. Inspection of the trace plots for all model parameters indicates quick convergence to a steady state. Thus, this research uses a burn-in period of 5,000 iterations and draws inferences based on the remaining 30,000 iterations. As is conventional practice in Bayesian analysis, a 95% credibility interval together with posterior mean and standard deviation associated with each model parameter are reported in Table 1.
Table 2 displays the results of several other techniques commonly used for the estimation of the gravity equation alongside those from the spatial OD threshold Tobit [10]. Column 1 presents ordianary least squares (OLS) estimates using the logarithm of exports as the dependent variable. As noted earlier, this requires dropping all observations of zero bilateral trade flow. Only 612 country pairs, or 61.7% of the current sample, record positive export flows. Column 2 shows the OLS estimates with
The signs of all of the parameter estimates are remarkably stable across all models except for the contiguity variable, which seems not substantially different from zero in these models. Inspecting the first three columns, we find that different approaches to log transforming the dependent variable lead to noticeable changes in OLS estimates. As shown in Column 1, the coefficients for exporter’s GDP and distance are almost equal to positive one and negative one, respectively, while the GDP coefficient for importer is also on a comparable scale. However, we obtained these results using positive export flows only. When we include the zero observations for estimation, the magnitude of conventional trade variables decreases noticeably. As illustrated in Column 3, when we set the added positive constant (i.e. fix the threshold parameter) as 0.0049, the sizes of the two income elasticities decrease by more than half, with exporter income-elasticity declining from 0.9970 to 0.4404 and importer income-elasticity decreasing from 0.8813 to 0.4013. As for the distance parameter, its magnitude changes from −1.0081 to −0.2006. Further, when we add an arbitrary constant of “1” to the export flow data before log transforming them as in some previous trade studies, the sizes of all parameters except for contiguity decrease to about one-twentieth of those estimated only with positive observations [11]. Once a threshold parameter is included, the sign of the coefficient on contiguity changes from negative to positive as shown in Columns 5 and 6, compared to the others, which is consistent with predictions of trade theory on bilateral trade costs. Though this coefficient seems not significantly different from zero in almost all the models. Also, the coefficient is quite consistent across these models. The magnitude of coefficient on exporter’s income is larger than that of importer’s; though this coefficient estimate itself is not directly comparable across the models, which we will discuss below.
Estimates from spatial OD threshold Tobit suggest that bilateral trade flows are correlated in space and the interdependence among export flows arises from multiple sources. Specifically, none of the 95% credible intervals for spatial coefficients contains the value zero, with
On the other hand, the negative sign of
The estimate of the threshold parameter is around 0.0049, and zero falls outside the 95% credible intervals. This implies that, on average, potential trade volumes need to be at least 4.9 million for an exporter country to be willing (i.e. for it to be profitable) to trade.
It appears that geographic distance negatively affects trade volume. Its coefficient estimate from the spatial OD threshold Tobit is −0.1842. However, this estimate is different from those obtained under standard OLS and Tobit models (columns 1 and 4), which are very close to unity, −1.0081 and −1.0079, respectively. It is also slightly smaller than the distance coefficient produced by Eaton and Tamura’s threshold Tobit. This is consistent with LeSage and Thomas-Agnan (2012)’s observation that the importance of distance diminishes after accounting for spatial dependence “often … for the spatial variants of gravity models” (p. 23). In a similar vein, Fotheringham and Webber (1980) note that in the presence of spatial autocorrelation, the estimated parameter on the distance variable captures both “a ‘true’ friction of distance effect” and a measure of the map pattern (p. 34). Joining their insight, Porojan (2001, p. 275) further explicates that spatial lag in his model captures an important part of the spatial effect, which the traditional formulation of the gravity model partially picked up through the distance variable. Since spatial OD modeling is better tailored to flow data in capturing spatial effects, it is expected that the estimated impact of distance weakens.
Contiguity shows no discernible impact on export flows. Although the respective coefficient takes a positive sign for both the spatial and non-spatial threshold Tobit, zero falls near the center of the intervals for this coefficient in all but one model. This is consistent with Ranjan and Tobias (2007)’s finding. While the authors do not offer a formal explanation for the insignificance of the contiguity effect, they draw attention to the difference in their new model specification which accounts for the discrete-continuous nature of bilateral trade data (p. 830). More importantly, in competition with spatial terms built on contiguity relationship, a bilateral contiguity dummy may prove inadequate to distinguish the involved effects of contiguity on trade flows.
Whether the spatial OD threshold Tobit model is estimated with or without observations on internal trade flows (i.e. columns 6 and 7), the estimation results are consistent in the sign and significance of coefficients. According to the design of spatial weight matrix
As LeSage and Thomas-Agnan (2012) point out, estimates for non-bilateral variables in spatial OD models (i.e. exporter-GDP and importer-GDP in the current application) are not directly comparable to those from OLS. Hence, it is more appropriate to calculate scalar summary effect estimates that reflect marginal effects associated with changes in regional characteristics on average flows that provide interpretation consistent with conventional linear regression models. Table 3 shows summary effect estimates of GDP for the spatial OD threshold Tobit model. The first column displays (averaged) marginal effects on the latent
As an exploratory step, Table 4 compares the marginal effects of GDP for the latent variable
For models with no spatial correlation (i.e. the first three columns), the origin effects and destination effects are the same as the coefficient estimates for exporter-GDP and importer-GDP and the network effects are zeros. As shown in Table 4, the marginal effects from these different models are dissimilar, though all four types of summary measures consistently identify positive impacts of GDP on export flows as expected. This implies that the different impacts estimated of GDP by the spatial OD threshold model are not statistical artifacts of the choice of
As the econometric models in Table 2 have different assumptions of underlying data distribution and are estimated using different techniques, model comparison is not straightforward. Thus, the second part of the Supplementary Material employs several measures of model fit as exploratory tools, which are helpful in evaluating how well the model represents the data [3].
Conclusion
We make two contributions in this study. Methodologically, we advance an econometric model by considering the complexity of spatial autocorrelation embedded in “directional” trade flows, while dealing with the corner solution where trade volumes are zero. Empirically, we provide evidence that bilateral trade flows are correlated in space and that conventional trade variables have lesser impact than previously reported, working through multiple channels due to multifaceted spatial dependence of trade flows. On the other hand, in fitting the sample data that contain both a sizable number of zeros as well as some particularly large values, we notice that our spatial OD threshold Tobit model performs better than the non-spatial threshold Tobit model. Future research should try to further improve the model by addressing issues related to zero and extreme trade values.
Bayesian estimates of the spatial OD threshold Tobit model of export Flows, Asia, 1990
Mean | S.D. | 2.5% | Median | 97.5% | Sample | |
---|---|---|---|---|---|---|
Intcpt | −6.7752 | 0.6666 | −8.0859 | −6.7740 | −5.4725 | 30,000 |
Log exporter’s GDP | 0.3286 | 0.0270 | 0.2767 | 0.3285 | 0.3816 | 30,000 |
Log importer’s GDP | 0.2877 | 0.0268 | 0.2359 | 0.2876 | 0.3410 | 30,000 |
Log distance | −0.1842 | 0.0660 | −0.3125 | −0.1839 | −0.0558 | 30,000 |
Contiguity | 0.0331 | 0.1876 | −0.3324 | 0.0333 | 0.4005 | 30,000 |
ρd | 0.3498 | 0.0299 | 0.2905 | 0.3499 | 0.4078 | 30,000 |
ρo | 0.3418 | 0.0323 | 0.2793 | 0.3420 | 0.4069 | 30,000 |
ρw | −0.1473 | 0.0371 | −0.2221 | −0.1476 | −0.0731 | 30,000 |
α | 0.0049 | 0.0001 | 0.0047 | 0.0049 | 0.0050 | 30,000 |
Regression estimates of the traditional gravity equation
Estimator | OLS | OLS | OLS | Tobit | Threshold Tobit | Spatial OD threshold Tobita | Spatial OD threshold Tobitb |
---|---|---|---|---|---|---|---|
Dep. Var. | |||||||
Intcpt | −15.8456 * (−18.2169, −13.4744) | −0.6689 * (−0.9225, −0.4153) | −10.7401* (−11.8838, −9.5964) | −15.8567 * (−18.2218, −13.4916) | −15.6865 * (−17.4427, −13.9303) | −6.7752 * (−8.10859, −5.4725) | −8.8987 * (−10.4636, −7.4026) |
Log exp-GDP | 0.9970 * (0.9084, 1.0856) | 0.0559 * (0.0477, 0.0641) | 0.4404 * (0.4030,0.4778) | 0.9979 * (0.9095, 1.0863) | 0.6473 * (0.5885, 0.7061) | 0.3286 * (0.2767, 0.3816) | 0.4920 * (0.4278, 0.5586) |
Log imp-GDP | 0.8813 * (0.7956, 0.9670) | 0.0594 * (0.0512, 0.0676) | 0.4013 * (0.3639, 0.4387) | 0.8812 * (0.7957, 0.9667) | 0.5740 * (0.5187, 0.6293) | 0.2877 * (0.2359, 0.3410) | 0.4638 * (0.4017, 0.5310) |
Log distance | −1.0081 * (−1.2925, −0.7237) | −0.0442 * (−0.0740, −0.0144) | −0.2006 * (−0.3351, −0.0661) | −1.0079 * (−1.2917, −0.7241) | −0.1907 * (−0.3536, −0.0278) | −0.1842 * (−0.3125, −0.0558) | −0.9395 * (−1.0535, −0.8297) |
Contiguity | −0.0982 (−0.8308, 0.6344) | −0.0931 * (−0.1786, −0.0076) | −0.0479 (−0.4334, 0.3376) | −0.0967 (−0.8274, 0.6340) | 0.1517 (−0.3069, 0.6103) | 0.0331 (−0.3324, 0.4005) | −0.4162 (−0.8763, 0.0427) |
ρd | 0.3498 * (0.2905, 0.4078) | 0.1514 * (0.0917, 0.2132) | |||||
ρo | 0.3418 * (0.2793, 0.4069) | 0.1131 * (0.0472, 0.1748) | |||||
ρw | −0.1473 * (−0.2221, −0.0731) | 0.0512 (−0.0209, 0.1153) | |||||
α | 0.0049 * (0.0033, 0.0065) | 0.0049 * (0.0047, 0.0050) | 0.0049 * (0.0048, 0.0050) |
Note(s): 95% confidence intervals for OLS and ML-based estimates, and 95% credible intervals for Bayesian estimates (sample size of 30,000)
* denotes zero not in interval
a considers bilateral trade flows only (
b includes both bilateral and internal trade flows (
Marginal estimates of GDP for the spatial OD threshold Tobit
Marginal effects on | Marginal effects on | |
---|---|---|
Origin effects | 0.5180 | 0.5941 |
Destination effects | 0.2877 | 0.3351 |
Network effects | 0.1993 | 0.2190 |
Total effects | 1.0050 | 1.1482 |
Effect estimates of GDP for the OLS models and for the latent variable in the spatial OD threshold Tobit
Estimator | OLS | OLS | OLS | Spatial OD threshold Tobit |
---|---|---|---|---|
Dep. Var | ||||
Origin effects | 0.9970 | 0.0559 | 0.4404 | 0.5180 |
destination effects | 0.8813 | 0.0594 | 0.4013 | 0.2877 |
Network effects | 0 | 0 | 0 | 0.1993 |
Total effects | 1.8783 | 0.1153 | 0.8417 | 1.0050 |
List of sample countries (abbreviations in parentheses)
Bahrain (BAH) | Jordan (JOR) | Russian Federation (RUS) |
Bangladesh (BNG) | Korea, Rep. (ROK) | Saudi Arabia (SAU) |
Bhutan (BHU) | Lao PDR (LAO) | Singapore (SIN) |
Brunei (BRU) | Lebanon (LEB) | Sri Lanka (SRI) |
Cambodia (CAM) | Malaysia (MAL) | Syrian Arab Rep. (SYR) |
China (CHN) | Maldives (MAD) | Thailand (THI) |
India (IND) | Mongolia (MON) | Turkey (TUR) |
Indonesia (INS) | Nepal (NEP) | United Arab Emirates (UAE) |
Iran (IRN) | Oman (OMA) | Vietnam (DRV) |
Israel (ISR) | Pakistan (PAK) | Yemen (YEM) |
Japan (JPN) | Philippines (PHI) |
First-order contiguity matrix
Notes
Applying a Bayesian procedure to the threshold gravity model proposed by Eaton and Tamura (1994), Ranjan and Tobias (2007) examine the impact of contract enforcement on bilateral trade flows. LeSage and Pace (2009) briefly mention the potential to combine their spatial Tobit model with the threshold value of trade idea proposed by Eaton and Tamura and later adopted by Ranjan and Tobias.
Similarly, Rauch and Trindade (2002, p. 119) think of
The Supplemental Material is available online at https://whanchoi.people.uic.edu/research.html
The explanatory variables are all log transformed except the contiguity variable.
Santos Silva and Tenreyro post their data and definition of variables at http://privatewww.essex.ac.uk/∼jmcss/LGW.html. When comparing different estimators using the Anderson and van Wincoop (2003) gravity model, which controls for multilateral resistance by including exporter- and importer-specific effects, Santos Silva and Tenreyro (2006) do not use countries’ GDPs as explanatory variables as the cross-sectional data employed can only identify bilateral variables.
In this study, lower case
As a crude measure, we calculates internal trade flows as the difference between GDP and trade balance as suggested by Lebreton and Roi (2009, p. 5). To maintain data consistency, we multiply GDP data by external balance on goods and services (% of GDP) to back calculate trade balance. We draw data on external balance of goods and services (% of GDP) from World Development Indicators (WDI) online version. For Cambodia and the United Arab Emirates, this data is not available for 1990, we use the year this information first becomes available (1993 for Cambodia, 2001 for UAE). We take data on internal distance from the GeoDist database compiled by Mayer and Zignago (2011), available at cepii.fr/anglaisgraph/bdd/distances.htm. We compute the internal distance of a country as
Since
To comply with the origin-centric ordering, the diagonal elements of the matrix
For non-Bayesian estimations, a 95% confidence interval is reported in parentheses below each point estimate, while for the Bayesian estimation a 95% credible interval is presented.
Although in this case, the value “1” is quite large given that export flows are measured in billions of US dollars, this exercise illustrates that the choice of the positive constant added to trade data in order to make use of the log-linearized gravity equation does affect the estimation results and therefore should not be made ad hoc. For instance, Behrens et al. (2012) augment zero trade flows by adding 1, which might have exerted an unduly impact on their estimates given that the Canada-US exports dataset is measured in million US dollars for the year 1993.
References
Anderson, J.E. (2011), “The gravity model”, American Review of Economics, Vol. 3, pp. 133-160.
Anderson, J.E. and van Wincoop, E. (2003), “Gravity with gravitas: a solution to the border puzzle”, American Economic Review, Vol. 93, pp. 170-192.
Behrens, K., Ertur, C. and Koch, W. (2012), “‘Dual’ gravity: using spatial econometrics to control for multilateral resistance”, Journal of Applied Econometrics, Vol. 27 No. 5, pp. 773-794.
Eaton, J. and Tamura, A. (1994), “Bilateralism and regionalism in Japanese and U.S. Trade and direct foreign investment patterns”, Journal of the Japanese and International Economies, Vol. 8, pp. 478-510.
Feenstra, R.C. (2004), Advanced International Trade, Princeton University Press, Princeton.
Fotheringham, A.S. and Webber, M.J. (1980), “Spatial structure and the parameters of spatial interaction models”, Geographical Analysis, Vol. 12 No. 1, pp. 33-46.
Grossman, G.M. (1998), “Comment on determinants of bilateral trade: does gravity work in a neoclassical world? By Alan V. Deardorff”, in Frankel, J.A. (Ed.), The Regionalization of the World Economy, Chicago University Press, London, pp. 29-31.
Helpman, E., Melitz, M. and Rubinstein, Y. (2008), “Estimating trade flows: Trading partners and trading volumes”, Quarterly Journal of Economics, Vol. 123 No. 2, pp. 441-487.
LeSage, J.P. and Pace, R.K. (2008), “Spatial econometric modeling of origin-destination flows”, Journal of Regional Science, Vol. 48 No. 5, pp. 941-967.
LeSage, J.P. and Pace, R.K. (2009), Introduction to Spatial Econometrics, Chapman & Hall/CRC, Boca Raton.
LeSage, J.P. and Thomas-Agnan, C. (2012), Interpreting Spatial Econometric Origin-Destination Flow Models, Texas State University, San Marcos, TX.
LeSage, J.P., Fischer, M.M. and Scherngell, T. (2007), “Knowledge spillovers across Europe: evidence from a poisson spatial interaction model with spatial effects”, Papers in Regional Science, Vol. 86 No. 3, pp. 393-421.
Luo, S. and Miller, J.I. (2014), “On the spatial correlation of international conflict initiation and other binary and dyadic dependent variables”, Regional Science and Urban Economics, Vol. 44, pp. 107-118.
Mayer, T. and Zignago, S. (2011), “Notes on CEPII's distance measures”, CEPII Working Paper 201-25.
McCallum, J. (1995), “National borders matter”, American Economic Review, Vol. 85 No. 3, pp. 615-623.
Pfaffermayr, M. (2019), “Gravity models, PPML estimation and the bias of the robust standard Errors”, Applied Economic Letter, Vol. 26 No. 18, pp. 1-5.
Porojan, A. (2001), “Trade flows and spatial effects: the gravity model revisited”, Open Economies Review, Vol. 12, pp. 265-280.
Ranjan, P. and Tobias, J.L. (2007), “Bayesian inference for the gravity model”, Journal of Applied Econometrics, Vol. 22, pp. 817-838.
Rauch, J.E. and Trindade, V. (2002), “Ethnic Chinese networks in international trade”, Review of Economics and Statistics, Vol. 84 No. 1, pp. 116-130.
Santos Silva, J.M.C. and Tenreyro, S. (2006), “The log of gravity”, Review of Economics and Statistics, Vol. 88 No. 4, pp. 641-658.
Thomas-Agnan, C. and LeSage, J.P. (2021), “Spatial econometric OD-flow models”, in Fischer, M.M. and Nijkamp, P. (Eds), Handbook of Regional Science, Springer-Verlag, GmbH, pp. 2179-2199.
Tinbergen, J. (1962), Shaping the World Economy, Twentieth Century Fund, New York.
Weidner, M. and Zylkin, T. (2021), “Bias and consistency in three-way gravity models”, Journal of International Economics, Vol. 132 No. 103513, pp. 1-22.
Acknowledgements
This study grew out of Shali Luo's dissertation at the University of Missouri–Columbia.