THE LOG OF GRAVITY - the University of Mauritius

644THE REVIEW OF ECONOMICS AND STATISTICSy i expx i ε i , (6)with y i 0 and E[ε i x] 0.As we mentioned before, the standard practice of loglinearizingequation (6) and estimating by OLS is inappropriatefor a number of reasons. First of all, y i can be 0, inwhich case log-linearization is infeasible. Second, even ifall observations of y i are strictly positive, the expected valueof the log-linearized error will in general depend on thecovariates, and hence OLS will be inconsistent. To see thepoint more clearly, notice that equation (6) can be expressedasy i expx i i ,with i 1 ε i /exp(x i ) and E[ i x] 1. Assuming for themoment that y i is positive, the model can be made linear inthe parameters by taking logarithms of both sides of theequation, leading toln y i x i ln i . (7)To obtain a consistent estimator of the slope parametersin equation (6) estimating equation (7) by OLS, it is necessarythat E[ln i x] does not depend on x i . 8 Because i 1 ε i /exp(x i ), this condition is met only if ε i can bewritten as ε i exp(x i ) v i , where v i is a random variablestatistically independent of x i . In this case, i 1 v i andtherefore is statistically independent of x i , implying thatE[ln i x] is constant. Thus, only under very specific conditionson the error term is the log linear representation ofthe constant-elasticity model useful as a device to estimatethe parameters of interest.When i is statistically independent of x i , the conditionalvariance of y i (and ε i ) is proportional to exp(2x i ). Althougheconomic theory generally does not provide any informationon the variance of ε i , we can infer some of its propertiesfrom the characteristics of the data. Because y i is nonnegative,when E[y i x] approaches 0, the probability of y i beingpositive must also approach 0. This implies that V[y i x], theconditional variance of y i , tends to vanish as E[y i x] passesto 0. 9 On the other hand, when the expected value of y is faraway from its lower bound, it is possible to observe largedeviations from the conditional mean in either direction,leading to greater dispersion. Thus, in practice, ε i willgenerally be heteroskedastic and its variance will depend onexp(x i ), but there is no reason to assume that V[y i x] isproportional to exp(2x i ). Therefore, in general, regressingln y i on x i by OLS will lead to inconsistent estimates of .8Consistent estimation of the intercept would also require E[ln i x] 0.9In the case of trade data, when E[y i x] is close to its lower bound (thatis, for pairs of small and distant countries), it is unlikely that large valuesof trade are observed, for they cannot be offset by equally large deviationsin the opposite direction, simply because trade cannot be negative.Therefore, for these observations, dispersion around the mean tends to besmall.It may be surprising that the pattern of heteroskedasticityand, indeed, the form of all higher-order moments of theconditional distribution of the error term can affect theconsistency of an estimator, rather than just its efficiency.The reason is that the nonlinear transformation of thedependent variable in equation (7) changes the properties ofthe error term in a nontrivial way because the conditionalexpectation of ln i depends on the shape of the conditionaldistribution of i . Hence, unless very strong restrictions areimposed on the form of this distribution, it is not possible torecover information about the conditional expectation of y ifrom the conditional mean of ln y i , simply because ln i iscorrelated with the regressors. Nevertheless, estimatingequation (7) by OLS will produce consistent estimates ofthe parameters of E[ln y i x] as long as E[ln (y i )x] is a linearfunction of the regressors. 10 The problem is that theseparameters may not permit identification of the parametersof E[y i x].In short, even assuming that all observations on y i arepositive, it is not advisable to estimate from the log linearmodel. Instead, the nonlinear model has to be estimated.A. EstimationAlthough most empirical studies use the log linear formof the constant-elasticity model, some authors [see Frankeland Wei (1993) for an example in the international tradeliterature] have estimated multiplicative models using nonlinearleast squares (NLS), which is an asymptotically validestimator for equation (6). However, the NLS estimator canbe very inefficient in this context, as it ignores the heteroskedasticitythat, as discussed before, is characteristic ofthis type of data.The NLS estimator of is defined byˆ arg minbni1y i expx i b 2 ,which implies the following set of first-order conditions:n y i expx iˆ expxiˆ xi 0. (8)i1These equations give more weight to observations whereexp(x i ˆ ) is large, because that is where the curvature of theconditional expectation is more pronounced. However,these are generally also the observations with larger variance,which implies that NLS gives more weight to noisierobservations. Thus, this estimator may be very inefficient,depending heavily on a small number of observations.If the form of V[y i x] were known, this problem could beeliminated using a weighted NLS estimator. However, in10When E[ln y i x] is not a linear function of the regressors, estimatingequation (7) by OLS will produce consistent estimates of the parametersof the best linear approximation to E[ln y i x] (see Goldberger, 1991, p.53).

THE LOG OF GRAVITY 645practice, all we know about V[y i x] is that, in general, it goesto0asE[y i x] passes to 0. Therefore, an optimal weightedNLS estimator cannot be used without further informationon the distribution of the errors. In principle, this problemcan be tackled by estimating the multiplicative model usinga consistent estimator, and then obtaining the appropriateweights estimating the skedastic function nonparametrically,as suggested by Delgado (1992) and Delgado andKniesner (1997). However, this nonparametric generalizedleast squares estimator is rather cumbersome to implement,especially if the model has a large number of regressors.Moreover, the choice of the first-round estimator is an openquestion, as the NLS estimator may be a poor starting pointdue to its considerable inefficiency. Therefore, the nonparametricgeneralized least squares estimator is not appropriateto use as a workhorse for routine estimation of multiplicativemodels. 11 Indeed, what is needed is an estimator that isconsistent and reasonably efficient under a wide range ofheteroskedasticity patterns and is also simple to implement.A possible way of obtaining an estimator that is moreefficient than the standard NLS without the need to usenonparametric regression is to follow McCullagh andNelder (1989) and estimate the parameters of interest usinga PML estimator based on some assumption on the functionalform of V[y i x]. 12 Among the many possible specifications,the hypothesis that the conditional variance isproportional to the conditional mean is particularly appealing.Indeed, under this assumption E[y i x] exp(x i ) V[y i x], and can be estimated by solving the following setof first-order conditions:n y i expx i ˜ x i 0. (9)i1Comparing equations (8) and (9), it is clear that, unlikethe NLS estimator, which is a PML estimator obtainedassuming that V[y i x] is constant, the PML estimator basedon equation (9) gives the same weight to all observations,rather than emphasizing those for which exp(x i ) is large.This is because, under the assumption that E[y i x] V[y i x],all observations have the same information on the parametersof interest as the additional information on the curvatureof the conditional mean coming from observations withlarge exp(x i ) is offset by their larger variance. Of course,this estimator may not be optimal, but without furtherinformation on the pattern of heteroskedasticity, it seems11A nonparametric generalized least squares estimator can also be usedto estimate linear models in the presence of heteroskedasticity of unknownform (Robinson, 1987). However, despite having been proposed morethan 15 years ago, this estimator has never been adopted as a standard toolby researchers doing empirical work, who generally prefer the simplicityof the inefficient OLS, with an appropriate covariance matrix.12See also Manning and Mullahy (2001). A related estimator is proposedby Papke and Wooldridge (1996) for the estimation of models forfractional data.natural to give the same weight to all observations. 13 Evenif E[y i x] is not proportional to V[y i x], the PML estimatorbased on equation (9) is likely to be more efficient than theNLS estimator when the heteroskedasticity increases withthe conditional mean.The estimator defined by equation (9) is numericallyequal to the Poisson pseudo-maximum-likelihood (PPML)estimator, which is often used for count data. 14 The form ofequation (9) makes clear that all that is needed for thisestimator to be consistent is the correct specification of theconditional mean, that is, E[y i x] exp(x i ). Therefore, thedata do not have to be Poisson at all—and, what is moreimportant, y i does not even have to be an integer—for theestimator based on the Poisson likelihood function to beconsistent. This is the well-known PML result first noted byGourieroux, Monfort, and Trognon (1984).The implementation of the PPML estimator is straightforward:there are standard econometric programs withcommands that permit the estimation of Poisson regression,even when the dependent variables are not integers. Becausethe assumption V[y i x] E[y i x] is unlikely to hold, thisestimator does not take full account of the heteroskedasticityin the model, and all inference has to be based on anEicker-White (Eicker, 1963; White, 1980) robust covariancematrix estimator. In particular, within Stata (StataCorp.,2003), the PPML estimation can be executed using thefollowing command:poisson export i, j lndist ij ln Y i ln Y j other variables ij , robustwhere export (or import) is measured in levels.Of course, if it were known that V[y i x] is a function ofhigher powers of E[y i x], a more efficient estimator could beobtained by downweighting even more the observationswith large conditional mean. An example of such an estimatoris the gamma PML estimator studied by Manning andMullahy (2001), which, like the log-linearized model, assumesthat V[y i x] is proportional to E[y i x] 2 . The first-orderconditions for the gamma PML estimator are given byn y i expx iˇ exp x iˇ x i 0.i1In the case of trade data, however, this estimator mayhave an important drawback. Trade data for larger countries(as gauged by GDP per capita) tend to be of higher quality(see Frankel & Wei, 1993; Frankel, 1997); hence, modelsassuming that V[y i x] is a function of higher powers ofE[y i x] might give excessive weight to the observations that13The same strategy is implicitly used by Papke and Wooldridge (1996)in their pseudo-maximum-likelihood estimator for fractional data models.14See Cameron and Trivedi (1998) and Winkelmann (2003) for moredetails on the Poisson regression and on more general models for countdata.

THE LOG OF GRAVITY 647E y i x x i exp 0 1 x 1i 2 x 2i ,i 1,...,1000. (14)Because, in practice, regression models often include amixture of continuous and dummy variables, we replicatethis feature in our experiments: x 1i is drawn from a standardnormal, and x 2 is a binary dummy variable that equals 1 witha probability of 0.4. 18 The two covariates are independent,and a new set of observations of all variables is generated ineach replication using 0 0, 1 2 1. Data on y aregenerated asy i x i i , (15)where i is a log normal random variable with mean 1 andvariance i 2 . As noted before, the slope parameters in equation(14) can be estimated using the log linear form of themodel only when i 2 is constant, that is, when V[y i x] isproportional to (x i ) 2 .In these experiments we analyzed PML estimators of themultiplicative model and different estimators of the loglinearizedmodel. The consistent PML estimators studiedwere: NLS, gamma pseudo-maximum-likelihood (GPML),and PPML. Besides these estimators, we also considered thestandard OLS estimator of the log linear model (here calledsimply OLS); the OLS estimator for the model where thedependent variable is y i 1 [OLS(y 1)]; a truncated OLSestimator to be discussed below; and the threshold tobit ofEaton and Tamura (1994) (ET-tobit). 19To assess the performance of the estimators under differentpatterns of heteroskedasticity, we considered the fourfollowing specifications of i 2 :Case 1: i 2 (x i ) 2 ; V[y i x] 1.Case 2: i 2 (x i ) 1 ; V[y i x] (x i ).Case 3: i 2 1; V[y i x] (x i ) 2 .Case 4: i 2 (x i ) 1 exp(x 2i ); V[y i x] (x i ) exp(x 2i ) (x i ) 2 .In case 1 the variance of ε i is constant, implying that theNLS estimator is optimal. Although, as argued before, thiscase is unrealistic for models of bilateral trade, it is includedin the simulations for completeness. In case 2, the conditionalvariance of y i equals its conditional mean, as in thePoisson distribution. The pseudo-maximum-likelihood estimatorbased on the Poisson distribution is optimal in thissituation. Case 3 is the special case in which OLS estimationof the log linear model is consistent for the slope parametersof equation (14). Moreover, in this case the log linear model18For example, in gravity equations, continuous variables (which are allstrictly positive) include income and geographical distance. In equation(14), x 1 can be interpreted as (the logarithm of) one of these variables.Examples of binary variables include dummies for free-trade agreements,common language, colonial ties, contiguity, and access to water.19We also studied the performance of other variants of the tobit model,finding very poor results.not only corrects the heteroskedasticity in the data, but,because i is log normal, it is also the maximum likelihoodestimator. The GPML is the optimal PML estimator in thiscase, but it should be outperformed by the true maximumlikelihood estimator. Finally, case 4 is the only one in whichthe conditional variance does not depend exclusively on themean. The variance is a quadratic function of the mean, asin case 3, but it is not proportional to the square of the mean.We carried out two sets of experiments. The first set wasaimed at studying the performance of the estimators of themultiplicative and the log linear models under differentpatterns of heteroskedasticity. In order to study the effect ofthe truncation on the performance of the OLS, and giventhat this data-generating mechanism does not produce observationswith y i 0, the log linear model was alsoestimated using only the observations for which y i 0.5[OLS(y 0.5)]. This reduces the sample size by approximately25% to 35%, depending on the pattern of heteroskedasticity.The estimation of the threshold tobit was alsoperformed using this dependent variable. Notice that, althoughthe dependent variable has to cross a threshold to beobservable, the truncation mechanism used here is not equalto the one assumed by Eaton and Tamura (1994). Therefore,in all these experiments the ET-tobit will be slightly misspecifiedand the results presented here should be viewed asa check of its robustness to this problem.The second set of experiments studied the estimators’performance in the presence of rounding errors in thedependent variable. For that purpose, a new random variablewas generated by rounding to the nearest integer thevalues of y i obtained in the first set of simulations. Thisprocedure mimics the rounding errors in official statisticsand generates a large number of zeros, a typical feature oftrade data. Because the model considered here generates alarge proportion of observations close to zero, roundingdown is much more frequent than rounding up. As theprobability of rounding up or down depends on the covariates,this procedure will necessarily bias the estimates, asdiscussed before. The purpose of the study is to gauge themagnitude of these biases. Naturally, the log linear modelcannot be estimated in these conditions, because the dependentvariable equals 0 for some observations. Followingwhat is the usual practice in these circumstances, the truncatedOLS estimation of the log-linear model was performeddropping the observations for which the dependentvariable equals 0. Notice that the observations discardedwith this procedure are exactly the same that are discardedby OLS(y 0.5) in the first set of experiments. Therefore,this estimator is also denoted OLS(y 0.5).The results of the two sets of experiments are summarizedin table 1, which displays the biases and standarderrors of the different estimators of obtained with 10,000replicas of the simulation procedure described above. Onlyresults for 1 and 2 are presented, as these are generally theparameters of interest.

648THE REVIEW OF ECONOMICS AND STATISTICSTABLE 1.—SIMULATION RESULTS UNDER DIFFERENT FORMS OF HETEROSKEDASTICITYResults Without Rounding ErrorResults with Rounding ErrorEstimator: 1 2 1 2Bias S.E. Bias S.E. Bias S.E. Bias S.E.Case 1: V[y i x] 1PPML 0.00004 0.016 0.00009 0.027 0.01886 0.017 0.02032 0.029NLS 0.00006 0.008 0.00003 0.017 0.00195 0.008 0.00274 0.018GPML 0.01276 0.068 0.00754 0.082 0.10946 0.096 0.09338 0.108OLS 0.39008 0.039 0.35568 0.054 — — — —ET-tobit 0.47855 0.030 0.47786 0.032 0.49981 0.030 0.49968 0.032OLS(y 0.5) 0.16402 0.027 0.15487 0.038 0.22121 0.026 0.21339 0.036OLS(y 1) 0.40237 0.014 0.37683 0.022 0.37752 0.015 0.34997 0.024Case 2: V[y i x] (x i )PPML 0.00011 0.019 0.00009 0.039 0.02190 0.020 0.02334 0.041NLS 0.00046 0.033 0.00066 0.057 0.00262 0.033 0.00360 0.057GPML 0.00376 0.043 0.00211 0.062 0.13243 0.073 0.11331 0.087OLS 0.21076 0.030 0.19960 0.049 — — — —ET-tobit 0.42394 0.028 0.42316 0.033 0.45518 0.028 0.45513 0.033OLS(y 0.5) 0.17868 0.026 0.17220 0.043 0.24405 0.026 0.23889 0.040OLS(y 1) 0.42371 0.015 0.39931 0.025 0.39401 0.016 0.36806 0.028Case 3: V[y i x] (x i ) 2PPML 0.00526 0.091 0.00228 0.130 0.02332 0.091 0.02812 0.133NLS 0.23539 3.066 0.07323 1.521 0.23959 3.082 0.07852 1.521GPML 0.00047 0.041 0.00029 0.083 0.17134 0.068 0.14442 0.104OLS 0.00015 0.032 0.00003 0.064 — — — —ET-tobit 0.31908 0.044 0.32161 0.058 0.36480 0.043 0.36789 0.056OLS(y 0.5) 0.34480 0.039 0.34614 0.064 0.41006 0.037 0.41200 0.060OLS(y 1) 0.51804 0.021 0.50000 0.038 0.48564 0.022 0.46597 0.040Case 4: V[y i x] (x i ) exp(x 2i ) (x i ) 2PPML 0.00696 0.103 0.00647 0.144 0.02027 0.104 0.01856 0.146NLS 0.35139 7.516 0.08801 1.827 0.35672 7.521 0.09239 1.829GPML 0.00322 0.057 0.00137 0.083 0.12831 0.085 0.10245 0.129OLS 0.13270 0.039 0.12542 0.075 — — — —ET-tobit 0.29908 0.049 0.42731 0.063 0.34351 0.047 0.46225 0.060OLS(y 0.5) 0.39217 0.042 0.41391 0.070 0.45188 0.040 0.46173 0.066OLS(y 1) 0.51440 0.021 0.58087 0.041 0.48627 0.022 0.56039 0.044As expected, OLS only performs well in case 3. In allother cases this estimator is clearly inadequate because,despite its low dispersion, it is often badly biased. Moreover,the sign and magnitude of the bias vary considerably.Therefore, even when the dependent variable is strictlypositive, estimation of constant-elasticity models using thelog-linearized model cannot generally be recommended. Asfor the modifications of the log-linearized model designedto deal with the zeros of the dependent variable—ET-tobit,OLS(y 1), and OLS(y 0.5)—their performance is alsovery disappointing. These results clearly emphasize theneed to use adequate methods to deal with the zeros in thedata and raise serious doubts about the validity of the resultsobtained using the traditional estimators based on the loglinear model. Overall, except under very special circumstances,estimation based on the log-linear model cannot berecommended.One remarkable result of this set of experiments is theextremely poor performance of the NLS estimator. Indeed,when the heteroskedasticity is more severe (cases 3 and 4),this estimator, despite being consistent, leads to very poorresults because of its erratic behavior. 20 Therefore, it is clearthat the loss of efficiency caused by some of the forms ofheteroskedasticity considered in these experiments is strongenough to render this estimator useless in practice.In the first set of experiments, the results of the gammaPML estimator are very good. Indeed, when no measurementerror is present, the biases and standard errors of theGPML estimator are always among the lowest. However,this estimator is very sensitive to the form of measurementerror considered in the second set of experiments, consistentlyleading to sizable biases. These results, like those ofthe NLS, clearly illustrate the danger of using a PMLestimator that gives extra weight to the noisier observations.As for the performance of the Poisson PML estimator, theresults are very encouraging. In fact, when no roundingerror is present, its performance is reasonably good in all20Manning and Mullahy (2001) report similar results.

THE LOG OF GRAVITY 649cases. Moreover, although some loss of efficiency is noticeableas one moves away from case 2, in which it is anoptimal estimator, the biases of the PPML are alwayssmall. 21 Moreover, the results obtained with rounded datasuggest that the Poisson-based PML estimator is relativelyrobust to this form of measurement error of the dependentvariable. Indeed, the bias introduced by the rounding-offerrors in the dependent variable is relatively small, and insome cases it even compensates the bias found in the firstset of experiments. Therefore, because it is simple to implementand reliable in a wide variety of situations, thePoisson PML estimator has the essential characteristicsneeded to make it the new workhorse for the estimation ofconstant-elasticity models.Obviously, the sign and magnitude of the bias of theestimators studied here depend on the particular specificationconsidered. Therefore, the results of these experimentscannot serve as an indicator of what can be expected inother situations. However, it is clear that, apart from thePoisson PML method, all estimators will often be verymisleading.These experiments were also used to study the finitesampleperformance of the Gauss-Newton regression(GNR) test for the adequacy of the Poisson PML based onequation (13) and of the Park test advocated by Manningand Mullahy (2001), which, as explained above, is validonly to check for the adequacy of the estimator based on thelog linear model. 22 Given that the Poisson PML estimator isthe only estimator with a reasonable behavior under all thecases considered, these tests were performed using residualsand estimates of (x i ) from the Poisson regression. Table2 contains the rejection frequencies of the null hypothesis atthe 5% nominal level for both tests in the four casesconsidered in the two sets of experiments. In this table therejection frequencies under the null hypothesis are given inbold.In as much as both tests have adequate behavior under thenull and reveal reasonable power against a wide range ofalternatives, the results suggest that these tests are importanttools to assess the adequacy of the standard OLS estimatorof the log linear model and of the proposed Poisson PMLestimator.V. The Gravity EquationIn this section, we use the PPML estimator to quantitativelyassess the determinants of bilateral trade flows, uncoveringsignificant differences in the roles of variousmeasures of size and distance from those predicted by the21These results are in line with those reported by Manning and Mullahy(2001).22To illustrate the pitfalls of the procedure suggested by Manning andMullahy (2001), we note that the means of the estimates of 1 obtainedusing equation (11) in cases 1, 2, and 3 (without measurement error) were0.58955, 1.29821, and 1.98705, whereas the true values of 1 in thesecases are, respectively, 0, 1, and 2.TABLE 2.—REJECTION FREQUENCIES AT THE 5% LEVELFOR THE TWO SPECIFICATION TESTSFrequencyCaseGNR TestPark TestWithout Measurement Error1 0.91980 1.000002 0.05430 1.000003 0.58110 0.066804 0.49100 0.40810With Measurement Error1 0.91740 1.000002 0.14980 1.000003 0.57170 1.000004 0.47580 1.00000logarithmic tradition. We perform the comparison of the twotechniques using both the traditional and the Anderson–vanWincoop (2003) specifications of the gravity equation.For the sake of completeness, we also compare the PPMLestimates with those obtained from alternative ways researchershave used to deal with zero values for trade. Inparticular, we present the results obtained with the tobitestimator used in Eaton and Tamura (1994), OLS estimatorapplied to ln(1 T ij ), and a standard nonlinear least squaresestimator. The results obtained with these estimators arepresented for both the traditional and the Anderson–vanWincoop specifications.A. The DataThe analysis covers a cross section of 136 countries in1990. Hence, our data set consists of 18,360 observations ofbilateral export flows (136 135 country pairs). The list ofcountries is reported in table A1 in the appendix. Informationon bilateral exports comes from Feenstra et al. (1997).Data on real GDP per capita and population come from theWorld Bank’s (2002) World Development Indicators. Dataon location and dummies indicating contiguity, commonlanguage (official and second languages), colonial ties (directand indirect links), and access to water are constructedfrom the CIA’s (2002) World Factbook. The data on languageand colonial links are presented on tables A2 and A3in the appendix. 23 Bilateral distance is computed using thegreat circle distance algorithm provided by Andrew Gray(2001). Remoteness—or relative distance—is calculated asthe (log of) GDP-weighted average distance to all othercountries (see Wei, 1996). Finally, information on preferentialtrade agreements comes from Frankel (1997), complementedwith data from the World Trade Organization. Thelist of preferential trade agreements (and stronger forms oftrade agreements) considered in the analysis is displayed intable A4 in the appendix. Table A5 in the appendix provides23Alternative estimates based on Boisso and Ferrantino’s (1997) indexof language similarity are available, at request, from the authors.

650THE REVIEW OF ECONOMICS AND STATISTICSTABLE 3.—THE TRADITIONAL GRAVITY EQUATIONEstimator: OLS OLS Tobit NLS PPML PPMLDependent Variable: ln(T ij ) ln(1 T ij ) ln(a T ij ) T ij T ij 0 T ijLog exporter’s GDP 0.938** 1.128** 1.058** 0.738** 0.721** 0.733**(0.012) (0.011) (0.012) (0.038) (0.027) (0.027)Log importer’s GDP 0.798** 0.866** 0.847** 0.862** 0.732** 0.741**(0.012) (0.012) (0.011) (0.041) (0.028) (0.027)Log exporter’s GDP per capita 0.207** 0.277** 0.227** 0.396** 0.154** 0.157**(0.017) (0.018) (0.015) (0.116) (0.053) (0.053)Log importer’s GDP per capita 0.106** 0.217** 0.178** 0.033 0.133** 0.135**(0.018) (0.018) (0.015) (0.062) (0.044) (0.045)Log distance 1.166** 1.151** 1.160** 0.924** 0.776** 0.784**(0.034) (0.040) (0.034) (0.072) (0.055) (0.055)Contiguity dummy 0.314* 0.241 0.225 0.081 0.202 0.193(0.127) (0.201) (0.152) (0.100) (0.105) (0.104)Common-language dummy 0.678** 0.742** 0.759** 0.689** 0.752** 0.746**(0.067) (0.067) (0.060) (0.085) (0.134) (0.135)Colonial-tie dummy 0.397** 0.392** 0.416** 0.036 0.019 0.024(0.070) (0.070) (0.063) (0.125) (0.150) (0.150)Landlocked-exporter dummy 0.062 0.106* 0.038 1.367** 0.873** 0.864**(0.062) (0.054) (0.052) (0.202) (0.157) (0.157)Landlocked-importer dummy 0.665** 0.278** 0.479** 0.471** 0.704** 0.697**(0.060) (0.055) (0.051) (0.184) (0.141) (0.141)Exporter’s remoteness 0.467** 0.526** 0.563** 1.188** 0.647** 0.660**(0.079) (0.087) (0.068) (0.182) (0.135) (0.134)Importer’s remoteness 0.205* 0.109 0.032 1.010** 0.549** 0.561**(0.085) (0.091) (0.073) (0.154) (0.120) (0.118)Free-trade agreement dummy 0.491** 1.289** 0.729** 0.443** 0.179* 0.181*(0.097) (0.124) (0.103) (0.109) (0.090) (0.088)Openness 0.170** 0.739** 0.310** 0.928** 0.139 0.107(0.053) (0.050) (0.045) (0.191) (0.133) (0.131)Observations 9613 18360 18360 18360 9613 18360RESET test p-values 0.000 0.000 0.204 0.000 0.941 0.331a description of the variables and displays the summarystatistics.B. Results24The reason why truncation has little effect in this case is thatobservations with zero trade correspond to pairs for which the estimatedvalue of trade is close to zero. Therefore, the corresponding residuals arealso close to zero, and their elimination from the sample has little effect.The Traditional Gravity Equation: Table 3 presents theestimation outcomes resulting from the various techniquesfor the traditional gravity equation. The first column reportsOLS estimates using the logarithm of exports as the dependentvariable; as noted before, this regression leaves outpairs of countries with zero bilateral trade (only 9,613country pairs, or 52% of the sample, exhibit positive exportflows).The second column reports the OLS estimates usingln(1 T ij ) as dependent variable, as a way of dealing withzeros. The third column presents tobit estimates based onEaton and Tamura (1994). The fourth column shows theresults of standard NLS. The fifth column reports Poissonestimates using only the subsample of positive-trade pairs.Finally, the sixth column shows the Poisson results for thewhole sample (including zero-trade pairs).The first point to notice is that PPML-estimated coefficientsare remarkably similar using the whole sample andusing the positive-trade subsample. 24 However, most coefficientsdiffer—oftentimes significantly—from those obtainedusing OLS. This suggests that in this case, heteroskedasticity(rather than truncation) is responsible for thedifferences between PPML results and those of OLS usingonly the observations with positive exports. Further evidenceon the importance of the heteroskedasticity is providedby the two-degrees-of-freedom special case ofWhite’s test for heteroskedasticity (see Wooldridge, 2002, p.127), which leads to a test statistic of 476.6 and to a p-valueof 0. That is, the null hypothesis of homoskedastic errors isunequivocally rejected.Poisson estimates reveal that the coefficients on importer’sand exporter’s GDPs in the traditional equation are not,as generally believed, close to 1. The estimated GDP elasticitiesare just above 0.7 (s.e. 0.03). OLS generatessignificantly larger estimates, especially on exporter’s GDP(0.94, s.e. 0.01). Although all these results are conditionalon the particular specification used, 25 it is worth pointing outthat unit income elasticities in the simple gravity frameworkare at odds with the observation that the trade-to-GDP ratiodecreases with increasing total GDP, or, in other words, thatsmaller countries tend to be more open to internationaltrade. 2625This result holds when one looks at the subsample of OECD countries.It is also robust to the exclusion of GDP per capita from the regressions.26Note also that PPML predicts almost equal coefficients for the GDPsof exporters and importers.

THE LOG OF GRAVITY 651TABLE 4.—RESULTS OF THE TESTS FOR TYPE OF HETEROSKEDASTICITY(p-VALUES)Test (Null Hypothesis) Exports 0 Full SampleGNR (V[y i x] (x i )) 0.144 0.115Park (OLS is valid) 0.000 0.00027The formula to compute this effect is (e bi 1) 100%, where b i isthe estimated coefficient.28To illustrate the role of remoteness, consider two pairs of countries, (i,j) and (k, l), and assume that the distance between the countries in eachpair is the same (D ij D kl ), but i and j are closer to other countries. In thiscase, the most remote countries, k and l, will tend to trade more betweeneach other because they do not have alternative trading partners. SeeDeardoff (1998).The role of geographical distance as trade deterrent issignificantly larger under OLS; the estimated elasticity is1.17 (s.e. 0.03), whereas the Poisson estimate is 0.78(s.e. 0.06). This lower estimate suggests a smaller role fortransport costs in the determination of trade patterns. Furthermore,Poisson estimates indicate that, after controllingfor bilateral distance, sharing a border does not influencetrade flows, whereas OLS, instead, generates a substantialeffect: It predicts that trade between two contiguous countriesis 37% larger than trade between countries that do notshare a border. 27We control for remoteness to allow for the hypothesis thatlarger distances to all other countries might increase bilateraltrade between two countries. 28 Poisson regressionssupport this hypothesis, whereas OLS estimates suggest thatonly exporter’s remoteness increases bilateral flows betweentwo given countries. Access to water appears to beimportant for trade flows, according to Poisson regressions;the negative coefficients on the land-locked dummies can beinterpreted as an indication that ocean transportation issignificantly cheaper. In contrast, OLS results suggest thatwhether or not the exporter is landlocked does not influencetrade flows, whereas a landlocked importer experienceslower trade. (These asymmetries in the effects of remotenessand access to water for importers and exporters arehard to interpret.) We also explore the role of colonialheritage, obtaining, as before, significant discrepancies:Poisson regressions indicate that colonial ties play no role indetermining trade flows, once a dummy variable for commonlanguage is introduced. OLS regressions, instead, generatea sizeable effect (countries with a common colonialpast trade almost 45% more than other pairs). Language isstatistically and economically significant under both estimationprocedures.Strikingly, in the traditional gravity equation, preferentialtradeagreements play a much smaller—although still substantial—roleaccording to Poisson regressions. OLS estimatessuggest that preferential trade agreements raiseexpected bilateral trade by 63%, whereas Poisson estimatesindicate an average enhancement below 20%.Preferential trade agreements might also cause trade diversion;if this is the case, the coefficient on the tradeagreementdummy will not reflect the net effect of tradeagreements. To account for the possibility of diversion, weinclude an additional dummy, openness, similar to that usedby Frankel (1997). This dummy takes the value 1 wheneverone (or both) of the countries in the pair is part of apreferential trade agreement, and thus it captures the extentof trade between members and nonmembers of a preferentialtrade agreement. The sum of the coefficients on the tradeagreement and the openness dummies gives the net creationeffect of trade agreements. OLS suggests that trade destructioncomes from trade agreements. Still, the net creationeffect is around 40%. In contrast, Poisson regressions provideno significant evidence of trade diversion, although thepoint estimates are of the same order of magnitude underboth methods.Hence, even when allowing for trade diversion effects, onaverage, the Poisson method estimates a smaller effect ofpreferential trade agreements on trade, approximately halfof that indicated by OLS. The contrast in estimates suggeststhat the biases generated by standard regressions can besubstantial, leading to misleading inferences and, perhaps,erroneous policy decisions.We now turn briefly to the results of the other estimationmethods. OLS on ln(1 T ij ) and tobit give very closeestimates for most coefficients. Like OLS, they yield largeestimates for the elasticity of bilateral trade with respect todistance. Unlike OLS, however, they produce insignificantcoefficients for the contiguity dummy. They both generateextremely large and statistically significant coefficients forthe trade-agreement dummy. The first method predicts thattrade between two countries that have signed a trade agreementis on average 266% larger than that between countrieswithout an agreement. The second predicts that trade betweencountries in such agreements is on average 100%larger. NLS tends to generate somewhat different estimates.The elasticity of trade with respect to the exporter’s GDP issignificantly smaller than with OLS, but the correspondingelasticity with respect to importer’s GDP is significantlylarger than with OLS. The estimated distance elasticity issmaller than with OLS and bigger than with Poisson. Likethe other methods, NLS predicts a significant and largeeffect for free-trade agreements.It is noteworthy that all methods, except the PPML, leadto puzzling asymmetries in the elasticities with respect toimporter and exporter characteristics (especially remotenessand access to water).To check the adequacy of the estimated models, weperformed a heteroskedasticity-robust RESET test (Ramsey,1969). This is essentially a test for the correct specificationof the conditional expectation, which is performed bychecking the significance of an additional regressor constructedas (xb) 2 , where b denotes the vector of estimatedparameters. The corresponding p-values are reported at thebottom of table 3. In the OLS regression, the test rejects thehypothesis that the coefficient on the test variable is 0. This

652THE REVIEW OF ECONOMICS AND STATISTICSTABLE 5.—THE ANDERSON–VAN WINCOOP GRAVITY EQUATIONEstimator: OLS OLS Tobit NLS PPML PPMLDependent variable: ln (T ij ) ln (1 T ij ) ln (a T ij ) T ij T ij 0 T ijLog distance 1.347** 1.332** 1.272** 0.582** 0.770** 0.750**(0.031) (0.036) (0.029) (0.088) (0.042) (0.041)Contiguity dummy 0.174 0.399* 0.253 0.458** 0.352** 0.370**(0.130) (0.189) (0.135) (0.121) (0.090) (0.091)Common-language dummy 0.406** 0.550** 0.485** 0.926** 0.418** 0.383**(0.068) (0.066) (0.057) (0.116) (0.094) (0.093)Colonial-tie dummy 0.666** 0.693** 0.650** 0.736** 0.038 0.079(0.070) (0.067) (0.059) (0.178) (0.134) (0.134)Free-trade agreement dummy 0.310** 0.174 0.137** 1.017** 0.374** 0.376**(0.098) (0.138) (0.098) (0.170) (0.076) (0.077)Fixed effects Yes Yes Yes Yes Yes YesObservations 9613 18360 18360 18360 9613 18360RESET test p-values 0.000 0.000 0.000 0.000 0.564 0.112means that the model estimated using the logarithmic specificationis inappropriate. A similar result is found for theOLS estimated using ln(1 T ij ) as the dependent variableand for the NLS. In contrast, the models estimated using thePoisson regressions pass the RESET test, that is, the RESETtest provides no evidence of misspecification of the gravityequations estimated using the PPML. With this particularspecification, the model estimated using tobit also passesthe test for the traditional gravity equation.Finally, we also check whether the particular pattern ofheteroskedasticity assumed by the models is appropriate. Asexplained in section III B, the adequacy of the log linearmodel was checked using the Park-type test, whereas thehypothesis V[y i x] (x i ) was tested by evaluating thesignificance of the coefficient of (ln y˘i)y˘i in the Gauss-Newton regression indicated in equation (13). The p-valuesof the tests are reported in table 4. Again, the log linearspecification is unequivocally rejected. On the other hand,these results indicate that the estimated coefficient on (ln y˘i)y˘ i is insignificantly different from 0 at the usual 5% level.This implies that the Poisson PML assumption V[y i x] 0 E[y i x] cannot be rejected at this significance level.The Anderson–van Wincoop Gravity Equation: Table 5presents the estimated coefficients for the Anderson–vanWincoop (2003) gravity equation, which controls moreproperly for multilateral resistance terms by introducingexporter- and importer-specific effects. As before, the columnsshow, respectively, the estimated coefficients obtainedusing OLS on the log of exports, OLS on ln(1 T ij ), tobit,NLS, PPML on the positive-trade sample, and PPML. Notethat, because this exercise uses cross-sectional data, we canonly identify bilateral variables. 2929Anderson and van Wincoop (2003) impose unit income elasticities byusing as the dependent variable the log of exports divided by the productof the countries’ GDPs. Because we are working with cross-sectional dataand the model specification includes importer and exporter fixed effects,income elasticities cannot be identified, and there is no need to imposerestrictions on them. Still, the estimation of the PML models could beperformed using as the dependent variable the ratio of exports to theproduct of the GDPs. This would downweight the observations with largeAs with the standard specification of the gravity equation,we find that, using the Anderson–van Wincoop (2003)specification, estimates obtained with the Poisson methodvary little when only the positive-trade subsample is used.Moreover, we find again strong evidence that the errors ofthe log linear model estimated using the sample with positivetrade are heteroskedastic. With this specification, thetwo-degree-of-freedom special case of White’s test for heteroskedasticityleads to a test statistic of 469.2 and a p-valueof 0.Because we are now conditioning on a much larger set ofcontrols, it is not surprising to find that most coefficients aresensitive to the introduction of fixed effects. For example, inthe Poisson method, although the distance elasticity remainsabout the same and the coefficient on common colonial tiesis still insignificant, the effect on common language is nowsmaller and the coefficient on free-trade agreements islarger. The results of the other estimation methods aregenerally much more sensitive to the inclusion of the fixedeffects.Comparing the results of PPML and OLS for the positivetradesubsample, the following observations are in order.The distance elasticity is substantially larger under OLS(1.35 versus 0.75). Sharing a border has a positive effecton trade under Poisson, but no significant effect under OLS.Sharing a common language has similar effects under thetwo techniques. Common colonial ties have strong effectsunder OLS (with an average enhancement effect of 100%),whereas Poisson predicts no significant effect. Finally, thevalues of the product of the GDPs, implicitly assuming that the varianceof the error term is proportional to the square of this product. This iscontrary to what is advocated by Frankel and Wei (1993) and Frankel(1997), who suggest that larger countries should be given more weight inthe estimation of gravity equations because they generally have betterdata. In any case, whether this should be done or not is an empiricalquestion, and the right course of action depends on the pattern ofheteroskedasticity. With our data, using the ratio of exports to the productof GDPs as the dependent variable leads to models that are rejected by thespecification tests. Therefore, the implied assumptions about the pattern ofheteroskedasticity are not supported by our data. Hence, we use exports asthe dependent variable of the gravity equation, and not the ratio of exportsto the product of GDPs.

THE LOG OF GRAVITY 653TABLE 6.—RESULTS OF THE TESTS FOR TYPE OF HETEROSKEDASTICITY(p-VALUES)Test (Null Hypothesis) Exports 0 Full SampleGNR (V[y i x] (x i )) 0.100 0.070Park (OLS is valid) 0.000 0.000two techniques produce reasonably similar estimates for thecoefficient on the trade-agreement dummy, implying a tradeenhancementeffect of the order of 40%.As before, the other estimation methods lead to somepuzzling results. For example, OLS on ln(1 T ij ) nowyields a significantly negative effect of contiguity, and underNLS, the coefficient on common colonial ties becomessignificantly negative.To complete the study, we performed the same set ofspecification tests used before. The p-values of the heteroskedasticity-robustRESET test at the bottom of table 5suggest that with the Anderson–van Wincoop (2003) specificationof the gravity equation, only the models estimatedby the PPML method are adequate. The p-values of the teststo check whether the particular pattern of heteroskedasticityassumed by the models is appropriate are reported in table6. As in the traditional gravity equation, the log linearspecification is unequivocally rejected. On the other hand,these results indicate that the estimated coefficient on (ln y˘i)y˘ i is insignificantly different from 0 at the usual 5% level.This implies that the Poisson PML assumption V[y i x] 0 E[y i x] cannot be rejected at this significance level.To sum up, whether or not fixed effects are used in thespecification of the model, we find strong evidence thatestimation methods based on the log-linearization of thegravity equation suffer from severe misspecification, whichhinders the interpretation of the results. NLS is also generallyunreliable. In contrast, the models estimated by PPMLshow no signs of misspecification and, in general, do notproduce the puzzling results generated by the other methods.30 VI. ConclusionsIn this paper, we argue that the standard empirical methodsused to estimate gravity equations are inappropriate.30It is worth noting that the large differences in estimates among thevarious methods persist when we look at a smaller subsample of countriesthat account for most of world trade and, quite likely, have better data.More specifically, we run similar regressions for the subsample of 63countries included in Frankel’s (1997) study. These countries accountedfor almost 90% of the world trade reported to the United Nations in 1992.One advantage of this subsample is that the number of zeros is significantlyreduced. Heteroskedasticity, however, is still a problem: The nullhypothesis of homoskedasticity is rejected in both the traditional and thefixed-effects gravity equations. As with the full sample, PPML generatesa smaller role for distance and common language than OLS, and, unlikeOLS, PPML predicts no role for colonial ties. In line with the findingsdocumented in Frankel (1997), the OLS estimated coefficient on thefree-trade-agreement dummy is negative in both specifications of thegravity equation, whereas PPML predicts a positive and significant effect(slightly bigger than that found for the whole sample). These results areavailable—on request—from the authors.The basic problem is that log-linearization (or, indeed, anynonlinear transformation) of the empirical model in thepresence of heteroskedasticity leads to inconsistent estimates.This is because the expected value of the logarithmof a random variable depends on higher-order moments ofits distribution. Therefore, if the errors are heteroskedastic,the transformed errors will be generally correlated with thecovariates. An additional problem of log-linearization is thatit is incompatible with the existence of zeros in trade data,which led to several unsatisfactory solutions, includingtruncation of the sample (that is, elimination of zero-tradepairs) and further nonlinear transformations of the dependentvariable.We argue that the biases are present both in the traditionalspecification of the gravity equation and in the Anderson–van Wincoop (2003) specification, which includes countryspecificfixed effects.To address the various estimation problems, we proposea simple Poisson pseudo-maximum-likelihood method andassess its performance using Monte Carlo simulations. Wefind that in the presence of heteroskedasticity the standardmethods can severely bias the estimated coefficients, castingdoubt on previous empirical findings. Our method,instead, is robust to different patterns of heteroskedasticityand, in addition, provides a natural way to deal with zeros intrade data.We use our method to reestimate the gravity equation anddocument significant differences from the results obtainedusing the log linear method. For example, income elasticitiesin the traditional gravity equation are systematicallysmaller than those obtained with log-linearized OLS regressions.In addition, in both the traditional and Anderson–vanWincoop specifications of the gravity equation, OLS estimationexaggerates the role of geographical proximity andcolonial ties. RESET tests systematically favor the PoissonPML technique. The results suggest that heteroskedasticity(rather than truncation of the data) is responsible for themain differences.Log-linearized equations estimated by OLS are of courseused in many other areas of empirical economics and econometrics.Our Monte Carlo simulations and the regression outcomesindicate that in the presence of heteroskedasticity thispractice can lead to significant biases. These results suggestthat, at least when there is evidence of heteroskedasticity, thePoisson pseudo-maximum-likelihood estimator should be usedas a substitute for the standard log linear model.REFERENCESAnderson, J., “A Theoretical Foundation for the Gravity Equation,”American Economic Review 69 (1979), 106–116.Anderson, J., and E. van Wincoop, “Gravity with Gravitas: A Solution tothe Border Puzzle,” American Economic Review 93 (2003), 170–192.Bergstrand, J., “The Gravity Equation in International Trade: SomeMicroeconomic Foundations and Empirical Evidence,” this RE-VIEW, 69 (1985), 474–481.

654THE REVIEW OF ECONOMICS AND STATISTICSBoisso, D., and M. Ferrantino, “Economic and Cultural Distance inInternational Trade: Empirical Puzzles,” Journal of EconomicIntegration 12 (1997), 456–484.Cameron, A. C., and P. K. Trivedi, Regression Analysis of Count Data(Cambridge: Cambridge University Press, 1998).Central Intelligence Agency, World Factbook, http://www.cia.gov/cia/publications/factbook/ (2002).Davidson, R., and J. G. MacKinnon, Estimation and Inference in Econometrics(Oxford: Oxford University Press, 1993).Davis, D., “Intra-industry Trade: A Hecksher-Ohlin-Ricardo Approach,”Journal of International Economics 39 (1995), 201–226.Deardoff, A., “Determinants of Bilateral Trade: Does Gravity Work in aNeoclassical World?” in Jeffrey Frankel (Ed.), The Regionalizationof the World Economy (Chicago: University of Chicago Press,1998).Delgado, M., “Semiparametric Generalized Least Squares Estimation inthe Multivariate Nonlinear Regression Model,” Econometric Theory8 (1992), 203–222.Delgado, M., and T. J. Kniesner, “Count Data Models with Variance ofUnknown Form: An Application to a Hedonic Model of WorkerAbsenteeism,” this REVIEW, 79 (1997), 41–49.Eaton, J., and S. Kortum, “Technology, Geography and Trade,” NBERworking paper no. 6253 (2001).Eaton, J., and A. Tamura, “Bilateralism and Regionalism in Japanese andUS Trade and Direct Foreign Investment Patterns,” Journal of theJapanese and International Economics 8 (1994), 478–510.Eichengreen, B., and D. Irwin, “Trade Blocs, Currency Blocs, and theReorientation of World Trade in the 1930’s,” Journal of InternationalEconomics, 38 (1995), 1–24.Eicker, F., “Asymptotic Normality and Consistency of the Least SquaresEstimators for Families of Linear Regressions,” The Annals ofMathematical Statistics 34 (1963), 447–456.Feenstra, R. C., R. E. Lipsey, and H. P. Bowen, “World Trade Flows,1970–1992, with Production and Tariff Data,” NBER workingpaper no. 5910 (1997).Feenstra, R., J. Markusen, and A. Rose, “Using the Gravity Equation toDifferentiate among Alternative Theories of Trade,” CanadianJournal of Economics 34 (2001), 430–447.Frankel, J., Regional Trading Blocs in the World Economic System(Washington, DC: Institute for International Economics, 1997).Frankel, J., and A. Rose, “An Estimate of the Effect of Common Currencieson Trade and Income,” Quarterly Journal of Economics 117(2002), 409–466.Frankel, J., E. Stein, and S. Wei, “Continental Trading Blocs: Are TheyNatural, or Super-Natural?” in J. Frankel (Ed.), The Regionalizationof the World Economy (Chicago: University of Chicago Press,1998).Frankel, J., and S. Wei, “Trade Blocs and Currency Blocs,” NBERworking paper no. 4335 (1993).Goldberger, A. “The Interpretation and Estimation of Cobb-DouglasFunctions,” Econometrica 36 (1968), 464–472.Goldberger, A., A Course in Econometrics (Cambridge, MA: HarvardUniversity Press, 1991).Gourieroux, C., A. Monfort, and A. Trognon, “Pseudo Maximum LikelihoodMethods: Applications to Poisson Models,” Econometrica 52(1984), 701–720.Gray, A., http://argray.fateback.com/dist/formula.html (2001).Hallak, J. C., “Product Quality and the Direction of Trade,” Journal ofInternational Economics 68 (2006), 238–265.Harrigan, J., “OECD Imports and Trade Barriers in 1983,” Journal ofInternational Economics 35 (1993), 95–111.Haveman, J., and D. Hummels, “Alternative Hypotheses and the Volumeof Trade: The Gravity Equation and the Extent of Specialization,”Purdue University mimeograph, (2001).Helpman, E., and P. Krugman, Market Structure and Foreign Trade(Cambridge, MA: MIT Press, 1985).Helpman, E., M. Melitz, and Y. Rubinstein, “Trading Patterns and TradingVolumes,” Harvard University mimeograph (2004).Koenker, R., and G. S. Bassett, Jr., “Regression Quantiles,” Econometrica46 (1978), 33–50.Manning, W. G., and J. Mullahy, “Estimating Log Models: To Transformor Not to Transform?” Journal of Health Economics 20 (2001),461–494.McCallum, J., “National Borders Matter: Canada-US Regional TradePatterns,” American Economic Review 85 (1995), 615–623.McCullagh, P., and J. A. Nelder, Generalized Linear Models, 2nd ed.(London: Chapman and Hall, 1989).Papke, L. E., and J. M. Wooldridge, “Econometric Methods for FractionalResponse Variables with an Application to 401(k) Plan ParticipationRates,” Journal of Applied Econometrics 11 (1996), 619–632.Park, R., “Estimation with Heteroskedastic Error Terms,” Econometrica34 (1966), 888.Ramsey, J. B., “Tests for Specification Errors in Classical Linear LeastSquares Regression Analysis,” Journal of the Royal StatisticalSociety B 31 (1969), 350–371.Robinson, P. M., “Asymptotically Efficient Estimation in the Presence ofHeteroskedasticity of Unknown Form,” Econometrica 55 (1987),875–891.Rose, A., “One Money One Market: Estimating the Effect of CommonCurrencies on Trade,” Economic Policy 15 (2000), 7–46.StataCorp., Stata Statistical Software: Release 8 (College Station, TX:StataCorp LP, 2003).Tenreyro, S., and R. Barro, “Economic Effects of Currency Unions,” FRBBoston series working paper no. 02–4 (2002).Tinbergen, J., The World Economy. Suggestions for an InternationalEconomic Policy (New York: Twentieth Century Fund, 1962).Wei, S., “Intra-national versus International Trade: How Stubborn AreNation States in Globalization?” NBER working paper no. 5331(1996).White, H., “A Heteroskedasticity-Consistent Covariance Matrix Estimatorand a Direct Test for Heteroskedasticity,” Econometrica 48 (1980),817–838.Winkelmann, R., Econometric Analysis of Count Data, 4th ed. (Berlin:Springer-Verlag, 2003).Windmeijer, F., and J. M. C. Santos Silva, “Endogeneity in Count DataModels: An Application to Demand for Health Care,” Journal ofApplied Econometrics 12 (1997), 281–294.Wooldridge, J. M., “Distribution-Free Estimation of Some NonlinearPanel Data Models,” Journal of Econometrics 90 (1999), 77–97.Econometric Analysis of Cross Section and Panel Data (Cambridge,MA: MIT Press, 2002).World Bank, World Development Indicators CD-ROM (The World Bank,2002).

THE LOG OF GRAVITY 655APPENDIXTABLE A1.—LIST OF COUNTRIESAlbania Denmark Kenya RomaniaAlgeria Djibouti Kiribati Russian FederationAngola Dominican Rep. Korea, Rep. RwandaArgentina Ecuador Laos P. Dem. Rep. Saudi ArabiaAustralia Egypt Lebanon SenegalAustria El Salvador Madagascar SeychellesBahamas Eq. Guinea Malawi Sierra LeoneBahrain Ethiopia Malaysia SingaporeBangladesh Fiji Maldives Solomon IslandsBarbados Finland Mali South AfricaBelgium-Lux. France Malta SpainBelize Gabon Mauritania Sri LankaBenin Gambia Mauritius St. Kitts and NevisBhutan Germany Mexico SudanBolivia Ghana Mongolia SurinameBrazil Greece Morocco SwedenBrunei Guatemala Mozambique SwitzerlandBulgaria Guinea Nepal Syrian Arab Rep.Burkina Faso Guinea-Bissau Netherlands TanzaniaBurundi Guyana New Caledonia ThailandCambodia Haiti New Zealand TogoCameroon Honduras Nicaragua Trinidad and TobagoCanada Hong Kong Niger TunisiaCentral African Rep. Hungary Nigeria TurkeyChad Iceland Norway UgandaChile India Oman United Arab Em.China Indonesia Pakistan United KingdomColombia Iran Panama United StatesComoros Ireland Papua New Guinea UruguayCongo Dem. Rep. Israel Paraguay VenezuelaCongo Rep. Italy Peru VietnamCosta Rica Jamaica Philippines YemenCôte D’Ivoire Japan Poland ZambiaCyprus Jordan Portugal Zimbabwe

656THE REVIEW OF ECONOMICS AND STATISTICSTABLE A2.—COMMON OFFICIAL AND SECOND LANGUAGESEnglish French Spanish DutchAustralia Belgium-Lux. Argentina Belgium-Lux.Bahamas Benin Belize NetherlandsBarbados Burkina Faso Bolivia SurinameBelize Burundi ChileBrunei Cameroon Colombia GermanCameroon Canada Costa RicaCanada Central African Rep. Dominican Rep. AustriaFiji Chad Ecuador GermanyGambia Comoros El Salvador SwitzerlandGhana Congo Dem. Rep. Eq. GuineaGuyana Congo Rep. Guatemala GreekHong Kong Côte D’Ivoire HondurasIndia Djibouti Mexico CyprusIndonesia Eq. Guinea Nicaragua GreeceIreland France PanamaIsrael Gabon Paraguay HungarianJamaica Guinea PeruJordan Haiti Spain HungaryKenya Lebanon Uruguay RomaniaKiribati Madagascar VenezuelaMalawiMaliItalianMalaysia Mauritania ArabicMaldivesMauritiusItalyMaltaMoroccoAlgeriaSwitzerlandMauritiusNew CaledoniaBahrainNew ZealandNigerChadLingalaNigeriaRwandaComorosOmanSenegalDjiboutiCongo Dem. Rep.PakistanSeychellesEgyptCongo Rep.PanamaSwitzerlandIsraelPapua New GuineaTogoJordanRussianPhilippinesTunisiaLebanonRwandaMauritaniaMongoliaSeychellesMalayMoroccoRussian FederationSierra LeoneSingaporeBruneiOmanSaudi ArabiaSwahiliSouth AfricaIndonesiaSudanSri LankaMalaysiaSyriaKenyaSt. HelenaSingaporeTanzaniaTanzaniaSt. Kitts and NevisSurinamePortugueseTunisiaUnited Arab Em.ChineseTanzaniaYemenTrinidad and TobagoAngolaChinaUgandaBrazilTurkishHong KongUnited KingdomGuinea-BissauMalaysiaUnited StatesMozambiqueCyprusSingaporeZambiaPortugalTurkeyZimbabwe

THE LOG OF GRAVITY 657TABLE A3.—COLONIAL TIESUnited Kingdom France SpainAustralia Mauritius Algeria ArgentinaBahamas New Zealand Benin BoliviaBahrain Nigeria Burkina Faso ChileBarbados Pakistan Cambodia ColombiaBelize Saint Kitts and Nevis Cameroon Costa RicaCameroon Seychelles Central African Rep. CubaCanada Sierra Leone Chad EcuadorCyprus South Africa Comoros El SalvadorEgypt Sri Lanka Congo Eq. GuineaFiji Sudan Djibouti GuatemalaGambia Tanzania Gabon HondurasGhana Trinidad and Tobago Guinea MexicoGuyana Uganda Haiti NetherlandsIndia United States Laos NicaraguaIreland Zambia Lebanon PanamaIsrael Zimbabwe Madagascar ParaguayJamaica Mali PeruJordan Mauritania VenezuelaKenya Morocco PortugalKuwaitNigerMalawiSenegalAngolaMalaysiaSyriaBrazilMaldivesTogoGuinea-BissauMaltaTunisiaMozambiqueVietnamOmanTABLE A4.—PREFERENTIAL TRADE AGREEMENTS IN 1990EEC/EC CARICOM CACMBelgium Bahamas Costa RicaDenmark Barbados El SalvadorFrance Belize GuatemalaGermany Dominican Rep. HondurasGreece Guyana NicaraguaIrelandHaitiItaly Jamaica Bilateral AgreementsLuxembourgTrinidad and TobagoNetherlandsSt. Kitts and NevisEC-CyprusPortugalSurinameEC-MaltaSpainEC-EgyptUnited KingdomSPARTECAEC-SyriaEC-AlgeriaEFTAAustraliaEC-NorwayNew ZealandEC-IcelandIceland Fiji EC-SwitzerlandNorway Kiribati Canada–United StatesSwitzerland Papua New Guinea Israel–United StatesLiechtensteinSolomon IslandsCERAustraliaNew ZealandPATCRAAustraliaPapua New Guinea

658THE REVIEW OF ECONOMICS AND STATISTICSTABLE A5.—SUMMARY STATISTICSFull Sample Exports 0VariableMean Std. Dev. Mean Std. Dev.Trade 172132.2 1828720 328757.7 2517139Log of trade — — 8.43383 3.26819Log of exporter’s GDP 23.24975 2.39727 24.42503 2.29748Log of importer’s GDP 23.24975 2.39727 24.13243 2.43148Log of exporter’s per capita GDP 7.50538 1.63986 8.09600 1.65986Log of importer’s per capita GDP 7.50538 1.63986 7.98602 1.68649Log of distance 8.78551 0.74168 8.69497 0.77283Contiguity dummy 0.01961 0.13865 0.02361 0.15185Common-language dummy 0.20970 0.40710 0.21284 0.40933Colonial-tie dummy 0.17048 0.37606 0.16894 0.37472Landlocked exporter dummy 0.15441 0.36135 0.10767 0.30998Landlocked importer dummy 0.15441 0.36135 0.11401 0.31784Exporter’s remoteness 8.94654 0.26389 8.90383 0.29313Importer’s remoteness 8.94654 0.26389 8.90787 0.28412Preferential–trade-agreement dummy 0.02505 0.15629 0.04452 0.20626Openness dummy 0.56373 0.49594 0.65796 0.47442

This article has been cited by:1. Jean-Fran##ois Arvis, Ben Shepherd. 2013. The Poisson quasi-maximum likelihood estimator: a solution to the ###adding up###problem in gravity models. Applied Economics Letters 20:6, 515-519. [CrossRef]2. Gabriel Felbermayr, Jasmin Gr##schl. 2013. Natural disasters and the effect of trade on income: A new panel IV approach.European Economic Review 58, 18-30. [CrossRef]3. Inmaculada Mart##nez-Zarzoso. 2013. The log of gravity revisited. Applied Economics 45:3, 311-327. [CrossRef]4. J.M.C. Santos Silva, S. TenreyroCurrency Unions 451-461. [CrossRef]5. DENNIS NOVY. 2013. GRAVITY REDUX: MEASURING INTERNATIONAL TRADE COSTS WITH PANEL DATA.Economic Inquiry 51:1, 101-121. [CrossRef]6. L. Cissokho, J. Haughton, K. Makpayo, A. Seck. 2013. Why Is Agricultural Trade within ECOWAS So High?. Journal of AfricanEconomies 22:1, 22-51. [CrossRef]7. Sophie Drogu##, Federica DeMaria. 2012. Pesticide residues and trade, the apple of discord?. Food Policy 37:6, 641-649.[CrossRef]8. Valentina Raimondi, Margherita Scoppola, Alessandro Olper. 2012. Preference erosion and the developing countries exports tothe EU: a dynamic panel gravity approach. Review of World Economics 148:4, 707-732. [CrossRef]9. Arvin Pirness, M. Rose Olfert, Mark D. Partridge, William Hartley Furtan. 2012. Assessing the Impact of State Trading Enterprises.International Economic Journal 26:4, 587-608. [CrossRef]10. Yoto V. Yotov. 2012. A simple solution to the distance puzzle in international trade. Economics Letters 117:3, 794-798. [CrossRef]11. Jos## de Sousa. 2012. The currency union effect on trade is decreasing over time. Economics Letters 117:3, 917-920. [CrossRef]12. Patrik Gustavsson Tingvall, Andreas Poldahl. 2012. Determinants of Firm R&D: The Role of Relationship-Specific Interactionsfor R&D Spillovers. Journal of Industry, Competition and Trade 12:4, 395-411. [CrossRef]13. Fabien Candau, Jean-Fran##ois Hoarau, Serge Rey. 2012. L###impact de la distance et de l###int##gration sur le commerced###une r##gion ultrap##riph##rique d###Europe: l#####le de La R##union. European Journal of Development Research 24:5,808-831. [CrossRef]14. Lars H##kanson, Douglas Dow. 2012. Markets and Networks in International Trade: On the Role of Distances in Globalization.Management International Review 52:6, 761-789. [CrossRef]15. Ludo Peeters. 2012. GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*.Journal of Regional Science 52:5, 819-856. [CrossRef]16. Fernando Ferreira, Joel Waldfogel. 2012. Pop Internationalism: Has Half a Century of World Music Trade Displaced LocalCulture?. The Economic Journal n/a-n/a. [CrossRef]17. Pedro Verga Matos, Hor##cio C. Faustino. 2012. Beta-convergence and sigma-convergence in corporate governance in Europe.Economic Modelling 29:6, 2198-2204. [CrossRef]18. Neil Foster. 2012. Preferential Trade Agreements and the Margins of Imports. Open Economies Review 23:5, 869-889. [CrossRef]19. Jason H. Grant. 2012. Is the growth of regionalism as significant as the headlines suggest? Lessons from agricultural trade.Agricultural Economics no-no. [CrossRef]20. Jos## de Sousa, Thierry Mayer, Soledad Zignago. 2012. Market access in global and regional trade. Regional Science and UrbanEconomics 42:6, 1037-1052. [CrossRef]21. Zhenhui Xu, Jianyong Fan. 2012. China's Regional Trade and Domestic Market Integrations. Review of International Economics20:5, 1052-1069. [CrossRef]22. Carol McAusland, Daniel L. Millimet. 2012. Do national borders matter? Intranational trade, international trade, and theenvironment. Journal of Environmental Economics and Management . [CrossRef]23. A. Cheptea. 2012. Border Effects and European Integration. CESifo Economic Studies . [CrossRef]24. Juan Blyde. 2012. Paving the Road to Export: Assessing the Trade Impact of Road Quality. International Economic Journal 1-19.[CrossRef]25. Giorgio Fagiolo, Tiziano Squartini, Diego Garlaschelli. 2012. Null models of economic networks: the case of the world trade web.Journal of Economic Interaction and Coordination . [CrossRef]26. D. V. Pahan Prasada. 2012. Domestic versus Multilateral Institutions in Bilateral Trade: A Comparative Gravity Analysis.International Economic Journal 1-16. [CrossRef]27. Mahmut Yasar, David Lisner, Roderick M. Rejesus. 2012. Bilateral trade impacts of temporary foreign visitor policy. Review ofWorld Economics 148:3, 501-521. [CrossRef]

28. Jean-Marc Siro##n, Aycil Yucer. 2012. The impact of MERCOSUR on trade of Brazilian states. Review of World Economics148:3, 553-582. [CrossRef]29. Myoung-jae Lee, Young-sook Kim. 2012. ZERO-INFLATED ENDOGENOUS COUNT IN CENSORED MODEL: EFFECTSOF INFORMAL FAMILY CARE ON FORMAL HEALTH CARE. Health Economics 21:9, 1119-1133. [CrossRef]30. Nelson Villoria. 2012. The effects of China's growth on the food prices and the food exports of other developing countries.Agricultural Economics 43:5, 499-514. [CrossRef]31. Oliver Falck, Stephan Heblich, Alfred Lameli, Jens S##dekum. 2012. Dialects, cultural identity, and economic exchange. Journalof Urban Economics 72:2-3, 225-239. [CrossRef]32. Theo S. Eicher, Lindy Helfman, Alex Lenkoski. 2012. Robust FDI determinants: Bayesian Model Averaging in the presence ofselection bias. Journal of Macroeconomics 34:3, 637-651. [CrossRef]33. B. Xiong, J. Beghin. 2012. Does European aflatoxin regulation hurt groundnut exporters from Africa?. European Review ofAgricultural Economics 39:4, 589-609. [CrossRef]34. Nicolas Berman, Philippe Martin. 2012. The Vulnerability of Sub-Saharan Africa to Financial Crises: The Case of Trade. IMFEconomic Review 60:3, 329-364. [CrossRef]35. DJETO ASSANE, ERIC P. CHIANG. 2012. TRADE, STRUCTURAL REFORM, AND INSTITUTIONS IN SUB-SAHARANAFRICA. Contemporary Economic Policy no-no. [CrossRef]36. Mark N. Harris, L##szl## K##nya, L##szl## M##ty##s. 2012. Some Stylized Facts about International Trade Flows. Review ofInternational Economics 20:4, 781-792. [CrossRef]37. Yue Ma, Baozhi Qu, Yifan Zhang. 2012. Complex Goods' Exports and Institutions: Empirics at the Firm Level. Review ofInternational Economics 20:4, 841-853. [CrossRef]38. Marco Fugazza, Alessandro Nicita. 2012. The direct and relative effects of preferential market access. Journal of InternationalEconomics . [CrossRef]39. Sean KaskModes of Open Innovation in Service Industries and Process Innovation 137-158. [CrossRef]40. Pascal L. Ghazalian. 2012. MERCOSUR enlargement: predicting the effects on trade in primary agricultural commodities.Economic Change and Restructuring . [CrossRef]41. Z. U. Haq, K. Meilke, J. Cranfield. 2012. Selection bias in a gravity model of agrifood trade. European Review of AgriculturalEconomics . [CrossRef]42. Faqin Lin, Nicholas C.S. Sim. 2012. Death of distance and the distance puzzle. Economics Letters 116:2, 225-228. [CrossRef]43. Aitor Garmendia, Carlos Llano, Asier Minondo, Francisco Requena. 2012. Networks and the disappearance of the intranationalhome bias. Economics Letters 116:2, 178-182. [CrossRef]44. Peter H. Egger, Andrea Lassmann. 2012. The language effect in international trade: A meta-analysis. Economics Letters 116:2,221-224. [CrossRef]45. Pascal L. Ghazalian, Lota D. Tamini, Bruno Larue, Jean-Philippe Gervais. 2012. A gravity model to account for vertical linkagesbetween markets with an application to the cattle/beef sector. The Journal of International Trade & Economic Development 21:4,579-601. [CrossRef]46. Gianfranco De Simone, Miriam Manchin. 2012. Outward Migration and Inward FDI: Factor Mobility between Eastern andWestern Europe. Review of International Economics 20:3, 600-615. [CrossRef]47. Segun Goh, Keumsook Lee, Jong Park, M. Choi. 2012. Modification of the gravity model and application to the metropolitanSeoul subway system. Physical Review E 86:2. . [CrossRef]48. Russell Thomson. 2012. National scientific capacity and R&D offshoring. Research Policy . [CrossRef]49. N. Voigtlander, H.-J. Voth. 2012. Persecution Perpetuated: The Medieval Origins of Anti-Semitic Violence in Nazi Germany.The Quarterly Journal of Economics 127:3, 1339-1392. [CrossRef]50. Derek Kellenberg. 2012. Trading wastes. Journal of Environmental Economics and Management 64:1, 68-87. [CrossRef]51. A. Klein, N. Crafts. 2012. Making sense of the manufacturing belt: determinants of U.S. industrial location, 1880-1920. Journalof Economic Geography 12:4, 775-807. [CrossRef]52. Celine Azemar, Julia Darby, Rodolphe Desbordes, Ian Wooton. 2012. Market Familiarity and the Location of South and NorthMNEs. Economics & Politics n/a-n/a. [CrossRef]53. Mohammad Mafizur Rahman, Dilip Dutta. 2012. The Gravity Model Analysis of Bangladesh's Trade: A Panel Data Approach.Journal of Asia-Pacific Business 13:3, 263-286. [CrossRef]54. Andrew B. Bernard, J. Bradford Jensen, Stephen J. Redding, Peter K. Schott. 2012. The Empirics of Firm Heterogeneity andInternational Trade. Annual Review of Economics 4:1, 283-313. [CrossRef]

55. Giulia Bettin, Alessia Lo Turco. 2012. A Cross-Country View on South-North Migration and Trade: Dissecting the Channels.Emerging Markets Finance and Trade 48:4, 4-29. [CrossRef]56. Pascal L. Ghazalian. 2012. Home Bias in Primary Agricultural and Processed Food Trade: Assessing the Effects of NationalDegree of Uncertainty Aversion. Journal of Agricultural Economics 63:2, 265-290. [CrossRef]57. J. de Sousa, J. Lochard. 2012. Trade and Colonial Status. Journal of African Economies 21:3, 409-439. [CrossRef]58. Andr## C. Jordaan, Joel H. Eita. 2012. Determinants of South Africa's exports of leather products. Agrekon 51:2, 38-52. [CrossRef]59. Yuan Li, John C. Beghin. 2012. A meta-analysis of estimates of the impact of technical barriers to trade. Journal of Policy Modeling34:3, 497-511. [CrossRef]60. Gordon H Hanson. 2012. The Rise of Middle Kingdoms: Emerging Economies in Global Trade. Journal of Economic Perspectives26:2, 41-64. [CrossRef]61. Kevin E. Staub, Rainer Winkelmann. 2012. CONSISTENT ESTIMATION OF ZERO-INFLATED COUNT MODELS. HealthEconomics n/a-n/a. [CrossRef]62. LEO H. KAHANE. 2012. UNDERSTANDING THE INTERSTATE EXPORT OF CRIME GUNS: A GRAVITY MODELAPPROACH. Contemporary Economic Policy no-no. [CrossRef]63. Kevin N. Alschuler, Laura E. Gibbons, Dori E. Rosenberg, Dawn M. Ehde, Aimee M. Verrall, Alyssa M. Bamer, Mark P.Jensen. 2012. Body mass index and waist circumference in persons aging with muscular dystrophy, multiple sclerosis, post-poliosyndrome, and spinal cord injury. Disability and Health Journal . [CrossRef]64. Axel Berger, Matthias Busse, Peter Nunnenkamp, Martin Roy. 2012. Do trade and investment agreements lead to more FDI?Accounting for key provisions inside the black box. International Economics and Economic Policy . [CrossRef]65. Guo-xue WEI, Ji-kun HUANG, Jun YANG. 2012. Honey Safety Standards and Its Impacts on China's Honey Export. Journal ofIntegrative Agriculture 11:4, 684-693. [CrossRef]66. John Francis, Yuqing Zheng. 2012. Trade, Geography, and Industry Growth in U.S. Manufacturing. Southern Economic Journal78:4, 1222-1241. [CrossRef]67. Estrella G##mez-Herrera. 2012. Comparing alternative methods to estimate gravity models of bilateral trade. Empirical Economics. [CrossRef]68. Katheryn Niles Russ. 2012. Exchange rate volatility and first-time entry by multinational firms. Review of World Economics .[CrossRef]69. Joaquim J. S. Ramalho, J. Vidigal Silva. 2012. Functional form issues in the regression analysis of financial leverage ratios.Empirical Economics . [CrossRef]70. Neil Foster. 2012. Intellectual property rights and the margins of international trade. The Journal of International Trade &Economic Development 1-30. [CrossRef]71. Michele Fratianni, Francesco Marchionne. 2012. Trade Costs and Economic Development. Economic Geography no-no.[CrossRef]72. Jean-Marie Grether, Nicole Andr##a Mathys, Jaime de Melo. 2012. Unravelling the worldwide pollution haven effect. The Journalof International Trade & Economic Development 21:1, 131-162. [CrossRef]73. Mar##a P##a Olivero, Yoto V. Yotov. 2012. Dynamic gravity: endogenous country size and asset accumulation. Canadian Journalof Economics/Revue canadienne d'##conomique 45:1, 64-92. [CrossRef]74. Simone Juhasz Silva, Douglas Nelson. 2012. Does Aid Cause Trade? Evidence from an Asymmetric Gravity Model. The WorldEconomy no-no. [CrossRef]75. C##line Carr##re, Jaime de Melo, John Wilson. 2012. THE DISTANCE PUZZLE AND LOW-INCOME COUNTRIES: ANUPDATE. Journal of Economic Surveys no-no. [CrossRef]76. Willem Thorbecke, Atsuyuki Kato. 2012. The effect of exchange rate changes on Japanese consumption exports. Japan and theWorld Economy . [CrossRef]77. Benedikt Heid, Mario Larch. 2012. Migration, Trade and Unemployment. Economics: The Open-Access, Open-Assessment E-Journal . [CrossRef]78. Athiwat Sukanuntathum. 2012. Robust Estimation of Gravity Models under Heteroskedasticity and Data Censoring. Procedia -Social and Behavioral Sciences 40, 731-735. [CrossRef]79. NIKOLAUS WOLF, MAX-STEPHAN SCHULZE, HANS-CHRISTIAN HEINEMEYER. 2011. On the Economic Consequencesof the Peace: Trade and Borders After Versailles. The Journal of Economic History 71:04, 915-949. [CrossRef]80. Gregory Corcos, Massimo Del Gatto, Giordano Mion, Gianmarco I.P. Ottaviano. 2011. Productivity and Firm Selection:Quantifying the ###New### Gains from Trade*. The Economic Journal no-no. [CrossRef]

81. Yoko Asuyama. 2011. Skill Distribution and Comparative Advantage: A Comparison of China and India. World Development. [CrossRef]82. Ivan T. Kandilov, Thomas Grennes. 2011. The determinants of service offshoring: Does distance matter?. Japan and the WorldEconomy . [CrossRef]83. Hyun-Hoon Lee, Hyeon-seung Huh, Won Joong Kim. 2011. Cross-border portfolio investment in the APEC region. Japan andthe World Economy . [CrossRef]84. Tomasz Michalski, Evren Ors. 2011. (Interstate) Banking and (interstate) trade: Does real integration follow financial integration?.Journal of Financial Economics . [CrossRef]85. J. H. Grant, K. A. Boys. 2011. Agricultural Trade and the GATT/WTO: Does Membership Make a Difference?. American Journalof Agricultural Economics . [CrossRef]86. Ines Buono, Guy Lalanne. 2011. The effect of the Uruguay round on the intensive and extensive margins of trade. Journal ofInternational Economics . [CrossRef]87. Carlos Llano-Verduras, Asier Minondo, Francisco Requena-Silvente. 2011. Is the Border Effect an Artefact of GeographicalAggregation?. The World Economy 34:10, 1771-1787. [CrossRef]88. YVES BOURDET, MARIA PERSSON. 2011. Completing the European Union Customs Union: The Effects of Trade ProcedureHarmonization*. JCMS: Journal of Common Market Studies no-no. [CrossRef]89. Andrew J. Cassey. 2011. State Foreign Export Patterns. Southern Economic Journal 78:2, 308-329. [CrossRef]90. Fr##d##ric Docquier, Hillel Rapoport, Sara Salomone. 2011. Remittances, migrants' education and immigration policy: Theoryand evidence from bilateral data. Regional Science and Urban Economics . [CrossRef]91. Jan Pettersson, Lars Johansson. 2011. Aid, Aid for Trade, and bilateral trade: An empirical study. The Journal of InternationalTrade & Economic Development 1-29. [CrossRef]92. Pierre Azoulay, Joshua S. Graff Zivin, Gustavo Manso. 2011. Incentives and creativity: evidence from the academic life sciences.The RAND Journal of Economics 42:3, 527-554. [CrossRef]93. Kazunobu Hayakawa. 2011. Measuring fixed costs for firms### use of a free trade agreement: Threshold regression approach.Economics Letters . [CrossRef]94. Valeria Costantini, Massimiliano Mazzanti. 2011. On the green and innovative side of trade competitiveness? The impact ofenvironmental policies and innovation on EU exports. Research Policy . [CrossRef]95. Raj Aggarwal, Colm Kearney, Brian Lucey. 2011. Gravity and culture in foreign portfolio investment. Journal of Banking &Finance . [CrossRef]96. Gabriel Felbermayr, Wilhelm KohlerModelling the Extensive Margin of World Trade: New Evidence on GATT and WTOMembership 92-130. [CrossRef]97. Peter Egger, Mario Larch, Kevin E Staub, Rainer Winkelmann. 2011. The Trade Effects of Endogenous Preferential TradeAgreements. American Economic Journal: Economic Policy 3:3, 113-143. [CrossRef]98. Rahul Giri. 2011. Local costs of distribution, international trade costs and micro evidence on the law of one price. Journal ofInternational Economics . [CrossRef]99. Wolfgang Hess, Maria Persson. 2011. Exploring the duration of EU imports. Review of World Economics . [CrossRef]100. Hajime Katayama, Mark Melatos. 2011. The nonlinear impact of currency unions on bilateral trade. Economics Letters 112:1,94-96. [CrossRef]101. Alfredo Jim##nez. 2011. Political Risk as a Determinant of Southern European FDI in Neighboring Developing Countries.Emerging Markets Finance and Trade 47:4, 59-74. [CrossRef]102. Natalie Chen, Dennis Novy. 2011. Gravity, trade integration, and heterogeneity across industries. Journal of InternationalEconomics . [CrossRef]103. Vincent Vicard. 2011. Trade, conflict, and political integration: Explaining the heterogeneity of regional trade agreements.European Economic Review . [CrossRef]104. Bernhard Herz, Marco Wagner. 2011. The ###Real### Impact of GATT/WTO - a Generalised Approach. The World Economy34:6, 1014-1041. [CrossRef]105. Bernard Hoekman, Alessandro Nicita. 2011. Trade Policy, Trade Costs, and Developing Country Trade. World Development .[CrossRef]106. Nikolaus Wolf, Albrecht O. Ritschl. 2011. Endogeneity of Currency Areas and Trade Blocs: Evidence from a Natural Experiment.Kyklos 64:2, 291-312. [CrossRef]

107. Peter Egger, David Greenaway, Tobias Seidel. 2011. Rigid labour markets with trade and capital mobility: theory and evidence.Canadian Journal of Economics/Revue canadienne d'##conomique 44:2, 509-540. [CrossRef]108. Peter Egger, Doina Maria Radulescu. 2011. Labor Taxation and Foreign Direct Investment*. Scandinavian Journal of Economicsno-no. [CrossRef]109. J.M.C. Santos Silva, Silvana Tenreyro. 2011. Further simulation evidence on the performance of the Poisson pseudo-maximumlikelihood estimator. Economics Letters . [CrossRef]110. Debasri Mukherjee, Susan Pozo. 2011. Exchange-rate volatility and trade: a semiparametric approach. Applied Economics 43:13,1617-1627. [CrossRef]111. Valentina Raimondi, Alessandro Olper. 2011. Trade Elasticity, Gravity and Trade Liberalisation: Evidence from the Food Industry.Journal of Agricultural Economics no-no. [CrossRef]112. Giovanni Pica, Jos## V. Rodr##guez Mora. 2011. Who's afraid of a globalized world? Foreign Direct Investments, local knowledgeand allocation of talents. Journal of International Economics . [CrossRef]113. Michel Beine, Fr##d##ric Docquier, ##a##lar ##zden. 2011. Diasporas###. Journal of Development Economics 95:1, 30-41.[CrossRef]114. Florian M##lders, Ulrich Volz. 2011. Trade creation and the status of FTAs: empirical evidence from East Asia. Review of WorldEconomics . [CrossRef]115. Neil Foster, Robert Stehrer. 2011. Preferential trade agreements and the structure of international trade. Review of WorldEconomics . [CrossRef]116. Imran Ullah Khan, Kaliappa Kalirajan. 2011. The impact of trade costs on exports: An empirical modeling###. EconomicModelling . [CrossRef]117. Gabriel Felbermayr, Julien Prat, Hans-J##rg Schmerer. 2011. Trade and unemployment: What do the data say?. EuropeanEconomic Review . [CrossRef]118. Joakim Westerlund, Fredrik Wilhelmsson. 2011. Estimating the gravity model without gravity using panel data. AppliedEconomics 43:6, 641-649. [CrossRef]119. Anca D. Cristea. 2011. Buyer-seller relationships in international trade: Evidence from U.S. States' exports and business-classtravel. Journal of International Economics . [CrossRef]120. David S. Jacks, Christopher M. Meissner, Dennis Novy. 2011. Trade booms, trade busts, and trade costs. Journal of InternationalEconomics 83:2, 185-201. [CrossRef]121. Gianluca Cafiso. 2011. Sectoral border effects and the geographic concentration of production. Review of World Economics .[CrossRef]122. P. Cardamone. 2011. The effect of preferential trade agreements on monthly fruit exports to the European Union. European Reviewof Agricultural Economics . [CrossRef]123. Mich##le Belot, Sjef Ederveen. 2011. Cultural barriers in migration between OECD countries. Journal of Population Economics. [CrossRef]124. Anna D'Souza. 2011. The OECD Anti-Bribery Convention: Changing the currents of trade. Journal of Development Economics. [CrossRef]125. Allen Dennis, Ben Shepherd. 2011. Trade Facilitation and Export Diversification. The World Economy 34:1, 101-122. [CrossRef]126. Pascal L. Ghazalian, Bruno Larue, Jean-Philippe Gervais. 2011. Assessing the implications of regional preferential market accessfor meat commodities. Agribusiness n/a-n/a. [CrossRef]127. Byron S. Gangnes, Alyson C. Ma, Ari Van Assche. 2011. China's exports in a world of increasing oil prices. Multinational BusinessReview 19:2, 133-151. [CrossRef]128. Luc Bauwens, Giordano Mion, Jacques-Fran##ois Thisse. 2011. The Resistible Decline of European Science. Recherches##conomiques de Louvain 77:4, 5. [CrossRef]129. Marilyne Huchet-Bourdon, Angela Cheptea. 2011. Informal barriers and agricultural trade: does monetary integration matter?.Agricultural Economics no-no. [CrossRef]130. Marcella Nicolini. 2010. On the Evolution of Institutional Comparative Advantages. Structural Change and Economic Dynamics. [CrossRef]131. Valeria Costantini, Francesco Crespi. 2010. Public policies for a sustainable energy sector: regulation, diversity and fostering ofinnovation. Journal of Evolutionary Economics . [CrossRef]132. Harald Badinger, Peter Egger. 2010. Horizontal vs. Vertical Interdependence in Multinational Activity*. Oxford Bulletin ofEconomics and Statistics 72:6, 744-768. [CrossRef]

133. Michael E Waugh. 2010. International Trade and Income Differences. American Economic Review 100:5, 2093-2124. [CrossRef]134. James E Anderson, Yoto V Yotov. 2010. The Changing Incidence of Geography. American Economic Review 100:5, 2157-2186.[CrossRef]135. Francesco Aiello, Paola Cardamone, Maria Rosaria Agostino. 2010. Evaluating the impact of nonreciprocal trade preferencesusing gravity models. Applied Economics 42:29, 3745-3760. [CrossRef]136. Innwon Park, Soonchan Park. 2010. Best practices for regional trade agreements. Review of World Economics . [CrossRef]137. L. D. Tamini, J.-P. Gervais, B. Larue. 2010. Trade liberalisation effects on agricultural goods at different processing stages.European Review of Agricultural Economics . [CrossRef]138. Giovanni Peri, Francisco Requena-Silvente. 2010. The trade creation effect of immigrants: evidence from the remarkable case ofSpain. Canadian Journal of Economics/Revue canadienne d'##conomique 43:4, 1433-1459. [CrossRef]139. Marie Daumal, Soledad Zignago. 2010. Measure and determinants of border effects of Brazilian states. Papers in Regional Science89:4, 735-758. [CrossRef]140. Gabriel Felbermayr, Wilhelm Kohler. 2010. Modelling the Extensive Margin of World Trade: New Evidence on GATT and WTOMembership. The World Economy 33:11, 1430-1469. [CrossRef]141. Davin Chor. 2010. Unpacking sources of comparative advantage: A quantitative approach. Journal of International Economics82:2, 152-167. [CrossRef]142. Oxana Babeck## Kuchar##ukov##, Jan Babeck##, Martin Raiser. 2010. Gravity Approach for Modelling International Tradein South-Eastern Europe and the Commonwealth of Independent States: The Role of Geography, Policy and Institutions. OpenEconomies Review . [CrossRef]143. L. Sun, M. R. Reed. 2010. Impacts of Free Trade Agreements on Agricultural Trade Creation and Trade Diversion. AmericanJournal of Agricultural Economics . [CrossRef]144. Nicolas Sauter. 2010. Talking trade: language barriers in intra-Canadian commerce. Empirical Economics . [CrossRef]145. Donata Bessey. 2010. International student migration to Germany. Empirical Economics . [CrossRef]146. Ivan T. Kandilov, Thomas Grennes. 2010. The determinants of service exports from Central and Eastern Europe. Economics ofTransition 18:4, 763-794. [CrossRef]147. Lucio Picci. 2010. The internationalization of inventive activity: A gravity model using patent data###. Research Policy 39:8,1070-1081. [CrossRef]148. J.M.C. Santos Silva, Silvana Tenreyro. 2010. Currency Unions in Prospect and Retrospect. Annual Review of Economics 2:1,51-74. [CrossRef]149. STEFAN BOES. 2010. Count Data Models with Correlated Unobserved Heterogeneity. Scandinavian Journal of Statistics 37:3,382-402. [CrossRef]150. Anne-C##lia Disdier, Lionel Fontagn##. 2010. Trade impact of European measures on GMOs condemned by the WTO panel.Review of World Economics 146:3, 495-514. [CrossRef]151. Jayjit Roy. 2010. Do Customs Union Members Engage in More Bilateral Trade than Free-Trade Agreement Members?. Reviewof International Economics 18:4, 663-681. [CrossRef]152. Daniele Fabbri, Silvana Robone. 2010. The geography of hospital admission in a national health service with patient choice.Health Economics 19:9, 1029-1047. [CrossRef]153. Mariarosaria Agostino, Federica Demaria, Francesco Trivieri. 2010. Non-Reciprocal Trade Preferences and the Role ofCompliance Costs in the Agricultural Sector: Exports to the EU. Journal of Agricultural Economics 61:3, 652-679. [CrossRef]154. James E. Anderson. 2010. The Gravity Model. Annual Review of Economics 3:1, 110301095653089. [CrossRef]155. Maarten Bosker, Harry Garretsen. 2010. Trade costs in empirical New Economic Geography. Papers in Regional Science 89:3,485-511. [CrossRef]156. S. Jayasinghe, J. C. Beghin, G. Moschini. 2010. Determinants of World Demand for U.S. Corn Seeds: The Role of Trade Costs.American Journal of Agricultural Economics 92:4, 999-1010. [CrossRef]157. FABIAN BARTHEL, MATTHIAS BUSSE, ERIC NEUMAYER. 2010. THE IMPACT OF DOUBLE TAXATION TREATIESON FOREIGN DIRECT INVESTMENT: EVIDENCE FROM LARGE DYADIC PANEL DATA. Contemporary EconomicPolicy 28:3, 366-377. [CrossRef]158. C. Bagoulla, E. Chevassus-Lozza, K. Daniel, C. Gaigne. 2010. Regional Production Adjustment to Import Competition: Evidencefrom the French Agro-Industry. American Journal of Agricultural Economics 92:4, 1040-1050. [CrossRef]159. Elisa Giuliani, Andrea Morrison, Carlo Pietrobelli, Roberta Rabellotti. 2010. Who are the researchers that are collaborating withindustry? An analysis of the wine sectors in Chile, South Africa and Italy. Research Policy 39:6, 748-761. [CrossRef]

160. Giorgio Fagiolo. 2010. The international-trade network: gravity equations and topological properties. Journal of EconomicInteraction and Coordination 5:1, 1-25. [CrossRef]161. Eric Neumayer. 2010. Visa Restrictions and Bilateral Travel. The Professional Geographer 62:2, 171-181. [CrossRef]162. Keith Head, Thierry Mayer, John Ries. 2010. The erosion of colonial trade linkages after independence. Journal of InternationalEconomics 81:1, 1-14. [CrossRef]163. Maria Bas, Ivan Ledezma. 2010. Trade integration and within-plant productivity evolution in Chile. Review of World Economics146:1, 113-146. [CrossRef]164. Matthias Busse, Jens K##niger, Peter Nunnenkamp. 2010. FDI promotion through bilateral investment treaties: more than a bit?.Review of World Economics 146:1, 147-177. [CrossRef]165. Christian Volpe Martincus, Antoni Estevadeordal, Andr##s Gallo, Jessica Luna. 2010. Information barriers, export promotioninstitutions, and the extensive margin of trade. Review of World Economics 146:1, 91-111. [CrossRef]166. RODOLPHE DESBORDES. 2010. GLOBAL AND DIPLOMATIC POLITICAL RISKS AND FOREIGN DIRECTINVESTMENT. Economics & Politics 22:1, 92-125. [CrossRef]167. Daniel Lederman, Marcelo Olarreaga, Lucy Payton. 2010. Export promotion agencies: Do they work?. Journal of DevelopmentEconomics 91:2, 257-265. [CrossRef]168. Miaojie Yu. 2010. Trade, democracy, and the gravity equation###. Journal of Development Economics 91:2, 289-300. [CrossRef]169. J##rn Kleinert, Farid Toubal. 2010. Gravity for FDI. Review of International Economics 18:1, 1-13. [CrossRef]170. Peter Egger. 2010. Bilateral FDI potentials for Austria. Empirica 37:1, 5-17. [CrossRef]171. Alberto Salvo. 2010. Trade flows in a spatial oligopoly: gravity fits well, but what does it explain?. Canadian Journal ofEconomics/Revue canadienne d'##conomique 43:1, 63-96. [CrossRef]172. Ting Chi, Peter P.D. Kilduff. 2010. An empirical investigation of the determinants and shifting patterns of US apparel importsusing a gravity model framework. Journal of Fashion Marketing and Management 14:3, 501-520. [CrossRef]173. H. Boulhol, A. de Serres. 2010. Have developed countries escaped the curse of distance?. Journal of Economic Geography 10:1,113-139. [CrossRef]174. Anne-C##lia Disdier, Silvio H. T. Tai, Lionel Fontagn##, Thierry Mayer. 2010. Bilateral trade of cultural goods. Review of WorldEconomics 145:4, 575-595. [CrossRef]175. T. S. Aidt, M. Gassebner. 2010. Do Autocratic States Trade Less?. The World Bank Economic Review 24:1, 38-76. [CrossRef]176. Mohammad Masudur Rahman, Laila Arjuman Ara. 2010. Bangladesh trade potential: a dynamic gravity approach. Journal ofInternational Trade Law and Policy 9:2, 130-147. [CrossRef]177. Kai Sun, Daniel J. Henderson, Subal C. Kumbhakar. 2010. Biases in approximating log production. Journal of AppliedEconometrics n/a-n/a. [CrossRef]178. Theo S. Eicher, Christian Henn, Chris Papageorgiou. 2010. Trade creation and diversion revisited: accounting for modeluncertainty and natural trading partner effects. Journal of Applied Econometrics n/a-n/a. [CrossRef]179. Simon W. Schlueter, Christine Wieck, Thomas Heckelei. 2009. Regulatory Policies in Meat Trade: Is There Evidence for LeastTrade-distorting Sanitary Regulations?. American Journal of Agricultural Economics 91:5, 1484-1490. [CrossRef]180. Markus Lampe. 2009. Effects of Bilateralism and the MFN Clause on International Trade: Evidence for the Cobden-ChevalierNetwork, 1860-1875. The Journal of Economic History 69:04, 1012. [CrossRef]181. Edmund Amann, Barry Lau, Frederick Nixson. 2009. Did China Hurt the Textiles and Clothing Exports of Other Asian Economies,1990-2005?. Oxford Development Studies 37:4, 333-362. [CrossRef]182. PIERRE AZOULAY, WAVERLY DING, TOBY STUART. 2009. THE IMPACT OF ACADEMIC PATENTING ON THERATE, QUALITY AND DIRECTION OF (PUBLIC) RESEARCH OUTPUT. The Journal of Industrial Economics 57:4, 637-676.[CrossRef]183. Charalambos Tsangarides, Pierre Ewenczyk, Michal Hulej, Mahvash Saeed Qureshi. 2009. Are Africa's Currency Unions Goodfor Trade?. IMF Staff Papers 56:4, 876-918. [CrossRef]184. N. B. Villoria. 2009. China and the Manufacturing Terms-of-Trade of African Exporters. Journal of African Economies 18:5,781-823. [CrossRef]185. W. Czubala, B. Shepherd, J. S. Wilson. 2009. Help or Hindrance? The Impact of Harmonised Standards on African Exports.Journal of African Economies 18:5, 711-744. [CrossRef]186. Rabin Hattari, Ramkishen S. Rajan. 2009. Understanding bilateral FDI flows in developing Asia. Asian-Pacific EconomicLiterature 23:2, 73-93. [CrossRef]

187. Marius Br##lhart, Federico Trionfetti. 2009. A test of trade theories when expenditure is home biased###. European EconomicReview 53:7, 830-845. [CrossRef]188. 2009. Simple Tests for Exogeneity of a Binary Explanatory Variable in Count Data Regression Models. Communications inStatistics - Simulation and Computation 38:9, 1834-1855. [CrossRef]189. Xuepeng Liu. 2009. GATT/WTO Promotes Trade Strongly: Sample Selection and Model Specification. Review of InternationalEconomics 17:3, 428-446. [CrossRef]190. Jihyung Hong, Frank Windmeijer, Diego Novick, Josep Maria Haro, Jacqueline Brown. 2009. The cost of relapse inpatients with schizophrenia in the European SOHO (Schizophrenia Outpatient Health Outcomes) study. Progress in Neuro-Psychopharmacology and Biological Psychiatry 33:5, 835-841. [CrossRef]191. Silvio H. T. Tai. 2009. Market structure and the link between migration and trade. Review of World Economics 145:2, 225-249.[CrossRef]192. 2009. Comments by Shigeyuki Abe. Asian Economic Papers 8:2, 143-146. [Citation] [PDF] [PDF Plus]193. Thomas L. Vollrath, Mark J. Gehlhar, Charles B. Hallahan. 2009. Bilateral Import Protection, Free Trade Agreements, and OtherFactors Influencing Trade Flows in Agriculture and Clothing. Journal of Agricultural Economics 60:2, 298-317. [CrossRef]194. Boriss Siliverstovs, Dieter Schumacher. 2009. Estimating gravity equations: to log or not to log?. Empirical Economics 36:3,645-669. [CrossRef]195. Martijn Burger, Frank van Oort, Gert-Jan Linders. 2009. On the Specification of the Gravity Model of Trade: Zeros, Excess Zerosand Zero-inflated Estimation. Spatial Economic Analysis 4:2, 167-190. [CrossRef]196. Brent Neiman, Phillip Swagel. 2009. The impact of post-9/11 visa policies on travel to the United States. Journal of InternationalEconomics 78:1, 86-99. [CrossRef]197. Katheryn N. Russ. 2009. The New Theory of Foreign Direct Investment: Merging Trade and Capital Flows. International Finance12:1, 107-119. [CrossRef]198. Hans-Martin Zademach, Andres Rodriguez-Pose. 2009. Cross-Border M&As and the Changing Economic Geography of Europe.European Planning Studies 17:5, 765-789. [CrossRef]199. Matthias Helble, Ben Shepherd, John S. Wilson. 2009. Transparency and Regional Integration in the Asia Pacific. World Economy32:3, 479-508. [CrossRef]200. S BAIER, J BERGSTRAND. 2009. Estimating the effects of free trade agreements on international trade flows using matchingeconometrics. Journal of International Economics 77:1, 63-76. [CrossRef]201. S BAIER, J BERGSTRAND. 2009. Bonus vetus OLS: A simple method for approximating international trade-cost effects usingthe gravity equation###. Journal of International Economics 77:1, 77-85. [CrossRef]202. Jos## De Sousa, Olivier Lamotte. 2009. S##paration politique et d##sint##gration commerciale. Revue ##conomique 60:4, 891.[CrossRef]203. Nicolas Coeurdacier, Roberto A. De Santis, Antonin Aviat. 2009. Cross-border mergers and acquisitions and European integration.Economic Policy 24:57, 55-106. [CrossRef]204. M. Bosker, H. Garretsen. 2008. Economic development and the geography of institutions. Journal of Economic Geography 9:3,295-328. [CrossRef]205. Isabel Proen##a, Maria Paula Fontoura, Enrique Mart##nez-Gal##n. 2008. Trade in the enlarged European Union: a new approachon trade potential. Portuguese Economic Journal 7:3, 205-224. [CrossRef]206. Hildegunn Kyvik Nord##s. 2008. Gatekeepers to consumer markets: the role of retailers in international trade. The InternationalReview of Retail, Distribution and Consumer Research 18:5, 449-472. [CrossRef]207. G.-J. M. Linders, M. J. Burger, F. G. van Oort. 2008. A rather empty world: the many faces of distance and the persistent resistanceto international trade. Cambridge Journal of Regions, Economy and Society 1:3, 439-458. [CrossRef]208. Samih Antoine Azar. 2008. Jensen###s Inequality in Finance. International Advances in Economic Research 14:4, 433-440.[CrossRef]209. Marissa D King, Heather A Haveman. 2008. Antislavery in America: The Press, the Pulpit, and the Rise of Antislavery Societies.Administrative Science Quarterly 53:3, 492-528. [CrossRef]210. C MAGEE. 2008. New measures of trade creation and trade diversion###. Journal of International Economics 75:2, 349-362.[CrossRef]211. B BALTAGI, P EGGER, M PFAFFERMAYR. 2008. Estimating regional trade agreement effects on FDI in an interdependentworld. Journal of Econometrics 145:1-2, 194-208. [CrossRef]

212. Richard Kneller, Mauro Pisu, Zhihong Yu. 2008. Overseas business costs and firm export performance. Canadian Journal ofEconomics/Revue canadienne d'##conomique 41:2, 639-669. [CrossRef]213. Doireann Fitzgerald. 2008. Can trade costs explain why exchange rate volatility does not feed into consumer prices?###. Journalof Monetary Economics 55:3, 606-628. [CrossRef]214. Daniel J. Henderson, Daniel L. Millimet. 2008. Is gravity linear?. Journal of Applied Econometrics 23:2, 137-172. [CrossRef]215. Massimo Del Gatto, Gianmarco I. P. Ottaviano, Marcello Pagnini. 2008. OPENNESS TO TRADE AND INDUSTRY COSTDISPERSION: EVIDENCE FROM A PANEL OF ITALIAN FIRMS*. Journal of Regional Science 48:1, 97-129. [CrossRef]216. Martin Knapp, Frank Windmeijer, Jacqueline Brown, Stathis Kontodimas, Spyridon Tzivelekis, Josep Maria Haro, Mark Ratcliffe,Jihyung Hong, Diego Novick. 2008. Cost-Utility Analysis of Treatment with Olanzapine Compared with Other AntipsychoticTreatments in Patients with Schizophrenia in the Pan-European SOHO Study. PharmacoEconomics 26:4, 341-358. [CrossRef]217. Markus LampeBilateral trade flows in Europe, 1857###1875: A new dataset 26, 81-155. [CrossRef]218. Keith Head, John Ries. 2008. FDI as an outcome of the market for corporate control: Theory and evidence###. Journal ofInternational Economics 74:1, 2-20. [CrossRef]219. Q DO, A LEVCHENKO. 2007. Comparative advantage, demand for external finance, and financial development###. Journal ofFinancial Economics 86:3, 796-834. [CrossRef]220. Boriss Siliverstovs, Dieter Schumacher. 2007. Using the gravity equation to differentiate among alternative theories of trade:another look. Applied Economics Letters 14:14, 1065-1073. [CrossRef]