The _RERGRO_ variable is the annual percentage change in the real effective exchange rate (REER) index of country _i_ . The REER has a base year of 2000 (i.e. _REERi,_ 2000 = 100) and is obtained from the WDI database of the World Bank. According to the WDI documentation, this variable is calculated in two steps. First, WDI computes a nominal effective exchange rate as a weighted average of a basket of foreign currencies.<sup>48</sup> Second, the nominal rate is deflated by an indicator of manufacturing unit labor costs for high income countries and changes in consumer prices for others. Since the definition of the REER series is based on the inverse quote of the nominal exchange rate, an increase in the value of the real exchange rate (that is, a positive value for _RERGRO_ ) implies a real appreciation of the domestic currency. Therefore, based on the discussion in the previous sub-section, we expect a negative relationship between changes in the real effective exchange rate and net FDI inflows.

The _WLDFDIadj_ variable represents an adjustment to the definition of global FDI discussed in the earlier sub-section. This new variable is calculated as ( _WLDFDIt − FDIit_ ) to remove the two-way causality between world FDI and the dependent variable. As before, this variable should pick up aggregate trends in FDI and globalization effects, and therefore we expect its coefficient to be positive.

The third new variable, _DISTA_ , is the log of average distance between country _i_ and all of its PTA partners at time _t_ . This variable is equal to zero when a country is not a member of any PTAs, and has a time series dimension since its value is updated every time a country enters into a new preferential agreement. It is calculated as �ln � _N_ <u>1</u> � _Nj_<sup>_distij_</sup> �� for each country _i_ and every year _t_ , where _distij_ is the great circle distance between the largest or capital cities of countries _i_ and _j_ and _N_ is the number of country _i_ ’s PTA partners.<sup>49</sup> For the reasons discussed previously, we expect to find a negative elasticity of net FDI inflows with respect to distance to PTA partners.

In order to simultaneously account for heteroscedasticity across panels and serial correlation within panels, we rely on a three-step feasible generalized least squares (FGLS) estimator. The advantage of this approach is that it allows estimation in the presence of AR(1) autocorrelation within panels and cross-sectional correlation and/or heteroscedasticity across panels. However, the use of this estimator is conditional on having a sufficient number of degrees of freedom, since it must generate additional estimates of the variance, covariance, and serial correlation parameters. The standard version of the FGLS estimator in the presence of both heteroscedasticity and autocorrelation is a three-step process: in the first step, the model assumes homoscedastic errors and calculates consistent estimates of the AR(1) parameter(s); in the second step, a groupwise heteroscedastic model is applied to the transformed data (which is now free of autocorrelation); and in the third step, the new moment matrix is used to solve the full FGLS system and obtain the correct asymptotic variance-covariance matrix for _β_<sup>**ˆ**</sup> . The autoregressive parameters can be cross-sectionspecific or constrained to be the same across all cross-sections, with the latter increasing efficiency and improving the small sample performance of the estimator. The third step can be iterated to convergence, although Greene (2000) notes that no asymptotic gains can be expected from iteration since the estimator is efficient at every step. Furthermore, while the iterated FGLS estimator

> 48The WDI provides the following information on this variable: “A nominal effective exchange rate index represents the ratio (expressed on the base 2000 = 100) of an index of a currency’s period-average exchange rate to a weighted geometric average of exchange rates for currencies of selected countries and the euro area. For most high-income countries, weights are derived from trade in manufactured goods among industrial countries. For selected other countries the nominal effective exchange rate index is based on each countrys trade in both manufactured goods and primary products with its partner or competitor countries.”

> 49The distance series has been obtained from Centre d’Etudes Prospectives et d’Informations Internationales (CEPII ). See Appendix A for more details.

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