14 are not statistically significant in either of the two regressions. This suggests that once the heterogeneity in returns to export promotion is modeled adequately, there is no endogeneity problem left when estimating the impact of export-promotion budgets on exports or GDP per capita. This is interesting because when equation (3) is run for exports and GDP per capita but without the heterogeneous impact of the export-promotion budget along EPAs’ characteristics it is found that the varying coefficients for the control functions become statistically significant. This suggests that, having all fixed effects and population size included, when explicitly modeling the heterogeneous impact of export-promotion budgets across EPA’s characteristics, there is no mean-dependency left between the error term and export-promotion budgets (i.e., no endogeneity problem left). This holds for both the export and GDP per capita equations.

The results provided in figs. 2 and 3 can help design more effective EPAs. For example the fact that the larger share of the budget seem to be spent on marketing activities (see fig. 3 in the supplementary appendix S1) is comforting, given that our results tend to suggest that a larger share spent on marketing generally is associated with higher returns in terms of exports and GDP per capita, even though there seems to be some nonmonotonicity in this relationship for very high shares. Nevertheless, the plots in figs. 2 and 3 suggest that the largest returns are observed when this variable takes the value 5, that is, a share corresponding to 50 to 75 percent of the total expenditure. This suggests that there is still room for increasing the share spent on marketing activities in most countries, given that in 75 percent of the countries in the sample this share is below 50 percent (see fig. 3 in the supplementary appendix S1).

More important, it is clear from figs. 2 and 3 that what may be effective in promoting exports (focusing in a few sectors and destinations or a large share of the budget coming from fees for services, for example) may be less effective in increasing GDP per capita. One important message that comes out of this is that trying to evaluate the performance of EPAs by looking at increases in exports may create the wrong incentives when the ultimate goal of EPAs is social and economic welfare proxied here with GDP per capita.

A potential concern with the sample is that the third wave of EPA surveys for the period 2010–2014 only concerns 14 European countries. The study therefore tested the robustness of the results to the exclusion of this third wave from the sample and found that the same variables that are statistically significant in the full sample are also statistically significant for the years 2005–2010 with the exception of the strategic focus on a few sectors and destinations in the export equation. Also, the share of budget spent on established exporters becomes statistically significant in the smaller sample in both the export and GDP per capita equations. Overall the results, which are available in the supplementary appendix, are qualitatively similar in the 2005–2010 sample.

Finally, this study is interested in computing the returns to export promotion in each country as a function of EPA’s characteristics. The study proceeds as follows. First, because the control function parameter is never statistically significant the control function is dropped from the estimation of (3). This makes it possible to avoid estimating standard errors over the two stages, which in this case would be inefficient. Then, for each country _c_ and year _t_ the returns to export promotion are estimated by adding the functions corresponding to each characteristic _i_ in that country and year. Finally, these yearly returns are averaged for each country. The result is provided in uu table 4. ii bb To estimate the standard errors the study uses a wild bootstrap version introduced by Mammen (1992) for nonlinear cross-sectional regression models, and studied in Franke, Kreiss, and Mammen (2002) for nonlinear time series data. A main advantage in this case is that it automatically accounts for the presence of unknown heteroscedasticity and potential non-normality. The procedure is as follows; for a sample {( _Yc , t , Xc , t_ )} _tT , c ,_ = _nt_ 1 with _nt_ countries in year _t_ , and estimates [ _Y , ct_ | _Xc , t_ ] bootstrap samples are generated: EE<sup>�</sup> _Yc_ ∗ _, t_<sup>=EE�[YYoo</sup> ,<sup>oo|XXoo</sup> ,<sup>oo] +�YYoo</sup> ,<sup>oo−EE�[YYoo</sup> ,<sup>oo|XXoo</sup> ,<sup>oo]�</sup> · _v , v_ ∼ _N_ (0 _,_ 1) _._