GLOBAL FACTOR TRADE: Implications for Net Factor Trade 6
There are a variety of robustness checks that we would like to make. The first notes that specifications T6 and T7 have included the ROW point even though both force the ROW production model to fit perfectly. We have already provided reasons for believing that adjustment of the ROW technology is appropriate. Nonetheless, it would be troubling if the steady improvement in the model owed solely to inclusion of the ROW points once this adjustment is made. Our check on this is to return to models T4 through T7, excluding ROW in each case. The results are presented in Table 6. Exclusion of ROW does tend to reduce the slope coefficients in each case. And the improvement of T6′ over T5′ seems somewhat less substantial than that of T6 over T5. Nonetheless, the key observation is that the results are broadly consistent across the two sets of tests.
Most importantly, the slope coefficient and the trade variance ratio rise consistently across both sets of tests, beginning and culminating at very similar levels. Even if we exclude ROW, the model correctly predicts the direction of net factor trade 90 percent of the time and the measured factor trade is over three-fourths the level predicted. Thus the results are highly robust to exclusion of ROW.
A second robustness check is to note that by sheer size, not only the ROW, but also the US, frequently provides influential data points. The US is a major exporter of capital and importer of labor while the reverse is true for the ROW. While these countries are extremely important to include in the analysis because they contribute so much variance, it would be troubling if our results were only a result of their inclusion. In Table 7 we drop the US and ROW and repeat our experiments. The slope coefficient in T7 rises to 0.64 and is precisely measured with an R2 of 0.76. The overall pattern is very similar to the tests including the US and ROW. Specifications T1 through T3 show little improvement in the HOV predictions. The movement to T4 provides a very substantial improvement, those to T5 and T6 somewhat smaller improvements, and finally a substantial improvement in the move to T7. Hence the amended HOV model works quite well even when we drop two points that contribute a great deal to the variance.
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A third robustness check is to consider the various ways that previous papers on factor service trade have weighted the data in order to account for heteroskedasticity. Up to now we have been focusing on untransformed data because all graphs and regressions have a clear interpretation in terms of actual factor service flows when these units are used. However, it is reasonable to ask whether our results are fragile when we shift weighting schemes.
The first weighting scheme that we try is one suggested by Trefler (1995). In that paper, Trefler deflates the data by the square root of a country’s absorption share multiplied by the standard deviation of the predicted factor service flows (expressed in natural units). This weighting scheme reduces the importance of large countries and factors with substantial variation in country abundance.