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February, 2015

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GLOBAL FACTOR TRADE: Implications for Net Factor Trade 5

Corrections on ROW Technology: T6

We have seen that production model P5 works quite well for most countries. There are a few countries for which the fit of the production model is less satisfying. There are relatively large prediction errors (ca. 10 percent) for both factors in Canada, for capital in Denmark, and for labor in Italy. Given the simplicity of the framework, the magnitude of these errors is not surprising. Since we would like to preserve this simplicity, neither do these errors immediately call for a revision of our framework. Here

There is one case, however, in which a closer review is appropriate. For the ten OECD countries, we have data on technology which enters into our broader estimation exercise. But this is not the case for ROW. The technology for ROW is projected from the OECD data based on the aggregate ROW endowments and the capital to labor ratio. Because the gap in capital to labor ratios between the ten and the ROW is large, there is a good measure of uncertainty about the adequacy of this projection. As it turns out, the prediction errors for ROW are large: the estimated technology matrix under-predicts labor usage by 9 percent, and over-predicts capital usage by 12 percent. Moreover, these errors may well matter because ROW is predicted to be the largest net trader in both factors and because its technology will matter for the implied factor content of absorption of all other countries.

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GLOBAL FACTOR TRADE: Implications for Net Factor Trade 4

The D-F-S Continuum Model with Industry Variation in Factor Employment: P4 and T4

As we discussed in the section on estimating the technologies, there is a robust feature of the data that has been completely ignored in formal tests of the HOV model: capital to labor input ratios by industry vary positively with country factor abundance. We consider this first within the framework of the Dornbusch-Fischer-Samuelson (1980) continuum model, as this allows us to conserve yet a while longer the assumption of (approximate) factor price equalization.
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Consider production specification P4, as in Figure 9. The production slope coefficient remains at 0.89, but the median production error falls slightly to 5 percent. What is most surprising is how the continuum model affects the trade specification T4. A plot appears as Figure 10. The proportion of correct sign tests rises sharply to 86 percent (19 of 22) — significantly better than a coin flip at the 1 percent level. The variance ratio remains relatively low, although at 7 percent it is much higher than in any of the previous tests. The most impressive statistic is the slope coefficient of 0.17, where all of the previous trade slopes were zero. Clearly, allowing country capital to labor ratios to affect industry coefficients is moving us dramatically in the right direction.

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GLOBAL FACTOR TRADE: Implications for Net Factor Trade 3

If we exclude the US as well, the slope falls to about 0.90. The R2 in each case is respectably above 0.9. Also, in both cases, the median production errors are approximately 20 percent. The ROW continues to be a huge outlier, given its significantly lower productivity. These results suggest that use of an average technology matrix is a substantial improvement over using that of the US, since median production errors fall by one-third to one-half. Nonetheless, the fact that prediction errors are still on the order of 20 percent for the OECD group, and much larger for the ROW, suggests that there remains a lot of room for improvement.
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Examination of T2 can be brief. The sign test correctly predicts the direction of net factor trade only 45 percent of the time. The variance ratio continues to be essentially zero, again indicating strong missing trade. The Slope Test coefficient is -0.006. In short, factor abundance continues to provide essentially no information about which factors a country will be measured to export. These statistics are reinforced by the pictures in Figure 5 and Figure 6. Overall, this model is a complete empirical failure.

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