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.
A Failure of FPE and Factor Usage in Non-Traded Production: P5 and T5
Our next specification considers what happens if the endowment differences are sufficiently large to leave the countries in different cones of production. In such a case, FPE will break down and non-tradables will no longer be produced with common input coefficients across countries. This specification of the production model was preferred in our statistical analysis of technology in Section IV. Our trade tests now require us to focus on the factor content of tradables after we have adjusted the HOV predictions to reflect the differences in factor usage in non-tradables arising from the failure of FPE.
This is our best model so far. Plots of production and trade specifications P5 and T5 appear in Figures 11 and 12. The production slope coefficient rises to 0.97, with an R2 of essentially unity. The median production error falls to just 3 percent. We again achieve 86 percent correct matches in the sign test. The variance ratio rises to 19 percent. The slope coefficient is 0.43 for all factors, and 0.57 and 0.42 for capital and labor respectively. Again, the slopes still fall well short of unity.
But this must be compared to prior work and specifications T1 to T3, all of which had a zero slope, and T4, which had a slope that is less than half as large. Under specification T5, for example, a rise of one unit in Canadian “excess” capital would lead to the export of nearly 0.6 units of capital services. The amended HOV model is not working perfectly, but given the prior results, the surprise is how well it does.