# GLOBAL FACTOR TRADE: Theory 5

Case Without Factor Price Equalization

Helpman (1998) proposes an account of the missing trade in the same spirit as the continuum model but which focuses on more substantial departures from FPE and the existence of specialization “cones” of production in tradables. One consequence of this is that the common set of non-traded goods will be produced using different techniques. In turn, this will affect our HOV factor content predictions. We now consider the implications review.

To arrive at a definite result, we need to apply a little more structure on demand than is standard. Consider a world with any number of countries, two factors (capital and labor) and in which the extent of differences in endowments is sufficient that at least some countries do not share factor price equalization. We do not restrict the number of non-traded goods, although we assume that the number of traded go

That is, under the conditions stated above, we get something very like the simple HOV equation so long as we restrict ourselves to world endowments devoted to tradable production and weight absorption according to the actual coefficients employed in production.

We now need to contemplate the implications of this model for what we will observe in the data. We know that input coefficients both in tradables and in non-tradables will differ across countries. The failure of FPE plays a role in both cases, but they have important differences. The input coefficients differ in tradables because the failure of FPE has led the countries to specialize

where the superscript in BcK reflects the fact that in the no-FPE model, all input coefficients in a country’s technology matrix will vary according to the country’s capital to labor ratio.

The first term on the RHS in T5 is the standard HOV prediction, while the second is an adjustment that accounts for departures in factor usage in non-tradable goods from the world average. Note, for example that a capital abundant country will have high wages, inducing substitution in non-tradables toward capital. The second term in brackets will typically be positive then for the case of capital, meaning that the simple HOV prediction overstates how much trade there really ought to be in capital services. In the same case, the actual labor usage in nontradables is less than the world average, and so the simple HOV equation will tend to overstate the expected level of labor service imports. In both cases, the new prediction for factor service trade will be less than that of the simple HOV model.