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September, 2014

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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

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Think now about how previous tests have been implemented. Call the capital abundant country the US. Prior tests have used the US technology matrix to measure the factor content of trade. Consider how the input coefficients are constructed for the empirical US industry 1. Let BX be the column of average input coefficients for goods in the X sector and BN be the column of average input coefficients for goods in the the N sector. Then the measured input coefficients for sector 1 will be:
The weight R is determined by the X-sector’s weight in US output in sector 1 and we include the zero-weighted term BY to emphasize that it does not figure at all into calculation of the US technical coefficients. Note that the coefficients so estimated are a weighted average of the goods that the US actually exports (X) and goods with much more labor-intensive coefficients (N). That is, the estimated technology matrix will tend to understate the capital content and overstate the labor content of US exports. The consequence is to bias our measures of net factor trade toward zero. A parallel calculation for industry 2 would reveal the same downward bias in the US net factor content read only.

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Assume that the point dividing the world endowments between the two countries lies within the FPE set. The factor content of production for each country is its endowment Vc. With identical homothetic preferences, common goods prices, and production with the integrated equilibrium techniques, the factor content of absorption is sc VW. Together these yield the standard HOV prediction for the net factor content of trade: Vc – S VW. However we also know that with more goods than factors, the pattern of goods production, so also the pattern of goods trade, is not determinate.

In order to make the trade and production patterns determinate, we resort to an artifice originally introduced by Samuelson (1954) and considered within the continuum framework by Xu (1993). Imagine that all goods have iceberg transport costs, so that if j > 1 units are shipped, only one unit arrives. We will think of these trade costs as being strictly positive but arbitrarily small. Goods prices will be arbitrarily close to those of the integrated equilibrium, as will absorption and so the net factor content of trade. However, as Samuelson suggested, trade will be arranged so as to minimize trade costs. Since all goods are assumed to have the same proportional costs, this is equivalent to minimizing the volume of trade subject to achieving (approximately) the HOV-required net factor content.

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Hicks-Neutral Technical Differences A wide body of literature, both in productivity and in trade, suggests that there are systematic cross-country differences in productivity, even among the richest countries [e.g. Jorgenson and Kuroda (1990)]. This is very likely an important reason why Trefler (1995) found that the data suggests poor countries are “abundant” in all factors and vice versa for the rich countries. Bowen, et al. (1987) and Trefler (1995) have focused attention on Hicks-Neutral technical differences as a parsimonious way to capture these effects. Under this hypothesis, the technologies of countries differ only by a Hicks-neutral shift term. This can be characterized via country-specific technology shifts 8c:

Bc 8 = 8cB V c

In order to implement an amended HOV equation, it is convenient to think of the productivity differences as reflecting efficiency differences of the factors themselves (rather than technology per se). For example, if we take the US as a base and US factors are twice as productive as Italian factors, then 8Italy E = 2. In general, we can express a country’s endowments in efficiency terms:

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A successful account should provide a parsimonious and plausible set of departures from the standard model. In order to understand the role played by each of the assumptions, it is important, both in the theory and empirics, to begin with the standard model, relaxing the assumptions one at a time. The theoretical departures are developed in this section and implemented empirically in the following section electronic-loan.com.

The Standard HOV Model

We begin by developing the standard HOV model from first principles. Assume that all countries have identical, constant returns to scale production functions. Markets for goods and factors are perfectly competitive. There are no barriers to trade and transport costs are zero. The number of tradable goods is at least as large as the number of primary factors. We assume that the distribution of these factors across countries is consistent with the world replicating the integrated equilibrium (cf. Helpman and Krugman 1985).

Then factor prices will be equalized, so all producers will choose the same techniques of production. Let the matrix of total factor inputs for country c be given by Bc. The foregoing implies that for all countries c:

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The salient feature of the recent research is to ask if parsimonious amendments allow the model to match the data. The research focuses on two classes of amendments: technology and absorption. The technological assumptions considered include cross-country differences, either Hicks-neutral or factor-augmenting, and industry-level economies of scale [Trefler 1993, 1995; Gabaix 1997; Antweiler and Trefler 1997]. The assumptions about absorption introduce non-homotheticities, most prominently a home-bias in demand [BLS, Trefler 1995].

The search for parsimonious amendments that allow the model to work is precisely the right research strategy. However, the existing literature has one major drawback. The hypothesized amendments concern technology and absorption. Yet the empirical tests draw on only a single direct observation on technology (typically that of the United States) and no observations whatsoever concerning absorption. Hence even if these hypotheses improve the model’s performance by selected statistical measures, it remains uncertain if the estimated parameters have a structural interpretation in terms of the economic fundamentals.

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Global Factor Service Trade

Theory strives to be simple, rich, and robust. When it succeeds, it attains extraordinary influence. No doubt this explains the ubiquity of Heckscher-Ohlin theory in the field of international trade, particularly in the Factor Price Equalization (FPE) version of Samuelson (1947).1 Countless theoretical and empirical studies have built on this foundation.

The FPE theory’s most impressive feature is its extraordinary ambition. It proposes to describe, with but a few parameters, and in a unified constellation, the endowments, technologies, production, absorption, and trade of all countries in the world. This juxtaposition of extraordinary ambition and parsimonious specification has made the theory irresistible to empirical researchers.

In recent years, empirical research has focused on a relatively robust version of the theory, embodied in the Heckscher-Ohlin-Vanek (HOV) theorem. The HOV theorem yields a simple prediction: The net export of factor services will be the difference between a country’s endowment and the endowment typical in the world for a country of that size. The prediction is elegant, intuitive, and spectacularly at odds with the data.

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