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Introduction to Modern Economic Growth and the residuals can be interpreted as estimates of technology differences Unfortunately, this approach is not particularly attractive, since the potential correlation between log Aj and log Kj or log Hj implies that the estimates of α need not be unbiased even though we impose the constant returns to scale assumption Moreover, if we not impose the assumption that these coefficients sum to one and test this restriction, it will be rejected Thus, this regression approach runs into the same difficulties as the Mankiw, Romer and Weil approach discussed previously What this discussion highlights is that, even if we are willing to presume that we know the functional form of the aggregate production function, it is difficult to directly estimate productivity differences So how can we improve over this naăve approach? The answer involves making more use of economic theory Estimating an equation of the form (3.28) does not make use of the fact that we are looking at the equilibrium of an economic system A more sophisticated approach would use more of the restrictions imposed by equilibrium behavior (and to bring additional relevant data) We next illustrate this using a specific attempt based on international trade The reader who is not familiar with trade theory may want to skip this subsection 3.6.2 Learning from International Trade* We will discuss models of growth in trade in Chapter 20 Even without a detailed discussion of international trade theory, we can use data from international trade flows and some simple principles of international trade theory to obtain another way of estimating productivity differences across countries Let us follow an important paper by Trefler (1993), which uses an augmented version of the standard Heckscher-Ohlin approach to international trade The Heckscher-Ohlin approach assumes that countries differ according to their factor proportions (e.g., some countries have much more physical capital relative to their labor supply than others) In a closed economy, this will lead to differences in relative factor costs and differences in the relative prices of products using these factors in different intensities International trade results as a way of taking advantage of these relative price differences The most extreme form of the theory assumes no cost of shipping goods and no policy impediments to trade, so that international trade can happen costlessly between countries 142