Knowledge that Transforms

where Yt and Xt are subject to random errors of measurement ut and vt, respectively, with E(u) = E(vt) = 0, E(u2) = u, E(v2) = 2, E(utvt) = , and E(utu')E(vtsv) = 0 for t # t', is applied to a simple system of difference equations. The paper treats two such models, which differ in that one system is specified as deterministic except for measurement error, while the second model includes random in the equations as well. The investigation focuses on the possible consistency of least squares estimates of structural parameters in both cases. Mann and Wald [3] have demonstrated the consistency property of least squares estimates in stochastic difference equations which contain a shock term, and T. W. Anderson [1] has more recently shown such estimates to possess asymptotic normal distributions. One way argue, and perhaps quite legitimately, against the inclusion of measurement errors and shocks as separate entities in systems such as those under consideration. This separation, however, does provide a useful contrast with regard to the consistency property of LS estimates as compared to the case when only shocks (which subsume measurement error) are present in the specification of the system. When measurement errors are separated from shocks, LS yields consistent estimates for the explosive case of cobweb equilibrium and inconsistent estimates under convergence. The above phenomenon rests on the perhaps more interesting results for a recursive model where only measurement errors are present. This change in how the random terms enter the system, as contrasted to the Mann and Wald or Anderson formulations, causes zero correlation between observed variables and inconsistent LS estimates in the equations under convergence. Again, under explosion, LS provides consistent estimators of structural parameters.

THE CELEBRATED factor price equalization theorem has a curious history. Ohlin (1933) introduced to English-speaking readers an important modification to international trade theory, replacing the classical simplification, of constant costs but differing production functions among countries, with the alternative simplification of identical production functions but differing factor endowments. While many economists have remarked on the unrealism of Ohlin's simplification, an important aspect of it has not, it would seem, always been sufficiently appreciated. This is the fact that the classical model assumed that production relations in different countries differed in a quite arbitrary fashion; no satisfactory way had been provided for explaining how such production relations differed. In the Ohlin model, on the other hand, an element of continuity was introduced, since continuous variation of factor endowments would yield continuous (rather than arbitrary) variation in production relations. Even if differences in production relations (specifically, in transformation functions) cannot be completely explained in terms of differences in factor endowments, the Ohlin model is nevertheless susceptible to amendments that preserve meaningful relationships between different countries' production functions. Ohlin's writings were greatly influenced by Heckscher (1919), whose work was not made available in English until 1949. Heckscher, in turn, acknowledged the influence on his thought of Wicksell (1919).' Ohlin asserted that there was a tendency towards factor price equalization as a result of free trade, but he tempered his argument with many qualifications, even to the point of asserting that equalization would never be complete. The partial equalization argument was taken up and made rigorous by Stolper and Samuelson (1941), and later Samuelson (1948,