Leon L. Wegge

On the Relation between Commodity Prices and Factor Rewards

1. 1. CONSIDER A COMPETITIVE ECONOMY with two commodities produced in positive amounts, two non-produced factors of production, and production functions concave and homogeneous of degree one. According to the StolperSamuelson Theorem [12], an autonomous increase in the price of one product gives rise to an increase in the real reward of one factor and to a decline in the real reward of the other. Specifically, an increase in the price of the i-th product results in an increase in the real reward of whichever factor is used vxith greater relative intensity in the i-th industry; and since one is free to number factors in any order, it is possible to associate the i-th factor with the i-th product (at least in a sufficiently small neighborhood of an initial equilibrium). 1.2. This is an exceedingly useful theorem. In a two-by-two model one finds oneself appealing to it in just about every exercise involving the distribution of income. The original article by Stolper and Samuelson was devoted to a single application of the theorem, the relation between tariff protection and real wages.2 But the theorem plays an equally important role in determining the incidence of a sales tax in a closed economy ([1], [4], [5]), and in making clear the distributional implications of capital accumulation [11]. The theorem would be even more useful if it could be extended to the case of n products and n factors. Can we in that more general case claim that an increase in the price of the i-th good results in an unambiguous increase

Identifiability criteria for Muth-rational expectations models

Abstract The authors deal with complete static linear models that contain current Muth-rational expectations. Rank, order and variety conditions for the identifiability of the structural parameter are derived under general restrictions. We also correct statements that appeared in the literature. Our main finding is that, in general, the standard rank and order conditions are sufficient also for the identifiability of the Muth-rational expectations model parameter, whenever there are enough not fully anticipated exogenous variables. If the number of imperfectly forecasted exogenous variables falls short of the number of endogenous variables by g , then g extra restrictions are needed on every equation and the restrictions must meet easily verifiable variety conditions as well as an augmented rank criterion.

CONSTRAINED INDIRECT LEAST SQUARES ESTIMATORS

An over-identified model could be defined as an exactly identified model that is subject to over-identifying restrictions. One could therefore define a constrained indirect least squares estimator for systems of equations similar to generalized least squares estimators under constraints for single equations. The estimator differs from three stage least squares in using the indirect least squares estimated covariance instead of the two stage least squares estimated covariance. With linear constraints, the estimator is linear. Under the overall null hypothesis with all constraints obtaining, the constrained indirect least squares estimator has the same asymptotic properties as the full infornhtation maximum likelihood estimator. The main advantage of the estimator lies in its easy adaptability to the multiple comparisonists preferred testing procedure given the exactly identified model as maintained hypothesis. In this paper we stay with the likelihood principle and the corresponding preliminary Wald-type multiple X tests. 1. PROPERTIES OF SEQUENTIALLY CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATORS BELOW WE DEFINE a family of estimators obtained by adding one or a group of constraints after another. To verify the properties of these estimators, we first compare the covariances in the asymptotic distribution of maximum likelihood estimators of models that differ in the number of prior constraints on the structural parameter. References are [1, 13, and 14], but we state the comparisons in a form that shows more of the details. Let f( ; xt, 0) be the density of the endogenous variables yt E R G conditional on the exogenous variables x, E R K and the reduced form parameter 0 E R m. For a sequence (yt), t = 1, . n of n independently selected endogenous variables,

Mean value theorem for convex functions

Abstract Closed proper convex functions have many properties in common with differentiable functions such as continuity and one-sided directional derivatives. In this paper it is shown that there exists a mean value theorem for such functions with the gradient vector in the differentiable case replaced by an element of the subdifferential in the convex case. Under compactness of the isoquant sets, (minus) the cost functions are convex and with the theorem above it is easy to show that under incomplete specialization and constant returns to scale the prices of international goods determine uniquely the prices of domestic goods if the isoquant sets are linearly independent.

A FAMILY OF FUNCTIONAL ITERATIONS AND THE SOLUTION OF MAXIMUM LIKELIHOOD ESTIMATING EQUATIONS

In this paper a family of functional iterations is introduced. One member of this family is the Newton-Raphson method and another member, obtained from a generalization of Steffensens method to a system of equations, has been considered in [7]. The general member of the family is derived from a regulafalsi construction, due to Gauss, for a particular choice of points in the iteration. From the computational point of view, all the members of the family of iterations, except the Newton-Raphson method, have the property that the partial derivatives of the system of equations are used almost never if a computing device with unlimited precision is utilized. Further, the asymptotic speed of convergence for any member is at least of order two. In view of the difficulties of obtaining the functional form of the second order partials of the likelihood function for general linear and nonlinear simultaneous systems, the method proposed here may be recommended in the computation of full information maximum likelih Dod estimates. Even if the partials of the system of equations are easily calculated, then some member of the family may still lead to convergence if the Newton-Raphson method does not. Practically speaking, the proposed method can be used to determine an approximate solution and this approximate solution will be closer to the solution if the precision of the computations is higher.

LOCAL IDENTIFIABILITY OF THE FACTOR ANALYSIS AND MEASUREMENT ERROR MODEL PARAMETER

Abstract Measurement error regression models are factor analysis models, the latent ‘correct’ regressors are the factors. There is however no common statistical method between the factor analysis and the regression model, because the covariance elements that are known identifying constituents of the former model are unknown in the latter. Instead, the idea that the data come from the same regression model, as with panel data, but can be grouped in two or more groups, each group having its own different regrressor generating process, is shown to supply credible restrictions. We generalize and compare relevant identifiability criteria and corresponding asymptotically efficient estimators that are recursive in the number of overidentifying restrictions.

Conjugate small country production equilibrium concepts

Abstract Conjugacy theory is utilized and developed to develop an interpretation of the production equilibrium in general equilibrium in terms of the properties of sectoral value added functions and in terms of the relative influence of each sector on all other sectors in a small countrys economy. The exact relationship between the comparative static system thus analyzed and the one traditionally built on equilibrium in terms of the vector of factor prices and gross output levels is delineated. The major contributions to the theory of effective protection are also illuminated.