Mean value theorem for convex functions

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.     

Identification with latent variables

This is an essay on a unified approach to the identifiability problem in static models with and without hidden endogenous variables. As is well known, when some of these variables are unobserved, the prior information requirements for models when all endogenous variables are observed, are still there. In addition, extra prior information that takes the place of the means and covariances of the missing variables will have to be supplied directly or indirectly by the statistical researcher. In the paper we characterize the quality and quantity of the required information for the general linear static model and apply it when the model is i) an econometric demand and supply model with missing observations on the quantity transacted, ii) a factor analysis model with observed characteristics of the test takers and iii) a LISREL Model without fixed exogenous variables. With unknown true parameters, the exact rank conditions are seldom verifiable but we do recommend an implementable check-list that is adequate for almost all parameters.     

Conjugate small country production equilibrium concepts

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 country's 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.     

Identifiability criteria for Muth-rational expectations models

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.