Knowledge that Transforms

[In the estimation of structural coefficients it is well-known that both two-stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators are consistent and asymptotically efficient, and that the exact mean of the LIML estimator does not exist. Then the TSLS estimator, which is computationally simpler, has appeared a proper choice to empirical researchers. In this article asymptotic properties of the k-class and related estimators are sorted out according to the ratio between the total number of exogenous variables and the number of observations. It is found that the TSLS distribution deviates far from its traditional asymptotic distribution; the LIML distribution stays stable about its traditional asymptotic distribution. The LIML estimator now seems more attractive than the TSLS estimator except for the fact that its exact moments do not exist. A modified estimator is proposed which is asymptotically better than the LIML estimator and whose exact moments exist.]

We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. These portfolios span the mean-variance efficient set. We resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available. Ross 112, 141 showed that if there is a factor structure, then the mean returns are approximately linear functions of factor loadings. We define an approximate factor structure and show that this weaker restriction is sufficient for Ross' result. If the covariance matrix of the asset returns has only K unbounded eigenvalues, then there is an approximate factor structure and it is unique. The corresponding K eigenvectors converge and play the role of factor loadings. Hence only a principal component analysis is needed in empirical work.

An index of Inequality is constructed which decomposes into two components, corresponding to vertical and "horizontal" equity respectively.Horizontal equity Is defined in terms of changes in the ordering of a distribution.The proposed index is a function to two inequality aversion parameters.One empirical application is for comparison of a pre-tax distribution with a post-tax distribution, and an example of this is given for the distribution of incomes in the UK in 1977.There is a trade-off between "horizontal" and vertical equity, and for particular combinations of the inequality aversion parameters the original distribution.willbe preferred to the final distribution.The paper concludes with an application of the proposed index to a model of optimal taxation.

[In this paper we develop a rational expectations exchange-rate model which is capable of confronting explicitly agents' beliefs about a future switch in exogenous driving processes. In our set-up the agents know with certainty both the initial exogenous process and the new process to be adopted when the switch occurs. However, they do not know with certainty the timing of future switch as it depends on the path followed by the (stochastic) exchange rate. The model is discussed in terms of the British return to pre-war parity, in 1925. However, our results are applicable to a variety of situations where process switching depends on the motion of a key endogenous variable.]

We analyze equilibria in exchange economies following the approach taken by Borch and Wilson. We correct Wilson's main result by showing that linear contracts are sufficient but not necessary for the existence of syndicates under heterogeneous beliefs. We introduce the concept of the decomposability of syndicates and demonstrate that linear contracts are necessary only for arbitrarily decomposable syndicates. This implies that groups that form syndicates under an arbitrary set of beliefs must also employ linear contracts.

When estimating a single equation with an error generated by an autoregressive process of higher order than one using a sequence of likelihood ratio tests to determine the correct order, the asymptotic size of the tests will be biased because of multiple optima of the likelihood function. A new type is suggested similar to the Durbin test [2] which is not biased in this way. IN HIS ARTICLE on testing for serial correlation in the presence of lagged endogenous variables [2] Durbin proved a general theorem which gives a significance test shown to be generally asymptotically equivalent to a likelihood ratio test. This paper proposes a generalization which gives a test criterion that may be preferred to the existing test criteria insofar as it can be set up using a less arbitrary choice of the parameters to be re-estimated, and also has the advantage of being relatively simple to compute. It seems more appropriate than the general Durbin form of test for application to the dynamic specification problem discussed in the third section of this article.

This paper presents the necessary and sufficient conditions for determining the signs of the solution variables of a system of linear equations based only upon a knowledge of the signs of the coefficient matrix and the signs of the right hand side variables. This problem was initially formulated in economics due to the idea that the signs of an equation's derivatives might have a stronger empirical basis than that of a particular functional form. A new interest in qualitative problems has arisen in connection with the need to develop analytic measures in order to better manage the understanding and use of large, computer-based mathematical systems. The conditions for the qualitative determinancy of nonhomogeneous systems are developed in terms of a small number of necessary conditions which are jointly sufficient. Algorithmic approaches are given for testing a given system for qualitative determinancy. For nonhomogeneous systems algorithms are given for constructing all possible qualitatively determinate systems of a given size. For the homogeneous case conditions are also given for the qualitative invertibility of the (irreducible) coefficient matrix. These conditions are then related to the problem of partially qualitatively determinate systems and the signs in the qualitative inverse of a matrix.