Knowledge that Transforms

This article is devoted to computable techniques for solving comparative static problems when only the sign of the partial derivatives of the model is considered. We first show how to extract unambiguously signed multipliers, or more generally qualitatively linked multipliers. This information then helps to reduce the size of the original system by means of a qualitative aggregation principle which we establish. As to the computation of solutions, a branch-and-bound algorithm is presented which considerably increases the efficiency of the Samuelson-Lancaster elimination principle. Finally we derive an efficient algorithm to check for signed determinants. The techniques are then applied to the analysis of an actual 20 equation model.

During the recent years, there is substantial interest in the econometric models with qualitative and censored dependent variables. The important contributions on these topics by Amemiya [1973J, McFadden [1973J and Heckman [1974J among others stimulate the recent

Edlefsen [3] has shown that a phenomenon of great similarity to the strong LeChatelier principle can be established when altering the feasible set of an optimizing agent by suitably replacing existing constraints rather than adding new ones. Here it was demonstrated that essentially the same phenomenon occurs when altering the objective function in a systematic manner rather than the.feasible set. The result obtained is general enough to allow a replication of Edlefsen's analysis of a household choosing between quantity and quality when facing hedonic prices, and served here furthermore in an application to the theory of the firm where it was demonstrated that a systematic relationship exists between the intensity of the reactions of a producer to changes in a conjugate parameter and the conditions prevailing in his markets.

Institutional and Behavioral Economics, Labor and Human Capital

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.

The effects of minimum wage legislation on the employment and wage rates of youth are estimated using a new statistical approach. We find that without the minimum, not only would the percent of out-of-school youth who are employed be 4 to 6 percent higher than it is, but also that these youth would earn more.

When is the Pareto optimal amount of public goods independent of income distribution? Subject to some regularity conditions, the answer is when preferences of every individual i can be represented by a utility function of the form U(X_i,Y)=A(Y)X_i+B_i(Y) where X_i is i's consumption of private goods and Y is the amount of public goods.