George M. Lady

A comparison of petroleum futures versus spot prices as predictors of prices in the future

Abstract Even though studies have indicated that the futures market leads the spot market in price discovery, this paper hypothesizes that the ‘predictive’ significance of each should be the same. A number of different statistical tests are presented to test this hypothesis. When deseasonalized data is employed the predictive significance of each series is found to be the same, but when actual prices are employed, futures prices did correctly anticipate the observed seasonal pattern.

Qualitatively invertible matrices

Abstract Our purpose is to describe the properties of the class of n × n matrices such that some or all of the signs of the nonzero elements of the inverse matrix can be determined based only upon the knowledge of the signs of the matrix being inverted. Applications of such matrices can be found in the study of the testibility of economic theory, the stability of economic systems and the general ‘quality’ of solutions to large computer models.

Topics in nonparametric comparative statics and stability

This paper presents the analysis of the Jacobian matrix of a small, macroeconomic model to determine the robustness of the models comparative statics. The values of the models coefficients are assessed with respect to seven alternative estimation strategies such as ordinary least squares or two-stage least squares. For each alternative version, the invertibility and stability of the Jacobian matrix is studied. The model is robust to the degree that these characteristics are shared by any matrix with the same sign pattern or other similar nonparametric conditions on its entries. One way to address the relative success of the different estimation strategies is through the robustness of the comparative statics of the resulting model.

Qualitative comparative statics and audits of model performance

Abstract It is often difficult to determine if large, computer based models actually conform to the mathematical descriptions given in their documentation. One way to study this problem is through a sensitivity, or comparative statics, analysis of the model. At issue is the degree to which characteristics of the Jacobian matrix associated with a solution to the model can be shown to imply characteristics of the inverse Jacobian matrix. Any necessary characteristics of the inverse Jacobian can be tested for via comparative statics. Sign nonsingularity of the Jacobian provides an opportunity to audit a models mathematical documentation through a comparative statics analysis. Prototype software was developed that tested for sign nonsingularity and applied to the Jacobian matrix corresponding to the U.S. Department of Energys Oil Market Simulation Model. It was found that the signs of all of the elements of the inverse Jacobian matrix could be found. This

Robust economic models

Abstract Economic models are robust to the degree to which an analysis of their comparative statics can be made without a full quantification of the models embodied interrelationships. This paper surveys the use of signed directed graphs in conducting nonquantitative comparative static analyses. The graph-theoretic techniques are extended to enable the use of additional, but not fully quantitative, information in signing the inverse Jacobian matrix and assessing stability.

ON ORGANIZING ANALYSIS

Publisher Summary This chapter discusses the proceedings of a symposium on computer-assisted analysis and model simplification held at the University of Colorado (Boulder). It describes the relationship between the inventory load carried by the submarine and its ability to perform mission assignments despite part failures. If a model of an entity refers to an explicit set of mathematical and logical statements, then the structure of the entity can be termed as the meta-model. Computer-assisted analysis, both in stimulating an identification of the rigorous correspondence between meta-model and model statements and in assisting in the actual comparison of models and meta-models, provides a direct means of approaching the important issue of the empirical bases for models developed in a nonexperimental environment. An important ramification of the confrontation of model/meta-model correspondences through computer-assisted analysis, in addition to helping build and audit models, is the enhanced understanding of models and model results.

Detecting stable matrices

Stable matrices are related to the values of their entries by the concept of an all negative quasi-dominant diagonal. Stable matrices are related to the signs of their entries by the signs of cycles in their corresponding signed directed graphs. This paper establishes relationships between stable matrices and conditions on the values of cycles. For some cases the conditions on the values of cycles are satisfied if and only if the matrix has a quasi-dominant diagonal.

Nearly sign-nonsingular matrices

Abstract A real matrix A is nearly sign-nonsingular if every term in the expansion of det A but one has the same sign. We show such matrices can be put into a normal form in which all diagonal entries are negative, all other nonzero entries are positive, and the directed graph of the matrix is intercyclic. With the help of recent results of Metzlar, McCuaig, and Thomassen on intercyclic digraphs, we are able to separate the nearly sign-nonsingular matrices into five classes and to characterize each of these classes. We also obtain two results showing where real matrices having intercyclic digraphs can or cannot be signed in such a way as to belong both to the class of sign-nonsingular matrices and the class of nearly sign-nonsingular matrices.

On measuring the effects of higher energy prices

Abstract The dramatic increases in world petroleum prices in the 1970s have been recognized as stimulating significant adverse economic consequences. Several simple partial equilibrium models have been constructed to analyse a portion of the expected consequences and some complex large-scale general equilibrium models have attempted the complete analysis. A simple and small general equilibrium model is developed and presented here that allows one to simply investigate and explain the effects of higher energy prices. The model is calibrated to the US experience over 1973–1979.

Econometric analysis of the 1974/75 decline in petroleum consumption in the USA: Some policy implications

Abstract A statistical estimate of the factors causing a reduction in petroleum consumption in 1974 and 1975 is presented on a factor by factor basis. It is shown that higher real prices accounted for the largest reduction in the 1974 decline while reduced macroeconomic activity directly accounted for the largest reduction in the 1975 decline. Weather and all other factors are shown to have had smaller roles in explaining reductions in those years. Such an analysis is useful in evaluating the potential of various policy actions to reduce petroleum consumption and imports.