William A. Barnett

The user cost of money

Abstract Prior imputations of a price to monetary asset services have not been basedupon an explicit assumption structure or an explicit model. We rigorously derive a unique user cost formula for that price; our results are consistent with Donovans (1977) formula.

Nonparametric and Semiparametric Methods in Econometrics and Statistics

This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

The Global Properties of the Miniflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms

Caves and Christensen [16] have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional forms. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models. We find that the new minflex Laurent model generally has the largest regular regions of the three fiexible functional forms. In addition, the regular region of the minflex Laurent model is found to expand as real income increases. As a result, that model is particularly well suited for use with time series data, which typically is characterized by positive long term growth trends in real income. In such applications, all recent data and future forecasts can be expected to lie within the regular region of the minflex Laurent model. Although it is possible for some of the earliest data to fall outside that regular region, the models regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets. The regular region of each of three models moves when the models parameters are changed. With the generalized Leontief or translog model, the regular regions shape, location, and size are unpredictable without prior knowledge of the models parameters. With either of those two models, the intersection of the models regular regions, as the parameters are changed, is contained within a very small neighborhood of the one point at which we require the model to be regular. With the minflex Laurent model, the primary properties of the regular regions are invariant to the values of the parameters, and the intersection of the displayed regular regions is a very large unbounded set. The width of that intersection increases without limit as real income increases.

New Indices of Money Supply and the Flexible Laurent Demand System

The article begins by surveying the existing results on the new Divisia monetary aggregates. Charts display the differences in behavior between the Divisia aggregates and the Federal Reserves official simple-sum monetary aggregates. The article then compares system-wide fit for the simple-sum and Divisia monetary aggregates when used as data in the joint estimation of a system of demand equations. The demand system is derived from a new Laurent expansion approximation to the reciprocal indirect utility function. The Laurent expansion provides a better-behaved remainder term than that of the more commonly used Taylor series. The results favor the Divisia aggregates.

The New Divisia Monetary Aggregates

Barnetts Divisia monetary aggregates were derived to be elements of Diewerts class of superlative quantity index numbers. Relative to aggregation theory, Barnetts resulting monetary aggregates are strictly preferable to the official sum monetary aggregates, since the component monetary assets are not perfect substitutes. Formal empirical tests based on the relevant aggregation-theoretic criteria have likewise uniformly favored the Divisia monetary aggregates. The current article compares the Divisia with the sum monetary aggregates relative to numerous conventional policy-relevant criteria. The Divisia monetary aggregates, especially at high levels of aggregation, usually perform best in these tests.

Martingales, nonlinearity, and chaos

In this paper we provide a review of the literature with respect to the efficient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that have arisen about the available tests and results, and raise the issue of whether dynamical systems theory is practical in finance.

Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity

The contents of this volume comprise the proceedings of the International Symposia in Economic Theory and Econometrics conference held in 1987 at the IC^T2 (Innovation, Creativity, and Capital) Institute at the University of Texas at Austin. The essays present fundamental new research on the analysis of complicated outcomes in relatively simple macroeconomic models. The book covers econometric modelling and time series analysis techniques in five parts. Part I focuses on sunspot equilibria, the study of uncertainty generated by nonstochastic economic models. Part II examines the more traditional examples of deterministic chaos: bubbles, instability, and hyperinflation. Part III contains the most current literature dealing with empirical tests for chaos and strange attractors. Part IV deals with chaos and informational complexity. Part V, Nonlinear Econometric Modelling, includes tests for and applications of nonlinearity.

A single-blind controlled competition among tests for nonlinearity and chaos

Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.

The Optimal Level of Monetary Aggregation

IN THIS PAPER, I have three objectives: (1) to describe the aggregation theoretic procedure for selecting the optimal monetary aggregateS (2) to survey the available empirical evidence for information on the optimal aggregateS and (3) to describe the procedures that should be followed to complete a redefinition of the monetary aggregates. Although all of the Federal Reserve Boards current official aggregates are rejected as targets, some newer aggregates are found to be substantially preferable to the official aggregates. The boards staff recently completed the official redefinition of its monetary aggregates in a manner largely unrelated to aggregation and index number theory. My own research in recent years has sought to remedy that shortcoming. Except for monetary aggregates, most of the data provided by governmental agencies are constructed in accordance with aggregation and index number theory. Since aggregation theory can be applied to monetary aggregation, 1 I constructed new monetary aggregates that are consistent with the economic theory.2 Recently the empiri-

A Monte Carlo Study of Tests of Blockwise Weak Separability

Separability assumptions on functional structure have received a great deal of attention from econometricians and economic theorists because (1) separability provides the fundamental linkage between aggregation over goods and the maximization principles in economic theory, (2) separability provides the theoretical basis for partitioning the economys structure into sectors and (3) separability provides a theoretical hypothesis, which can produce parameter restrictions, permitting great simplification in estimation of large demand systems. The power of the various available tests for separability has never been determined, however. We conduct Monte Carlo studies to examine the capability of currently available methods to provide correct inferences about separability.