Euler equation models represent an important class of macroeconomic systems. Our ongoing research [He, Y., Barnett, W.A., 2003. New phenomena identified in a stochastic dynamic macroeconometric model: A bifurcation perspective. Working Paper, University of Kansas] on the Leeper and Sims [Leeper, E., Sims, C., 1994. Toward a modern macro model usable for policy analysis. NBER Macroeconomics Annual, National Bureau of Economic Research, New York, pp. 81–117] Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model’s parameters are within a confidence region about the parameter estimates. Although known to engineers, singularity bifurcation has not previously been seen in the economics literature. Knowledge of the nature of singularity-induced bifurcations is likely to become important in understanding the dynamics of modern macroeconometric models. This paper explains singularity-induced bifurcation, its nature, and its identification and contrasts this class of bifurcations with the more common forms of bifurcation we have previously encountered within the parameter space of the Bergstrom and Wymer [Bergstrom, A.R., Wymer, C.R., 1976. A model of disequilibrium neoclassic growth and its application to the United Kingdom. In: Bergstrom, A.R. (Ed.), Statistical Inference in Continuous Time Economic Models, North-Holland, Amsterdam, pp. 267–327] continuous time macroeconometric model of the UK economy (see, e.g., [Barnett, W.A., He, Y., 1999. Stability analysis of continuous-time, macroeconometric systems. Studies in Nonlinear Dynamics and Econometrics 3, 169–188; Barnett, W.A., He, Y., 2002. Stabilization policy as bifurcation selection: Would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics 6, 713–747]).

Taken literally, the concept of “stabilization policy” implicitly assumes that the macroeconomy is unstable without imposition of a policy. Hence, selection of a “stabilization policy” can be viewed as selection of a policy to bifurcate the system from an unstable to a stable operating regime. The literature on dynamics of high-dimensional systems suggests that successful bifurcation selection is challenging. As an experiment to investigate this point of view, we use the continuous-time UK dynamic macroeconometric model. Under assumptions designed to be most favorable to stabilization policy, we find that policies that would produce successful bifurcation are very complicated. We also find that less complicated policies based upon reasonable economic intuition can be counterproductive, since such policies can contract the size of the stable subset of the parameter space. In fact, an economy that is dynamically stable without policy, but subject to stochastic shocks, could be bifurcated to instability with imposition of a poorly designed “stabilization” policy.

We estimate the generalized McFadden (generalized quadratic) production function by GMM for a manufacturing firm that uses risky monetary assets among its inputs and for a bank that produces risky monetary assets as outputs. We impose curvature globally and monotonicity at a point, as is the capability of the model. We find that monotonicity is violated at many data points away from the one point at which it is imposed. We conclude that the model's inability to impose monotonicity globally is a serious limitation, despite the ability to impose curvature globally.

In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. We compare two statistical index numbers—the Divisia monetary aggregate and the simple-sum monetary aggregate—with the exact rational expectations monetary aggregate, using actual data. Because we are not using simulated data, we estimate the parameters of the Euler equations, and thereby of the nested monetary aggregator function, using the generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors.

Some economists continue to insist that linearity is a good assumption for all economic time series, despite the fact that economic theory provides virtually no support for the assumption of linearity; see, e.g., Barnett and Chen (1986, 1988). The controversy is partly due to the fact that the currently available tests do not test for the existence of chaos or nonlinearity produced from within the structure of the economy. As recently pointed out by Day (1992), the tests have no way of determining the sources of the chaos or nonlinearity. In other words, even if the economy is totally linear and stable, the current tests, such as the Brock–Dechert–Scheinkman (Brock 1986), could still catch evidence of nonlinearity or even chaos in economic data if the economy is affected by a chaotic and unstable surrounding weather system. Therefore it is interesting if we can identify some sources of potential nonlinearity and instability within the economic system.

Franco Modigliani's contributions in economics and finance have transformed both fields. Although many other major contributions in those fields have come and gone, Modigliani's contributions seem to grow in importance with time. His famous 1944 article on liquidity preference has not only remained required reading for generations of Keynesian economists but has become part of the vocabulary of all economists. The implications of the life-cycle hypothesis of consumption and saving provided the primary motivation for the incorporation of finite lifetime models into macroeconomics and had a seminal role in the growth in macroeconomics of the overlapping generations approach to modeling of Allais, Samuelson, and Diamond. Modigliani and Miller's work on the cost of capital transformed corporate finance and deeply influenced subsequent research on investment, capital asset pricing, and recent research on derivatives. Modigliani received the Nobel Memorial Prize for Economics in 1985. In macroeconomic policy, Modigliani has remained influential on two continents. In the United States, he played a central role in the creation of a the Federal Reserve System's large-scale quarterly macroeconometric model, and he frequently participated in the semiannual meetings of academic consultants to the Board of Governors of the Federal Reserve System in Washington, D.C. His visibility in European policy matters is most evident in Italy, where nearly everyone seems to know him as a celebrity, from his frequent appearances in the media. In the rest of Europe, his visibility has been enhanced by his publication, with a group of distinguished European and American economists, of “An Economists' Manifesto on Unemployment in the European Union,” which was signed by a number of famous economists and endorsed by several others. This interview was conducted in two parts on different dates in two different locations, and later unified. The initial interview was conducted by Robert Solow at Modigliani's vacation home in Martha's Vineyard. Following the transcription of the tape from that interview, the rest of the interview was conducted by William Barnett in Modigliani's apartment on the top floor of a high-rise building overlooking the Charles River near Harvard University in Cambridge, Massachusetts. Those concluding parts of the interview in Cambridge continued for the two days of November 5–6, 1999 with breaks for lunch and for the excellent espresso coffee prepared by Modigliani in an elaborate machine that would be owned only by someone who takes fine coffee seriously. Although the impact that Modigliani has had on the economics and finance professions is clear to all members of those professions, only his students can understand the inspiration that he has provided to them. However, that may have been adequately reflected by Robert Shiller at Yale University in correspondence regarding this interview, when he referred to Modigliani as: “my hero.”

There has been increasing interest in continuous-time macroeconometric models. This research investigates stability of the Bergstrom, Nowman, and Wymer continuous-time model of the U.K. when system parameters change. This particularly well-regarded continuous-time macroeconometric model is chosen to assure the empirical and potential policy relevance of the results. Stability analysis is important with this model for understanding the dynamic properties of the system and for determining which parameters are the most important to those dynamic properties. The main objective of this paper is to determine the boundaries of parameters at which instability occurs. Two types of boundaries are found: the transcritical bifurcation boundary and the Hopf bifurcation boundary, corresponding to two different ways that instability occurs when parameter values cross the bifurcation boundary.The existence of the Hopf bifurcation boundary is particularly useful, since Hopf bifurcation may provide explanations for some cyclical phenomena in macroeconomy. Numerical algorithms are designed to locate the stability boundaries, which are displayed in three-dimensional diagrams. A notable and perhaps surprising fact is that both types of bifurcations can coexist with this well-regarded U.K. model-in the same neighborhood of the parameter space.

In this study it is shown that money velocity in a monetary equilibrium model is deterministically nonlinear when there are no exogenous uncertainties. Under some conditions, the asymptotic motion of money velocity is chaotic. When interest rates are stochastic and money and income growth are uncertain, the dynamics of money velocity are nonlinear and its coefficients are stochastic. We simulate the slope coefficient of the money velocity function and find that it is quite volatile. The Swamy and Tinsley (1980) random coefficient model is then estimated to compare the results with those from model simulation. It is found that the estimated stochastic slope coefficient has important similarity with the simulation results. The findings of this paper provide some useful information on the nature of the instability of money velocity.

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 non-chaotic 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 2000 observation case was large enough to support the use of asymptotic inference, and (3) the inclusion of a noisy chaotic case. But the computational burdens upon the participants in this competition were already pressing the limits that could reasonably be expected of those courageous enough to subject their tests to this professionally risky competition.

We investigate bifurcation phenomena in the Bergstrom-Nowman-Wymer (1992) continuous time macroeconometric model of the United Kingdom. Both transcritical and Hopf bifurcations are considered with this model within the model's region of plausible parameter settings. Hopf bifurcations are particularly useful since they may provide explanations for some cyclical phenomena in the macroeconomy. Numerical algorithms are designed to locate the bifurcation boundaries. To the best of our knowledge, this is the first work on numerical determination of bifurcation boundaries for large scale macroeconomic systems. A notable and perhaps surprising fact is that both types of bifurcations can coexist with this well-regarded UK model-in the same neighborhood of the parameter space. Effect of the usual fiscal policy control on bifurcations is also examined

This paper denies that the demand for money function is any more unstable than other demand functions and maintains that the controversies regarding unstable money demand are produce by poor methodology that is not shared by other areas of the field of economics, when investigating demand function properties.

Fellows of the Journal of Econometrics are invited to publish personal opinions regarding the field of econometrics in that journal. This paper is a statement of my personal opinion about the potential role of the World Wide Web in improving data quality and availability in economics. The paper also relates to current controversies regarding federal data quality and biases in index numbers produced by federal government agencies, as well as potential proposals for governmental reform in the areas of data production.

Interest has been growing in testing for nonlinearity and chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We apply five tests for nonlinearity or chaos to various monetary aggregate data series. We find that the inferences vary across tests for the same data, and within tests for varying sample sizes and various methods of aggregation of the data. Robustness of inferences in this area of research seems to be low and may account for the controversies surrounding empirical claims of nonlinearity and chaos in economics.

An alternative monetary-production model of financial firms is employed to investigate supply-side monetary aggregation. Financial firms are conceived to produce monetary services as outputs through financial intermediation. A new method for testing the existence of consistent monetary-output aggregates in financial firms' production technology is developed in terms of a multiproduct firm's variable profit function, and the method does not require homotheticity of the aggregator function. We use a generalized symmetric Barnett flexible functional form. That specification satisfies global curvature conditions and retains its flexibility under the null hypothesis of weak separability. Neither of those properties is possessed by other flexible functional forms.

Historically, microeconomics was the domain of scientific methodology in economics, while macroeconomics attacted less mathematically oriented economists. In recent years, the level of sophistication of macroeconomics has grown dramatically, and that field now attracts many of the most mathematically oriented economists. Nevertheless, the field's set of shared views (i.e. maintained hypotheses) has not grown. The purpose of the scientific method is to permit the maintained hypotheses within a field to grow by establishing a rigorous methodology for deductively deriving and empirically testing hypotheses. The field of macroeconomics has failed that test of scientific success during precisely the decades of most rapid growth in the use of scientific methodology. It is argued that the source of the paradox lies in the fact that the inroads of science into macroeconomics have been asymmetrical. Central to the definition and objectives of macroeconomics is dimension reduction and dynamics. Rigorous dimension reduction is impossible without formal aggregration, and complex dynamics is impossible without non-linearity. Yet applications of formal aggregation theory and non-linear dynamics to macroeconomics have progressed very slowly, at a time when scientific methodology in other areas of macroeconomics has advanced rapidly. This asymmetry explains the paradox.

Recently it has been shown that seminonparametric methods can be used to produced high-quality approximations to a firm's technology. Unlike the local approximations provided by the conventional class of ‘flexible functional forms’, seminonparametric methods generate global spans within large classes of functions. However, that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling. An exception is the asymptotically ideal model (AIM) generated from the Müntz-Szatz series expansion. Since every basis function in that expansion is within the neoclassical function space, a straightforward method exists for imposing neoclassical regularity, when all factors are substitutes. Since the relevant constraints are inequality restrictions, we implement the approach using Bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods. We further discuss the relevant extensions that would permit complementary factors, nonconstant returns to scale, and technological change.

We survey the recent advances in monetary aggregation theory as well as the earlier literature on the subject. We discuss the limitations in the current state of our knowledge about monetary aggregation and speculate about productive areas for future research.

It is well known that specification error within a model's equations can produce a remainder term consisting of higher-order terms. We find similarly that specification error from inexact aggregation over goods or over economic agents can produce within a model an additive remainder term; but it consists of higher-order moments of the distribution of component growth rates, for aggregation over goods, or it consists of higher-order moments of the distribution of income, for aggregation over consumers. We use this result to create diagnostic tests for aggregation error in causality testing, reduced form modeling, and consumer demand system modeling. We apply the tests to monetary data. We call our approach dispersion-dependency diagnostic testing (DDT), and we advocate application of DDT to all modeling and forecasting procedures in econometrics as an effective diagnostic treatment for aggregation error.

Separability assumptions on functional structure have received a great deal of attention from econometricians and economic theorists because (a) separability provides the fundamental linkage between aggregation over goods and the maximization principles in economic theory, (b) separability provides the theoretical basis for partitioning the economy's structure into sectors, and (c) 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.