Estimation of Continuous Time Models in Economics: an Overview

The dynamics of economic behaviour is often developed in theory as a continuous time system. Rigorous estimation and testing of such systems, and the analysis of some aspects of their properties, is of particular importance in distinguishing between competing hypotheses and the resulting models. The consequences for the international economy during the past eighteen months of failures in the financial sector, and particularly the banking sector, make it essential that the dynamics of financial and commodity markets and of macro-economic policy are well understood. The nonlinearity of the economic system means that it’s properties are heavily dependent on it’s parameter values. The estimators discussed here are tools to provide those parameter estimates.

Investment, Productivity and Employment in the Italian Economy

none3openTRAVAGLINI G.; E. Saltari; C. WymerTravaglini, Giuseppe; E., Saltari; C., Wyme

Science and Ideology in Economic, Political, and Social Thought

This paper has two sources: One is my own research in three broad areas: business cycles, economic measurement and social choice. In all of these fields I attempted to apply the basic precepts of the scientific method as it is understood in the natural sciences. I found that my effort at using natural science methods in economics was met with little understanding and often considerable hostility. I found economics to be driven less by common sense and empirical evidence, then by various ideologies that exhibited either a political or a methodological bias, or both. This brings me to the second source: Several books have appeared recently that describe in historical terms the ideological forces that have shaped either the direct areas in which I worked, or a broader background. These books taught me that the ideological forces in the social sciences are even stronger than I imagined on the basis of my own experiences. The scientific method is the antipode to ideology. I feel that the scientific work that I have done on specific, long standing and fundamental problems in economics and political science have given me additional insights into the destructive role of ideology beyond the history of thought orientation of the works I will be discussing

Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed

Rapidly measured indicators of recreational water quality and swimming-associated illness at marine beaches: a prospective cohort study

<p>Abstract</p> <p>Introduction</p> <p>In the United States and elsewhere, recreational water quality is monitored for fecal indicator bacteria to help prevent swimming-associated illnesses. Standard methods to measure these bacteria take at least 24 hours to obtain results. Molecular approaches such as quantitative polymerase chain reaction (qPCR) can estimate these bacteria faster, in under 3 hours. Previously, we demonstrated that measurements of the fecal indicator bacteria <it>Enterococcus </it>using qPCR were associated with gastrointestinal (GI) illness among swimmers at freshwater beaches. In this paper, we report on results from three marine beach sites.</p> <p>Methods</p> <p>We interviewed beach-goers and collected water samples at marine beaches affected by treated sewage discharges in Mississippi in 2005, and Rhode Island and Alabama in 2007. Ten to twelve days later, we obtained information about gastrointestinal, respiratory, eye, ear and skin symptoms by telephone. We tested water samples for fecal indicator organisms using qPCR and other methods.</p> <p>Results</p> <p>We enrolled 6,350 beach-goers. The occurrence of GI illness among swimmers was associated with a log₁₀-increase in exposure to qPCR-determined estimates of fecal indicator organisms in the genus <it>Enterococcus </it>(AOR = 2.6, 95% CI 1.3-5.1) and order <it>Bacteroidales </it>(AOR = 1.9, 95% CI 1.3-2.9). Estimates of organisms related to <it>Clostridium perfringens </it>and a subgroup of organisms in the genus <it>Bacteroides </it>were also determined by qPCR in 2007, as was F+ coliphage, but relationships between these indicators and illness were not statistically significant.</p> <p>Conclusions</p> <p>This study provides the first evidence of a relationship between gastrointestinal illness and estimates of fecal indicator organisms determined by qPCR at marine beaches.</p

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

STRUCTURAL NONLINEAR CONTINUOUS-TIME MODELS IN ECONOMETRICS

Economic theory indicates the need for nonlinear structuralmodels to study medium-term and long-run dynamic behavior of aneconomy. This paper argues that economic systems can be betterspecified and estimated using differential-equation rather thandifference-equation systems and briefly reviews the estimators ofcontinuous models. This approach of specifying structural models onthe basis of economic theory and institutional structure explicitlyand then testing the underlying hypothesis to verify the structuralform is contrasted with a general-to-specific approach ofsuccessively more restricted VARMAX processes. Previous analyses ofstability about the steady state or fixed point in phasespace are extended to more general attractors to allowan investigation of complexity in economicsystems. The critical dependence of some attractors, andparticularly strange attractors, on parameter valuesemphasizes the need for consistent, efficientestimation. A structural approachprovides a rigorous alternative to using single time series todetermine whether economic systems exhibit aperiodic or chaoticdynamical behavior.

APERIODIC DYNAMICS IN THE BERGSTROM/WYMER MODEL OF THE UNITED KINGDOM

Lyapunov exponents may be used to provide information on attractors of nonlinear models and, if strange, their aperiodic dynamics, in much the same way as eigenvalues of a linear model. An advantage of calculating these from an estimated model, rather than calculating the largest ones from a time series, is that economic theory is used to help distinguish between deterministic and stochastic behavior. Estimates of the Bergstrom/Wymer model of the United Kingdom, and of some other models of a similar form, were unstable in a classical sense, to some extent being caused by policy parameters. The Lyapunov exponents show that this model, and variants of it, have strange attractors in the neighborhood of the estimated parameter values and hence are stable but with aperiodic oscillations.

Endogenizing the ICT sector: a multisector approach

In this paper, we present a nonlinear model where the information and communication technology (ICT ) sector is endogenized. In the model, there are two intermediate goods: a traditional good produced by capital and labor and the ICT good produced by innovative capital and skilled labor. The final good is obtained combining the two intermediate goods. The model is specified and estimated as continuous-time general disequilibrium framework. Our main results are the following. We find that the elasticity of substitution of the aggregate sector has a value intermediate between that of the ICT sector and that of the traditional sector, indicating that the input complementarity is tighter in the former than in the latter. Moreover, in all the sectors elasticities are well below 1. As for the traditional sector, whose share is predominant in the production of the final good, the input complementarity helps explain most of the labor share decline of Italian economy as a consequence of the slowdown in the growth of capital intensity. In the ICT sector, technological progress, both in the form of capital augmenting and capital bias, showed a decline over the sample period with an obvious negative consequence on the global evolution of the technical progress. The results about the dynamics of the two intermediate sectors allow to interpret the “Italian paradox” of an industrial structure marked by an increasing weight of the traditional sector and the difficulties encountered by the Italian economy in exiting from its actual worst recession since the 1930s

A Macroeconomic Model of the United Kingdom (Un modèle macroéconomique du Royaume-Uni) (Modelo macroeconómico del Reino Unido)

The model that is specified and estimated in this study describes the dynamic behavior of major economic aggregates in the economy of the United Kingdom. In the real sector of the model, the markets for output and labor services are linked by a production function that both constrains the long-run relation between domestic output and inputs of labor and capital and influences the short-run behavior of wages, prices, and investment in fixed capital. A detailed financial sector that specifies the determinants of domestic money balances, advances, Eurocurrency deposits, and government debt is also included. A basic feature of the model is that it allows government monetary and fiscal policies (taxes, government spending, open market operations, and Bank rate) to respond to changes in target variables, such as income, the balance of payments, and employment. The budget constraints of the government sector are incorporated explicitly, so that the government borrowing requirement is financed by changes in the volume of base money and government securities. Thus, the model is well-suited to detailed policy analysis. The model is also designed both to capture the short-run adjustment processes of the U. K. economy and to have steady-state properties consistent with macroeconomic theory and with empirical observation over periods longer than the sample used for estimation. Thus, the steady-state solution of the model and the implications for both estimation and policy analysis are considered in detail. The model is estimated subject to the overidentifying restrictions of the theoretical structure. The parameter estimates and other statistics, including insample forecasts, indicate that the model is a plausible representation of the U. K. economy. A general analysis of the dynamic properties of the model is provided and is integrated with a discussion of the effects of the authorities' policy reactions on the stability of the system. /// Le modèle qui est spécifié et estimé dans la présente étude décrit le comportement dynamique des principaux agrégats économiques dans l'économie du Royaume-Uni. Dans le secteur réel du modèle, les marchés pour la production finale et les services de la main-d'Å“uvre sont liés par une fonction de production qui exerce une contrainte sur la relation à long terme entre la production intérieure et les inputs main-d'Å“uvre et capital et influence le comportement à court terme des salaires, des prix et de la formation de capital fixe. Les auteurs ont également inclus un secteur financier détaillé qui spécifie les déterminants des encaisses monétaires intérieures, du crédit au secteur privé, des dépôts en euro-monnaies et du volume des emprunts publics. L'une des caractéristiques essentielles du modèle est qu'il permet aux politiques monétaire et budgétaire de l'Etat (impôts, dépenses publiques, opérations d'open market et taux d'escompte) de réagir aux variations de variables-objectifs telles que le revenu, la balance des paiements et l'emploi. Les contraintes budgétaires du secteur public sont explicitement incorporées, de sorte que les besoins de financement de l'Etat sont couverts par la variation du volume de la base monétaire et des valeurs d'Etat. Le modèle se prête donc bien à une étude détaillée de la politique économique. Il est également conçu pour à la fois appréhender les processus d'ajustement à court terme de l'économie du Royaume-Uni et avoir des propriétés de croissance équilibrée compatibles avec la théorie macroéconomique et l'observation empirique sur des périodes plus longues que l'échantillon utilisé pour l'estimation. Ainsi, la solution de croissance équilibrée du modèle et les implications qui en découlent tant pour l'estimation que pour l'analyse de la politique économique sont examinées en détail. Le modèle est estimé sous réserve des restrictions suridentificatrices imposées par la structure théorique. Les estimations des paramètres et autres statistiques, y compris les prévisions effectuées dans l'échantillon, indiquent que le modèle constitue une représentation plausible de l'économie du Royaume-Uni. La présente étude comporte une analyse générale des propriétés dynamiques du modèle, qui est intégrée dans le cadre d'une discussion de l'impact des réactions des mesures économiques adoptées par les autorités sur la stabilité du système. /// El modelo especificado y estimado en este estudio describe el comportamiento dinámico de importantes agregados económicos del Reino Unido. En el sector real del modelo, los mercados del producto y de los servicios laborales están vinculados por una función de producción que limita la relación a largo plazo entre el producto y los insumos internos del trabajo y el capital e influye en el comportamiento a corto plazo de los salarios, los precios y la inversión en capital fijo. Se incluye también un sector financiero detallado en el cual se especifican las determinantes de la liquidez monetaria interna, créditos bancarios, depósitos en euromonedas y deuda del gobierno. Una característica básica del modelo es que permite que las políticas monetarias y fiscales del gobierno (impuestos, gasto público, operaciones de mercado abierto y tasa de descuento) respondan ante los cambios de variables metas tales como el ingreso, la balanza de pagos y el empleo. Se incorporan explícitamente las limitaciones presupuestarias del sector gubernamental, de modo que la necesidad de endeudamiento del gobierno se financia mediante modificaciones del volumen de la base monetaria y las obligaciones del gobierno. Por lo tanto, el modelo se presta muy bien para el análisis de política detallado. El modelo se ha concebido de tal manera que, además de captar los procesos de ajuste a corto plazo de la economía del Reino Unido, sus características respecto al estado estacionario ("steady state") son compatibles con la teoría macroeconómica y con la observación empírica durante períodos más largos que los de la muestra usada para fines de estimación. De este modo, se consideran en detalle la solución de marco estable del modelo y las repercusiones desde el punto de vista tanto de la estimación como del análisis de política. Se ha estimado el modelo con sujeción a restrictiones que superidentifican la estructura teórica. Las estimaciones de los parámetros y otras estadísticas, inclusive los pronósticos obtenidos en la muestra, indican que el modelo constituye una representación plausible de la economía del Reino Unido. Se presenta un análisis general de las propiedades dinámicas del modelo y dicho análisis se integra en el examen de los efectos que tienen en la estabilidad del sistema las decisiones de las autoridades en materia de política.