A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends

Bergstrom, A. R.; Nowman, K. Ben

doi:10.1017/cbo9780511664687

Cited by 36 publications

(42 citation statements)

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“…Interest rate equations in the form of second-order stochastic differential equations are not without precedent. A CARMA(2, 0) specification (in effect) was used in the continuous time macroeconometric model of the United Kingdom by Bergstrom and Nowman (2007) while Andresen, Benth, Koekebakker and Zakamulin (2014) have more recently developed more general CARMA specifications.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

The exact discretisation of CARMA models with applications in finance

Thornton

Chambers

2016

Journal of Empirical Finance

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The problem of estimating a continuous time model using discretely observed data is common in empirical finance. This paper uses recently developed methods of deriving the exact discrete representation for a continuous time ARMA (autoregressive moving average) system of order p, q to consider three popular models in finance. Our results for two benchmark term structure models show that higher order ARMA processes provide a significantly better fit than standard Ornstein-Uhlenbeck processes. We then explore present value models linking stock prices and dividends in the presence of cointegration. Our methods enable us to take account of the fact that the two variables are observed in fundamentally different ways by explicitly modelling the data as mixed stock-flow type, which we then compare with the (more common, but incorrect) treatment of dividends as a stock variable.

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Section: Accepted Manuscriptmentioning

confidence: 99%

The exact discretisation of CARMA models with applications in finance

Thornton

Chambers

2016

Journal of Empirical Finance

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“…The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy's data, and is clearly policy relevant. See Bergstrom and Wymer (1976), Bergstrom (1996), Bergstrom, Nowman, and Wandasiewicz (1994), Bergstrom, Nowman, and Wymer (1992), and Bergstrom and Nowman (2006). Barnett and He found that bifurcation boundaries cross confidence regions of parameter estimates in that model, such that both stability and instability are possible within the confidence regions.…”

Section: The Historymentioning

confidence: 99%

“…As parameters change within that neighborhood, one eigenvalue of the linearized part of the model can move quickly from finite to infinite and back again to finite. A large stable eigenvalue characterizes the case in which some variables can respond rapidly to changes of other variables, while a large unstable 2 Among those models that have direct relevance to this research are the high-dimensional continuoustime macroeconometric models of Bergstrom, Nowman and Wymer (1992), Bergstrom, Nowman, and Wandasiewicz (1994), Bergstrom and Wymer (1976), Bergstrom and Nowman (2006), Grandmont (1998), Leeper and Sims (1994), Powell and Murphy (1997) and Kim (2000). Surveys of relevant macroeconomic models are available in Bergstrom (1996) and in several textbooks such as Gandolfo (1996) and Medio (1992).…”

Section: The Leeper and Sims Modelmentioning

confidence: 99%

Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right

Barnett

2010

Economic Modelling

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Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between.But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002 investigated a Keynesian structural model, and found results supporting Grandmont's conclusions within the parameter space of the BergstromWymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy's data, and is clearly policy relevant. In addition, results by Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models.Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the pathbreaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont's views.Beginning with Grandmont's findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters.

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Section: The Historymentioning

confidence: 99%

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

Barnett

Duzhak

2008

Physica A: Statistical Mechanics and its Applications

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Grandmont (1985) found that the parameter space of the most classical dynamic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. The econometric implications of Grandmont's findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences.But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002 investigated a Keynesian structural model, and found results supporting Grandmont's conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That highly regarded, prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy's data, and is clearly policy relevant.Criticism of Keynesian structural models by the Lucas critique have motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, Barnett and He (2006) chose to continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations macroeconometric models: the Leeper and Sims (1994) model. The results further confirm Grandmont's views.Even more recently, interest in policy in some circles has moved to New Keynesian models. As a result, in this paper we explore bifurcation within the class of New Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Empirical implementation will be the subject of a future paper, in which we shall solve numerically for the location and properties of the bifurcation boundaries and their dependency upon policy-rule parameter settings. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider. We provide the proofs of those propositions in this paper. One surprising result from these proofs is the finding that a common setting of a parameter in the future-looking New-Keynesian model can put the model directly onto a Hopf bifurcation boundary.Beginning with Grandmont's findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesia...

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A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends

Cited by 36 publications

References 0 publications

The exact discretisation of CARMA models with applications in finance

The exact discretisation of CARMA models with applications in finance

Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

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