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Formulating and estimating continuous time rational expectations models
This paper proposes a method for estimating the parameters of continuous time, stochastic rational expectations models from discrete time observations. The method is important since various heuristic procedures for deducing the implications for discrete time data of continuous time models, such as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. Our proposal is to express the restrictions imposed by the rational expectations model on the continuous time process generating the observable variables. Then the likelihood ...
Report
Rational expectations models and the aliasing phenomenon
This paper shows how the cross-equation restrictions delivered by the hypothesis of rational expectations can serve to solve the aliasing identification problem. It is shown how the rational expectations restrictions uniquely identify the parameters of a continuous time model from statistics of discrete time models.
Report
The dimensionality of the aliasing problem in models with rational spectral densities
This paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data. It analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models. It focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of the time series data.
Report
On the mechanics of forming and estimating dynamic linear economies
This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.
Report
Mechanics of forming and estimating dynamic linear economies
This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman's (1994) model of cattle cycles.
Working Paper
Examining macroeconomic models through the lens of asset pricing
Dynamic stochastic equilibrium models of the macro economy are designed to match the macro time series including impulse response functions. Since these models aim to be structural, they also have implications for asset pricing. To assess these implications, we explore asset pricing counterparts to impulse response functions. We use the resulting dynamic value decomposition (DVD) methods to quantify the exposures of macroeconomic cash flows to shocks over alternative investment horizons and the corresponding prices or compensations that investors must receive because of the exposure to such ...
Working Paper
Formulating and estimating dynamic linear rational expectations models
This paper describes methods for conveniently formulating and estimating dynamic linear econometric models under the hypothesis of rational expectations. An econometrically convenient formula for the cross-equation rational expectations restrictions is derived. Models of error terms and the role of the concept of Granger causality in formulating rational expectations models are both discussed. Tests of hypothesis of strict econometric exogeneity along the lines of Sim?s are compared with a test that is related to Wu?s.
Discussion Paper
Implications of security market data for models of dynamic economies
We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. Our approach is (i) nonparametric and applies to a rich class of models of dynamic economies; (ii) characterizes the duality between the mean-standard deviation frontier for IMRSs and the familiar mean-standard deviation frontier for asset returns; and (iii) exploits the restriction that IMRSs are positive random variables. The region provides a convenient summary of the sense in which asset market data are anomalous ...