Risk premia in general equilibrium

Schrimpf

2022

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This paper shows that the consumption‐based capital asset pricing model (C‐CAPM) with low‐probability disaster risk rationalizes pricing errors. We find that implausible estimates of risk aversion and time preference are not puzzling if market participants expect a future catastrophic change in fundamentals, which just happens not to occur in the sample (a “peso problem”). A bias in structural parameter estimates emerges as a result of pricing errors in quiet times. While the bias essentially removes the pricing error in the simple models when risk‐free rates are constant, time‐variation may also generate large and persistent estimated pricing errors in simulated data. We also show analytically how the problem of biased estimates can be avoided in empirical research by resolving the misspecification in moment conditions.

R P = γ {\overset{σ}{true}}^{2} + e^{- γ \overset{ν}{true}} true2.4ex2.4ex(1 - e^{\overset{ν}{true}} true2.4ex2.4ex) λ = γ {\overset{σ}{true}}^{2} + \log true2.4ex2.4ex(true2.4ex2.4ex(1 + e_{R}^{c} true2.4ex2.4ex) false/ true2.4ex2.4ex(1 + e_{R}^{f} true2.4ex2.4ex) true2.4ex2.4ex) .

Hence, in the endowment economy, the ratio of pricing errors in (19) measures the implicit risk premium RP related to the disaster risk (cf. Posch (2011)).…”

Section: Resultsmentioning

confidence: 99%

Peso problems in the estimation of the C‐CAPM

Parra-Alvarez

Schrimpf

2022

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Estimating dynamic equilibrium models using mixed frequency macro and financial data

Christensen

Journal of Econometrics

Wel

2016

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency, along with macro series at standard lower frequency. Our formulation of the macro-finance model in continuous-time conveniently accounts for the difference in observation frequency. We suggest the use of martingale estimating functions (MEF) to infer the structural parameters of the model directly through a nonlinear optimization scheme. This method is compared to regression-based methods and the general method of moments (GMM). We illustrate our approaches by estimating the AK-Vasicek model with mean-reverting interest rates. We provide Monte Carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of U.S. macro and financial data. Terms of use: Documents inJEL-Code: C130, E320, O400.

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Journal of Economic Dynamics and Control

Trimborn

2013

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households. Terms of use: Documents inJEL-Code: C630, E210, O410.