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Working Paper
Computing DSGE models with recursive preferences and stochastic volatility
This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989 and 1991) and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value ...
Working Paper
A, B, C’s, (and D’s) for understanding VARs
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state-space system. An associated state space system (A, K, C, S) determines a vector autoregression (VAR) for observables available to an econometrician. We review circumstances in which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there ...
Working Paper
Estimating nonlinear dynamic equilibrium economies: a likelihood approach
This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. The authors develop a sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. The authors show consistency of the estimate and its good performance in finite simulations. This new algorithm is important because the existing ...
Working Paper
Search Complementarities, Aggregate Fluctuations, and Fiscal Policy
We develop a quantitative business cycle model with search complementarities in the inter-firm matching process that entails a multiplicity of equilibria. An active equilibrium with strong joint venture formation, large output, and low unemployment coexists with a passive equilibrium with low joint venture formation, low output, and high unemployment. {{p}} Changes in fundamentals move the system between the two equilibria, generating large and persistent business cycle fluctuations. The volatility of shocks is important for the selection and duration of each equilibrium. Sufficiently adverse ...
Working Paper
Estimating dynamic equilibrium economies: linear versus nonlinear likelihood
This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter proposed by Fernndez-Villaverde and Rubio-Ramrez (2004) and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. The authors report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a ...
Working Paper
Some results on the solution of the neoclassical growth model
This paper presents some new results on the solution of the stochastic neoclassical growth model with leisure. We use the method of Judd (2003) to explore how to change variables in the computed policy functions that characterize the behavior of the economy. We find a simple closed-form relation between the parameters of the linear and the loglinear solution of the model. We extend this approach to a general class of changes of variables and show how to find the optimal transformation. We thus reduce the average absolute Euler equation errors of the solution of the model by a factor of three. ...
Working Paper
Comparing solution methods for dynamic equilibrium economies
This paper compares solution methods for dynamic equilibrium economies. The authors compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. The authors document the performance of the methods in terms of computing time, implementation complexity and accuracy and they present some conclusions about their preferred approaches based on the reported evidence.
Working Paper
Comparing dynamic equilibrium economies to data
This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, the authors show that Bayesian methods have a classical interpretation: asymptotically the parameter point estimates converge to their pseudotrue values, and the best model under the Kullback-Leibler will have the highest posterior probability. Second, they illustrate the strong small sample behavior of the approach using a well-known application: the U.S. cattle cycle. ...
Working Paper
On the solution of the growth model with investment-specific technological change
Recent work by Greenwood, Hercowitz, and Krusell (1997 and 2000) and Fisher (2003) has emphasized the importance of investment-specific technological change as a main driving force behind long-run growth and the business cycle. This paper shows how the growth model with investment-specific technological change has a closed-form solution if capital fully depreciates. This solution furthers our understanding of the model, and it constitutes a useful benchmark to check the accuracy of numerical procedures to solve dynamic macroeconomic models in cases with several state variables.
Working Paper
Convergence properties of the likelihood of computed dynamic models
This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, economists approximate the policy functions of the agents in the model with numerical methods. But this implies that, instead of the exact likelihood function, the researcher can evaluate only an approximated likelihood associated with the approximated policy function. What are the consequences for inference of the use of approximated likelihoods? First, we show that as the approximated policy function converges to the exact policy, the approximated likelihood also ...