Juan Francisco Rubio-Ramirez

Risk Matters: The Real Effects of Volatility Shocks

This paper shows how changes in the volatility of the real interest rate at which small open emerging economies borrow have a quantitatively important effect on real variables like output, consumption, investment, and hours worked. To motivate our investigation, we document the strong evidence of time-varying volatility in the real interest rates faced by a sample of four emerging small open economies: Argentina, Ecuador, Venezuela, and Brazil. We postulate a stochastic volatility process for real interest rates using T-bill rates and country spreads and estimate it with the help of the Particle filter and Bayesian methods. Then, we feed the estimated stochastic volatility process for real interest rates in an otherwise standard small open economy business cycle model. We calibrate eight versions of our model to match basic aggregate observations, two versions for each of the four countries in our sample. We find that an increase in real interest rate volatility triggers a fall in output, consumption, investment, and hours worked, and a notable change in the current account of the economy.

Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.

Fiscal Volatility Shocks and Economic Activity

We study the effects of changes in uncertainty about future fiscal policy on aggregate economic activity. Fiscal deficits and public debt have risen sharply in the wake of the financial crisis. While these developments make fiscal consolidation inevitable, there is considerable uncertainty about the policy mix and timing of such budgetary adjustment. To evaluate the consequences of this increased uncertainty, we first estimate tax and spending processes for the U.S. that allow for time-varying volatility. We then feed these processes into an otherwise standard New Keynesian business cycle model calibrated to the U.S. economy. We find that fiscal volatility shocks have an adverse effect on economic activity that is comparable to the effects of a 25-basis-point innovation in the federal funds rate.

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 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. We report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, although relatively small in absolute values, have important effects on the moments of the model. We conclude that the nonlinear filter is a superior procedure for taking models to the data. Copyright

Nonlinear Adventures at the Zero Lower Bound

Motivated by the recent experience of the U.S. and the Eurozone, we describe the quantitative properties of a New Keynesian model with a zero lower bound (ZLB) on nominal interest rates, explicitly accounting for the nonlinearities that the bound brings. Besides showing how such a model can be efficiently computed, we find that the behavior of the economy is substantially affected by the presence of the ZLB. In particular, we document 1) the unconditional and conditional probabilities of hitting the ZLB; 2) the unconditional and conditional probabilty distributions of the duration of a spell at the ZLB; 3) the responses of output to government expenditure shocks at the ZLB, 4) the distribution of shocks that send the economy to the ZLB; and 5) the distribution of shocks that keep the economy at the ZLB.

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 function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

Markov-Switching Structural Vector Autoregressions: Theory and Application

This paper develops a new and easily implementable necessary and sufficient condition for the exact identification of a Markov-switching structural vector autoregression (SVAR) model. The theorem applies to models with both linear and some nonlinear restrictions on the structural parameters. We also derive efficient MCMC algorithms to implement sign and long-run restrictions in Markov-switching SVARs. Using our methods, four well-known identification schemes are used to study whether monetary policy has changed in the euro area since the introduction of the European Monetary Union. We find that models restricted to only time-varying shock variances dominate the other models. We find a persistent post-1993 regime that is associated with low volatility of shocks to output, prices, and interest rates. Finally, the output effects of monetary policy shocks are small and uncertain across regimes and models. These results are robust to the four identification schemes studied in this paper.

Cointegrated TFP processes and international business cycles

A puzzle in international macroeconomics is that observed real exchange rates are highly volatile. Standard international real business cycle (IRBC) models cannot reproduce this fact. We show that total factor productivity processes for the United States and the rest of the world are characterized by a vector error correction model (VECM) and that adding cointegrated technology shocks to the standard IRBC model helps explaining the observed high real exchange rate volatility. Also, we show that the observed increase of the real exchange rate volatility with respect to output in the past twenty years can be explained by changes in the parameter of the VECM.

Fortune or Virtue: Time-Variant Volatilities Versus Parameter Drifting in U.S. Data

This paper compares the role of stochastic volatility versus changes in monetary policy rules in accounting for the time-varying volatility of U.S. aggregate data. Of special interest to us is understanding the sources of the great moderation of business cycle fluctuations that the U.S. economy experienced between 1984 and 2007. To explore this issue, we build a medium-scale dynamic stochastic general equilibrium (DSGE) model with both stochastic volatility and parameter drifting in the Taylor rule and we estimate it non-linearly using U.S. data and Bayesian methods. Methodologically, we show how to confront such a rich model with the data by exploiting the structure of the high-order approximation to the decision rules that characterize the equilibrium of the economy. Our main empirical findings are: 1) even after controlling for stochastic volatility (and there is a fair amount of it), there is overwhelming evidence of changes in monetary policy during the analyzed period; 2) however, these changes in monetary policy mattered little for the great moderation; 3) most of the great performance of the U.S. economy during the 1990s was a result of good shocks; and 4) the response of monetary policy to inflation under Burns, Miller, and Greenspan was similar, while it was much higher under Volcker.

Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors

This paper shows how to build algorithms that use graphics processing units (GPUs) installed in most modern computers to solve dynamic equilibrium models in economics. In particular, we rely on the compute unified device architecture (CUDA) of NVIDIA GPUs. We illustrate the power of the approach by solving a simple real business cycle model with value function iteration. We document improvements in speed of around 200 times and suggest that even further gains are likely.