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My research interest are in the formulation of dynamic
equilibrium models, their efficient computation,
and their estimation.
Below you can get pdf copies of my papers and codes for reproducing some of the computations involved.
New Items
May, 29th, 2007. A first draft of a paper forthcoming in the NBER Macroeconomics Annual 2007 with Juan Rubio-Ramirez, at Duke, "How Structural Are Structural Parameters?" can be found here.
October, 5th, 2006. A description of my research agenda with Juan Rubio-Ramirez, at Duke, on the estimation of DSGE models is here. Also, the final version of the paper Economic and VAR Shocsk: What Can Go Wrong?, recently published in JEEA.
February, 24th, 2006. A new paper with Francisco Barillas, at NYU, "A Generalization of the Endogenous Grid Method" can be found here.
January, 26th, 2006. Among some new material, a new draft of the paper "Estimating Macroeconomic Models: A Likelihood Approach" can be found here. We have changed the application and now we estimate a business cycle more with investment-specific technological change and stochasic volatility.
Dynamic Macroeconomics
Joint with Juan F. Rubio-Ramirez (Duke University), Thomas Sargent (New York University), and Mark Watson (Princeton University).
An approximation to the equilibrium of a complete 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,I) determines a vector autoregression for fixed observables available to an econometrician. We review circumstances under which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple special condition for checking whether the mapping from VAR shocks to economic shocks is invertible.
The older working paper version is here.
Joint with Dirk Krueger (University of Pennsylvania).
Micro data show two key patterns of consumption and asset holdings over the life cycle. First, consumption expenditures on both durable and nondurable goods are hump-shaped. Second, young households keep very few liquid assets and hold most of their wealth in consumer durables. The first pattern persists even after controlling for family size and constitutes a puzzle from the perspective of complete market models, in which individuals smooth consumption over their lifetime. The second pattern suggests that we need to explicitly model durables to understand households' life cycle consumption and portfolio allocation. This paper studies the introduction of consumer durables into a dynamic general equilibrium life cycle model with idiosyncratic income shocks and endogenous borrowing constraints. In this setting durables play a dual role: they provide both consumption services and act as collateral for loans. A plausibly parameterized version of the model predicts that the interaction of consumer durables and endogenous borrowing constraints induces durables accumulation early in life and higher consumption of nondurables and accumulation of financial assets later in the life cycle, in an order of magnitude consistent with observed data. We thus conclude that durables are a key feature to explain both the hump in consumption of durables and nondurables and the optimal asset allocation of households.
Joint with Dirk Krueger (University of Pennsylvania).
This paper uses Consumer Expenditure Survey data and a seminonparametric statistical model to estimate life-cycle profiles of consumption, controlling for demographics, cohort, and time effects. We construct age profiles for total and nondurable consumption as well as expenditure patterns for consumer durables. Special emphasis is placed on the comparison of different approaches to control for changes in demographics over the life cycle. We find significant humps over the life cycle for total, nondurable, and durable expenditures. Changes in household size account for roughly half of these humps. Bootstrap simulations suggest that our empirical estimates are tight in that standard errors are small.
Here you can find the technical appendix of the paper with further details about our estimation.Joint with Dirk Krueger (University of Pennsylvania).
Joint with Aleh Tsyvinski (University of Minnesota and Federal Reserve Bank of Minneapolis).
This paper develops the quantitative implications of optimal fiscal policy
in a business cycle model when government does not have access to a commitment
technology. For an economy calibrated to the
This paper studies the relationship between population dynamics and economic
growth. Prior to the Industrial Revolution increases in total output were
roughly matched by increases in population. In contrast, during the last 150
years, increments in per capita income have coexisted with slow population
growth. Why are income and population growth no longer positively correlated?
This paper presents a new answer, based on the role of capital-specific
technological change, that provides a unifying account of lower population
growth and sustained economic growth. An overlapping generations model with
capital-skill complementarity and endogenous fertility, mortality and education
is constructed and parametrized to match English data from 1536 to 1920. The
key finding is that the observed fall in the relative price of capital can
account for more than 60% of the fall in fertility and over 50% of the increase
in income per capita in
These notes present further discussion and details of several aspects of "Was Malthus Right? Economic Growth and Population Dynamics". They should be readed following each particular section of the main paper.
Joint with the late Arijit Mukherji.
This paper proposes a new, more robust experiment to test for the presence of hyperbolic discounting. We motivate the experiment by pointing out the problems in interpreting the existing evidence caused by uncertainty. In the design of our experiment, we control for uncertainty by exploiting the demand of hyperbolic discounting agents for commitment. The experiment offers two choice sets, the second being a strict subset of the first. Exponential discounters will (possibly weakly) prefer the largest one. Hyperbolic discounters, in contrast, will (strictly) prefer the second set because its design makes it equivalent to a commitment technology. The experiment is conducted on a sample of undergraduate students. Our results suggest that hyperbolic behavior might be more difficult to find than implied by previous experiments.
Joint with Cesar Alonso-Borrego (Universidad Carlos III de Madrid) and Jose E. Galdon-Sanchez (Universidad Publica de Návarra).
Job security provisions are commonly invoked to explain the high and
persistent European unemployment rates. This belief has led several countries
to reform their labor markets and liberalize the use of fixed-term contracts.
Despite how common such contracts have become after deregulation, there is a
lack of quantitative analysis of their impact on the economy. To fill this gap,
we build a general equilibrium model with heterogeneous agents and firing costs
in the tradition of Hopenhayn and Rogerson (1993). We calibrate our model to
Spanish data, choosing in part parameters estimated with firm-level
longitudinal data.
Joint with Luis Carranza (Universidad de Navarra) and Jose E. Galdon-Sanchez (Universidad Publica de Navarra).
This paper studies the effects of credit market imperfections on output, the average size and distribution of firms and the level of financial intermediation of the economy. We build a dynamic general equilibrium model with heterogeneous agents. Households choose whether to become workers or entrepreneurs depending on their own productivity shock and asset level. If they decide to operate a firm, they will not be able to borrow as much as needed because of the imperfect enforceability of borrowing contracts. As a consequence, the output level of the firm will depend on the assets level of the owner. Our main finding is that income per capita would increase a 30% if we could move to an economy with perfect capital markets for firms. Also the number of firms would go up around 33% and their average size as measured by their capital by a factor of four.
Joint with Juan F. Rubio-Ramirez (Duke University).
Recent work by
Computation of Dynamic Equilibrium Models
Joint with S. Boragan Aruoba (University of Maryland) and Juan F. Rubio-Ramirez (Duke University).
This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using first, second, and fifth order perturbations in levels and in logs, the finite elements method, Chebyshev polynomials, and value function iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy, and we present some conclusions based on the reported evidence.
Click on this link to go to the companion web page where you can find the codes used in this paper.
Joint with Juan F. Rubio-Ramirez (Duke University).
This paper explores the application of the changes of variables technique to solve the stochastic neoclassical growth model. We use the method of Judd [2003. Perturbation methods with nonlinear changes of variables. Mimeo, Hoover Institution] to change variables in the computed policy functions that characterize the behavior of the economy. We report how the optimal change of variables reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first-order policy functions and how we can keep a linear representation of the laws of motion of the model if we use a nearly optimal transformation. We discuss how to apply our results to estimate dynamic equilibrium economies.
Joint with Francisco Barillas (New York University).
This paper extends Carroll's (2005) endogenous grid method to perform value function iteration in models with more than one control variable. We propose to mix the endogenous grid method with standard value function iteration to achieve higher efficiency. We illustrate the method using the stochastic neoclassical growth model with and without labor-leisure choice. We report important gains in efficiency that make value function iteration an attractive computational method in terms of both computing time and accuracy.
Joint with Francisco Barillas (New York University) and Juan F. Rubio-Ramirez (Duke University).
In this paper we propose a new solution algorithm for models with heterogeneous agents. The main idea of our method is to use a mixture of normal distributions to approximate the cross-sectional distribution of consumers and projection methods to approximate its law of motion.
Estimation of Dynamic Equilibrium Models
Joint with Juan F. Rubio-Ramirez (Duke University).
This note, which will appear in the newsletter of the Review of Economic Dynamics, fall 2006, describes our agenda on the estimation of DSGE Models. We discuss our different papers and explain how they fit together.
Joint with Juan F. Rubio-Ramirez (Duke University).
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, we 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 distance will have the highest posterior probability.
Second, we illustrate the strong small sample behavior of the approach using a
well-known application: the
Joint with Juan F. Rubio-Ramirez (Duke University).
This paper shows how particle filtering allows us to undertake likelihood-based inference in dynamic macroeconomic models. The models can be nonlinear and/or non-normal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.
Here you can find a simple example of how to use a Sequential Monte Carlo to evaluate the likelihood function of a nonlinear and non-normal process.
Joint with Juan F. Rubio-Ramirez (Duke University).
This paper compares two methods to undertake likelihood-based inference in dynamic equilibrium economies, a Sequential Monte Carlo filter proposed by Fernandez-Villaverde Rubio-Ramirez (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. 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, even if relatively small in absolute values, have important effects in the moments of the model. We conclude that the nonlinear filter is a superior procedure to take models to the data.
Joint with Juan F. Rubio-Ramirez (Duke University).
This paper studies how stable over time are the so-called "structural parameters" of dynamic stochastic general equilibrium (DSGE) models. To answer this question, we estimate a medium-scale DSGE model with real and nominal rigidities using U.S. data. In our model, we allow for parameter drifting and rational expectations of the agents with respect to this drift. We document that there is strong evidence that parameters change within our sample. We illustrate variations in the parameters describing the monetary policy reaction function and in the parameters characterizing the pricing behavior of firms and households. Moreover, we show how the movements in the pricing parameters are correlated with inflation. Thus, our results cast doubts on the empirical relevance of Calvo models.
Also, NBER Working Paper version, with more details.
Joint with Juan F. Rubio-Ramirez (Duke University) and Manuel Santos (Arizona State University).
This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, the policy functions are approximated by numerical methods. But then the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact 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 converges to the exact likelihood. Second, we find that the error in the approximated likelihood gets compounded with the sample size. As a consequence, second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. We illustrate our results with an application based on the Neoclassical Growth Model.