Abstract. We propose a linear approximation to the solution of DSGE models that is sensitive to the effects of risk. If variables remain close to the approximation point in expectation, a second-order Taylor expansion to the equilibrium conditions reduces to a system of linear equations that depends on the second-order moments of the variables. The latter can be solved using standard linear rational expectation methods. The resulting approximation captures the effects of risk in models with constant volatility, stochastic volatility, and GARCH effects through the intercept and/or the slopes of the decision rules. Relative to alternative approximations, our method yields approximation errors that are up to two orders of magnitude smaller, all while preserving a linear structure in the state variables. Finally, we show how to accommodate asymmetric effects from non-normal shocks within our linear approximation using information from a third-order Taylor expansion.
Abstract. We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from data that are only available at discrete points in time. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, which allows avoiding discretization errors. Using the Kalman filter, we construct the exact likelihood for data sampled either as stocks or flows, and estimate frequency-invariant parameters by maximum likelihood. We address the aliasing problem arising in multivariate settings and provide conditions for precluding it, which is required for local identification of the parameters in the continuous-time economic model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links imposed by the economic theory and the information content of the discrete-time observations. We illustrate our approach using an off-the-shelf real business cycle model. We conduct extensive Monte Carlo experiments to study the finite sample properties of the estimator based on the exact discrete-time representation, and show they are superior to those based on a naive Euler-Maruyama discretization of the economic model. Finally, we estimate the model using postwar U.S. macroeconomic data, and offer examples of applications of our approach, including historical shock decomposition at different frequencies, and estimation based on mixed-frequency data.
Abstract. This paper revisits the fit of disaster risk models where a representative agent has recursive preferences and the probability of a macroeconomic disaster changes over time. We calibrate the model as in Wachter (2013) and perform two sets of tests to assess the empirical performance of the model in long run simulations. The model is solved using a two step projection-based method that allows us to find the equilibrium consumption-wealth ratio and dividend-yield for different values of the intertemporal elasticity of substitution. By fixing the elasticity of substitution to one, the first experiment indicates that the overall fit of the model is adequate. However, we find that the amount of aggregate stock market volatility that the model can generate is sensible to the method used to solve the model. We also find that the model generates near unit root interest rates and a puzzling ranking of volatilities between the risk free rate and the expected return on government bills. We later solve the model for values of the elasticity of substitution that differ from one. This second experiment shows that while a higher elasticity of substitution helps to increase the aggregate stock market volatility and hence to reduce the Sharpe Ratio, a lower elasticity of substitution generates a more reasonable level for the equity risk premium and for the volatility of the government bond returns without compromising the ability of the price-dividend ratio to predict excess returns.
Abstract. En este documento se presentan los resultados obtenidos de un ejercicio empírico que pretende extraer los principales hechos estilizados de la economía colombiana para el período 1994: I 2007: I. El objetivo es servir de apoyo tanto para el diseño y especificación como para la evaluación de un modelo de equilibrio general dinámico y estocástico (DSGE) que actualmente desarrolla el Departamento de Modelos Macroeconómicos del Banco de la República. Para ello se emplea una base de datos que permite descomponer algunos de los principales agregados macroeconómicos calculados por el DANE a través del sistema de cuentas nacionales anuales en sus componentes doméstico e importado, así como construir una medida de los márgenes de comercialización adicionados a los bienes de consumo e inversión importados. Una vez se dispone de los datos, se analiza la estructura de la economía colombiana por componentes de oferta y demanda siguiendo de cerca la metodología empleada por Restrepo y Soto (2004) en Chile y Restrepo y Reyes (2000) en Colombia.
Abstract. There is now an impetus to apply dynamic stochastic general equilibrium models to forecasting. But these models typically rely on purpose-built data, for example on tradable and nontradable sector outputs. How then do we know that the model will forecast well, in advance? We develop an early warning test of the database-model match and apply that to a Colombian model. Our test reveals where the combination should work (consumption) and where not (in investment). The test can be adapted to look at many likely sources of DSGE model failure.
Abstract. In this document we apply the Business Cycle Accounting (BCA) procedure in order to study which mechanisms are more relevant to interpret the dynamics of the Colombian GDP between 1994 and 2009. The neoclassical growth model with endogenous variable capital utilization of Cavalcanti et al. (2008) is used as a benchmark model. This reference model can be seen as a reduced form of a greater number of DSGE models with different frictions commonly used in the literature. This equivalence allows us to assess the importance of each of those detailed models in explaining the fluctuation in the economic activity. The results suggest that in order to achieve better predictions for the GDP, macroeconomic models should include distortions that alter the consumption-savings decisions and the labor supply of the households. These distortions can be obtained with the inclusion of capital and labor wedges on the benchmark model. Furthermore, frictions related to movements in the total factor productivity tend to overestimate periods of persistent economic downturn such as the one registered between 1998 and 2000 after the Asian crisis.