Statistical Estimation and Moment Evaluation of a Stochastic Growth Model with Asset Market

Martin Lettau - University of Tilburg, Gang Gong - University of Bielefeld and Willi Semmler - New School for Social Research and University of Bielefeld

This paper estimates the parameters of a stochastic growth model and contrasts the model's moments with moments of the actual data. More specifically, we pursue the following objectives:

First, we introduce a GMM estimation of the model's parameters. This estimation is conducted through a numerical procedure that allows us to iteratively compute the solution of the decision variables for given parameters (inner algorithm) and to revise the parameters through a numerical optimization procedure (outer algorithm). For the latter we use the simulated annealing. Two different solution methods to obtain the decision variables in feedback form will be employed; a local linearization method proposed by Semmler and Gong (1996) and the projection method by Judd (1992). We explore the sensitivity of the estimated parameters with respect to different solution methods.

Second, we employ a diagnostic procedure which is closely related to Watson (1993) and Diebold, Ohanian and Berkowitz (1995) to test whether the moments predicted by the model for the estimated parameters can match the moments of the actual macroeconomic time series data. For this purpose we generate the forecasted series from which the moment statistics are derived. We then use the variance-covariance matrix from our estimation of the parameters to infer the intervals of the moment statistics and to study whether the actual moments derived from the data sample fall within the intervals. The moment statistics that we will compare include the means (the first moments) and the spectrum at various frequencies (the second moments).

Third, we pursue the above objectives by employing simulated data, generated from a stochastic simulation of the model, and then apply them to the actual data. The purpose of the first step is to test whether our proposed method works well. As actual data we employ two data sets currently used in RBC studies: the data set constructed by Christiano (1987) and employed in Christiano (1988) and Christiano and Eichenbaum (1992) and the data set obtained from NIPA as used in King et al. (1988), Watson (1993), Chow (1993) and Semmler and Gong (1996).

Fourth, beside exploring the sensitivity of the estimated parameters to the solution methods and data sets we also study the sensitivity of the estimates for a model with one shock sequence, technology shocks, and a model with two shock sequences, technology and government spending shocks.

Scheduled for Session 2.4 Rational Expectations Analysis - I