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

This paper estimates the parameters of a stochastic growth model with asset market and contrasts the model's moments with moments of the actual data. We solve the model through log-linearization along the line of Campbell (1994) and estimate the model without and with asset pricing restrictions. As asset pricing restrictions we employ the risk-free interest rate and the Sharpe-ratio. To estimate the parameters we employ, as in Semmler and Gong (1996a), a ML estimation. The estimation is conducted through the simulated annealing. We introduce a diagnostic procedure which is closely related to Watson (1993) and Diebold, Ohanian and Berkowitz (1995) to test whether the second moments of the actual macroeconomic time series data are matched by the model's time series. Several models are explored. The overall results are that sensible parameter estimates may be obtained when the actual and computed risk-free rate is included in the moments to be matched. The attempt, however, to include the Sharpe-ratio as restriction in the estimation does not produce sensible estimates. The paper thus shows, by employing statistical estimation techniques, that the baseline real business cycle (RBC) model is not likely to give correct predictions on asset market pricing when parameters are estimated from actual time series data. The paper has been presented at the International Conference on "Computing in Economics and Finance", Stanford University, July 1997. We want to thank the participants for comments. The views expressed are those of the authors and do not necessarily re ect those of the Federal Reserve Bank of New York or the Federal Reserve System. Research Department, Federal Reserve Bank of New York, 33 Liberty St., New York, NY 10045; [email protected] and CEPR, London Department of Economics, New School for Social Research, 65 Fifth Ave, New York, NY 10003 Department of Economics, University of Bielefeld, Germany and Department of Economics, New School University, 65 Fifth Ave., New York, NY 10003