Estimation and Stochastic Simulation of Large-Scale Econometric Models with Rational Expectations

Giuseppe Bruno, Giancarlo Marra, and Andrea Cividini - Bank of Italy and Carlo Bianchi - University of Pisa

Expectations are a crucial issue in Macroeconomics and Rational Expectations has revolutionised research in this field. The elementary Rational Expectation Hypothesis, which states that economic agents do not make systematic mistakes in forecasting, has generated numerous modifications to both theory and methodology.

The purpose of this work is to present some of the results obtained by the joint application of an extended version of the Limited Information Instrumental Variables Efficient (LIVE) proposed by Brundy and Jorgenson (1971) for the estimation of a simultaneous model and a modified version of the Extended Path (EP) method proposed by Fair and Taylor (1983) for the solution of a dynamic nonlinear Rational Expectations model. The latter model can be written as

$$f_i(y_t,y_{t-1},\cdots, y_{t-p},E_{t-1}y_t,E_{t-1}y_{t+1},\cdots,E_{t-1}y_{t+h},x_t,\alpha_i) = u_{it},\quad i=1,\cdots,n\quad t=1,\cdots,T.$$

A Rational Expectations or Forward Looking model provides leads for endogenous variables representing solution values from future periods. These leads introduce simultaneity across different time periods, so that the model cannot be consistently and efficiently estimated using of OLS; furthermore the model cannot be solved recursively, period by period, as is usually the case when the endogenous variables may have lags but not leads.

Full Information estimation is clearly more efficient than Limited Information estimation. Nevertheless, for very large scale non-linear models, the Limited Information method is the only viable procedure on account of its computational simplicity and its robustness with regard to mis-specified restrictions (Full Information methods spreads inconsistency throughout the system). Among Limited Information algorithms LIVE does not require a direct estimation of the reduced form because the instruments are evaluated by solving the model numerically.

A model solver, therefore becomes the main inferential tool. The presence of non-linearities introduces some bias in the solution through a deterministic simulation; in this case the Certainty Equivalence no longer holds (Begg 1982) and the solution obtained on the basis of Perfect Foresight assumptions would give results different from those obtained using a stochastic simulation of models with rational expectations (Fair and Taylor 1983). Although this was not computationally feasible, computational difficulties should not deter researchers from adopting the more suitable procedure as computer time becomes increasingly cheap. Here we present an implementation of the forward-looking solver that makes use of the stochastic simulation. The proposed technique is slightly different from that proposed in Fair and Taylor (1989). The algorithm has been coded in FORTRAN and then embedded as an add-on in a user-friendly general purpose interactive package called Speakeasy.

The paper presents some of the numerical results of estimates and simulations of large scale (almost 1000 equations) dynamic nonlinear Rational Expectations models currently used at the Bank of Italy; these are compared with those obtained using models assuming the classical hypothesis of Adaptive Expectations.

Scheduled for Session 6.1 Computation And Econometrics - III