On propose une methode analytique simplifiee qui autorise le calcul, meme pour des systemes de dimension moyenne

IT IS WELL KNOWN that in an econometric model, under general assumptions, the ex-post forecast error (conditional on predetermined variables) can be decomposed into the sum of two independent terms; the former is the component due to error in estimated coefficients, while the latter depends on the random error terms. The asymptotic covariance matrix of the first component can be analytically derived through intermediate computation of the covariance matrix of restricted reduced form coefficients. However, in the case of overidentified models, this may lead to a great increase in the problem's dimensions, the number of reduced form parameters being larger (often much larger) than the number of structural parameters. This intermediate step is, however, unnecessary; this note discusses a straightforward analytic derivation of the desired matrix directly from the estimated structural parameters, without any increase in the dimensions of the problem, thus facilitating the computation even for medium to large econometric models. Let

On cherche a exposer aux utilisateurs des techniques d'estimation par le maximum de vraisemblance a information complete. Pourquoi le choix de l'estimateur de la matrice de covariance des coefficients n'est pas aussi neutre qu'on peut l'esperer

model. Many results (observed value, deterministic solution, computed mean among the replications, minimum and maximum of the stochastic solution, first relative differences of the observed, deterministic and mean stochastic values) are displayed and several empirical indicators of goodness of fit are computed: (1) the mean over the simulation period of the actual, deterministic and mean stochastic values; (2) the root mean square error (RMSE) of the deterministic and mean stochastic solutions; (3) the mean absolute percentage error (MAPE) of the deterministic and mean stochastic solutions; (4) Theil's inequality coefficient (U) of the deterministic and mean stochastic solutions; (5) the coefficients and standard errors of the regression (with intercept) of the observed values on the deterministic or mean stochastic solutions; (6) the coefficients and standard errors of the regression (without intercept) of the first relative differences of the observed values over those of the deterministic or mean stochastic solutions. The package is written in FORTRAN IV and ASSEMBLER 370 languages. It consists of approximately one thousand statements, in addition to the statements necessary to formalize the model. The required storage for the program is 60 kilobytes. A large work matrix is then required to hold intermediate and final results of the computation; its dimensions depend on the parameters specified in the input file (number of equations, simulation period, number of variables, etc.). The stochastic simulation of the Klein I model requires about 13 seconds of CPU time for 100 replications over 21 years of the sample period.

We develop generalized indirect estimation procedures that handle equality and inequality constraints on the auxiliary model parameters by extracting information from the relevant multipliers, and compare their asymptotic efficiency to maximum likelihood. We also show that, regardless of the validity of the restrictions, the asymptotic efficiency of such estimators can never decrease by explicitly considering the multipliers associated with additional equality constraints. Furthermore, we discuss the variety of effects on efficiency that can result from imposing constraints on a previously unrestricted model. As an example, we consider a stochastic volatility process estimated through a garch model with Gaussian or t distributed errors.

We develop generalized indirect estimation procedures that handle equality and inequality constraints on the auxiliary model parameters by extracting information from the relevant multipliers, and compare their asymptotic efficiency to maximum likelihood. We also show that, regardless of the validity of the restrictions, the asymptotic efficiency of such estimators can never decrease by explicitly considering the multipliers associated with additional equality constraints. Furthermore, we discuss the variety of effects on efficiency that can result from imposing constraints on a previously unrestricted model. As an example, we consider a stochastic volatility process estimated through a garch model with Gaussian or t distributed errors.