Mode predictors in nonlinear systems with identities

For a nonlinear system of simultaneous equations, the mode of the joint distribution of the endogenous variables in the forecast period is proposed as alternative to the more usual deterministic or mean predictors. A first method follows from maximizing the joint density of a subset of the endogenous variables, corresponding to stochastic equations only (analogously to FIML estimation, where identities are first substituted into stochastic equations). Then a more general approach is developed, which maintains the identities. The model with identities is viewed as a mapping between the space of the random errors and a hypersurface in the space of the endogenous variables; the probability density is defined, and maximization is performed on such a hypersurface. Experimental results on these two mode predictors (and comparisons with deterministic and mean predictors) are provided for a macro model of the Italian economy.