Forecasts from Reduced-form Models under the Zero-Lower-Bound Constraint

In this paper, I consider forecasting from a reduced-form VAR under the zero lower bound (ZLB) for the short-term nominal interest rate. The ZLB constraint expands the number of states exponentially, making the exact computation of forecast moments infeasible. I develop a method that a) computes the exact moments for the first n + 1 periods when n previous periods are tracked and b) approximates moments for the periods beyond n + 1 period using techniques for truncated normal distributions and approximations a la Kim (1994). In its simplest form, the algorithm tracks only the previous forecast period. The approximations become more accurate as additional previous periods are tracked at the cost of longer computational time, although when the method is tracking two or three previous periods, it is competitive with Monte Carlo simulation in terms computational time. I show that the algorithm produces satisfactory results for VAR systems with moderate to high persistence even when only one previous period is tracked. For very persistent VAR systems, however, tracking more periods is needed in order to obtain reliable approximations. I also show that the method is suitable for affine term-structure modeling, where the underlying state vector includes the short-term interest rate as in Taylor rules with inertia.