  Conditional forecasts, i.e. projections of a set of variables of interest on
the future paths of some other variables, are used routinely by empirical
macroeconomists in a number of applied settings. In spite of this, the existing
algorithms used to generate conditional forecasts tend to be very
computationally intensive, especially when working with large Vector
Autoregressions or when multiple linear equality and inequality constraints are
imposed at once. We introduce a novel precision-based sampler that is fast,
scales well, and yields conditional forecasts from linear equality and
inequality constraints. We show in a simulation study that the proposed method
produces forecasts that are identical to those from the existing algorithms but
in a fraction of the time. We then illustrate the performance of our method in
a large Bayesian Vector Autoregression where we simultaneously impose a mix of
linear equality and inequality constraints on the future trajectories of key US
macroeconomic indicators over the 2020--2022 period.
