  A local projection model is defined by a set of linear regressions that
account for the associations between exogenous variables and an endogenous
variable observed at different time points. While it is standard practice to
separately estimate individual regressions using the ordinary least squares
estimator, some recent studies treat a local projection model as a multivariate
regression with correlated errors, i.e., seemingly unrelated regressions, and
propose Bayesian and non-Bayesian methods to improve the estimation accuracy.
However, it is not clear how and when this way of treatment of local projection
models is justified. The primary purpose of this paper is to fill this gap by
showing that the likelihood of local projection models can be analytically
derived from a stationary vector moving average process. By means of numerical
experiments, we confirm that this treatment of local projections is tenable for
finite samples.
