  When a finite order vector autoregressive model is fitted to VAR($\infty$)
data the asymptotic distribution of statistics obtained via smooth functions of
least-squares estimates requires care. L\"utkepohl and Poskitt (1991) provide a
closed-form expression for the limiting distribution of (structural) impulse
responses for sieve VAR models based on the Delta method. Yet, numerical
simulations have shown that confidence intervals built in such way appear
overly conservative. In this note I argue that these results stem naturally
from the limit arguments used in L\"utkepohl and Poskitt (1991), that they
manifest when sieve inference is improperly applied, and that they can be
"remedied" by either using bootstrap resampling or, simply, by using standard
(non-sieve) asymptotics.
