Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint...

In this note, I extend the optimal asymptotic least squares estimation framework to deal with singularities in the asymptotic covariance of the distance function. Further, the relationship between the asymptotic least squares and maximum likelihood estimation frameworks in such a singular set-up...

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures,...

The general Gauss–Markov model, Y = Xβ + e, E(e) = 0, Cov(e) = σ <Superscript>2</Superscript> V, has been intensively studied and widely used. Most studies consider covariance matrices V that are nonsingular but we focus on the most difficult case wherein C(X), the column space of X, is not contained in C(V)....</superscript>

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures,...