The Long-Run Phillips Curve: A Structural VAR Investigation

Both cointegration methods, and non-cointegrated structural VARs identified based on either long-run restrictions, or a combination of long-run and sign restrictions, are used in order to explore the long-run trade-off between inflation and the unemployment rate in the post-WWII U.S., U.K., Euro area, Canada, and Australia. Overall, neither approach produces clear evidence of a non-vertical trade-off. The extent of uncertainty surrounding the estimates is however substantial, thus implying that a researcher holding alternative priors about what a reasonable slope of the long-run trade-off might be will likely not see her views falsified

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.