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This paper provides methods for estimating a variety of retrospective measures of causal e¤ects in systems of dynamic structural equations. These equations need not be linear or separable. Structural identi…cation of e¤ects of interest is ensured by certain conditional exogeneity conditions, an extension of the notion of strict exogeneity. The covariates ensuring conditional exogeneity can contain not only lags but also leads of suitable proxies for unobservables. We focus on covariate-conditioned average and quantile e¤ects, together with counterfactual objects that are associated with these, such as point bands and path bands. The latter are useful for constructing con…dence intervals and testing hypotheses. We show how these objects can be estimated using state-space methods and illustrate with a study of the impact of crude oil prices on gasoline prices.

This paper puts forward the proposition that failure to take account of stochastic seasonality results in dynamic misspeci®cation. This point is illustrated by estimating various versions of a simple Australian consumption function using seasonally unadjusted data covering the period 1959(3)± 1993(3). It is demonstrated that only the equation modelling stochastic seasonality as an unobserved component shows no dynamic misspeci®cation unlike other equations. This equation is also shown to have the highest explanatory power and, unlike other equations, to be structurally stable.

They left without him! Len wanted to be with his unit, but he missed his starting point for The March. He was too late. He walked with two sticks now and there was no chance of catching up.Len didn't want to be late. Not today. Reluctantly he said to the boys that he couldn't make the Dawn Service this year, and Len always went to the Dawn Service, but he'd definitely be there for The March.

No abstract