This paper aims to provide a unified treatment of the properties of two stage estimators. General conditions are set forth for consistency, efficiency and correct inferences. Applications of the general theorems are made to models with expectations and diagnostic tests. The general approach frequently enables much simpler derivation of existing results, and provides a number of new ones.

THIS NOTE SUGGESTS that the components models employed in [2, 3, 10, 11, 12 and 17] may be usefully analyzed within the state space framework found in the literature of control engineering. Such a formulation has the distinct advantage that a large corpus of filtering and estimation theory may then be brought to bear upon such models and has secondary benefits in the form of a greater lucidity of, and flexibility in, the exposition of the extraction problem. Further, by relating such models to a format that has widespread use in other fields, it is possible to exploit any future computational and theoretical advances therein.

The paper provides a review of the estimation of structural vector autoregressions with sign restrictions. It is shown how sign restrictions solve the parametric identification problem present in structural systems but leaves the model identification problem unresolved. A market and a macro model are used to illustrate these points. Suggestions have been made on how to find a unique model. These are reviewed. An analysis is provided of whether one can recover the true impulse responses and what difficulties might arise when one wishes to use the impulse responses found with sign restrictions. (JEL C32, C51, E12)

The tail index of a density has been widely used as an indicator of the probability of getting a large deviation in a random variable. Most of the theory underlying popular estimators of it assume that the data are independently and identically distributed (i.i.d.). However, many recent applications of the estimator have been to financial data, and such data tend to exhibit long-range dependence. We show, via Monte Carlo simulations, that conventional measures of the precision of the estimator, which are based on the i.i.d. assumption, are greatly exaggerated when such dependent data are used. This conclusion also has implications for estimates of the likelihood of getting some extreme values, and we illustrate the changed conclusions one would get using equity return data.