Solutions to Bestvina & Feighn's Exercises on Limit Groups

This article gives solutions to the exercises in Bestvina and Feighn's paper on Sela's work on limit groups. We prove that all constructible limit groups are limit groups and give an account of the shortening argument of Rips and Sela.Comment: 31 pages, 2 figures. To appear in `Geometry and Cohomology in Group Theory (Durham, 2003)

The membership problem for 3-manifold groups is solvable

We show that the Membership Problem for finitely generated subgroups of 3-manifold groups is solvable.Comment: 19 page

Moving-Average Transformations in Classical Linear Models

Economists are frequently compelled to use data which take inappropriate forms. One particular deficiency is discussed in the paper below; namely, the prior adjustment of economic time-series by moving average transformations. This discussion is restricted to regression analyses and data which satisfy the conditions for the classical linear model.

Temporal Spillover and Autocorrelation in Some Aggregate Models of Wage-Determination

In a recent paper, we discussed the possible availability of prior information with respect to the source of the moving-average components of mixed moving-average autoregressive processes in the context of empirical investigations of wage-determination. The earlier discussion of this generalization of the Yule-Slutsky effect ignores the possible presence of lagged endogenous variables, which may be due to explicit temporal spillovers between different wage-bargains in the labour market. This omission is remedied in this paper, and several final equations for models with temporal spillovers are given below. These can be contrasted with the final equation for a simple model in which the spillover feedback is restricted to autoregressive processes for the stochastic errors of theoretical relations. Also, in this paper the different specifications can be associated with a collection of linear hypotheses for which conventional least-squares statistics provide suitable test statistics if samples of data are sufficiently large. Knowledge of the weights for the moving-average components is an essential framework for the procedures which are outlined.