A model is considered in which a covariance-stationary exogenous process is related to an endogenous process by an unrestricted, infinite, linear distributed lag. It is shown that when an underlying continuous time model is sampled at unit intervals to yield endogenous and exogenous discrete time processes, the discrete time processes are related by a discrete time equivalent of the underlying continuous model. The relationship between the underlying continuous lag distribution and its discrete time equivalent is close when the exogenous process is smooth. Even then, however, it is interesting to note that (i) a monotone continuous time distribution does not in general have a monotone discrete time equivalent and (ii) a one-sided continuous time distribution does not in general have a one-sided discrete time equivalent. The implications of the results for statistical practice are considered in the latter part of the paper.

This paper presents an empirical analysis of the determinants of negotiated wage changes using a pooled sample of time series observations for fourteen Canadian manufacturing industries. Data on individual contracts are used in an attempt to allow for the discontinuity of wage adjustments given the predominance of collective bargaining and variable contract length. Using a nonlinear formulation, profit levels, the unemployment rate, the rate of change of prices, and other variables are found to be statistically significant. DURING THE PAST decade a considerable amount of econometric research has been devoted to the explanation of movements in wages. Most empirical studies have used a basic disequilibrium model, first suggested by Phillips [11] in which the change in money wage rates is related to the level of unemployment. By relaxing some of the more rigid theoretical assumptions, the basic Phillips curve explanation has been expanded to include a number of other variables such as profits, prices, productivity, employment mix, etc. While many of these studies have provided valuable insights into the wage determining process, the statistical approaches used have often failed to deal adequately with the institutional features of the labor market. These statistical problems are briefly discussed in Section 1 of the paper and our own empirical analysis using data on individual contracts in Canada is presented in Section 2. The main implications of our study for the aggregate Phillips curve are given in Section 3.

[Using a general definition of a generalized inverse of a singular matrix we generalized the k class and three stage least squares procedures so that they can be applied when the sample size, say T, is smaller than the number of exogenous variables, say K, in a system of equations. These generalized k class and three stage least squares estimators, in usual cases, coincide with ordinary least squares and Zellner's [7] efficient estimators respectively as long as T @ extless K and coincide with the usual k class and three stage least squares estimators respectively as T exceeds K.]