T. S. Breusch, A. R. Pagan; The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics, The Review of Economic Studies, Volume 47,

A. R. Pagan, D. F. Nicholls; Exact Maximum Likelihood Estimation of Regression Models with Finite Order Moving Average Errors, The Review of Economic Studies, V

A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

In this paper we examine a number of recent studies that claim to have obtained a well-defined liquidity effect using structural VAR models based on broad measures of money. These studies can be distinguished in terms of the identifying restrictions, sample periods, and frequency of data used. We show that estimation of the structural coefficients of all these models can be achieved by instrumental-variable methods, where the instruments are predetermined variables and the estimated structural errors from other equations in the system. Overall, our judgment is that the evidence for a liquidity effect from these studies is much less certain than suggested in the original papers, primarily because of the poor quality of the instruments used in estimation and the sensitivity of the estimates to the sample period used.

Although there has been much argument over the impact of variable inflation rates upon economic performance, there has been surprisingly little attempt to define the term "variability of inflation" carefully or to test proposed hypotheses connecting variability and the level of inflation. Precise definitions are given in the paper and a model is constructed showing that the level/variability hypothesis may be formulated in terms of the presence of heteroscedasticity in a regression model. This theoretical model is used to criticize existing studies, while an empirical study with Australian data illustrates the application of the approach.