A Note on Models with Generated Covariances
| Published date | 01 May 1988 |
| DOI | http://doi.org/10.1111/j.1468-0084.1988.mp50002009.x |
| Date | 01 May 1988 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 50,2(1988)
0305-9049 $3.00
A Note on Models with Generated Covariances
Tiff Macklemt
I. INTRODUCTION
Second moments are appearing as regressors with increasing frequency in the
applied macro literature. The initial impetus appears to have been Friedman's
Nobel Lecture (1977), in which he argued that a variable rate of inflation will
reduce economic efficiency. To test this hypothesis several researchers (e.g.
Blejer and Liederman (1980) and Makin (1982)) have employed the variance
of unanticipated inflation as an explanatory variable in an output equation.
More recently, the variances of unanticipated money growth, interest rates
and exchange rates, as well as inflation, have featured as regressors in
reduced forms for output, money demand and trade volumes (e.g. Evans
(1984), Slovin and Sushka (1983), and Cushman(1983)).
A common econometric problem faced by each of these researchers is that
variances are not directly observable and must therefore be replaced by a
constructed variable. One approach has been to replace unknown variances
with the squared residuals from a supplementary forecast equation. Pagan
(1984), however, has demonstrated that this two-step procedure combined
with OLS estimation will yield inconsistent estimates and the error may be
large. To correct this problem he suggests an IV estimator. Since then, Pagan
and Ullah (1986) have extended Pagan's initial analysis to provide a thorough
treatment of the econometric issues surrounding generated variances.
The purpose of this note is to extend Pagan's (1984) analysis to the case of
generated covariances. Though less common than variances, covariances
have also begun appearing as regressors, and have been constructed follow-
ing a similar two step approach. Two examples are Mascaro and Meltzer
(1983) and Koskela and Viren (1987). Mascaro and Meltzer (1983) include
the covariance of unanticipated money and unanticipated velocity growth in
interest rates and money demand equations to test their hypothesis that
interest rates and money demand depend positively on risk. Risk is measured
as the variance of unanticipated nominal income growth, which, via the
quantity equation, is decomposed into the sum of the variances of unanti-
cipated money and unanticipated velocity growth, plus twice their covari-
ance. This decomposition allows Mascaro and Meltzer to distinguish
between monetary and non-monetary sources of variability, as well as their
I would like to thank David Hendry for his comments and Aman Ullah for his suggestions
and encouragement. Any errors are my own.
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