The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
August 15, 2022
Econometrica: Oct, 1964, Volume 32, Issue 4
https://doi.org/0012-9682(196410)32:4<652:SCDTDV>2.0.CO;2-F
p. 652-655
Albert Madansky
This paper shows that when a homogeneous linear regression of a normally distributed variable Y on two normally distributed variables X and Z is deflated by Z, and when X and Y are uncorrelated, the deflated dependent variable Y/Z and independent variable X/Z are either uncorrelated or perfectly correlated. Thus, existing approximations to the covariance of these deflated variables are poor. A new approximation to this covariance is given that has the same defect for normally distributed variables, but that should otherwise be better than existing ones.
