Proxy and Instrumental Variable Methods in a Regression Model with One of the Regressors Missing

✍ Scribed by R.N. Bhattacharya; D.K. Bhattacharyya

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 435 KB
• Volume: 47
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1993.1074

✦ Synopsis

Suppose (Y) has a linear regression on (X_{1}, X_{2}), but observations are only available on (\left(Y, X_{1}\right)). If large scale data on (\left(X_{1}, X_{2}\right)) are available, which do not include (Y), and if the regression of (X_{2}), given (X_{1}), is nonlinear, then one may estimate the regression coefficients of (Y) by using the proxy (g\left(X_{1}\right):=E\left(X_{2} \mid X_{1}\right)) for (X_{2}), or an instrument (\varphi\left(X_{1}\right)) which is uncorrelated with (X_{2}). Both methods provide estimators which are asymptotically normal around the true parameter values under appropriate assumptions. A computation of the optimal instrument is provided, and the asymptotic relative efficienties of the two types of estimators compared. C 1993 Academic Press, Inc.