Proxy and instrumental variable methods in a regression model with one of the regressors missing

Rabi N. Bhattacharya, Dilip K. Bhattacharyya

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Suppose Y has a linear regression on X1, X2, but observations are only available on (Y, X1). If large scale data on (X1, X2) are available, which do not include Y, and if the regression of X2, given X1, is nonlinear, then one may estimate the regression coefficients of Y by using the proxy g(X1) {colon equals} E(X2|X1) for X2, or an instrument φ(X1) which is uncorrelated with X2. 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.

Original languageEnglish (US)
Pages (from-to)123-138
Number of pages16
JournalJournal of Multivariate Analysis
Volume47
Issue number1
DOIs
StatePublished - Oct 1993

Keywords

  • Efficiency
  • Linear regression
  • Nonlinear regression
  • Optimal instrument
  • Proxy

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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