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Adeola Oyenubi
''A note on Covariate Balancing Propensity Score and Instrument-like variables''
( 2020, Vol. 40 No.1 )
We use the term instrument-like variables to describe a variable that is highly correlated with treatment (or programme participation) and weakly correlated with outcome. This kind of variable cannot be used in instrumental variable estimation because they are not instruments and the literature also show that they should not also be used in Propensity Score Matching (PSM) because of their high correlation with treatment. The literature is therefore silent on the estimation approach that performs better when it is necessary to control for such an instrument-like variable. In this paper, we consider the estimation of treatment effect in the presence of an instrument-like variable and an unobserved confounder. The result shows that a particular variant of propensity score estimation namely Covariate Balancing Propensity Score (CBPS) performs better than alternatives in the presence of instrument-like variable and an unmeasured confounder. Our simulation result suggests that by trading off treatment prediction for balance CBPS reduces the influence of instrument-like variables on the propensity scores. This leads to lower bias and mean square error for the estimate that is based on the CBPS model.
Keywords: Causal inference, Instrumental variables, Observational studies, Propensity score matching
JEL: C2 - Single Equation Models; Single Variables: General
C4 - Econometric and Statistical Methods: Special Topics
Manuscript Received : Aug 24 2019 Manuscript Accepted : Feb 05 2020

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