## Abstract

We propose a new method, the confidence interval (CI) method,

to select valid instruments from a larger set of potential instruments

for instrumental variables (IV) estimation of the causal effect of

an exposure on an outcome. Invalid instruments are such that they

fail the exclusion conditions and enter the model as explanatory variables.

The CI method is based on the confidence intervals of the per instrument

causal effects estimates and selects the largest group with all confidence

intervals overlapping with each other as the set of valid instruments.

Under a plurality rule, we show that the resulting standard IV, or

two-stage least squares (2SLS) estimator has oracle properties. This

result is the same as for the hard thresholding with voting (HT) method

of Guo et al. (2018). Unlike the HT method, the number of

instruments selected as valid by the CI method is guaranteed to be

monotonically decreasing for decreasing values of the tuning parameter.

For the CI method, we can therefore use a downward testing procedure

based on the Sargan (1958) test for overidentifying restrictions

and a main advantage of the CI downward testing method is that it

selects the model with the largest number of instruments selected

as valid that passes the Sargan test.

to select valid instruments from a larger set of potential instruments

for instrumental variables (IV) estimation of the causal effect of

an exposure on an outcome. Invalid instruments are such that they

fail the exclusion conditions and enter the model as explanatory variables.

The CI method is based on the confidence intervals of the per instrument

causal effects estimates and selects the largest group with all confidence

intervals overlapping with each other as the set of valid instruments.

Under a plurality rule, we show that the resulting standard IV, or

two-stage least squares (2SLS) estimator has oracle properties. This

result is the same as for the hard thresholding with voting (HT) method

of Guo et al. (2018). Unlike the HT method, the number of

instruments selected as valid by the CI method is guaranteed to be

monotonically decreasing for decreasing values of the tuning parameter.

For the CI method, we can therefore use a downward testing procedure

based on the Sargan (1958) test for overidentifying restrictions

and a main advantage of the CI downward testing method is that it

selects the model with the largest number of instruments selected

as valid that passes the Sargan test.

Original language | English |
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Number of pages | 50 |

Journal | Journal of the Royal Statistical Society: Series B |

Publication status | Accepted/In press - 13 Jan 2021 |