arXiv 4 Dec 2018 · Statistics — Methodology · 6 citations (OpenAlex)
arXiv:1812.01412 · PDF · DOI · OpenAlex · Extracted main text
Can instrumental variables be found from data? While instrumental variable (IV) methods are widely used to identify causal effect, testing their validity from observed data remains a challenge. This is because validity of an IV depends on two assumptions, exclusion and as-if-random, that are largely believed to be untestable from data. In this paper, we show that under certain conditions, testing for instrumental variables is possible. We build upon prior work on necessary tests to derive a test that characterizes the odds of being a valid instrument, thus yielding the name "necessary and probably sufficient". The test works by defining the class of invalid-IV and valid-IV causal models as Bayesian generative models and comparing their marginal likelihood based on observed data. When all variables are discrete, we also provide a method to efficiently compute these marginal likelihoods. We evaluate the test on an extensive set of simulations for binary data, inspired by an open problem for IV testing proposed in past work. We find that the test is most powerful when an instrument follows monotonicity---effect on treatment is either non-decreasing or non-increasing---and has moderate-to-weak strength; incidentally, such instruments are commonly used in observational studies. Among as-if-random and exclusion, it detects exclusion violations with higher power. Applying the test to IVs from two seminal studies on instrumental variables and five recent studies from the American Economic Review shows that many of the instruments may be flawed, at least when all variables are discretized. The proposed test opens the possibility of data-driven validation and search for instrumental variables.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Blai Bonet (2001) Instrumentality tests revisited | 1.000 | 8 | 3 | 100% |
| 2 | Joshua D Angrist and Jörn-Steffen Pischke (2008) Mostly harmless econometrics: An empiricist's companion | 0.928 | 4 | 3 | 100% |
| 3 | Tom M Palmer, Roland R Ramsahai, Vanessa Didelez, Nuala A Sheehan, e… (2011) Nonparametric bounds for the causal effect in a binary instrumental-variable model | 0.928 | 4 | 3 | 100% |
| 4 | Toru Kitagawa (2015) A test for instrument validity | 0.874 | 5 | 2 | 100% |
| 5 | Judea Pearl (1995) On the testability of causal models with latent and instrumental variables | 0.811 | 4 | 2 | 100% |
| 6 | Joshua D Angrist and Alan B Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.737 | 3 | 2 | 100% |
| 7 | Alexander Balke and Judea Pearl (1993) Nonparametric bounds on causal effects from partial compliance data | 0.737 | 3 | 2 | 100% |
| 8 | RR Ramsahai and SL Lauritzen (2011) Likelihood analysis of the binary instrumental variable model | 0.737 | 3 | 2 | 100% |
| 9 | Joshua Angrist and Guido Imbens (1994) Identification and estimation of local average treatment effects | 0.644 | 2 | 2 | 100% |
| 10 | John Bound, David A Jaeger, and Regina M Baker (1995) Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory vari… | 0.644 | 2 | 2 | 100% |
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