Experiments are the gold standard for causal identification but often have limited scale, while observational datasets are large  but often violate standard identification assumptions. To improve the estimation efficiency, we propose a new method that combines experimental and observational data by leveraging covariates that satisfy the first-stage relevance condition in the observational data . We first use the observational data to derive a biased estimate of the causal effect and then correct this bias using the experimental data. We show thatthis bias-corrected estimator is uncorrelated with the benchmark estimator that only uses the experimental data, and can thus be combined with the benchmark estimator to improve efficiency. Under a common experimental design that randomly assigns units into the experimental group, our method can reduce the variance by up to 50\% , so that only half of the experimental sample is required to attain the same accuracy. This accuracy can be further improved if the experimental design accounts for this relevant first-stage covariate and select the experimental group differently .
Randomized controlled trials generate experimental variation that can credibly identify causal effects, but often suffer from limited scale, while observational datasets are large , but often violate desired identification assumptions. To improve estimation efficiency, I propose a method that combines experimental and observational datasets when 1) units from these two datasets are sampled from the same population and 2) some characteristics of these units are observed. I show that if these characteristics can partially explain treatment assignment in the observational data , they can be used to derive moment restrictions that, in combination with the experimental data, improve estimation efficiency. I outline three estimators (weighting, shrinkage, or GMM) for implementing this strategy, and show that my methods can reduce variance by up to 50\% in typical experimental designs; therefore, only half of the experimental sample is required to attain the same statistical precision. If researchers are allowed to design experiments differently, I show that they can further improve the precision by directly leveraging this correlation between characteristics and assignment. I apply the method to a search listing dataset from Expedia that studies the causal effect of search rankings, and show that my method can substantially improve the precision .
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Experiments are the gold standard for causal identification but often have
Randomized controlled trials generate experimental variation that can credibly identify causal effects, but often suffer from
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,
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standard
desired
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the
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we propose a new
I propose a
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data by leveraging covariates that satisfy the first-stage relevance condition
datasets when 1) units from these two datasets are sampled from the same population and 2) some characteristics of these units are observed. I show that if these characteristics can partially explain treatment assignment
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. We first use the observational data to derive a biased estimate of the causal effect and then correct this bias using the experimental data. We show thatthis bias-corrected estimator is uncorrelated with the benchmark estimator that only uses the
, they can be used to derive moment restrictions that, in combination with the
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and can thus be combined with the benchmark estimator to improve efficiency. Under a common experimental design that randomly assigns units into the experimental group, our method can reduce the
improve estimation efficiency. I outline three estimators (weighting, shrinkage, or GMM) for implementing this strategy, and show that my methods can reduce
R
, so that
in typical experimental designs; therefore,
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accuracy. This accuracy can be further improved if the experimental design accounts for this relevant first-stage covariate and select the experimental group differently
statistical precision. If researchers are allowed to design experiments differently, I show that they can further improve the precision by directly leveraging this correlation between characteristics and assignment. I apply the method to a search listing dataset from Expedia that studies the causal effect of search rankings, and show that my method can substantially improve the precision