Publications

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Short and Simple Confidence Intervals when the Directions of Some Effects are Known (with Philipp Ketz), revise and resubmit at Review of Economics and Statistics

Matlab Code

Stata code available from SSC archive: type "ssc install ssci"

We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs.  The confidence intervals are adaptive in the sense that they tend to be short at and near the points where the nuisance parameters are equal to zero.  We focus our results primarily on the practical problem of inference on a coefficient of interest in the linear regression model when it is unclear whether or not it is necessary to include a subset of control variables whose partial effects on the dependent variable have known directions (signs).  Our confidence intervals are trivial to compute and can provide significant length reductions relative to standard confidence intervals in cases for which the control variables do not have large effects.  At the same time, they entail minimal length increases at any parameter values.  We prove that our confidence intervals are asymptotically valid uniformly over the parameter space and illustrate their length properties in an empirical application to a factorial design field experiment and a Monte Carlo study calibrated to the empirical application.

Hybrid Confidence Intervals for Informative Uniform Asymptotic Inference After Model Selection

I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified.  This hybrid confidence interval is constructed by combining techniques from the selective inference and post-selection inference literatures to yield a short confidence interval across a wide range of data realizations.  I show that hybrid confidence intervals have correct asymptotic coverage, uniformly over a large class of probability distributions that do not bound scaled model parameters.  I illustrate the use of these confidence intervals in the problem of inference after using the LASSO objective function to select a regression model of interest and provide evidence of their desirable length and coverage properties in small samples via a set of Monte Carlo experiments that entail a variety of different data distributions as well as an empirical application to the predictors of diabetes disease progression.

Incentive-Compatible Critical Values (with Pascal Michaillat)

Statistically significant results are more rewarded than insignificant ones, so researchers have the incentive to pursue statistical significance. Such p-hacking reduces the informativeness of hypothesis tests by making significant results much more common than they are supposed to be in the absence of true significance. To address this problem, we construct critical values of test statistics such that, if these values are used to determine significance, and if researchers optimally respond to these new significance standards, then significant results occur with the desired frequency. Such incentive-compatible critical values allow for p-hacking so they are larger than classical critical values. Calibrating the model's parameters with evidence from the social and medical sciences, we find that the incentive-compatible critical value for any test and any significance level is the classical critical value for the same test with approximately one fifth of the significance level---a form of Bonferroni correction. For instance, for a z-test with a significance level of 5%, the incentive-compatible critical value is 2.31 instead of 1.65 if the test is one-sided and 2.57 instead of 1.96 if the test is two-sided.

Inference on Winners (with Isaiah Andrews and Toru Kitagawa), revise and resubmit at Quarterly Journal of Economics

R Code

2019 Version (referenced in "Inference After Estimation of Breaks")

Many empirical questions concern target parameters selected through optimization.  For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data.  Such settings give rise to a winner's curse, where conventional estimates are biased and conventional confidence intervals are unreliable.  This paper develops optimal confidence intervals and median-unbiased estimators that are valid conditional on the target selected and so overcome this winner's curse. If one requires validity only on average over targets that might have been selected, we develop hybrid procedures that combine conditional and projection confidence intervals to offer further performance gains relative to existing alternatives.