Abstract This paper proposes a procedure for assessing the sensitivity of inferential conclusions for functionals of sparse high-dimensional models following model selection. The proposed procedure is called targeted undersmoothing. Functionals considered include dense functionals that may depend on many or all elements of the high-dimensional parameter vector. The sensitivity analysis is based on systematic enlargements of an initially selected model. By varying the enlargements, one can conduct sensitivity analysis about the strength of empirical conclusions to model selection mistakes. We illustrate the procedure's performance through simulation experiments and two empirical examples.

We develop a new approach for the identification of Pareto‐improving tax reforms. This approach yields necessary and sufficient conditions for the existence of Pareto‐improving reform directions. A main insight is that “Two brackets are enough”: When the system cannot be improved by altering tax rates in one or two income brackets, then there is no continuous reform direction that is Pareto‐improving. We also show how to check whether a given tax reform is Pareto‐improving. We use these tools to study the introduction of the Earned Income Tax Credit (EITC) in the United States in 1975. A robust finding is that, prior to the EITC, the U.S. tax‐transfer system was not Pareto‐efficient. Under plausible assumptions about behavioral responses, the 1975 reform was not Pareto‐improving. Qualitatively, though, it had the right properties: A similar reform with earnings subsidies made available to a broader range of incomes would have been Pareto‐improving.

We document the phenomenon that average excess returns of out-of-the-money puts and calls on bond futures are negative, both unconditionally and conditionally on economic states. To explain these findings, we develop economically motivated restrictions in the context of a theory in which the pricing kernel is a general diffusion process with spanned and unspanned components. Our reconciliation is a framework that introduces market incompleteness and priced unspanned volatility risks, allowing for time-varying downside and upside futures risk premiums. The estimated model shows consistency with data on bond yields, yield volatilities, bond futures return volatilities, option prices, and option risk premiums.