The low-frequency movements of economic variables play a prominent role in policy analysis and decision-making. We develop a robust estimation approach for these slow-moving trend processes which is guided by a judicious choice of priors and is characterized by sparsity. We present novel stylized facts from longer-run survey expectations that inform the structure of the estimation procedure. The general version of the proposed Bayesian estimator with a spike-and-slab prior accounts explicitly for cyclical dynamics. We show that it performs well in simulations against relevant benchmarks and report empirical estimates of trend growth for U.S. output and annual mean temperature.

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of five or ten. To illustrate the relevance of our results, we revisit the size and momentum anomalies.

In this paper we develop two nonparametric tests of treatment effect heterogeneity. The first test is for the null hypothesis that the treatment has a zero average effect for all subpopulations defined by covariates. The second test is for the null hypothesis that the average effect conditional on the covariates is identical for all subpopulations, that is, that there is no heterogeneity in average treatment effects by covariates. We derive tests that are straightforward to implement and illustrate the use of these tests on data from two sets of experimental evaluations of the effects of welfare-to-work programs.