We cast the problem of communicating scientific uncertainty as one of reporting a posterior distribution on an unknown parameter to an audience of Bayesian decision‐makers. We establish novel bounds on the audience's regret when the analyst reports an approximation to a posterior that the audience treats as exact. Under a palatable restriction on the audience's decision problems, the bounds take an especially convenient form. Under a further restriction on the audience's priors, a bootstrap distribution can be used as a stand‐in posterior. We propose a practical recipe for checking whether a conventional statistical report (say, a normal parameterized by a point estimate and standard error) is a good approximation, and for improving the report if it is not. We illustrate our proposals using the articles in the 2021 American Economic Review that use a bootstrap for inference.

We propose a positive model of empirical science in which an analyst makes a report to an audience after observing some data. Agents in the audience may differ in their beliefs or objectives, and may therefore update or act differently following a given report. We contrast the proposed model with a classical model of statistics in which the report directly determines the payoff. We identify settings in which the predictions of the proposed model differ from those of the classical model, and seem to better match practice.

We construct a new index of media slant that measures the similarity of a news outlet's language to that of a congressional Republican or Democrat. We estimate a model of newspaper demand that incorporates slant explicitly, estimate the slant that would be chosen if newspapers independently maximized their own profits, and compare these profit-maximizing points with firms' actual choices. We find that readers have an economically significant preference for like-minded news. Firms respond strongly to consumer preferences, which account for roughly 20 percent of the variation in measured slant in our sample. By contrast, the identity of a newspaper's owner explains far less of the variation in slant. Copyright 2010 The Econometric Society.

We propose a way to formalize the relationship between descriptive analysis and structural estimation. A researcher reports an estimate ĉ of a structural quantity of interest c that is exactly or asymptotically unbiased under some base model. The researcher also reports descriptive statistics<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>γ</a:mi><a:mo>ˆ</a:mo></a:mover></a:math>that estimate features γ of the distribution of the data that are related to c under the base model. A reader entertains a less restrictive model that is local to the base model, under which the estimate ĉ may be biased. We study the reduction in worst‐case bias from a restriction that requires the reader's model to respect the relationship between c and γ specified by the base model. Our main result shows that the proportional reduction in worst‐case bias depends only on a quantity we call the informativeness of<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mover accent="true"><d:mi>γ</d:mi><d:mo>ˆ</d:mo></d:mover></d:math>for ĉ . Informativeness can be easily estimated even for complex models. We recommend that researchers report estimated informativeness alongside their descriptive analyses, and we illustrate with applications to three recent papers.

We study the problem of measuring group differences in choices when the dimensionality of the choice set is large. We show that standard approaches suffer from a severe finite‐sample bias, and we propose an estimator that applies recent advances in machine learning to address this bias. We apply this method to measure trends in the partisanship of congressional speech from 1873 to 2016, defining partisanship to be the ease with which an observer could infer a congressperson's party from a single utterance. Our estimates imply that partisanship is far greater in recent years than in the past, and that it increased sharply in the early 1990s after remaining low and relatively constant over the preceding century.