The decisions of judges, lenders, journal editors, and other gatekeepers often lead to significant disparities across affected groups. An important question is whether, and to what extent, these group-level disparities are driven by relevant differences in underlying individual characteristics or by biased decision makers. Becker (1957, 1993) proposed an outcome test of bias based on differences in post-decision outcomes across groups, inspiring a large and growing empirical literature. The goal of our paper is to offer a methodological blueprint for empirical work that seeks to use outcome tests to detect bias. We show that models of decision making underpinning outcome tests can be usefully recast as Roy models, since heterogeneous potential outcomes enter directly into the decision maker’s choice equation. Different members of the Roy model family, however, are distinguished by the tightness of the link between potential outcomes and decisions. We show that these distinctions have important implications for defining bias, deriving logically valid outcome tests of such bias, and identifying the marginal outcomes that the test requires.

We study how Americans respond to idiosyncratic and exogenous changes in household wealth and unearned income. Our analyses combine administrative data on U.S. lottery winners with an event study design. We first examine individual and household earnings responses to these windfall gains, finding significant and sizable wealth and income effects. On average, an extra $1 of unearned income in a given period reduces household labor earnings by about 50 cents, decreases total labor taxes by 10 cents, and increases consumption expenditure by 60 cents. These effects are heterogeneous across the income distribution, with households in higher quartiles of the income distribution reducing their earnings by a larger amount. Next we examine margins of adjustment other than earnings and, in the course of doing so, address a number of important economic questions about how additional wealth or unearned income affect retirement decisions and labor market dynamics, family formation and dissolution, entrepreneurship and self-employment, and geographic mobility and neighborhood choice. Last, we carefully compare our findings to those reported in existing lottery studies. This comparison reveals that existing U.S. studies substantially underestimate wealth and income effects because they use measures that understate the earnings responses and overstate the after-tax wealth changes associated with lottery wins.

It is often desired to rank different populations according to the value of some feature of each population. For example, it may be desired to rank neighbourhoods according to some measure of intergenerational mobility or countries according to some measure of academic achievement. These rankings are invariably computed using estimates rather than the true values of these features. As a result, there may be considerable uncertainty concerning the rank of each population. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each population. We consider both the problem of constructing marginal confidence sets for the rank of a particular population as well as simultaneous confidence sets for the ranks of all populations. We show how to construct such confidence sets under weak assumptions. An important feature of all of our constructions is that they remain computationally feasible even when the number of populations is very large. We apply our theoretical results to re-examine the rankings of both neighbourhoods in the U.S. in terms of intergenerational mobility and developed countries in terms of academic achievement. The conclusions about which countries do best and worst at reading, math, and science are fairly robust to accounting for uncertainty. The confidence sets for the ranking of the fifty most populous commuting zones by measures of mobility are also found to be small. These confidence sets, however, become much less informative if one includes all commuting zones, if one considers neighbourhoods at a more granular level (counties, census tracts), or if one uses movers across areas to address concerns about selection.

We study the effects of broadband internet use on the investment decisions of individual investors. A public program in Norway provides plausibly exogenous variation in internet use. Our instrumental variables estimates show that internet use causes a substantial increase in stock market participation, driven primarily by increased fund ownership. Existing investors tilt their portfolios toward funds, thereby obtaining more diversified portfolios and higher Sharpe ratios, and do not increase their trading activity in stocks. Overall, access to high‐speed internet spurs a “democratization of finance,” with individuals making investment decisions that are more in line with the advice from portfolio theory.