We obtain a necessary and sufficient condition under which random-coefficient discrete choice models such as the mixed logit models are rich enough to approximate any nonparametric random utility models across choice sets. The condition turns out to be very simple and tractable. When the condition is not satisfied and, hence, there exists a random utility model that cannot be approximated by any random-coefficient discrete choice model, we provide algorithms to measure the approximation errors. After applying our theoretical results and the algorithms to real data, we find that the approximation errors can be large in practice.
Many centralized school admissions systems use lotteries to ration limited seats at oversubscribed schools. The resulting random assignment is used by empirical researchers to identify the effects of schools on outcomes like test scores. I first find that the two most popular empirical research designs may not successfully extract a random assignment of applicants to schools. When are the research designs able to overcome this problem? I show the following main results for a class of data-generating mechanisms containing those used in practice: The first-choice research design extracts a random assignment under a mechanism if the mechanism is strategy-proof for schools. In contrast, the other qualification instrument research design does not necessarily extract a random assignment under any mechanism. The former research design is therefore more compelling than the latter. Many applications of the two research designs need some implicit assumption, such as large-sample approximately random assignment, to justify their empirical strategy.
Democracy is widely believed to contribute to economic growth and public health in the 20th and earlier centuries. We find that this conventional wisdom is reversed in this century, i.e., democracy has persistent negative impacts on GDP growth during 2001-2020. This finding emerges from five different instrumental variable strategies. Our analysis suggests that democracies cause slower growth through less investment and trade. For 2020, democracy is also found to cause more deaths from Covid-19.
Algorithms produce a growing portion of decisions and recommendations both in policy and business. Such algorithmic decisions are natural experiments (conditionally quasirandomly assigned instruments) since the algorithms make decisions based only on observable input variables. We use this observation to develop a treatment-eﬀect estimator for a class of stochastic and deterministic algorithms. Our estimator is shown to be consistent and asymptotically normal for well-deﬁned causal eﬀects. A key special case of our estimator is a high-dimensional regression discontinuity design. The proofs use tools from diﬀerential geometry and geometric measure theory, which may be of independent interest.
The practical performance of our method is ﬁrst demonstrated in a high-dimensional simulation resembling decision-making by machine learning algorithms. Our estimator has smaller mean squared errors compared to alternative estimators. We ﬁnally apply our estimator to evaluate the eﬀect of Coronavirus Aid, Relief, and Economic Security (CARES) Act, where more than $10 billion worth of relief funding is allocated to hospitals via an algorithmic rule. The estimates suggest that the relief funding has little eﬀect on COVID- 19-related hospital activity levels. Naive OLS and IV estimates exhibit substantial selection bias.
Countries with more democratic political regimes experienced greater GDP loss and more deaths from COVID-19 in 2020. Using ﬁve diﬀferent instrumental variable strategies, we ﬁnd that democracy is a major cause of the wealth and health losses. This impact is global and is not driven by China and the US alone. A key channel for democracy’s negative impact is weaker and narrower containment policies at the beginning of the outbreak, not the speed of introducing policies.
Democracy is widely believed to contribute to economic growth and public health. However, we ﬁnd that this conventional wisdom is no longer true and even reversed; democracy has persistent negative impacts on GDP growth since the beginning of this century. This ﬁnding emerges from ﬁve diﬀerent instrumental variable strategies. Our analysis suggests that democracies cause slower growth through less investment, less trade, and slower value-added growth in manufacturing and services. For 2020, democracy is also found to cause more deaths from Covid-19.
Randomized controlled trials (RCTs) enroll hundreds of millions of subjects and involve many human lives. To improve subjects’ welfare, I propose a design of RCTs that I call Experiment-as-Market (EXAM). EXAM produces a welfare-maximizing allocation of treatment-assignment probabilities, is almost incentive-compatible for preference elicitation, and unbiasedly estimates any causal effect estimable with standard RCTs. I quantify these properties by applying EXAM to a water-cleaning experiment in Kenya. In this empirical setting, compared to standard RCTs, EXAM improves subjects’ predicted well-being while reaching similar treatment-effect estimates with similar precision.
Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores, grades, and interviews to rank applicants to screened schools, combined with lottery tie-breaking at unscreened schools. We show how to identify causal eﬀects of school attendance in such settings. Our approach generalizes regression discontinuity designs to allow for multiple treatments and multiple running variables, some of which are randomly assigned. Lotteries generate assignment risk at screened as well as unscreened schools. Centralized assignment also identiﬁes screened school eﬀects away from screened school cutoﬀs. These features of centralized assignment are used to assess the predictive value of New York City’s school report cards. Grade A schools improve SAT math scores and increase the likelihood of graduating, though by less than OLS estimates suggest. Selection bias in OLS estimates is egregious for Grade A screened schools.
Many countries face growing concerns that population aging may make voting and policy-making myopic. This concern begs for electoral reform to better reflect voices of the youth, such as weighting votes by voters' life expectancy. This paper predicts the effect of the counterfactual electoral reform on the 2016 U.S. presidential election. Using the American National Election Studies (ANES) data, I find that Hillary Clinton would have won the election if votes were weighted by life expectancy. I also discuss limitations due to data issues.