We propose a novel model of stochastic choice: the single-crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single-crossing property. We o↵er a characterization of SCRUMs based on two easy-to-check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single-peaked and single-dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.

The availability of high frequency financial data has generated a series of estimators based on intra-day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θt dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two-scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.

This paper develops a theory of randomization tests under an approximate symmetry as-sumption. Randomization tests provide a general means of constructing tests that control size in finite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis. Here, by exhibits symmetry we mean that the distribution remains invariant under a group of transformations. In this paper, we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis. An important application of this idea is in settings where the data may be grouped into a fixed number of “clusters ” with a large number of observations within each cluster. In such settings, we show that the distribution of the observed data satisfies our ap-proximate symmetry requirement under weak assumptions. In particular, our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster, but also across clusters. This approach enjoys several advantages over other approaches in these settings. Among other things, it leads to a test that is asymptotically similar, which, as shown in a simulation study, translates into improved power at many alternatives. Finally, we use our results to revisit the analysis of Angrist and Lavy (2009), who examine the impact of a cash award on exam performance for low-achievement students in Israel.

We use variation in historical state centralization to examine the long-term impact of institutions on cultural norms. The Kuba Kingdom, established in Central Africa in the early 17th century by King Shyaam, had more developed state institutions than the other independent villages and chieftaincies in the region. It had an unwritten constitution, separation of political powers, a judicial system with courts and juries, a police force, a military, taxation, and significant public goods provision. Comparing individuals from the Kuba Kingdom to those from just outside the Kingdom, we find that centralized formal institutions are associated with weaker norms of rule following and a greater propensity to cheat for material gain. This finding is consistent with recent models where endogenous investments to inculcate values in children decline when there is an increase in the effectiveness of formal institutions that enforce socially desirable behavior. Consistent with such a mechanism, we find that Kuba parents believe it is less important to teach children values related to rule-following behaviors.

The accepted manuscript version (last revised 5 Jan 2018 (v8)) has 118 pages, 3 tables, 11 figures, and includes supplementary appendix. This version corrects some typos in Example 2 of the published version. This supplement contains 11 appendices with additional results and some omitted proofs. Appendices F-J include additional results for Sections 2-7, respectively. Appendix K gathers auxiliary results on algebra of covering entropies. Appendices L and M contain the proofs of Sections 4 and 5 omitted from the main text. Appendix N contains the proofs of Sections 6 omitted from the main text, together with the proofs of the additional results for Section 6 in Appendix I. Appendix O reports the results of a simulation experiment.

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi-experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery-generated randomization integral to such designs from non-random preferences and priorities remains open. This paper develops easily-implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.