Knowledge that Transforms

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high‐frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes, and data frequencies.

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

We study the optimal design of corporate taxation and R&D policies as a dynamic mechanism design problem with spillovers. Firms have heterogeneous research productivity, and that research productivity is private information. There are non‐internalized technological spillovers across firms, but the asymmetric information prevents the government from correcting them in the first best way. We highlight that key parameters for the optimal policies are (i) the relative complementarities between observable R&D investments, unobservable R&D inputs, and firm research productivity, (ii) the dispersion and persistence of firms' research productivities, and (iii) the magnitude of technological spillovers across firms. We estimate our model using firm‐level data matched to patent data and quantify the optimal policies. In the data, high research productivity firms get disproportionately higher returns to R&D investments than lower productivity firms. Very simple innovation policies, such as linear corporate taxes combined with a nonlinear R&D subsidy—which provides lower marginal subsidies at higher R&D levels—can do almost as well as the unrestricted optimal policies. Our formulas and theoretical and numerical methods are more broadly applicable to the provision of firm incentives in dynamic settings with asymmetric information and spillovers, and to firm taxation more generally.

This paper studies the optimal conduct of monetary policy in a multisector economy in which firms buy and sell intermediate goods over a production network. We first provide a necessary and sufficient condition for the monetary policy's ability to implement flexible‐price equilibria in the presence of nominal rigidities and show that, generically, no monetary policy can implement the first‐best allocation. We then characterize the optimal policy in terms of the economy's production network and the extent and nature of nominal rigidities. Our characterization result yields general principles for the optimal conduct of monetary policy in the presence of input‐output linkages: it establishes that optimal policy stabilizes a price index with greater weights assigned to larger, stickier, and more upstream industries, as well as industries with less sticky upstream suppliers but stickier downstream customers. In a calibrated version of the model, we find that implementing the optimal policy can result in quantitatively meaningful welfare gains.

We propose and implement a new method to estimate treatment effects in settings where individuals need to be in a certain state (e.g., unemployment) to be eligible for a treatment, treatments may commence at different points in time, and the outcome of interest is realized after the individual left the initial state. An example concerns the effect of training on earnings in subsequent employment. Any evaluation needs to take into account that some of those who are not trained at a certain time in unemployment will leave unemployment before training while others will be trained later. We are interested in effects of the treatment at a certain elapsed duration compared to “no treatment at any subsequent duration.” We prove identification under unconfoundedness and propose inverse probability weighting estimators. A key feature is that weights given to outcome observations of nontreated depend on the remaining time in the initial state. We study effects of a training program for unemployed workers in Sweden. Estimates are positive and sizeable, exceeding those obtained with common static methods. This calls for a reappraisal of training as a tool to bring unemployed back to work.

Facing several decisions, people may consider each one in isolation or integrate them into a single optimization problem. Isolation and integration may yield different choices, for instance, if uncertainty is involved, and only one randomly selected decision is implemented. We investigate whether the random incentive system in experiments that measure ambiguity aversion provides a hedge against ambiguity, making ambiguity‐averse subjects who integrate behave as if they were ambiguity neutral. Our results suggest that about half of the ambiguity averse subjects integrated their choices in the experiment into a single problem, whereas the other half isolated. Our design further enables us to disentangle properties of the integrating subjects' preferences over compound objects induced by the random incentive system and the choice problems in the experiment.

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris (1983b)) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1 − α on average across the n EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.

WE CORRECT A BOUND in the definition of approximate truthfulness used in the body of the paper of Jackson and Sonnenschein (2007). The proof of their main theorem uses a different permutation-based definition, implicitly claiming that the permutation-version implies the bound-based version. We show that this claim holds only if the bound is loosened. The new bound is still strong enough to guarantee that the fraction of lies vanishes as the number of problems grows, so the theorem is correct as stated once the bound is loosened.

How large economic stimuli generate individual and aggregate responses is a central question in economics, but has not been studied experimentally. We provided one‐time cash transfers of about USD 1000 to over 10,500 poor households across 653 randomized villages in rural Kenya. The implied fiscal shock was over 15 percent of local GDP. We find large impacts on consumption and assets for recipients. Importantly, we document large positive spillovers on non‐recipient households and firms, and minimal price inflation. We estimate a local transfer multiplier of 2.5. We interpret welfare implications through the lens of a simple household optimization framework.