This comment includes a solution to a problem in Section 8 in Andrews (1991) and points out a method to generalize the mean‐squared error (MSE) bounds appearing in Andrews (1988) and Andrews (1991).
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.
We demonstrate that characterizing the minimal dimension of the term structure of interest rates is more challenging than currently appreciated. The highly structured polynomial patterns of the factor loadings, which are widely reported and discussed in the literature, reflect local correlations of smooth curves across maturities. We derive analytical expressions for the loadings of cross‐sectionally dependent processes that tend to favor a much lower dimension than the true dimension of the underlying factor space. Numerical examples illustrate the significant economic costs of erroneously committing to a parsimoniously parameterized factor space that is informed by standard metrics of goodness‐of‐fit. Our results apply to other assets with a finite maturity structure.
This paper develops a model of Bayesian learning from online reviews and investigates the conditions for learning the quality of a product and the speed of learning under different rating systems. A rating system provides information about reviews left by previous customers. observe the ratings of a product and decide whether to purchase and review it. We study learning dynamics under two classes of rating systems: full history , where customers see the full history of reviews, and summary statistics , where the platform reports some summary statistics of past reviews. In both cases, learning dynamics are complicated by a selection effect —the types of users who purchase the good, and thus their overall satisfaction and reviews depend on the information available at the time of purchase. We provide conditions for complete learning and characterize and compare its speed under full history and summary statistics. We also show that providing more information does not always lead to faster learning, but strictly finer rating systems do.
We show that demanding team incentives to be robust to nonquantifiable uncertainty about the game played by the agents leads to contracts that align the agents' interests. Such contracts have a natural interpretation as team‐based compensation. Under budget balance they reduce to linear contracts, thus identifying profit‐sharing, or equity, as an optimal contract absent a sink or a source of funds. A linear contract also gives the best profit guarantee to an outside residual claimant. These contracts still suffer from the free‐rider problem, but a positive guarantee obtains if and only if the technology known to the contract designer is sufficiently productive.
We study the educational choices of children of immigrants in a tracked school system. We first show that immigrants in Italy enroll disproportionately into vocational high schools, as opposed to technical and academically‐oriented ones, compared to natives of similar ability. The gap is greater for male students and it mirrors an analogous differential in grade retention. We then estimate the impact of a large‐scale, randomized intervention providing tutoring and career counseling to high‐ability immigrant students. Male treated students increase their probability of enrolling into the high track to the same level of natives, also closing the gap in grade retention. There are no significant effects on immigrant girls, who exhibit similar choices and performance as native ones in absence of the intervention. Increases in academic motivation and changes in teachers' recommendation regarding high school choice explain a sizable portion of the effect. Finally, we find positive spillovers on immigrant classmates of treated students, while there is no effect on native classmates.
The operation of markets and of politics are in practice deeply intertwined. Political decisions set the rules of the game for market competition and, conversely, market competitors participate in and influence political decisions. We develop an integrated model to capture the circularity between the two domains. We show that a positive feedback loop emerges such that market power begets political power, and political power begets market power, but that this feedback loop is bounded. With too much market power, the balance between politics and markets itself becomes lopsided and this drives a wedge between the interests of a policymaker and the dominant firm. Although such a wedge would seem pro‐competitive, we show how it can exacerbate the static and dynamic inefficiency of market outcomes. More generally, our model demonstrates that intuitions about market competition can be upended when competition is intermediated by a strategic policymaker.
Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The regressions may be high‐dimensional, making machine learning useful. Plugging machine learners into identifying equations can lead to poor inference due to bias from regularization and/or model selection. This paper gives automatic debiasing for linear and nonlinear functions of regressions. The debiasing is automatic in using Lasso and the function of interest without the full form of the bias correction. The debiasing can be applied to any regression learner, including neural nets, random forests, Lasso, boosting, and other high‐dimensional methods. In addition to providing the bias correction, we give standard errors that are robust to misspecification, convergence rates for the bias correction, and primitive conditions for asymptotic inference for estimators of a variety of estimators of structural and causal effects. The automatic debiased machine learning is used to estimate the average treatment effect on the treated for the NSW job training data and to estimate demand elasticities from Nielsen scanner data while allowing preferences to be correlated with prices and income.