Knowledge that Transforms

Certain extremum estimators have asymptotic distributions that are non‐Gaussian, yet characterizable as the distribution of the arg max of a Gaussian process. This paper presents high‐level sufficient conditions under which such asymptotic distributions admit a continuous distribution function. The plausibility of the sufficient conditions is demonstrated by verifying them in three examples, namely, maximum score estimation, empirical risk minimization, and threshold regression estimation. In turn, the continuity result buttresses several recently proposed inference procedures whose validity seems to require a result of the kind established herein. A notable feature of the high‐level assumptions is that one of them is designed to enable us to employ the Cameron–Martin theorem. In a leading special case, the assumption in question is demonstrably weak and appears to be close to minimal.

We investigate how formularies used by pharmacy benefit managers (PBMs) affect equilibrium manufacturer rebates for branded drugs through tiering and exclusion. We develop a theoretical model of multidimensional contracting in which a PBM negotiates with drug manufacturers over menus of formulary‐contingent rebates and chooses a formulary. We then estimate consumer demand responses to tier placement for statins using claims data from Princeton University, a large employer contracting with a single PBM to offer prescription drug coverage to its employees. Combining the theoretical model with demand estimates and observed list prices, we quantify how allowing for differential tier placement and exclusion affect equilibrium rebates. Our predictions are consistent with available aggregate rebate data, and we find that allowing a PBM to place branded drugs on preferred‐ and non‐preferred tiers can substantially increase negotiated rebate payments.

Apprenticeships play a key role in enabling successful school‐to‐work transitions in many countries, but in the presence of imperfect information, the specificity of this type of training may entail important costs for those working outside their training fields. I study this issue in one of the most prominent training settings, the German apprenticeship system. Using administrative data and a broad occupational classification, I find that 40% of individuals work in occupations different from their training. I estimate the cost of mismatch using vacancy instruments and extend methodological approaches in high‐dimensional selection settings. Lacking training in one's occupation entails an average wage penalty of 14%, the equivalent of two years of work experience. The penalty increases with the task distance between training and occupation. My findings suggest that retraining is crucial to mitigate the adverse consequences from imperfect information in specialized training settings.

Studies on agricultural technology adoption often focus on one input, practice, or package, which is analytically useful, but may overlook the complexities involved with multidimensional learning needed for a lot of agricultural decisions. In Kenya, we study farmers' dynamic learning (from oneself and others) and adoption decisions over six seasons after randomly inviting them to participate in agronomic research trials, comparing different combinations of inputs during three consecutive seasons. As a response to the trials, adoption increases steadily despite the absence of positive profits multiple seasons after exposure to the trials. Know‐how increases rapidly and faster for high skill farmers who experiment the most, at the cost of making new mistakes. The findings are consistent with a theoretical model with multidimensionality of input and practice decisions and differential learning from one's own experience by skills, where complementarities imply that adoption of an input requires finding how to re‐optimize other dimensions, which adds to the cost of adoption.

We derive a novel decomposition of the Gini coefficient into within‐ and between‐group inequality terms that sum to the aggregate Gini coefficient. This decomposition is derived from a set of axioms that ensure desirable behavior for the within‐ and between‐group inequality terms. The decomposition of the Gini coefficient is unique given our axioms, easy to compute, and can be interpreted geometrically.

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over‐accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady‐state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

We develop an optimal policy assignment rule that integrates two distinctive approaches commonly used in economics—targeting by observables and targeting through self‐selection . Our method can be used with experimental or quasi‐experimental data to identify who should be treated, be untreated, and self‐select to achieve a policymaker's objective. Applying this method to a randomized controlled trial on a residential energy rebate program, we find that targeting that optimally exploits both observable data and self‐selection outperforms conventional targeting. We use the Local Average Treatment Effect (LATE) framework (Imbens and Angrist (1994)) to investigate the mechanism in our approach. By estimating several key LATEs based on the random variation created by our experiment, we demonstrate how our method allows policymakers to identify whose self‐selection would be valuable and harmful to social welfare.

This paper studies the economic effects of rural‐urban migration on Brazilian cities. Using a shift‐share IV design, we show that, over a decade, drought‐induced immigration reduces informality, has no effect on unemployment, and increases the number of formal firms and jobs. Downward formal wage adjustments play a key role, as these long‐run effects are weaker in regions with stronger wage rigidity. In the short run, when wage rigidity is strongest, we replicate the informality‐increasing effects documented in the literature. We develop and estimate a model of firm dynamics and informality that rationalizes these results. The counterfactuals reveal that, in the short run, the informal sector absorbs the expanding labor force and acts as a “stepping‐stone” to formality for firms and workers. In the long run, however, it reduces the aggregate benefits from immigration by allowing the least productive firms to survive.

This paper studies how the risk of hold‐up affects procurement. I use data on the universe of solar power auctions in India. The Indian context allows clean estimates of counterparty risk, because solar plants set up in the same states, by the same firms, are procured in auctions intermediated by either risky states themselves or the trusted central government. I find that the counterparty risk of an average state increases solar prices by 10%. This risk premium sharply reduces investment, because demand for green energy is elastic. Contract intermediation by the central government eliminates the counterparty risk premium.