We propose a method to consistently estimate production functions in the presence of input price dispersion when intermediate input quantities are not observed. The traditional approach to dealing with unobserved input quantities-using deflated expenditure as a proxy-requires strong assumptions for consistency. Instead, we control for heterogeneous input prices by exploiting the first order conditions of the firm's profit maximization problem. Our approach applies to a wide class of production functions and can be extended to accommodate a variety of heterogeneous intermediate input types. A Monte Carlo study illustrates that the omitted price bias is significant in the traditional approach, while our method consistently recovers the production function parameters. We apply our method to a firm-level data set from Colombian manufacturing industries. The empirical results are consistent with the prediction that the use of expenditure as a proxy for quantities biases the elasticity of substitution downward. Moreover, using our preferred method, we provide evidence of significant input price dispersion and even wider productivity dispersion than is estimated using proxy methods.

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COVID-19 outbreak had a major impact on the organization of care in Italy, and a survey to evaluate provision of for arrhythmia during COVID-19 outbreak (March-April 2020) was launched. A total of 104 physicians from 84 Italian arrhythmia centres took part in the survey. The vast majority of participating centres (95.2%) reported a significant reduction in the number of elective pacemaker implantations during the outbreak period compared to the corresponding two months of year 2019 (50.0% of centres reported a reduction of > 50%). Similarly, 92.9% of participating centres reported a significant reduction in the number of implantable cardioverter-defibrillator (ICD) implantations for primary prevention, and 72.6% a significant reduction of ICD implantations for secondary prevention (> 50% in 65.5 and 44.0% of the centres, respectively). The majority of participating centres (77.4%) reported a significant reduction in the number of elective ablations (> 50% in 65.5% of the centres). Also the interventional procedures performed in an emergency setting, as well as acute management of atrial fibrillation had a marked reduction, thus leading to the conclusion that the impact of COVID-19 was disrupting the entire organization of health care, with a massive impact on the activities and procedures related to arrhythmia management in Italy.

Game‐theoretic models are frequently employed to study strategic interaction between agents. Empirical research has focused on estimating payoff functions while maintaining strong assumptions regarding the information structure of the game. I show how to relax informational assumptions to enhance the credibility of empirical analysis in discrete games. I apply the method to data on the entry and exit patterns of grocery stores. The model provides useful bounds on equilibrium outcomes. In addition, the empirical analysis indicates that more restrictive informational assumptions can generate qualitatively misleading counterfactual outcomes.

We show that healthcare providers face a tradeoff between increasing the number of patients they treat and improving their quality of care, with those providers facing the strongest incentives to treat more patients delivering the lowest quality of care. To measure the magnitude of this quality-quantity tradeoff, we estimate a model of dialysis provision that explicitly incorporates a center's endogenous choice of treatment quality and allows for unobserved differences in productivity across centers. We find that centers may treat 1 percent more patients by allowing their expected infection rate to increase by 0.8 percentage points (6 percent), holding inputs and productivity fixed. Our approach provides unbiased estimates of productivity, whereas traditional methods misattribute lower-quality care to greater productivity. We also find (i) extensive quality-adjusted productivity dispersion across providers, (ii) better outcomes among non-profit entities, and (iii) comparatively little effect from competition. JEL: D24, I1, L2

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Researchers make hundreds of decisions about data collection, preparation, and analysis in their research. We use a many-analysts approach to measure the extent and impact of these decisions. Two published causal empirical results are replicated by seven replicators each. We find large differences in data preparation and analysis decisions, many of which would not likely be reported in a publication. No two replicators reported the same sample size.Statistical significance varied across replications, and for one of the studies the effect's sign varied as well. The standard deviation of estimates across replications was 3-4 times the mean reported standard error.

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