We propose a framework for identification and estimation of a private values model with unobserved heterogeneity from bid data in English auctions, using variation in the number of bidders across auctions, and extend the framework to settings where the number of bidders is not cleanly observed in each auction. We illustrate our method on data from eBay Motors auctions. We find that unobserved heterogeneity is important, accounting for two thirds of price variation after controlling for observables, and that welfare measures would be dramatically misestimated if unobserved heterogeneity were ignored.

Pollution in urban areas has been one of the most relevant problems of the last decade since it represents a threat to public health. Specifically, particulate matter (PM2.5) is a pollutant that causes serious health complications, such as heart and lung diseases. Centers for monitoring contaminants and climatic variables have been established to adopt measures to control the consequences of high levels of air pollution. However, these monitoring centers sometimes make decisions when pollution levels are already harmful to health, which may be related to sensor miscalibration and failures. This study presents a PM2.5 prediction system based on a state-space model—developed with real data from 2019—plus a Kalman filter to improve the prediction. The system was subsequently validated using real data captured in 2018 in Valle de Aburrá. Therefore, this is an important first step towards a more robust PM diagnosis and prediction system in the presence of false and mismatched data in the measurement.

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