Consumption surveys often record zero purchases of a good because of a short observation window. Only mean consumption rates can then be inferred. We show that propensity scores can be used to estimate each unit's consumption rate, revealing the distribution. We demonstrate the method using the...

This paper develops a micro-founded city systems model with an endogenous number of cities to explore whether local governments establish the optimal city size when production processes involve environmental pollution. Our analysis delivers two key insights. First, if an optimal scheme to...