This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

We derive exact conditions relating the distributions of firm productivity, sales, output, and markups to the form of demand in monopolistic competition. Applications include a new “CREMR” demand function (Constant Revenue Elasticity of Marginal Revenue): it is necessary and sufficient for...

Estimates of the trade elasticity based on actual trade policy changes are scarce, and the few that exist are all over the place. This paper offers a setting where an exogenous increase in a border tax can be used to estimate the trade elasticity. It shows theoretically and empirically that if...

This paper analyzes the stability and distribution of ambiguity attitudes using a broad population sample. Using high-powered incentives, we collected six waves of data on ambiguity attitudes about financial markets—our main application—and climate change. Estimating a structural stochastic...

We propose a Generalized Poisson-Pseudo Maximum Likelihood (G-PPML) estimator that relaxes the PPML estimator’s assumption that the dependent variable’s conditional variance is proportional to its conditional mean. Instead, we employ an iterated Generalized Method of Moments (iGMM) to...

News reports and communication are inherently constrained by space, time, and attention. As a result, news sources often condition the decision of whether to share a piece of information on the similarity between the signal and the prior belief of the audience, which generates a sample selection...

We study the small sample properties of conditional quantile estimators such as classical and IV quantile regression. First, we propose a higher-order analytical framework for comparing competing estimators in small samples and assessing the accuracy of common inference procedures. Our framework...

Multicollinearity, especially in combination with errors-in-variables, can increase the likelihood of a Type-I error by inflating the value of the estimated coefficients by more than it magnifies their standard errors, thereby increasing the likelihood of obtaining statistically significant...