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...

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...

Exploiting the cascade structure of cities and based on a dataset for U.S. cities between 1840 and 2016, the aim of this short paper is to answer three important questions: First, do we observe that the U.S. city size distribution exhibits a smooth transition to Zipf's law from the beginning or...

The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm in applied microeconomics. However, as is well known, it...

This paper investigates the predictive power of the shadow rate for the inflation rate in countries with a zero lower bound (the US, the UK and Canada) and in those with negative rates (Japan, the Euro Area and Switzerland). Using shadow rates obtained from two different models (the Wu-Xia...

The conditional equity premium in the model with production is often approximated by assuming a jointly log-normal distribution of the marginal rate of substitution in consumption and the marginal productivity of capital. We show that, for standard parameterization, this premium is about one...