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...

This paper analyzes the generalized quality differentiation model in multi-sided markets with positive externalities, which leads to new insights into the optimal pricing structure of the firm. We find that quality differentiation for users on one side affects not only the side involving...

A monopolist producing vertically differentiated durable goods can offer in each period a sequence of price-quality menus to segment the market. We show that, contrary to the Coase conjecture for the homogeneous durable good monopoly, thanks to the ability to produce differentiated durable...

In a standard adverse selection world, asymmetric information about product quality leads to quality deterioration in the market. Suppose that a higher investment level makes the realization of high quality more likely. Then, if consumers observe the investment (but not the realization of...

We analyse optimal environmental policies in a market that is vertically differentiated in terms of the energy efficiency of products. Considering energy taxes, subsidies to firms for investment in more eco-friendly products, and product standards, we are particularly interested in how...

This paper studies the interactions between the structure of product demand, relative wages, and the allocation of economic activity across two sectors. The agrarian sector produces a homogeneous good and consists of informal firms employing adults and children. The modern sector produces a...