Chase Abram

Public Discussion

• Blog post about measuring inequality with Ben Marrow

Works in Progress

• Job Market Paper: Linking Firm Size and Skill Composition: Theory and Evidence from Australia (Feb 26, 2025)

• Urban development dynamics and zoning. (with Jordan Rosenthal-Kay ) Slides : How do local housing markets interact across space and time? To answer this question, we develop a tractable dynamic spatial equilibrium model with continuous space and time and computable transition dynamics. Our model features fixed housing developers that build housing subject to adjustment costs, and interact in a spatial equilibrium generated by freely mobile households. The spatial equilibrium is key, because it reduces the dimensionality of the problem: rather than solving for the price at every location at every instant (an N x T dimensional problem), we only need to solve for the common household utility at each instant (a T dimensional problem). We show numerically that following a demand shock, housing adjustment paths may be nonmonotonic, as short-run demand increases may induce some developers to overshoot their long-run housing supply. In ongoing work, we apply our model to study how zoning restrictions affect the dynamics following local housing demand shocks in San Francisco. We infer de facto zoning restrictions using bunching in the building height distribution over different zoning classifications, and use our estimates of latent zoning parameters to quantify the model.

• Mortality and Income Inequality Slides : I ask why the United States has higher GDP per capita than Great Britain, but lower life expectancy. I propose a theory of mortality risk depending on income, and aggregate productivity depending on population size. I derive the stationary population size, life expectancy, and income per capita in closed form. When aggregate productivity depends positively on population size, this feedback increases the equilibrium population size. As the productivity distribution becomes more dispersed, life expectancy falls and income per capita rises, and these effects are more pronounced the more convex is the mapping from income to mortality risk. Under the assumption that mortality risk is more convex in income in the United States than Great Britain, aggregate time trends in life expectancy and income inequality are in accord with the model's predictions.

• Tractable Dynamics in Models of Location Choice Paper : I lay out a dynamic model of location choice wherein the arrival of moving opportunities is random, and provide analytic results concerning equilibrium dynamics. The stationary distribution is isomorphic to standard static quantitative spatial models, and therefore can be calibrated similarly. I also show that in the baseline case of constant elasticity externalities across space, the transition path following a permanent change in fundamentals is efficient in the decentralized economy. Finally, I motivate the baseline model's potential usefulness going forward by considering a few extensions which maintain tractability while addressing more complex economic mechanisms.

Some Miscellaneous Notes

• UChicago Econ PhD Math Camp Lecture Notes (+ solutions): Notes I used while teaching the introductory math camp for PhD students in the economics department in Fall 2021 and 2022.

• Extreme Value Derivations: Handy reference for a handful of extreme value results, including a derivation of choice probabilities.

• Simple Sticky Wage New Keynesian Model: Derivation of a RANK model in continuous-time with sticky wages and monopsonistic competition in the labor market.

• Markov Processes: Some introductory notes on Markov Processes. Prepared for a TA session for Nancy Stokey's Theory of Income I.

• Conditioning with Normal Random Variables: A few lines of linear algebra to find the distribution of a normal vector, conditional on observing another normal vector, when they are drawn from an arbitrary joint process. Prepared for a TA session for Lars Hansen and Tom Sargent's Empirical Analysis II.

• Generalized Method of Moments: The bare basics of GMM, with some examples. Prepared for a TA session for Lars Hansen and Tom Sargent's Empirical Analysis II.

• Welfare Theorems: Some notes on the welfare theorems. Prepared for a TA session for Nancy Stokey's Theory of Income I.

Code

• hopenhayn.jl: Julia implementation of Hopenhayn (1992).

External Links

Here are some other websites I like.

• Ben Moll's website: Lots of excellent notes and codes.

• Jordan Rosenthal-Kay's website: Great spatial thinker.

• QuantEcon : Superb resource for economic programming. I particularly like the textbook on economic networks.

• EconGraphs : Pretty graphs for lots of fundamental economics concepts.