Publications
Logs with zeros? Some problems and solutions, with Jonathan Roth
[2024, Quarterly Journal of Economics] [Paper (final manuscript)] [arXiv] [Development Impact Blog] [Twitter TL;DR]
It turns out that one can’t define away the $\log(0)$ problem. Fundamentally, there is a trilemma on defining scale-invariant average effects. We discuss a few fixes.
Abstract
Many economic settings involve an outcome $Y$ that is weakly positive but can equal zero (e.g. earnings). In such settings, it is common to estimate an average treatment effect (ATE) for a transformation of the outcome that behaves like $\log(Y)$ when $Y$ is large but is defined at zero (e.g. $\log(1+Y)$, $\mathrm{arcsinh}(Y)$). This paper argues that ATEs for such log-like transformations should not be interpreted as approximating a percentage effect, since unlike a percentage, they depend arbitrarily on the units of the outcome when the treatment affects the extensive margin. Intuitively, this dependence arises because an individual-level percentage effect is not well-defined for individuals whose outcome changes from zero to non-zero when receiving treatment, and the units of the outcome implicitly determine how much weight the ATE places on such extensive margin changes. We further establish that when the outcome can equal zero, there is no treatment effect parameter that is an average of individual-level treatment effects, unit-invariant, and point-identified. We discuss a variety of alternative approaches that may be sensible in settings with an intensive and extensive margin, including (i) expressing the ATE in levels as a percentage (e.g. using Poisson regression), (ii) explicitly calibrating the value placed on the intensive and extensive margins, and (iii) estimating separate effects for the two margins (e.g. using Lee bounds). We illustrate these approaches in three empirical applications.Semiparametric Estimation of Long-Term Treatment Effects, with David M. Ritzwoller
[2023, Journal of Econometrics] [arXiv] [Twitter TL;DR] [Code]
We compute the semiparametric efficiency bounds for two models of long-term treatment effects and introduce the accompanying double/debiased machine learning estimators as well as sieve two-step estimators. Simulation evidence shows that our estimation strategies improve bias and variance properties.
Abstract
Long-term outcomes of experimental evaluations are necessarily observed after long delays. We develop semiparametric methods for combining the short-term outcomes of an experimental evaluation with observational measurements of the joint distribution of short-term and long-term outcomes to estimate long-term treatment effects. We characterize semiparametric efficiency bounds for estimation of the average effect of a treatment on a long-term outcome in several instances of this problem. These calculations facilitate the construction of semiparametrically efficient estimators. The finite-sample performance of these estimators is analyzed with a simulation calibrated to a randomized evaluation of the long-term effects of a poverty alleviation program.Synthetic Control As Online Linear Regression
[2023, Econometrica] [arXiv] [Twitter TL;DR] [NBER SI 2022 Labor Studies Method Session]
It turns out that synthetic control has a connection with online convex optimization, which I use to derive novel guarantees.
Abstract
This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow‐The‐Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference‐in‐differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.Efficient estimation of average derivatives in NPIV models: Simulation comparisons of neural network estimators, with Xiaohong Chen and Elie Tamer
[2023, Journal of Econometrics] [arXiv]
We conduct a large Monte Carlo study on using neural networks to estimate models of nonparametric instrumental variables.
Abstract
Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional variables more effectively than linear sieves. We investigate the performance of various ANNs in nonparametric instrumental variables (NPIV) models of moderately high dimensional covariates that are relevant to empirical economics. We present two efficient procedures for estimation and inference on a weighted average derivative (WAD): an orthogonalized plug-in with optimally-weighted sieve minimum distance (OP-OSMD) procedure and a sieve efficient score (ES) procedure. Both estimators for WAD use ANN sieves to approximate the unknown NPIV function and are $\sqrt{n}$-asymptotically normal and first-order equivalent. We provide a detailed practitioner’s recipe for implementing both efficient procedures. We compare their finite-sample performances in various simulation designs that involve smooth NPIV function of up to 13 continuous covariates, different nonlinearities and covariate correlations. Some Monte Carlo findings include: (1) tuning and optimization are more delicate in ANN estimation; (2) given proper tuning, both ANN estimators with various architectures can perform well; (3) easier to tune ANN OP-OSMD estimators than ANN ES estimators; (4) stable inferences are more difficult to achieve with ANN (than spline) estimators; (5) there are gaps between current implementations and approximation theories. Finally, we apply ANN NPIV to estimate average partial derivatives in two empirical demand examples with multivariate covariates.JUE Insight: The (Non-) Effect of Opportunity Zones on Housing Prices, with Edward L. Glaeser and David Wessel
[2022, Journal of Urban Economics] [NBER Working Paper] [Replication files] [Updated Working Paper (updated data)] [Bloomberg] [Brookings]
We rule out large immediate price effects on residential real estate from the Opportunity Zone program.
Abstract
Will the Opportunity Zones (OZ) program, America’s largest new place-based policy in decades, generate neighborhood change? We compare single-family housing price growth in OZs with price growth in areas that were eligible but not included in the program. We also compare OZs to their nearest geographic neighbors. Our most credible estimates rule out price impacts greater than 0.5 percentage points with 95% confidence, suggesting that, so far, home buyers don’t believe that this subsidy will generate major neighborhood change. OZ status reduces prices in areas with little employment, perhaps because buyers think that subsidizing new investment will increase housing supply. Mixed evidence suggests that OZs may have increased residential permitting.Auctioneers Sometimes Prefer Entry Fees to Extra Bidders, with Scott Duke Kominers
[2021, International Journal of Industrial Organization (EARIE Special Issue)]
Auctioneers can profit from entry fees, even though they create a thin market by doing so.
Abstract
We investigate a market thickness–market power tradeoff in an auction setting with endogenous entry. We find that charging admission fees can sometimes dominate the benefit of recruiting additional bidders, even though the fees themselves implicitly reduce competition at the auction stage. We also highlight that admission fees and reserve prices are different instruments in a setting with uncertainty over entry costs, and that optimal mechanisms in such settings may be more complex than simply setting a reserve price. Our results provide a counterpoint to the broad intuition of Bulow and Klemperer (1996) that market thickness often takes precedence over market power in auction design.A Semantic Approach to Financial Fundamentals with Suproteem K. Sarkar
[ACL 2020, Proceedings of the Second Workshop on Financial Technology and NLP (FinNLP)]
We explore using embeddings from large language models (BERT) for financial applications.