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 August 2022
 Article
Contract Duration and the Costs of Market Transactions
By: Alexander MacKay
The optimal duration of a supply contract balances the costs of reselecting a supplier against the costs of being matched to an inefficient supplier when the contract lasts too long. I develop a structural model of contract duration that captures this tradeoff and...
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Keywords:
Supply Contracts;
Intermediate Goods;
Switching Costs;
Vertical Relationships;
Transaction Costs;
Contract Duration;
Identification;
Supply Chain;
Cost;
Contracts;
Auctions;
Mathematical Methods
MacKay, Alexander. "Contract Duration and the Costs of Market Transactions." American Economic Journal: Microeconomics 14, no. 3 (August 2022): 164–212.
 2022
 Article
Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis.
By: Martin Pawelczyk, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay and Himabindu Lakkaraju
As machine learning (ML) models become more widely deployed in highstakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a...
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Keywords:
Machine Learning Models;
Counterfactual Explanations;
Adversarial Examples;
Mathematical Methods
Pawelczyk, Martin, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay, and Himabindu Lakkaraju. "Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
 Article
How Much Should We Trust Staggered DifferenceInDifferences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
Differenceindifferences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the...
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Keywords:
Difference In Differences;
Staggered Differenceindifferences Designs;
Generalized Differenceindifferences;
Dynamic Treatment Effects;
Mathematical Methods
Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered DifferenceInDifferences Estimates?" Journal of Financial Economics 144, no. 2 (May 2022): 370–395. (Editor's Choice, May 2022.)
 2022
 Article
Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods.
By: Chirag Agarwal, Marinka Zitnik and Himabindu Lakkaraju
As Graph Neural Networks (GNNs) are increasingly employed in realworld applications, it becomes critical to ensure that the stakeholders understand the rationale behind their predictions. While several GNN explanation methods have been proposed recently, there has...
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Keywords:
Graph Neural Networks;
Explanation Methods;
Mathematical Methods;
Framework;
Theory;
Analysis
Agarwal, Chirag, Marinka Zitnik, and Himabindu Lakkaraju. "Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
 2022
 Working Paper
A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure
By: Jesse M. Shapiro and Liyang Sun
Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the twoway fixed effects (TWFE) estimator, in...
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Shapiro, Jesse M., and Liyang Sun. "A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure." NBER Working Paper Series, No. 29976, April 2022.
 April 2022
 Article
Predictable Financial Crises
Using historical data on postwar financial crises around the world, we show that crises are substantially predictable. The combination of rapid credit and asset price growth over the prior three years, whether in the nonfinancial business or the household sector, is...
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Greenwood, Robin, Samuel G. Hanson, Andrei Shleifer, and Jakob Ahm Sørensen. "Predictable Financial Crises." Journal of Finance 77, no. 2 (April 2022): 863–921.
 March 2022 (Revised July 2022)
 Module Note
Linear Regression
This note provides an overview of linear regression for an introductory data science course. It begins with a discussion of correlation, and explains why correlation does not necessarily imply causation. The note then describes the method of least squares, and how to...
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 March 2022 (Revised July 2022)
 Module Note
Statistical Inference
This note provides an overview of statistical inference for an introductory data science course. First, the note discusses samples and populations. Next the note describes how to calculate confidence intervals for means and proportions. Then it walks through the logic...
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Keywords:
Data Science;
Statistics;
Mathematical Modeling;
Mathematical Methods;
Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Statistical Inference." Harvard Business School Module Note 622099, March 2022. (Revised July 2022.)
 Article
Eliminating Unintended Bias in Personalized Policies Using BiasEliminating Adapted Trees (BEAT)
By: Eva Ascarza and Ayelet Israeli
An inherent risk of algorithmic personalization is disproportionate targeting of individuals from certain groups (or demographic characteristics such as gender or race), even when the decision maker does not intend to discriminate based on those “protected”... View Details
Keywords:
Algorithm Bias;
Personalization;
Targeting;
Generalized Random Forests (GRF);
Discrimination;
Customization and Personalization;
Decision Making;
Fairness;
Mathematical Methods
Ascarza, Eva, and Ayelet Israeli. "Eliminating Unintended Bias in Personalized Policies Using BiasEliminating Adapted Trees (BEAT)." e2115126119. Proceedings of the National Academy of Sciences 119, no. 11 (March 8, 2022).
 March 2022
 Article
Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models
By: Fiammetta Menchetti and Iavor Bojinov
Researchers regularly use synthetic control methods for estimating causal effects when a subset of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless...
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Keywords:
Causal Inference;
Partial Interference;
Synthetic Controls;
Bayesian Structural Time Series;
Mathematical Methods
Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
 March 2022
 Article
Sensitivity Analysis of Agentbased Models: A New Protocol
By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow
Agentbased models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such...
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Keywords:
Agentbased Modeling;
Sensitivity Analysis;
Design Of Experiments;
Total Order Sensitivity Indices;
Organizations;
Behavior;
Decision Making;
Mathematical Methods
Borgonovo, Emanuele, Marco Pangallo, Jan Rivkin, Leonardo Rizzo, and Nicolaj Siggelkow. "Sensitivity Analysis of Agentbased Models: A New Protocol." Computational and Mathematical Organization Theory 28, no. 1 (March 2022): 52–94.
 March 2022
 Article
Targeting High Ability Entrepreneurs Using Community Information: Mechanism Design in the Field
Identifying highgrowth microentrepreneurs in lowincome countries remains a challenge due to a scarcity of verifiable information. With a cash grant experiment in India we demonstrate that community knowledge can help target highgrowth microentrepreneurs; while the...
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Keywords:
Microentrepreneurs;
Community Information;
Field Experiment;
Loans;
Entrepreneurship;
Developing Countries and Economies;
Financing and Loans;
Information;
Mathematical Methods;
India
Hussam, Reshmaan, Natalia Rigol, and Benjamin N. Roth. "Targeting High Ability Entrepreneurs Using Community Information: Mechanism Design in the Field." American Economic Review 112, no. 3 (March 2022): 861–898.
 2022
 Working Paper
The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective
By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju
As various post hoc explanation methods are increasingly being leveraged to explain complex models in highstakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how...
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Krishna, Satyapriya, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu, and Himabindu Lakkaraju. "The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective." Working Paper, 2022.
 Article
A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects
By: Edward McFowland III, Sandeep Gangarapu, Ravi Bapna and Tianshu Sun
We define a prescriptive analytics framework that addresses the needs of a constrained decisionmaker facing, ex ante, unknown costs and benefits of multiple policy levers. The framework is general in nature and can be deployed in any utility maximizing context, public...
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Keywords:
Prescriptive Analytics;
Heterogeneous Treatment Effects;
Optimization;
Observed Rank Utility Condition (OUR);
Betweentreatment Heterogeneity;
Machine Learning;
Decision Making;
Analysis;
Mathematical Methods
McFowland III, Edward, Sandeep Gangarapu, Ravi Bapna, and Tianshu Sun. "A Prescriptive Analytics Framework for Optimal Policy Deployment Using Heterogeneous Treatment Effects." MIS Quarterly 45, no. 4 (December 2021): 1807–1832.
 November 2021
 Article
Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective
By: Iavor Bojinov, Ashesh Rambachan and Neil Shephard
In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative...
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Keywords:
Panel Data;
Dynamic Causal Effects;
Potential Outcomes;
Finite Population;
Nonparametric;
Mathematical Methods
Bojinov, Iavor, Ashesh Rambachan, and Neil Shephard. "Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective." Quantitative Economics 12, no. 4 (November 2021): 1171–1196.
 September–October 2021
 Article
Frontiers: Can an AI Algorithm Mitigate Racial Economic Inequality? An Analysis in the Context of Airbnb
By: Shunyuan Zhang, Nitin Mehta, Param Singh and Kannan Srinivasan
We study the effect of Airbnb’s smartpricing algorithm on the racial disparity in the daily revenue earned by Airbnb hosts. Our empirical strategy exploits Airbnb’s introduction of the algorithm and its voluntary adoption by hosts as a quasinatural experiment. Among...
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Keywords:
Smart Pricing;
Pricing Algorithm;
Machine Bias;
Discrimination;
Racial Disparity;
Social Inequality;
Airbnb Revenue;
Revenue;
Race;
Equality and Inequality;
Prejudice and Bias;
Price;
Mathematical Methods;
Accommodations Industry
Zhang, Shunyuan, Nitin Mehta, Param Singh, and Kannan Srinivasan. "Frontiers: Can an AI Algorithm Mitigate Racial Economic Inequality? An Analysis in the Context of Airbnb." Marketing Science 40, no. 5 (September–October 2021): 813–820.
 September 2021
 Article
Diagnostic Bubbles
By: Pedro Bordalo, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We introduce diagnostic expectations into a standard setting of price formation in which investors learn about the fundamental value of an asset and trade it. We study the interaction of diagnostic expectations with two wellknown mechanisms: learning from prices and...
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Bordalo, Pedro, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "Diagnostic Bubbles." Journal of Financial Economics 141, no. 3 (September 2021).
 September 2021
 Article
Oh's 8Universality Criterion Is Unique
Using the methods developed for the proof that the 2universality criterion is unique, we partially characterize criteria for the nuniversality of positivedefinite integermatrix quadratic forms. We then obtain the uniqueness of Oh’s 8universality criterion as an...
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Keywords:
Nuniversal Lattice;
8universal Lattice;
Universality Criteria;
Quadratic Forms;
Additively Indecomposable;
Mathematical Methods
Kominers, Scott Duke. "Oh's 8Universality Criterion Is Unique." Kyungpook Mathematical Journal 61, no. 3 (September 2021): 455–459.
 Article
Learning Models for Actionable Recourse
By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
As machine learning models are increasingly deployed in highstakes domains such as legal and financial decisionmaking, there has been growing interest in posthoc methods for generating counterfactual explanations. Such explanations provide individuals adversely...
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Ross, Alexis, Himabindu Lakkaraju, and Osbert Bastani. "Learning Models for Actionable Recourse." Advances in Neural Information Processing Systems (NeurIPS) 34 (2021).
 June 2021
 Technical Note
Introduction to Linear Regression
By: Michael Parzen and Paul Hamilton
This technical note introduces (from an applied point of view) the theory and application of simple and multiple linear regression. The motivation for the model is introduced, as well as how to interpret the summary output with regard to prediction and statistical...
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