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  • 2023
  • Working Paper

Large Shocks Travel Fast
By: Alberto Cavallo, Francesco Lippi and Ken Miyahara
We leverage the inflation upswing of 2022 and various granular datasets to identify robust price-setting patterns following a large supply shock. We show that the frequency of price changes increases dramatically after a large shock. We set up a parsimonious New...  View Details
Keywords: Macroeconomics; Analytics and Data Science; Inflation and Deflation; Cost; Mathematical Methods
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  • 2023
  • Working Paper

How People Use Statistics
By: Pedro Bordalo, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We document two new facts about the distributions of answers in famous statistical problems: they are i) multi-modal and ii) unstable with respect to irrelevant changes in the problem. We offer a model in which, when solving a problem, people represent each hypothesis...  View Details
Keywords: Decision Choices and Conditions; Microeconomics; Mathematical Methods; Behavioral Finance
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  • July 2023 (Revised July 2023)
  • Background Note

Generative AI Value Chain
By: Andy Wu and Matt Higgins
Generative AI refers to a type of artificial intelligence (AI) that can create new content (e.g., text, image, or audio) in response to a prompt from a user. ChatGPT, Bard, and Claude are examples of text generating AIs, and DALL-E, Midjourney, and Stable Diffusion are...  View Details
Keywords: AI; Artificial Intelligence; Model; Hardware; Data Centers
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  • 2023
  • Article

Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse
By: Martin Pawelczyk, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci and Himabindu Lakkaraju
As machine learning models are increasingly being employed to make consequential decisions in real-world settings, it becomes critical to ensure that individuals who are adversely impacted (e.g., loan denied) by the predictions of these models are provided with a means...  View Details
Keywords: AI and Machine Learning; Decision Choices and Conditions; Mathematical Methods
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  • 2022
  • Article

Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations
By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This...  View Details
Keywords: Mathematical Methods; Decision Choices and Conditions; Analytics and Data Science
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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...  View Details
Keywords: Supply Contracts; Intermediate Goods; Switching Costs; Vertical Relationships; Transaction Costs; Contract Duration; Identification; Supply Chain; Cost; Contracts; Auctions; Mathematical Methods
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  • 2022
  • Article

Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations
By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju
As post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it...  View Details
Keywords: Prejudice and Bias; Mathematical Methods; Research; Analytics and Data Science
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  • 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 high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a...  View Details
Keywords: Machine Learning Models; Counterfactual Explanations; Adversarial Examples; Mathematical Methods
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  • 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 two-way fixed effects (TWFE) estimator, in...  View Details
Keywords: Econometric Models; Mathematical Methods
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  • March 2022 (Revised July 2022)
  • Module Note

Linear Regression
By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
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...  View Details
Keywords: Data Science; Linear Regression; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
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  • March 2022 (Revised July 2022)
  • Module Note

Statistical Inference
By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
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...  View Details
Keywords: Data Science; Statistics; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
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  • 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 sub-set 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...  View Details
Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods
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  • March 2022
  • Article

Sensitivity Analysis of Agent-based Models: A New Protocol
By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow
Agent-based 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...  View Details
Keywords: Agent-based Modeling; Sensitivity Analysis; Design Of Experiments; Total Order Sensitivity Indices; Organizations; Behavior; Decision Making; Mathematical Methods
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  • 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 high-stakes 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...  View Details
Keywords: AI and Machine Learning; Analytics and Data Science; Mathematical Methods
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  • October 1, 2021
  • Article

An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance.
By: B.M. Balk, M.R. De Koster, Christian Kaps and J.L. Zofio
Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a...  View Details
Keywords: Efficiency Analysis; Performance Benchmarking; Warehousing; Analytics and Data Science; Performance Evaluation; Measurement and Metrics; Mathematical Methods
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  • 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 well-known mechanisms: learning from prices and...  View Details
Keywords: Bubble; Speculation; Diagnostic Expectations; Price Bubble; Mathematical Methods
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  • Article

Learning Models for Actionable Recourse
By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations provide individuals adversely...  View Details
Keywords: Machine Learning Models; Recourse; Algorithm; Mathematical Methods
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  • 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...  View Details
Keywords: Linear Regression; Regression; Analysis; Forecasting and Prediction; Risk and Uncertainty; Theory; Compensation and Benefits; Mathematical Methods; Analytics and Data Science
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  • April 2021
  • Article

A Model of Multi-Pass Search: Price Search Across Stores and Time
By: Navid Mojir and K. Sudhir
In retail settings with price promotions, consumers often search across stores and time. However, the search literature typically only models one pass search across stores, ignoring revisits to stores; the choice literature using scanner data has modeled search across...  View Details
Keywords: Consumer Search; Multi-pass Search; Price Search; Store Search; Spatial Search; Temporal Search; Spatiotemporal Search; Dynamic Structural Models; MPEC; Price Promotions; Store Loyalty; Consumer Behavior; Price; Spending; Marketing; Mathematical Methods
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  • February 2021
  • Tutorial

What is AI?
By: Tsedal Neeley
This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of...  View Details
Keywords: Artificial Intelligence; Digital; Technological Innovation; Leadership; AI and Machine Learning; Mathematical Methods
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