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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...
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Keywords:
Macroeconomics;
Analytics and Data Science;
Inflation and Deflation;
Cost;
Mathematical Methods
Cavallo, Alberto, Francesco Lippi, and Ken Miyahara. "Large Shocks Travel Fast." NBER Working Paper Series, No. 31659, September 2023.
- 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...
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Bordalo, Pedro, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "How People Use Statistics." NBER Working Paper Series, No. 31631, August 2023.
- 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...
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Wu, Andy, and Matt Higgins. "Generative AI Value Chain." Harvard Business School Background Note 724-355, July 2023. (Revised July 2023.)
- 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...
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Pawelczyk, Martin, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci, and Himabindu Lakkaraju. "Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse." Proceedings of the International Conference on Learning Representations (ICLR) (2023).
- 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...
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Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information Processing Systems (NeurIPS) (2022). (Best Paper Award, International Conference on Machine Learning (ICML) Workshop on Interpretable ML in Healthcare.)
- 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
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...
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Dai, Jessica, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach, and Himabindu Lakkaraju. "Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society (2022): 203–214.
- 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...
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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).
- 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...
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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.
- 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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Keywords:
Data Science;
Linear Regression;
Mathematical Modeling;
Mathematical Methods;
Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Linear Regression." Harvard Business School Module Note 622-100, March 2022. (Revised July 2022.)
- 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 622-099, March 2022. (Revised July 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 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...
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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 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...
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Keywords:
Agent-based 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 Agent-based Models: A New Protocol." Computational and Mathematical Organization Theory 28, no. 1 (March 2022): 52–94.
- 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...
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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.
- 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...
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Keywords:
Efficiency Analysis;
Performance Benchmarking;
Warehousing;
Analytics and Data Science;
Performance Evaluation;
Measurement and Metrics;
Mathematical Methods
Balk, B.M., M.R. De Koster, Christian Kaps, and J.L. Zofio. "An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance." Art. 126261. Applied Mathematics and Computation 406 (October 1, 2021).
- 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...
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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).
- 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...
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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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- 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...
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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
Mojir, Navid, and K. Sudhir. "A Model of Multi-Pass Search: Price Search Across Stores and Time." Management Science 67, no. 4 (April 2021): 2126–2150.
- 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...
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