Publications

Publications

Filter Results : (388) Arrow Down

Show Results For

Mathematical Methods Remove Mathematical Methods →

Page 1 of 388 Results →

Are you looking for?

→ Search All HBS Web
  • 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
Related
  • 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
Related
  • Article

How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
Difference-in-differences 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...  View Details
Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
Related
  • 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 real-world 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...  View Details
Keywords: Graph Neural Networks; Explanation Methods; Mathematical Methods; Framework; Theory; Analysis
Related
  • 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
Related
  • April 2022
  • Article

Predictable Financial Crises
By: Robin Greenwood, Samuel G. Hanson, Andrei Shleifer and Jakob Ahm Sørensen
Using historical data on post-war 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...  View Details
Keywords: Financial Crisis; Global Range; Forecasting and Prediction; Mathematical Methods
Related
  • 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
Related
  • 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
Related
  • Article

Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating 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
Related
  • 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
Related
  • 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
Related
  • March 2022
  • Article

Targeting High Ability Entrepreneurs Using Community Information: Mechanism Design in the Field
By: Reshmaan Hussam, Natalia Rigol and Benjamin N. Roth
Identifying high-growth microentrepreneurs in low-income 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 high-growth microentrepreneurs; while the...  View Details
Keywords: Microentrepreneurs; Community Information; Field Experiment; Loans; Entrepreneurship; Developing Countries and Economies; Financing and Loans; Information; Mathematical Methods; India
Related
  • 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
Related
  • 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 decision-maker 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...  View Details
Keywords: Prescriptive Analytics; Heterogeneous Treatment Effects; Optimization; Observed Rank Utility Condition (OUR); Between-treatment Heterogeneity; Machine Learning; Decision Making; Analysis; Mathematical Methods
Related
  • 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...  View Details
Keywords: Panel Data; Dynamic Causal Effects; Potential Outcomes; Finite Population; Nonparametric; Mathematical Methods
Related
  • 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 smart-pricing 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 quasi-natural experiment. Among...  View Details
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
Related
  • 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
Related
  • September 2021
  • Article

Oh's 8-Universality Criterion Is Unique
By: Scott Duke Kominers
Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh’s 8-universality criterion as an...  View Details
Keywords: N-universal Lattice; 8-universal Lattice; Universality Criteria; Quadratic Forms; Additively Indecomposable; Mathematical Methods
Related
  • 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
Related
  • 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
Related

Are you looking for?

→ Search All HBS Web