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  • All HBS Web  (855)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
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  • July 1999
  • Background Note

Note on Statistical Tests for a Randomized Matched Pair Experimental Design, A

By: Alvin J. Silk
Concerns understanding the conditions under which an experimental design that employs matching and randomization may result in gains in precision as compared to a design that utilizes randomization and independent samples--i.e., no matching. An empirical example is... View Details
Keywords: Marketing; Performance Efficiency; Mathematical Methods
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Silk, Alvin J. "Note on Statistical Tests for a Randomized Matched Pair Experimental Design, A." Harvard Business School Background Note 500-007, July 1999.
  • 1981
  • Chapter

Sparsity and Piecewise Linearity in Large Portfolio Optimization Problems

By: André Perold and Harry M. Markowitz
Keywords: Investment Portfolio; Mathematical Methods
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Perold, André, and Harry M. Markowitz. "Sparsity and Piecewise Linearity in Large Portfolio Optimization Problems." In Sparse Matricies and Their Uses, edited by I. S. Duff. Academic Press, 1981.
  • 1981
  • Chapter

Risk Aversion and Solutions to Nash's Bargaining Problem

By: R. Kihlstrom, A. E. Roth and D. Schmeidler
Keywords: Risk and Uncertainty; Negotiation; Mathematical Methods
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Kihlstrom, R., A. E. Roth, and D. Schmeidler. "Risk Aversion and Solutions to Nash's Bargaining Problem." In Game Theory and Mathematical Economics, edited by O. Moeschlin and D. Pallaschke, 65–71. Amsterdam: North-Holland Publishing Company, 1981.
  • May 2020
  • Article

Inventory Auditing and Replenishment Using Point-of-Sales Data

By: Achal Bassamboo, Antonio Moreno and Ioannis Stamatopoulos
Spoilage, expiration, damage due to employee/customer handling, employee theft, and customer shoplifting usually are not reflected in inventory records. As a result, records often report phantom inventory, i.e., units of good not available for sale. We derive an... View Details
Keywords: Shelf Availability; Inventory Record Inaccuracy; Optimal Replenishment; Retail Analytics; Performance Effectiveness; Analysis; Mathematical Methods
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Bassamboo, Achal, Antonio Moreno, and Ioannis Stamatopoulos. "Inventory Auditing and Replenishment Using Point-of-Sales Data." Production and Operations Management 29, no. 5 (May 2020): 1219–1231.
  • April 1979
  • Article

Statistical Models of Bond Ratings: A Methodological Inquiry

By: Robert S. Kaplan and Gabriel Urwitz
Keywords: Mathematical Methods; Bonds
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Kaplan, Robert S., and Gabriel Urwitz. "Statistical Models of Bond Ratings: A Methodological Inquiry." Journal of Business (April 1979): 231–261.
  • Article

Mitigating Bias in Adaptive Data Gathering via Differential Privacy

By: Seth Neel and Aaron Leon Roth
Data that is gathered adaptively—via bandit algorithms, for example—exhibits bias. This is true both when gathering simple numeric valued data—the empirical means kept track of by stochastic bandit algorithms are biased downwards—and when gathering more complicated... View Details
Keywords: Bandit Algorithms; Bias; Analytics and Data Science; Mathematical Methods; Theory
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Neel, Seth, and Aaron Leon Roth. "Mitigating Bias in Adaptive Data Gathering via Differential Privacy." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
  • June 2005 (Revised March 2006)
  • Case

E Ink in 2005

By: David B. Yoffie and Barbara Mack
Explores the challenges of commercializing a bleeding-edge technology. After seven years, E Ink has spent more than $100 million to commercialize electronic ink. With business momentum picking up, but resources running out, the case examines the key trade-offs in... View Details
Keywords: Technological Innovation; Commercialization; Mathematical Methods; Consumer Products Industry; Technology Industry
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Yoffie, David B., and Barbara Mack. "E Ink in 2005." Harvard Business School Case 705-506, June 2005. (Revised March 2006.)
  • January 1995 (Revised January 1995)
  • Case

USAA: Business Process Review for the Great Lakes Region (Abridged)

By: James L. Heskett
Presents the results of a service process analysis of USAA's claims processing activity in its Great Lakes Region. Explores not only issues of redesigning the process but also the organizational implications of various alternatives. View Details
Keywords: Restructuring; Mortgages; Management Practices and Processes; Business Processes; Organizational Design; Mathematical Methods; Real Estate Industry; North America
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Heskett, James L. "USAA: Business Process Review for the Great Lakes Region (Abridged)." Harvard Business School Case 395-026, January 1995. (Revised January 1995.)
  • 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
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Ascarza, Eva, and Ayelet Israeli. "Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating Adapted Trees (BEAT)." e2115126119. Proceedings of the National Academy of Sciences 119, no. 11 (March 8, 2022).
  • January 2006
  • Tutorial

Cost-Volume Profit Models

By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
Keywords: Volume; Cost; Profit; Mathematical Methods
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"Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
  • 2007
  • Working Paper

Mental Accounting and Small Windfalls: Evidence from an Online Grocer

By: Katherine L. Milkman, John Beshears, Todd Rogers and Max H. Bazerman
We study the effect of small windfalls on consumer spending decisions by examining the purchasing behavior of a sample of online grocery shoppers over the course of a year. We compare the purchases customers make when redeeming a $10-off coupon they received from their... View Details
Keywords: Spending; Consumer Behavior; Mathematical Methods; Food and Beverage Industry; Retail Industry
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Milkman, Katherine L., John Beshears, Todd Rogers, and Max H. Bazerman. "Mental Accounting and Small Windfalls: Evidence from an Online Grocer." Harvard Business School Working Paper, No. 08-024, September 2007. (Revised March 2008.)
  • 2010
  • Working Paper

Medium Term Business Cycles in Developing Countries

By: Diego A. Comin, Norman Loayza, Farooq Pasha and Luis Serven
We build a two-country asymmetric DSGE model with two features: (i) endogenous and slow diffusion of technologies from the developed to the developing country, and (ii) adjustment costs to investment flows. We calibrate the model to match the Mexico-U.S. trade and FDI... View Details
Keywords: Business Cycles; Developing Countries and Economies; Trade; International Finance; Foreign Direct Investment; Mathematical Methods; Mexico; United States
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Comin, Diego A., Norman Loayza, Farooq Pasha, and Luis Serven. "Medium Term Business Cycles in Developing Countries." Harvard Business School Working Paper, No. 10-029, October 2009. (Revise and resubmit at the American Economic Journal: Macroeconomics.)
  • July 1987
  • Case

Altoona Corp.: Computer Products Division

By: Roger E. Bohn and Robert H. Hayes
A relatively small manufacturer of computer memory disks has achieved a major market position through the use of its statistical quality control (SQC) program. It is now expanding the production of a new line of disks and is encountering problems getting the process... View Details
Keywords: Factories, Labs, and Plants; Volatility; Performance Consistency; Performance Improvement; Performance Productivity; Quality; Mathematical Methods; Hardware; Manufacturing Industry
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Bohn, Roger E., and Robert H. Hayes. "Altoona Corp.: Computer Products Division." Harvard Business School Case 688-010, July 1987.
  • May 1988
  • Background Note

Roles and Relationships of Business and Government

By: George C. Lodge
Synthesizes a wide range of literature and experience concerning comparative government-business relations, focusing especially on Japan, Europe, and the United States with some references to Brazil and Mexico. Designed for discussion in two consecutive class sessions.... View Details
Keywords: Economic Systems; Framework; Government and Politics; Mission and Purpose; Organizational Structure; Business and Government Relations; Mathematical Methods; System; Japan; Europe; Mexico; United States; Brazil
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Lodge, George C. "Roles and Relationships of Business and Government." Harvard Business School Background Note 388-159, May 1988.
  • Article

An Optimization-based Econometric Framework for the Evaluation of Monetary Policy

By: Julio J. Rotemberg and Michael Woodford
Keywords: Framework; Mathematical Methods; Money; Policy
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Rotemberg, Julio J., and Michael Woodford. "An Optimization-based Econometric Framework for the Evaluation of Monetary Policy." NBER Macroeconomics Annual 12 (1997): 297–344.
  • March 1989 (Revised April 1998)
  • Case

Marriott Corporation: The Cost of Capital (Abridged)

By: Richard S. Ruback
Gives students the opportunity to explore how a company uses the Capital Asset Pricing Model (CAPM) to compute the cost of capital for each of its divisions. The use of Weighted Average Cost of Capital (WACC) formula and the mechanics of applying it are stressed. View Details
Keywords: Cost of Capital; Mathematical Methods
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Ruback, Richard S. "Marriott Corporation: The Cost of Capital (Abridged)." Harvard Business School Case 289-047, March 1989. (Revised April 1998.)
  • November 2019
  • Article

Full Substitutability

By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of... View Details
Keywords: Substitutability; Mathematical Methods; Auctions; Market Design
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Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Theoretical Economics 14, no. 4 (November 2019): 1535–1590.
  • July 2008 (Revised May 2009)
  • Teaching Note

The Springfield Nor'easters: Maximizing Revenues in the Minor Leagues (Brief Case)

By: Frank V. Cespedes, Christopher H. Lovelock and Laura Winig
Teaching Note for 2510 View Details
Keywords: Market Research; Quantitative Analysis; Consumer Marketing; Pricing Strategy; Price; Mathematical Methods; Marketing Channels
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Cespedes, Frank V., Christopher H. Lovelock, and Laura Winig. "The Springfield Nor'easters: Maximizing Revenues in the Minor Leagues (Brief Case)." Harvard Business School Teaching Note 082-511, July 2008. (Revised May 2009.)
  • November 2012
  • Article

The Variance of Non-Parametric Treatment Effect Estimators in the Presence of Clustering

By: Samuel G. Hanson and Adi Sunderam
Non-parametric estimators of treatment effects are often applied in settings where clustering may be important. We provide a general methodology for consistently estimating the variance of a large class of non-parametric estimators, including the simple matching... View Details
Keywords: Treatment Effects; Matching Estimators; Clustering; Applications and Software; Mathematical Methods
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Hanson, Samuel G., and Adi Sunderam. "The Variance of Non-Parametric Treatment Effect Estimators in the Presence of Clustering." Review of Economics and Statistics 94, no. 4 (November 2012). (Stata and Matlab Code Here.)
  • 18 Sep 2019
  • Working Paper Summaries

Using Models to Persuade

Keywords: by Joshua Schwartzstein and Adi Sunderam
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