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  • All HBS Web  (70)
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    • All HBS Web  (70)
      • Faculty Publications  (19)

      Econometric ModelsRemove Econometric Models →

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      • April 2025
      • Article

      Crisis Interventions in Corporate Insolvency

      By: Samuel Antill and Christopher Clayton
      We model the optimal resolution of insolvent firms in general equilibrium. Collateral-constrained banks lend to (i) solvent firms to finance investments and (ii) distressed firms to avoid liquidation. Liquidations create negative fire-sale externalities. Liquidations... View Details
      Keywords: Insolvent Firms; Government Intervention; Liquidation; Econometric Models; Insolvency and Bankruptcy; Policy
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      Antill, Samuel, and Christopher Clayton. "Crisis Interventions in Corporate Insolvency." Journal of Finance 80, no. 2 (April 2025): 875–910.
      • November 2024
      • Article

      Preference Externality Estimators: A Comparison of Border Approaches and IVs

      By: Xi Ling, Wesley R. Hartmann and Tomomichi Amano
      This paper compares two estimators—the Border Approach and an Instrumental Variable (IV) estimator—using a unified framework where identifying variation arises from “preference externalities,” following the intuition in Waldfogel (2003). We highlight two dimensions in... View Details
      Keywords: Econometrics; Casual Inference; Marketing; Economics; Advertising; Mathematical Methods
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      Ling, Xi, Wesley R. Hartmann, and Tomomichi Amano. "Preference Externality Estimators: A Comparison of Border Approaches and IVs." Management Science 70, no. 11 (November 2024): 7892–7910.
      • October–December 2022
      • Article

      Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem

      By: Mochen Yang, Edward McFowland III, Gordon Burtch and Gediminas Adomavicius
      Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to "mine" variables of interest from available data, followed... View Details
      Keywords: Machine Learning; Econometric Analysis; Instrumental Variable; Random Forest; Causal Inference; AI and Machine Learning; Forecasting and Prediction
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      Yang, Mochen, Edward McFowland III, Gordon Burtch, and Gediminas Adomavicius. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem." INFORMS Journal on Data Science 1, no. 2 (October–December 2022): 138–155.
      • 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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      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.
      • January 2021
      • Article

      A Model of Relative Thinking

      By: Benjamin Bushong, Matthew Rabin and Joshua Schwartzstein
      Fixed differences loom smaller when compared to large differences. We propose a model of relative thinking where a person weighs a given change along a consumption dimension by less when it is compared to bigger changes along that dimension. In deterministic settings,... View Details
      Keywords: Relative Thinking; Econometric Models; Behavior; Cognition and Thinking
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      Bushong, Benjamin, Matthew Rabin, and Joshua Schwartzstein. "A Model of Relative Thinking." Review of Economic Studies 88, no. 1 (January 2021): 162–191.
      • 2021
      • Working Paper

      Real Credit Cycles

      By: Pedro Bordalo, Nicola Gennaioli, Andrei Shleifer and Stephen J. Terry
      We incorporate diagnostic expectations, a psychologically founded model of overreaction to news, into a workhorse business cycle model with heterogeneous firms and risky debt. A realistic degree of diagnosticity, estimated from the forecast errors of managers of U.S.... View Details
      Keywords: Econometric Models; Business Cycles; Credit
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      Bordalo, Pedro, Nicola Gennaioli, Andrei Shleifer, and Stephen J. Terry. "Real Credit Cycles." NBER Working Paper Series, No. 28416, January 2021.
      • November 2020
      • Article

      Taxation in Matching Markets

      By: Arnaud Dupuy, Alfred Galichon, Sonia Jaffe and Scott Duke Kominers
      We analyze the effects of taxation in two-sided matching markets, i.e., markets in which all agents have heterogeneous preferences over potential partners. In matching markets, taxes can generate inefficiency on the allocative margin by changing who is matched to whom,... View Details
      Keywords: Matching Markets; Labor Markets; Taxation; Labor; Markets
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      Dupuy, Arnaud, Alfred Galichon, Sonia Jaffe, and Scott Duke Kominers. "Taxation in Matching Markets." International Economic Review 61, no. 4 (November 2020): 1591–1634.
      • Fall 2020
      • Article

      Business Credit Programs in the Pandemic Era

      By: Samuel G. Hanson, Jeremy C. Stein, Adi Sunderam and Eric Zwick
      We develop a pair of models that speak to the goals and design of the sort of business-lending and corporate-bond purchase programs that have been introduced by governments in response to the ongoing COVID-19 pandemic. An overarching theme is that, in contrast to the... View Details
      Keywords: COVID-19; Business Lending; Government Intervention; Econometric Models; Health Pandemics; Credit; Governance; Policy
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      Hanson, Samuel G., Jeremy C. Stein, Adi Sunderam, and Eric Zwick. "Business Credit Programs in the Pandemic Era." Brookings Papers on Economic Activity (Fall 2020).
      • August 2020 (Revised September 2020)
      • Technical Note

      Assessing Prediction Accuracy of Machine Learning Models

      By: Michael W. Toffel, Natalie Epstein, Kris Ferreira and Yael Grushka-Cockayne
      The note introduces a variety of methods to assess the accuracy of machine learning prediction models. The note begins by briefly introducing machine learning, overfitting, training versus test datasets, and cross validation. The following accuracy metrics and tools... View Details
      Keywords: Machine Learning; Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Forecasting and Prediction; Analytics and Data Science; Analysis; Mathematical Methods
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      Toffel, Michael W., Natalie Epstein, Kris Ferreira, and Yael Grushka-Cockayne. "Assessing Prediction Accuracy of Machine Learning Models." Harvard Business School Technical Note 621-045, August 2020. (Revised September 2020.)
      • 2020
      • Working Paper

      A General Theory of Identification

      By: Iavor Bojinov and Guillaume Basse
      What does it mean to say that a quantity is identifiable from the data? Statisticians seem to agree on a definition in the context of parametric statistical models — roughly, a parameter θ in a model P = {Pθ : θ ∈ Θ} is identifiable if the mapping θ 7→ Pθ is injective.... View Details
      Keywords: Identification; Econometric Models; Analytics and Data Science; Theory
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      Bojinov, Iavor, and Guillaume Basse. "A General Theory of Identification." Harvard Business School Working Paper, No. 20-086, February 2020.
      • 2008
      • Chapter

      Allocating Marketing Resources

      By: Sunil Gupta and Thomas J. Steenburgh

      Companies spend billions of dollars on marketing every year because it is essential to organic growth. Given these large investments, marketing managers have the responsibility to optimally allocate resources and to demonstrate that their investments generate... View Details

      Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods
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      Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." In Marketing Mix Decisions: New Perspectives and Practices, edited by Roger A. Kerin and Rob O'Regan. Chicago, IL: American Marketing Association, 2008.
      • 2008
      • Working Paper

      Allocating Marketing Resources

      By: Sunil Gupta and Thomas J. Steenburgh
      Marketing is essential for the organic growth of a company. Not surprisingly, firms spend billions of dollars on marketing. Given these large investments, marketing managers have the responsibility to optimally allocate these resources and demonstrate that these... View Details
      Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods
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      Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." Harvard Business School Working Paper, No. 08-069, February 2008.
      • 2005
      • Working Paper

      Additive Rules for the Quasi-linear Bargaining Problem

      By: Christopher P. Chambers and Jerry R. Green
      We study the class of additive rules for the quasi-linear bargaining problem introduced by Green. We provide a characterization of the class of all rules that are e¢ cient, translation invariant, additive, and continuous. We present several subfamilies of rules: the... View Details
      Keywords: Econometric Models
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      Chambers, Christopher P., and Jerry R. Green. "Additive Rules for the Quasi-linear Bargaining Problem." Working Paper, January 2005.
      • October 1982 (Revised June 1994)
      • Background Note

      Data Resources, Inc.: Note on Econometric Models

      By: Arthur Schleifer Jr.
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      Schleifer, Arthur, Jr. "Data Resources, Inc.: Note on Econometric Models." Harvard Business School Background Note 183-097, October 1982. (Revised June 1994.)
      • 1980
      • Working Paper

      Components of Manufacturing Inventories: A Structural Model of the Production Process

      By: Alan J. Auerbach and Jerry R. Green
      This paper presents a structural model of production and inventory accumulation based on the hypothesis of cost minimization. It differs from previous attempts in several respects. First, it integrates the analysis of input inventories with output inventories, treating... View Details
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      Auerbach, Alan J., and Jerry R. Green. "Components of Manufacturing Inventories: A Structural Model of the Production Process." NBER Working Paper Series, No. 491, June 1980.
      • 1977
      • Working Paper

      Mitigating Demographic Risk Through Social Insurance

      By: Jerry R. Green
      A two-period lifetime overlapping generations growth model is used to evaluate the possibility that social insurance can effectively offset economic risks associated with uncertainty about the rate of population growth. Crude measures of the seriousness of this type of... View Details
      Keywords: Social Insurance; Econometric Models; Public Sector; Government Administration; Policy; Human Needs; Social Issues; Risk and Uncertainty
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      Green, Jerry R. "Mitigating Demographic Risk Through Social Insurance." NBER Working Paper Series, No. 215, November 1977.
      • Article

      The Nature of Stochastic Equilibria

      By: Jerry R. Green and Mukul Majumdar
      This paper formulates the notion of stochastic equilibria as invariant probability distributions consistent with the behavior patterns of individuals and the disequilibrium adjustment mechanism of the economy. Conditions for existence, uniqueness, and stability of such... View Details
      Keywords: Stochastic Equilibria; Econometric Models
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      Green, Jerry R., and Mukul Majumdar. "The Nature of Stochastic Equilibria." Econometrica 43, no. 4 (July 1975): 647–660.
      • Article

      Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions

      By: Jerry R. Green
      The existence of an equilibrium is proven for a two-period model in which there are spot transactions and futures transactions in the first period and spot markets in the second period. Prices at that date are viewed with subjective uncertainty by all traders. This... View Details
      Keywords: Equilibrium; Sequential Trading; Econometric Models
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      Green, Jerry R. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions." Econometrica 41, no. 6 (November 1973): 1103–1123.
      • Research Summary

      The Connection Between Volatility and Leverage

      By: Emil N. Siriwardane

      Professor Siriwardane has co-developed a new econometric model that captures the link between equity volatility and financial leverage, driven by the desire to incorporate the record levels of both leverage and volatility that characterized the 2008 financial crisis... View Details

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