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Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices

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  • Eric Auerbach
  • Yong Cai

Abstract

We are interested in the distribution of treatment effects for an experiment where units are randomized to a treatment but outcomes are measured for pairs of units. For example, we might measure risk sharing links between households enrolled in a microfinance program, employment relationships between workers and firms exposed to a trade shock, or bids from bidders to items assigned to an auction format. Such a double randomized experimental design may be appropriate when there are social interactions, market externalities, or other spillovers across units assigned to the same treatment. Or it may describe a natural or quasi experiment given to the researcher. In this paper, we propose a new empirical strategy that compares the eigenvalues of the outcome matrices associated with each treatment. Our proposal is based on a new matrix analog of the Fr\'echet-Hoeffding bounds that play a key role in the standard theory. We first use this result to bound the distribution of treatment effects. We then propose a new matrix analog of quantile treatment effects that is given by a difference in the eigenvalues. We call this analog spectral treatment effects.

Suggested Citation

  • Eric Auerbach & Yong Cai, 2022. "Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices," Papers 2205.01246, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2205.01246
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    References listed on IDEAS

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    1. Margherita Comola & Silvia Prina, 2021. "Treatment Effect Accounting for Network Changes," The Review of Economics and Statistics, MIT Press, vol. 103(3), pages 597-604, July.
    2. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
    3. Abhijit Banerjee & Emily Breza & Arun G Chandrasekhar & Esther Duflo & Matthew O Jackson & Cynthia Kinnan, 2024. "Changes in Social Network Structure in Response to Exposure to Formal Credit Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(3), pages 1331-1372.
    4. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    5. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2006. "What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments," American Economic Review, American Economic Association, vol. 96(4), pages 988-1012, September.
    6. Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2014. "Complementarity and aggregate implications of assortative matching: A nonparametric analysis," Quantitative Economics, Econometric Society, vol. 5, pages 29-66, March.
    7. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    8. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    9. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    10. Patrick Bajari & Brian Burdick & Guido W. Imbens & Lorenzo Masoero & James McQueen & Thomas Richardson & Ido M. Rosen, 2021. "Multiple Randomization Designs," Papers 2112.13495, arXiv.org.
    11. Susan Athey & Jonathan Levin & Enrique Seira, 2011. "Comparing open and Sealed Bid Auctions: Evidence from Timber Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 207-257.
    12. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    13. Charles F. Manski, 1997. "The Mixing Problem in Programme Evaluation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 537-553.
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