IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2109.11647.html
   My bibliography  Save this paper

Treatment Effects in Market Equilibrium

Author

Listed:
  • Evan Munro
  • Stefan Wager
  • Kuang Xu

Abstract

When randomized trials are run in a marketplace equilibriated by prices, interference arises. To analyze this, we build a stochastic model of treatment effects in equilibrium. We characterize the average direct (ADE) and indirect treatment effect (AIE) asymptotically. A standard RCT can consistently estimate the ADE, but confidence intervals and AIE estimation require price elasticity estimates, which we provide using a novel experimental design. We define heterogeneous treatment effects and derive an optimal targeting rule that meets an equilibrium stability condition. We illustrate our results using a freelance labor market simulation and data from a cash transfer experiment.

Suggested Citation

  • Evan Munro & Stefan Wager & Kuang Xu, 2021. "Treatment Effects in Market Equilibrium," Papers 2109.11647, arXiv.org, revised Jan 2023.
  • Handle: RePEc:arx:papers:2109.11647
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2109.11647
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    2. Susan Athey & Dean Eckles & Guido W. Imbens, 2018. "Exact p-Values for Network Interference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 230-240, January.
    3. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    4. Coate, Stephen & Johnson, Stephen & Zeckhauser, Richard, 1994. "Pecuniary redistribution through in-kind programs," Journal of Public Economics, Elsevier, vol. 55(1), pages 19-40, September.
    5. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    6. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    7. Alberto Abadie & Susan Athey & Guido W Imbens & Jeffrey M Wooldridge, 2023. "When Should You Adjust Standard Errors for Clustering?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 1-35.
    8. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    9. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63, Elsevier.
    10. George E. Johnson, 1997. "Changes in Earnings Inequality: The Role of Demand Shifts," Journal of Economic Perspectives, American Economic Association, vol. 11(2), pages 41-54, Spring.
    11. Susan M. Dynarski, 2003. "Does Aid Matter? Measuring the Effect of Student Aid on College Attendance and Completion," American Economic Review, American Economic Association, vol. 93(1), pages 279-288, March.
    12. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    13. Johari, Ramesh & Li, Hannah & Weintraub, Gabriel, 2020. "Experimental Design in Two-Sided Platforms: An Analysis of Bias," Research Papers 3859, Stanford University, Graduate School of Business.
    14. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 499-527.
    15. Raj Chetty, 2009. "Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 451-488, May.
    16. Abhijit Banerjee & Rema Hanna & Benjamin A Olken & Elan Satriawan & Sudarno Sumarto, "undated". "Food vs. Food Stamps: Evidence from an At-Scale Experiment in Indonesia," Working Papers 2373, Publications Department.
    17. Stefan Wager & Kuang Xu, 2019. "Experimenting in Equilibrium," Papers 1903.02124, arXiv.org, revised Jun 2020.
    18. Michael P. Leung, 2020. "Treatment and Spillover Effects Under Network Interference," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 368-380, May.
    19. G W Basse & A Feller & P Toulis, 2019. "Randomization tests of causal effects under interference," Biometrika, Biometrika Trust, vol. 106(2), pages 487-494.
    20. Richard B. Freeman, 1982. "Elasticities of Demand for Educated Labor and Elasticities of Supply of Educated Labor," NBER Working Papers 1042, National Bureau of Economic Research, Inc.
    21. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    22. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    23. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    24. Lan Liu & Michael G. Hudgens, 2014. "Large Sample Randomization Inference of Causal Effects in the Presence of Interference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 288-301, March.
    25. Hudgens, Michael G. & Halloran, M. Elizabeth, 2008. "Toward Causal Inference With Interference," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 832-842, June.
    26. Claudia Allende & Francisco Gallego & Christopher Neilson, 2019. "Approximating The Equilibrium Effects of Informed School Choice," Working Papers 2019-16, Princeton University. Economics Department..
    27. Sarah Baird & J. Aislinn Bohren & Craig McIntosh & Berk Özler, 2018. "Optimal Design of Experiments in the Presence of Interference," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 844-860, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Roshni Sahoo & Stefan Wager, 2022. "Policy Learning with Competing Agents," Papers 2204.01884, arXiv.org, revised Apr 2024.
    3. Toru Kitagawa & Guanyi Wang, 2023. "Individualized Treatment Allocation in Sequential Network Games," Papers 2302.05747, arXiv.org, revised Jul 2023.
    4. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    2. Zhaonan Qu & Ruoxuan Xiong & Jizhou Liu & Guido Imbens, 2021. "Efficient Treatment Effect Estimation in Observational Studies under Heterogeneous Partial Interference," Papers 2107.12420, arXiv.org, revised Jun 2022.
    3. Julius Owusu, 2023. "Randomization Inference of Heterogeneous Treatment Effects under Network Interference," Papers 2308.00202, arXiv.org, revised Jan 2024.
    4. Ariel Boyarsky & Hongseok Namkoong & Jean Pouget-Abadie, 2023. "Modeling Interference Using Experiment Roll-out," Papers 2305.10728, arXiv.org, revised Aug 2023.
    5. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
    6. Denis Fougère & Nicolas Jacquemet, 2020. "Policy Evaluation Using Causal Inference Methods," SciencePo Working papers Main hal-03455978, HAL.
    7. Guido W. Imbens, 2020. "Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics," Journal of Economic Literature, American Economic Association, vol. 58(4), pages 1129-1179, December.
    8. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    9. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    10. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    11. Davide Viviano & Jess Rudder, 2020. "Policy design in experiments with unknown interference," Papers 2011.08174, arXiv.org, revised Dec 2023.
    12. Domenico Depalo, 2020. "Explaining the causal effect of adherence to medication on cholesterol through the marginal patient," Health Economics, John Wiley & Sons, Ltd., vol. 29(S1), pages 110-126, October.
    13. Gonzalo Vazquez-Bare, 2020. "Causal Spillover Effects Using Instrumental Variables," Papers 2003.06023, arXiv.org, revised Dec 2021.
    14. Michael P. Leung, 2020. "Treatment and Spillover Effects Under Network Interference," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 368-380, May.
    15. Bora Kim, 2020. "Analysis of Randomized Experiments with Network Interference and Noncompliance," Papers 2012.13710, arXiv.org.
    16. Carlos Daniel Santos, 2009. "Recovering the Sunk Costs of R&D: the Moulds Industry Case," CEP Discussion Papers dp0958, Centre for Economic Performance, LSE.
    17. Gonzalo Vazquez-Bare, 2017. "Identification and Estimation of Spillover Effects in Randomized Experiments," Papers 1711.02745, arXiv.org, revised Jan 2022.
    18. Eric Auerbach & Max Tabord-Meehan, 2021. "The Local Approach to Causal Inference under Network Interference," Papers 2105.03810, arXiv.org, revised Jun 2023.
    19. Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2020. "Treatment Effects With Heterogeneous Externalities," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 826-838, October.
    20. Yi Zhang & Kosuke Imai, 2023. "Individualized Policy Evaluation and Learning under Clustered Network Interference," Papers 2311.02467, arXiv.org, revised Feb 2024.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2109.11647. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.