IDEAS home Printed from https://ideas.repec.org/p/zur/econwp/413.html
   My bibliography  Save this paper

A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health

Author

Listed:
  • Giampiero Marra
  • Matteo Fasiolo
  • Rosalba Radice
  • Rainer Winkelmann

Abstract

Previous evidence shows that better insurance coverage increases medical expenditure. However, formal studies on the effect of spending on health outcomes, and especially mental health, are lacking. To fill this gap, we reanalyze data from the Rand Health Insurance Experiment and estimate a joint non-linear model of spending and mental health. We address the endogeneity of spending in a flexible copula regression model with Bernoulli and Tweedie margins and discuss its implementation in the freely available GJRM R package. Results confirm the importance of accounting for endogeneity: in the joint model, a $1000 spending in mental care is estimated to reduce the probability of low mental health by 1.3 percentage points, but this effect is not statistically significant. Ignoring endogeneity leads to a spurious (upwardly biased) estimate.

Suggested Citation

  • Giampiero Marra & Matteo Fasiolo & Rosalba Radice & Rainer Winkelmann, 2022. "A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health," ECON - Working Papers 413, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:413
    as

    Download full text from publisher

    File URL: https://www.zora.uzh.ch/id/eprint/218638/1/econwp413.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. John Mullahy, 1998. "Much Ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Economics," NBER Technical Working Papers 0228, National Bureau of Economic Research, Inc.
    3. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
    4. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.
    5. Deb, Partha & Trivedi, Pravin K., 2002. "The structure of demand for health care: latent class versus two-part models," Journal of Health Economics, Elsevier, vol. 21(4), pages 601-625, July.
    6. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    7. Partha Deb & Pravin K. Trivedi, 2006. "Specification and simulated likelihood estimation of a non-normal treatment-outcome model with selection: Application to health care utilization," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 307-331, July.
    8. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    9. Helmut Farbmacher & Peter Ihle & Ingrid Schubert & Joachim Winter & Amelie Wuppermann, 2017. "Heterogeneous Effects of a Nonlinear Price Schedule for Outpatient Care," Health Economics, John Wiley & Sons, Ltd., vol. 26(10), pages 1234-1248, October.
    10. Aviva Aron-Dine & Liran Einav & Amy Finkelstein, 2013. "The RAND Health Insurance Experiment, Three Decades Later," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 197-222, Winter.
    11. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    12. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    13. Manning, Willard G, et al, 1987. "Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment," American Economic Review, American Economic Association, vol. 77(3), pages 251-277, June.
    14. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
    15. United Nations UN, 2015. "Transforming our World: the 2030 Agenda for Sustainable Development," Working Papers id:7559, eSocialSciences.
    16. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    17. Brad R. Humphreys & Logan McLeod & Jane E. Ruseski, 2014. "Physical Activity And Health Outcomes: Evidence From Canada," Health Economics, John Wiley & Sons, Ltd., vol. 23(1), pages 33-54, January.
    18. Giampiero Marra & Rosalba Radice & David M. Zimmer, 2020. "Estimating the binary endogenous effect of insurance on doctor visits by copula‐based regression additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 953-971, August.
    19. Lin, Haizhen & Sacks, Daniel W., 2019. "Intertemporal substitution in health care demand: Evidence from the RAND Health Insurance Experiment," Journal of Public Economics, Elsevier, vol. 175(C), pages 29-43.
    20. Keeler, Emmett B. & Rolph, John E., 1988. "The demand for episodes of treatment in the health insurance experiment," Journal of Health Economics, Elsevier, vol. 7(4), pages 337-367, December.
    21. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.
    22. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    23. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
    Full references (including those not matched with items on IDEAS)

    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. Giampiero Marra & Rosalba Radice & David M. Zimmer, 2020. "Estimating the binary endogenous effect of insurance on doctor visits by copula‐based regression additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 953-971, August.
    2. Kurt Lavetti & Thomas DeLeire & Nicolas R. Ziebarth, 2023. "How do low‐income enrollees in the Affordable Care Act marketplaces respond to cost‐sharing?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(1), pages 155-183, March.
    3. Dunn, Abe, 2016. "Health insurance and the demand for medical care: Instrumental variable estimates using health insurer claims data," Journal of Health Economics, Elsevier, vol. 48(C), pages 74-88.
    4. Galina Besstremyannaya, 2014. "Heterogeneous effect of coinsurance rate on healthcare costs: generalized finite mixtures and matching estimators," Discussion Papers 14-014, Stanford Institute for Economic Policy Research.
    5. Nicolas R. Ziebarth, 2018. "Social Insurance and Health," Contributions to Economic Analysis, in: Health Econometrics, volume 127, pages 57-84, Emerald Group Publishing Limited.
    6. Manos Matsaganis & Theodore Mitrakos & Panos Tsakloglou, 2009. "Modelling health expenditure at the household level in Greece," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 10(3), pages 329-336, July.
    7. Amanda Kowalski, 2016. "Censored Quantile Instrumental Variable Estimates of the Price Elasticity of Expenditure on Medical Care," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 107-117, January.
    8. Stefan Boes & Michael Gerfin, 2016. "Does Full Insurance Increase the Demand for Health Care?," Health Economics, John Wiley & Sons, Ltd., vol. 25(11), pages 1483-1496, November.
    9. Carole Roan Gresenz & Jeanette A. Rogowski & Jose Escarce, 2004. "Healthcare Markets, the Safety Net and Access to Care Among the Uninsured," NBER Working Papers 10799, National Bureau of Economic Research, Inc.
    10. Jay Dev Dubey, 2021. "Measuring Income Elasticity of Healthcare-Seeking Behavior in India: A Conditional Quantile Regression Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(4), pages 767-793, December.
    11. Hao Yu, 2017. "China’s medical savings accounts: an analysis of the price elasticity of demand for health care," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 18(6), pages 773-785, July.
    12. Andrew Briggs & Richard Nixon & Simon Dixon & Simon Thompson, 2005. "Parametric modelling of cost data: some simulation evidence," Health Economics, John Wiley & Sons, Ltd., vol. 14(4), pages 421-428, April.
    13. Jones, A.M, 2010. "Models For Health Care," Health, Econometrics and Data Group (HEDG) Working Papers 10/01, HEDG, c/o Department of Economics, University of York.
    14. Toni Mora & Joan Gil & Antoni Sicras-Mainar, 2015. "The influence of obesity and overweight on medical costs: a panel data perspective," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 16(2), pages 161-173, March.
    15. Benali, Marwan & Brümmer, Bernhard & Afari-Sefa, Victor, 2017. "Small producer participation in export vegetable supply chains and household labour allocation in Tanzania: an age-disaggregated approach," GlobalFood Discussion Papers 257513, Georg-August-Universitaet Goettingen, GlobalFood, Department of Agricultural Economics and Rural Development.
    16. Shang-Yin Yang & Chou-Wen Wang & Hong-Chih Huang, 2016. "The Valuation of Lifetime Health Insurance Policies with Limited Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 777-800, September.
    17. Randall P. Ellis & Pooja G. Mookim, 2013. "K-Fold Cross-Validation is Superior to Split Sample Validation for Risk Adjustment Models," Boston University - Department of Economics - Working Papers Series wp2013-026, Boston University - Department of Economics.
    18. Nyman, John A. & Koc, Cagatay & Dowd, Bryan E. & McCreedy, Ellen & Trenz, Helen Markelova, 2018. "Decomposition of moral hazard," Journal of Health Economics, Elsevier, vol. 57(C), pages 168-178.
    19. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.
    20. Buntin, Melinda Beeuwkes & Zaslavsky, Alan M., 2004. "Too much ado about two-part models and transformation?: Comparing methods of modeling Medicare expenditures," Journal of Health Economics, Elsevier, vol. 23(3), pages 525-542, May.

    More about this item

    Keywords

    Binary response; co-payment; copula; health expenditures; penalized regression spline; Rand experiment; simultaneous estimation; Tweedie distribution;
    All these keywords.

    JEL classification:

    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

    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:zur:econwp:413. 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: Severin Oswald (email available below). General contact details of provider: https://edirc.repec.org/data/seizhch.html .

    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.