IDEAS home Printed from https://ideas.repec.org/a/spr/hecrev/v10y2020i1d10.1186_s13561-020-00294-9.html
   My bibliography  Save this article

Nonparametric estimation of a primary care production function in urban Brazil

Author

Listed:
  • Bruno Wichmann

    (University of Alberta)

  • Roberta Wichmann

    (World Bank
    Department of Public Health University of Brasília)

Abstract

Background The Brazilian public health system is one of the largest health systems in the world, with a mandate to deliver medical care to more than 200 million Brazilians. The objective of this study is to estimate a production function for primary care in urban Brazil. Our goal is to use flexible estimates to identify heterogeneous returns and complementarities between medical capital and labor. Methods We use a large dataset from 2012 to 2016 (with more than 400 million consultations, 270 thousand physicians, and 11 thousand clinics) to nonparametrically estimate a primary care production function and calculate the elasticity of doctors’ visits (output) to two inputs: capital stock (number of clinics) and labor (number of physicians). We benchmark our nonparametric estimates against estimates of a Cobb-Douglas (CD) production function. The CD model was chosen as a baseline because it is arguably the most popular parametric production function model. By comparing our nonparametric results with those from the CD model, our paper shed some light on the limitations of the parametric approach, and on the novelty of nonparametric insights. Results The nonparametric results show significantly heterogeneity of returns to both capital and labor, depending on the scale of operation. We find that diseconomies of scale, diminishing returns to scale, and increasing returns to scale are possible, depending on the input range. Conclusions The nonparametric model identifies complementarities between capital and labor, which is essential in designing efficient policy interventions. For example, we find that the response of primary care consultations to labor is steeper when capital level is high. This means that, if the goal is to allocate labor to maximize increases in consultations, adding physicians in cities with a high number of clinics is preferred to allocating physicians to low medical infrastructure municipalities. The results highlight how the CD model hides useful policy information by not accounting for the heterogeneity in the data.

Suggested Citation

  • Bruno Wichmann & Roberta Wichmann, 2020. "Nonparametric estimation of a primary care production function in urban Brazil," Health Economics Review, Springer, vol. 10(1), pages 1-10, December.
    • Handle: RePEc:spr:hecrev:v:10:y:2020:i:1:d:10.1186_s13561-020-00294-9
    DOI: 10.1186/s13561-020-00294-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s13561-020-00294-9
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s13561-020-00294-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Sisira Sarma & Rose Anne Devlin & William Hogg, 2010. "Physician's production of primary care in Ontario, Canada," Health Economics, John Wiley & Sons, Ltd., vol. 19(1), pages 14-30, January.
    2. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(2), pages 358-389, April.
    3. Douglas, Paul H, 1976. "The Cobb-Douglas Production Function Once Again: Its History, Its Testing, and Some New Empirical Values," Journal of Political Economy, University of Chicago Press, vol. 84(5), pages 903-915, October.
    4. Timothy J. Coelli & D.S. Prasada Rao & Christopher J. O’Donnell & George E. Battese, 2005. "An Introduction to Efficiency and Productivity Analysis," Springer Books, Springer, edition 0, number 978-0-387-25895-9, March.
    5. Niek Stadhouders & Xander Koolman & Christel van Dijk & Patrick Jeurissen & Eddy Adang, 2019. "The marginal benefits of healthcare spending in the Netherlands: Estimating cost‐effectiveness thresholds using a translog production function," Health Economics, John Wiley & Sons, Ltd., vol. 28(11), pages 1331-1344, November.
    6. Henderson,Daniel J. & Parmeter,Christopher F., 2015. "Applied Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521279680, January.
    7. Helmut Herwartz & Christoph Strumann, 2014. "Hospital efficiency under prospective reimbursement schemes: an empirical assessment for the case of Germany," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(2), pages 175-186, March.
    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. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2023. "Optimal interventions in networks during a pandemic," Journal of Population Economics, Springer;European Society for Population Economics, vol. 36(2), pages 847-883, April.
    2. Pongou, Roland & Tchuente, Guy & Tondji, Jean-Baptiste, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," GLO Discussion Paper Series 957, Global Labor Organization (GLO).
    3. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.

    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. Anne-Kathrin Last & Heike Wetzel, 2009. "Effizienzmessverfahren – eine Einführung," Working Paper Series in Economics 145, University of Lüneburg, Institute of Economics.
    2. Bornmann, Lutz & Gralka, Sabine & Anegón, Félix de Moya & Wohlrabe, Klaus, 2023. "Efficiency of universities and research-focused institutions worldwide: The introduction of a new input indicator reflecting institutional staff numbers," Journal of Informetrics, Elsevier, vol. 17(2).
    3. Galina Besstremyannaya, 2015. "Heterogeneous effect of residency matching and prospective payment on labor returns and hospital scale economies," Discussion Papers 15-001, Stanford Institute for Economic Policy Research.
    4. Christian von Hirschhausen & Astrid Cullmann, 2008. "Next Stop: Restructuring?: A Nonparametric Efficiency Analysis of German Public Transport Companies," Discussion Papers of DIW Berlin 831, DIW Berlin, German Institute for Economic Research.
    5. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    6. Juan Piedra-Peña & Diego Prior, 2023. "Analyzing the effect of health reforms on the efficiency of Ecuadorian public hospitals," International Journal of Health Economics and Management, Springer, vol. 23(3), pages 361-392, September.
    7. Lundgren, Tommy & Marklund, Per-Olov & Zhang, Shanshan, 2016. "Industrial energy demand and energy efficiency – Evidence from Sweden," Resource and Energy Economics, Elsevier, vol. 43(C), pages 130-152.
    8. Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & de Pinho Matos, Giordano Bruno Braz, 2015. "Statistical evaluation of Data Envelopment Analysis versus COLS Cobb–Douglas benchmarking models for the 2011 Brazilian tariff revision," Socio-Economic Planning Sciences, Elsevier, vol. 49(C), pages 47-60.
    9. David H. Bernstein & Christopher F. Parmeter, 2017. "Returns to Scale in Electricity Generation: Revisited and Replicated," Working Papers 2017-08, University of Miami, Department of Economics.
    10. Helmi Hammami & Thanh Ngo & David Tripe & Dinh-Tri Vo, 2022. "Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking sector," Annals of Operations Research, Springer, vol. 311(2), pages 675-694, April.
    11. Xu, Xianghui & Chen, Yingshan & Zhou, Yan & Liu, Wuyuan & Zhang, Xinrui & Li, Mo, 2023. "Sustainable management of agricultural water rights trading under uncertainty: An optimization-evaluation framework," Agricultural Water Management, Elsevier, vol. 280(C).
    12. Almeida, Alexandre N. & Bravo-Ureta, Boris E., 2019. "Agricultural productivity, shadow wages and off-farm labor decisions in Nicaragua," Economic Systems, Elsevier, vol. 43(1), pages 99-110.
    13. Figueiredo De Oliveira, Gabriel & Cariou, Pierre, 2015. "The impact of competition on container port (in)efficiency," Transportation Research Part A: Policy and Practice, Elsevier, vol. 78(C), pages 124-133.
    14. Kox, Henk L.M. & Leeuwen, George van & Wiel, Henry van der, 2010. "Competitive, but too small - productivity and entry-exit determinants in European business services," MPRA Paper 24389, University Library of Munich, Germany.
    15. Battisti, Michele & Gatto, Massimo Del & Parmeter, Christopher F., 2022. "Skill-biased technical change and labor market inefficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    16. Silvia Saravia-Matus & T. S. Amjath-Babu & Sreejith Aravindakshan & Stefan Sieber & Jimmy A. Saravia & Sergio Gomez y Paloma, 2021. "Can Enhancing Efficiency Promote the Economic Viability of Smallholder Farmers? A Case of Sierra Leone," Sustainability, MDPI, vol. 13(8), pages 1-17, April.
    17. Jael, Paul, 2019. "Does Marginal Productivity Mean Anything in Real Economic Life ?," MPRA Paper 97968, University Library of Munich, Germany, revised Jan 2020.
    18. Fall, François Seck & Tchakoute Tchuigoua, Hubert & Vanhems, Anne & Simar, Léopold, 2022. "Investigating the unobserved heterogeneity effect on microfinance social efficiency," LIDAM Discussion Papers ISBA 2022010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Norman Gemmell & Patrick Nolan & Grant Scobie, 2017. "Public sector productivity: Quality adjusting sector-level data on New Zealand schools," Working Papers 2017/02, New Zealand Productivity Commission.
    20. Töpfer, Marina, 2017. "Detailed RIF decomposition with selection: The gender pay gap in Italy," Hohenheim Discussion Papers in Business, Economics and Social Sciences 26-2017, University of Hohenheim, Faculty of Business, Economics and Social Sciences.

    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:spr:hecrev:v:10:y:2020:i:1:d:10.1186_s13561-020-00294-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com/economics/journal/13561 .

    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.