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

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

Abstract

We develop a flexible two‐equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post‐program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.

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  • Giampiero Marra & Matteo Fasiolo & Rosalba Radice & Rainer Winkelmann, 2023. "A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health," Health Economics, John Wiley & Sons, Ltd., vol. 32(6), pages 1305-1322, June.
    • Handle: RePEc:wly:hlthec:v:32:y:2023:i:6:p:1305-1322
    DOI: 10.1002/hec.4668
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    More about this item

    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

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