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Standard errors for the retransformation problem with heteroscedasticity.

C Ai1, E C Norton

  • 1University of Florida, USA.

Journal of Health Economics
|February 24, 2001
PubMed
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Economists can now calculate the variance for retransformed log-dependent variable models. This provides more accurate estimates for the conditional mean, slope, and average slope on the original scale.

Area of Science:

  • Econometrics
  • Statistical modeling
  • Health economics

Background:

  • Log-transformed dependent variables are common in economic models.
  • Retransformation to the original scale is often necessary but lacks variance estimation.
  • Existing methods provide consistent estimates but not their variances.

Purpose of the Study:

  • Derive variance equations for retransformed estimates.
  • Provide accurate variance estimates for the conditional mean, slope, and average slope.
  • Illustrate the practical application of these methods.

Main Methods:

  • Developed analytical methods to derive variance equations for retransformed variables.
  • Applied the derived variance equations to specific estimates: conditional mean, slope, and average slope.

Related Experiment Videos

  • Utilized skewed health expenditure data for empirical illustration.
  • Main Results:

    • Successfully derived variance equations for the conditional mean, slope, and average slope on the retransformed scale.
    • Demonstrated the utility of the proposed variance estimation procedures.
    • Highlighted the importance of accurate variance estimation in economic modeling.

    Conclusions:

    • The derived variance equations enable more precise statistical inference on the original scale.
    • Accurate variance estimation is crucial for interpreting results from log-transformed models.
    • The methods are applicable to skewed data, such as health expenditures.