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Matching and Regression to the Mean in Difference-in-Differences Analysis.

Jamie R Daw1, Laura A Hatfield1

  • 1Department of Health Care Policy, Harvard Medical School, Boston, MA.

Health Services Research
|June 30, 2018
PubMed
Summary
This summary is machine-generated.

Matching on preperiod variables in difference-in-differences studies can introduce regression to the mean bias. This bias is significant when preperiod levels differ and outcome serial correlation is weak.

Keywords:
Observational researchdifference-in-differencesmatching

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Area of Science:

  • Epidemiology
  • Econometrics
  • Biostatistics

Background:

  • Difference-in-differences (DiD) is a quasi-experimental method used to estimate treatment effects.
  • Matching is often employed in DiD to improve covariate balance and reduce bias.
  • Regression to the mean is a statistical phenomenon where extreme values tend to be closer to the average upon subsequent measurement.

Purpose of the Study:

  • To investigate the potential for regression to the mean bias when matching on preperiod variables in difference-in-differences analyses.
  • To quantify the impact of matching on preperiod levels and trends under various simulation conditions.

Main Methods:

  • A Monte Carlo simulation was conducted using longitudinal data.
  • Placebo interventions were applied to simulated treatment and control groups.
  • Difference-in-differences analyses were performed with and without matching on preperiod variables.
  • Bias was assessed by the mean absolute deviation of estimated effects from zero, varying preperiod differences and serial correlation.

Main Results:

  • Unmatched DiD analyses are unbiased when preperiod outcome level is correlated with treatment assignment.
  • Matching on preperiod outcome levels introduces bias, which increases with larger preperiod level differences and weaker outcome serial correlation.
  • This bias extends to matching on preperiod levels of time-varying covariates.
  • Matching does not introduce additional bias when treatment assignment is correlated only with preperiod trend.

Conclusions:

  • Researchers must consider the risk of regression to the mean bias when using matching in difference-in-differences studies.
  • Guidance is provided on the appropriate use of matching within this study design to mitigate bias.