Deploying Differential Distance as an Instrumental Variable: Alternative Forms, Estimators, and Specifications.

Area of Science:

• Health Economics
• Econometrics
• Causal Inference

Background:

• Instrumental variable (IV) methods are crucial for causal inference in health research.
• The specific type of treatment effect estimated by various IV approaches is often under-examined.
• Differential distance (DD) is a commonly used IV in health studies, but its application varies.

Purpose of the Study:

• To investigate how different instrumental variable (IV) approaches, specifically differential distance (DD), affect the estimation of treatment effects in health economics.
• To evaluate the causal impact of for-profit (FP) versus not-for-profit (NFP) hospital choice on psychiatric inpatient stay costs.
• To clarify the identification of parameters when using DD as an IV in diverse econometric models.

Main Methods:

• Literature review summarizing the use of differential distance (DD) as an instrumental variable (IV).
• Theoretical reasoning and a case study comparing two-stage least squares (2SLS) with binary vs. continuous DD.
• Application of two-stage residual inclusion (2SRI) with binary and continuous DD, and comparison with local IV approaches.

Main Results:

• Estimates of treatment effects varied significantly when using two-stage least squares (2SLS) with binary versus continuous differential distance (DD).
• Two-stage residual inclusion (2SRI) approaches yielded similar treatment effect estimates with both binary and continuous DD, provided adequate control function modeling.
• 2SRI estimates aligned closely with average treatment effect estimates from local IV approaches, indicating potential for understanding selection heterogeneity.

Conclusions:

• The choice of instrumental variable (IV) method, particularly the implementation of differential distance (DD), critically influences causal effect estimates in health research.
• Two-stage residual inclusion (2SRI) offers a more robust approach with differential distance (DD) compared to two-stage least squares (2SLS) for estimating treatment effects.
• Understanding the heterogeneity of treatment effects is essential for accurately assessing the impact of hospital type (for-profit vs. not-for-profit) on healthcare costs.