Instrument-Free Approach: Copula Correction
Because credible instruments are often difficult to find, instrument-free approaches have attracted increasing attention. The most prominent is copula correction.
How It Works
Copula correction follows the same logic as the control function approach: decompose the predictor’s variation into exogenous and endogenous components. But instead of using an external instrument, it constructs a copula-based control term from the conditional distribution of the predictor itself — typically its cumulative distribution function.
This term is included alongside the predictor in the outcome equation. By capturing the dependence between the predictor and the error term, the copula term removes the regressor–error correlation and enables consistent estimation. Its coefficient also serves as a diagnostic: if it is statistically significant, this signals endogeneity is present.
Untestable Assumptions
Copula correction relies on assumptions about unobservables that cannot be verified:
- The structural error (or its endogenous component) is approximately normally distributed
- The dependence between the endogenous predictor and the error, conditional on controls, is adequately captured by a Gaussian copula