The Ridge Path Estimator for Linear Instrumental Variables
This work addresses parameter estimation in econometrics and statistics, offering an incremental improvement for instrumental variables analysis.
The paper tackles the problem of selecting the regularization tuning parameter for a ridge-penalized linear instrumental variables estimator by proposing an empirical data-splitting method, resulting in an asymptotic distribution for the tuning parameter and showing through Monte Carlo simulations that this estimator can outperform two-stage least squares in certain cases.
This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates a path from the IV estimator to a prior. The optimal tuning parameter is the value along this path that minimizes the IV objective function for the test sample. The empirically selected regularization tuning parameter becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution of the tuning parameter is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares.