Bayesian Factor Model Shrinkage for Linear IV Regression With Many Instruments
针对线性工具变量模型中工具变量过多的问题，提出一种贝叶斯方法，包含新的切片采样器和基于因子模型的收缩先验，能高效处理大量工具变量，并通过模拟和三个实证例子展示效果。
A Bayesian approach for the many instruments problem in linear instrumental variable models is presented. The new approach has two components. First, a slice sampler is developed, which leverages a decomposition of the likelihood function that is a Bayesian analogue to two-stage least squares. The new sampler permits nonconjugate shrinkage priors to be implemented easily and efficiently. The new computational approach permits a Bayesian analysis of problems that were previously infeasible due to computational demands that scaled poorly in the number of regressors. Second, a new predictor-dependent shrinkage prior is developed specifically for the many instruments setting. The prior is constructed based on a factor model decomposition of the matrix of observed instruments, allowing many instruments to be incorporated into the analysis in a robust way. Features of the new method are illustrated via a simulation study and three empirical examples.