Standard Error Estimation for Clustered Data

In causal inference, experimental data is often collected from groups of individuals which form clusters. When estimating a statistical quantity from grouped data it is important for statisticians to take the clustering structure into account when performing standard error (SE) estimation. Literature suggests many conventional SE estimation methods ignore or underestimate grouping and which can cause severe downward bias in parameter estimation. This analysis uses Monte Carlo simulations to evaluate the downward bias claim from literature under a variety of data generating conditions such as different numbers of clusters, observations per cluster among others. In addition, a new bootstrap based estimation method using a Gaussian kernel is proposed in an effort to counteract the downward bias present under non-zero inter-cluster correlation observed in conventional estimation methods. Lastly, three estimation techniques were applied to a real-world data set consisting of home prices in Ames, IA, clustered by neighborhood which demonstrates the effect of downward bias on real research.