Efficient Solution of Large Fixed Effects Problems with Clustered Standard Errors

• Activity Number: 240 - Computationally Intensive Methods for Estimation and Inference
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Thomas Balmat* and Jerry Reiter
• Companies: Duke University and Department of Statistical Science, Duke University
• Keywords: Large data least squares ; fixed effects estimation ; clustered standard errors ; sparse matrix methods ; high performance computing ; parallel computing

Abstract

Large fixed effects regression problems, involving 100 million observations and thousands of effects levels, present special computational challenges but, also, a special performance opportunity because of the large proportion of entries in the expanded design matrix that are zero. For many problems, the proportion of zero entries is above 0.99995, which would be considered sparse. In this presentation, we demonstrate an efficient method for solving large, sparse fixed effects OLS problems without creation of the expanded design matrix and avoiding computations involving zero-level effects. This leads to minimal memory usage and optimal execution time. A feature, often desired in social science applications, is to estimate parameter standard errors clustered about a key identifier, such as employee ID. For large problems, with ID counts in the millions, this presents a significant computational challenge. We present a sparse matrix indexing algorithm that produces clustered standard error estimates that, for large fixed effects problems, is many times more efficient than standard sandwich matrix operations.