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Flexible and hyper-fast grouped regressions in Stata

version 0.51 31jul2018

## Overview

regressby is a fast and efficient method to run grouped OLS regressions; that is, it estimates a given OLS regression model on a collection of subsets of your dataset, returning the coefficients and standard errors associated with each regression. Functionally, it is very similar to the built-in -statsby- program, however, -regressby- runs between 10 and 1000 times faster than -statsby- in most use cases. The performance increases are particularly large when there are many groups, when the number observations in each group is relatively small, and when the regression model only contains a few parameters.

regressby supports a number of useful bells and whistles: subsetting with if/in, analytical weights, heteroskedasticity-robust and clustered standard errors. Furthermore, unlike statsby, regressby (optionally) allows users to access to the full variance-covariance matrix associated with each regression by returning the sampling covariance associated with each pair of estimated parameters.

## Motivation

It is easiest to explain how regressby functions by way of example. Suppose you want to estimate a regression describing how the relationship between a person's income (y) and their parent's income (x) varies across place of birth (g). More concretely, you want to run a regression of y on x with separate slopes and intercepts for each group g.

You can accomplish this in one step by regressing y on a vector of dummy variables for each distinct value of g and a vector of interactions between these dummies and x, suppressing the constant to avoid interpreting the coefficients with respect to an omitted reference group. This approach is convenient, but suffers from a number of drawacks. Most importantly, Stata does not allow the direct estimation of more than 10,998 parameters simultaneously, which in this case means that this one-step estimator can only be computed when there are fewer than 5,500 groups. Second, it turns out that directly estimating thousands of parameters is quite slow.

If the number of groups is relatively large, an alternative strategy is to estimate a univariate regression of y on x separately within each group g. There are at least two easy ways to do this in Stata, either by manually iterating over groups or by using the built-in -statsby- function. Unfortunately, both of these methods are excruciatingly slow when the number of groups is large.

Regressby is intended primarily as a replacement for these built-in methods. In my use cases, this program has been hundreds of times faster than -statsby-, reducing the runtime of scripts that would previously take days or weeks into less than an hour.

## Installation

There are two options for installing regressby.

1. The most recent version can be installed from Github with the following Stata command:
net install regressby, from(https://raw.githubusercontent.com/mdroste/stata-regressby/master/)
1. A ZIP containing the program can be downloaded and manually placed on the user's adopath from Github.

## Usage

The following two commands are equivalent:

regressby y x, by(byvars)
statsby, by(byvars) clear: reg y x	

More on this soon. See the help file in Stata.

## Benchmarks ## Todo

The following items will be addressed soon:

• Finish off this readme.md and the help file
• Finish benchmarking
• Provide script to validate results / example datasets
• Add support for frequency weights

Porting this program into a compiled C plugin for Stata would yield a significant increase in performance; I have no plans to do that in the near future.

## Acknowledgements

This program is based off of internal code from the illustrious Michael Stepner's health inequality project. This program also benefited from contributions provided by the inimitable Dr. Wilbur Townsend, who helped elegantly generalize the code to allow for an arbitrary number of regressors. Finally, this program benefited greatly from the guidance and advice of Raj Chetty.

Super fast grouped regressions in Stata spread retract
MIT

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