by Joachim Gassen and David Veenman
This repository provides Stata programs for multiway standard error clustering of robust regression estimators. The repository accompanies our paper (https://ssrn.com/abstract=3880942).
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robcluster2: this program produces multiway cluster-robust standard errors for a robust regression estimator. It computes standard errors for robust estimators based on equation 3.11 of Croux, Dhaene, and Hoorelbeke 2003. Multiway clustered standard errors are obtained based on (1) the intuition of Zeileis, Koll, and Graham (2020) for sandwich estimators to obtain cluster-robust standard errors and (2) the formulas for multiway cluster-robust standard errors from Thompson (2011), Cameron, Gelbach, and Miller (2011), and Gu and Yoo (2019). Significance levels of reported t-values are based on the degrees of freedom defined by the cluster dimension with the lowest number of unique clusters (G-1). -
roboot: this program produces bootstrapped standard errors for MM-estimators using the fast bootstrap procedure described by Salibian-Barrera and Zamar (2002). The robust estimator inrobootis the MM-estimator defined byrobreg mm, but the program requires an explicit input for the level of normal efficiency. The program produces MM-estimates with bootstrapped standard errors without cluster-adjustment, one-way cluster-robust standard errors, or twoway cluster-robust standard errors. The bootstrapped standard errors are derived from the standard deviations of B bootstrap samples drawn from the sample with replacement. One-way cluster-robust bootstrapped standard errors are obtained similarly by drawing entire clusters of data from the sample with replacement. Twoway cluster-robust standard errors are obtained using the formula from Thompson (2011) and Cameron, Gelbach, and Miller (2011). The cluster-robust versions rely on the computational efficiency of drawing low-dimensional matrices per cluster as described by MacKinnon (2022), which further speeds up the bootstrap procedure.
The programs can be installed by simply saving the *.ado files into your local Stata directory that contains additional ado programs. To identify this folder, type and execute "sysdir" in your Stata command window and go to the folder listed at "PLUS:". Make sure you place the program in the folder with the correct starting letter of the program (i.e., the folder names "r" for all programs) and the file extension is correctly specified as *.ado.
The robcluster2 and roboot programs require the latest versions of moremata and robreg to be installed in Stata:
ssc inst moremata, replace
ssc inst robreg, replace
Syntax: robcluster2 subcmd depvar indepvars, cluster(varlist) [options]
This program can be used to estimate a robust regression with cluster-robust standard errors in the two or three dimensions specified in cluster(varlist).
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The subcommand options available in [subcmd] follow robreg and include mm, s, m, and q. When not followed by any of these subcommands, the program can be used as a post-estimation tool after use of robreg mm, robreg s, or robreg m.
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The options available in [options] are:
- eff(value): specifies the desired level of estimation efficiency of the estimator in case the regression errors follow a normal distribution. This option is required for the default MM-estimator and the M-estimator when using the m option.
- biweight (optional): when combined with option m, this option replaces the default Huber objective function in the M-estimator with the biweight objective function.
- tol(value) (optional): specifies the tolerance for iterative algorithms (default is 1e-6).
- m() (optional): specifies the (indicator/categorical) variables to be partialled out with the S-estimator (applicable to S-estimation and MM-estimation).
- weightvar(name) (optional): stores the robust regression weights in new variable ''name''.
Output: The program produces standard regression output, with the number of observations used in the estimation, the degrees of freedom used to compute the critical values of the t-statistics (G-1, where G is the number of clusters in the dimension with lowest number of clusters), as well as the number of clusters in each dimension. Below the regression output, the program also lists information on the average weights assigned to observations in the final weighted least squares estimation, as well as the fraction of observations with weights below 0.5 and weights equal to zero. Illustration of output:
Examples of syntax with standard implementation:
robcluster2 mm y x x2 x3 x4 x5 x6, eff(95) cluster(firm year)
robcluster2 m y x x2 x3 x4 x5 x6, eff(70) cluster(firm year)
robcluster2 m y x x2 x3 x4 x5 x6, eff(95) cluster(firm year) biweight
robcluster2 s y x x2 x3 x4 x5 x6, cluster(firm year)
robcluster2 mm y i.year x x2 x3 x4 x5 x6, eff(95) cluster(firm year) m(i.year)
robcluster2 mm y x x2 x3 x4 x5 x6, eff(95) cluster(firm year dimension3)
Example of syntax with post-estimation implementation:
robreg mm y x x2 x3 x4 x5 x6, eff(95) cluster(firm)
robcluster2, cluster(firm year)
Syntax: roboot depvar indepvars, nboot(value) [cluster(varlist)] [options]
This program uses a fast-bootstrap procedure to produce bootstrapped standard errors for MM-estimators based on B bootstrap samples defined in nboot(value), with a potential adjustment for clustering up to two dimensions specified in option cluster(varlist).
- The options available in [options] are:
- nboot(value): the number of bootstrap samples to be drawn.
- eff(value): specifies the desired level of estimation efficiency of the estimator in case the regression errors follow a normal distribution.
- tol(value) (optional): specifies the tolerance for iterative algorithms (default is 1e-6).
- sopts(options) (optional): specifies additional options to be passed to the initial S-estimator in MM-estimation.
- weightvar(name) (optional): stores the robust regression weights in new variable ''name''.
- seed(value) (optional): sets the seed to ensure reproducibility of the results. Not required but highly recommended.
Output: The bootstrapped standard errors are adjusted for a finite-sample correction similar to robcluster2 and p-values rely on critical values from a t-distribution with G-1 degrees of freedom following the recommendations of Cameron and Miller (2015). Example output:
Examples:
roboot y x x2 x3 x4 x5 x6, eff(95) cluster(firm year) nboot(1000)
roboot y x x2 x3 x4 x5 x6, eff(70) cluster(firm) nboot(1000)
roboot y x x2 x3 x4 x5 x6, eff(70) nboot(1000) seed(1234)
roboot y i.year x x2 x3 x4 x5 x6, eff(95) cluster(firm year) nboot(1000) sopts(m(i.year))