## 46.4 Standard Errors

sandwich vignette

Type Applicable Usage Reference
const Assume constant variances
HC HC0 vcovCL

Heterogeneity

White’s estimator

All other heterogeneity SE methods are derivatives of this.

HC1 vcovCL

Uses a degrees of freedom-based correction

When the number of clusters is small, HC2 and HC3 are better

HC2 vcovCL

Better with the linear model, but still applicable for Generalized Linear Models

Needs a hat (weighted) matrix

HC3 vcovCL

Better with the linear model, but still applicable for Generalized Linear Models

Needs a hat (weighted) matrix

HC4 vcovHC
HC4m vcovHC
HC5 vcovHC
data(cars)
model <- lm(speed ~ dist, data = cars)
summary(model)
#>
#> Call:
#> lm(formula = speed ~ dist, data = cars)
#>
#> Residuals:
#>     Min      1Q  Median      3Q     Max
#> -7.5293 -2.1550  0.3615  2.4377  6.4179
#>
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  8.28391    0.87438   9.474 1.44e-12 ***
#> dist         0.16557    0.01749   9.464 1.49e-12 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 3.156 on 48 degrees of freedom
#> Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438
#> F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12
lmtest::coeftest(model, vcov. = sandwich::vcovHC(model, type = "HC1"))
#>
#> t test of coefficients:
#>
#>             Estimate Std. Error t value  Pr(>|t|)
#> (Intercept) 8.283906   0.891860  9.2883 2.682e-12 ***
#> dist        0.165568   0.019402  8.5335 3.482e-11 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

### References

Cameron, A Colin, Jonah B Gelbach, and Douglas L Miller. 2008. “Bootstrap-Based Improvements for Inference with Clustered Errors.” The Review of Economics and Statistics 90 (3): 414–27.
Cribari-Neto, Francisco. 2004. “Asymptotic Inference Under Heteroskedasticity of Unknown Form.” Computational Statistics & Data Analysis 45 (2): 215–33.
Cribari-Neto, Francisco, and Wilton Bernardino da Silva. 2011. “A New Heteroskedasticity-Consistent Covariance Matrix Estimator for the Linear Regression Model.” AStA Advances in Statistical Analysis 95: 129–46.
Cribari-Neto, Francisco, Tatiene C Souza, and Klaus LP Vasconcellos. 2007. “Inference Under Heteroskedasticity and Leveraged Data.” Communications in Statistics—Theory and Methods 36 (10): 1877–88.
MacKinnon, James G, and Halbert White. 1985. “Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties.” Journal of Econometrics 29 (3): 305–25.
White, Halbert. 1980. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica: Journal of the Econometric Society, 817–38.