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Finance Research

Heteroskedasticity-robust standard errors in R

Writing a financial paper is often associated with an OLS regression model. One major issue can be heteroskedasticity: the variance of the error terms vary. I show you how you can detect heteroskedasticity and how to implement robust standard errors in R.

Step 1: Implement a regression model in R

model1 <- lm(dist ~ speed, data=cars) # initial model using car data

Step 2: Detect heteroskedasticity using the Breush Pagan Test. When the p-value is below the 10% we can reject the null hypothesis that the variance of the residuals is constant. 

require(lmtest)  # load the package
require(vars)

The p-value is below the critical value of 10%.

lmtest::bptest(model1)
	studentized Breusch-Pagan test

data: model1
BP = 3.2149, df = 1, p-value = 0.07297

Step 3: Use Newey-West to correct the standard errors

model2 <- lm(dist~speed,data=cars)
model2$coefficients <- unclass(coeftest(model2, vcov. = NeweyWest))

Step 4: Compare the results

summary(model1)
Call:
lm(formula = dist ~ speed, data = cars)

Residuals:
Min 1Q Median 3Q Max
-29.069 -9.525 -2.272 9.215 43.201

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -17.5791 6.7584 -2.601 0.0123 *
speed 3.9324 0.4155 9.464 1.49e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.38 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
model2
Call:
lm(formula = dist ~ speed, data = cars)

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.758e+01 7.018e+00 -2.505e+00 1.570e-02
speed 3.932e+00 5.509e-01 7.138e+00 4.526e-09

Notice that the estimated coefficients are the same but the standard errors of the two models differ! Hence, this affects the statistical significance.