HeteroskedasticConsistent Standard Errors
The least squares estimator can be used to estimate the linear model even when the errors are heteroskedastic with good results. As mentioned in the first part of this chapter, the problem with using least squares in a heteroskedastic model is that the usual estimator of precision (estimated variancecovariance matrix) is not consistent. The simplest way to tackle this problem is to use least squares to estimate the intercept and slopes and use an estimator of least squares covariance that is consistent whether errors are heteroskedastic or not. This is the socalled heteroskcedasticity robust estimator of covariance that gretl uses.
In this example, the food expenditure data is used to estimate the model using least squares with both the usual and the robust sets of standard errors. Start by estimating the food expenditure model using least squares and add the estimates to the model table the estimates (Usual). Reestimate the model using the —robust option and store the results (modeltab add).
The model table, which I edited a bit, is
OLS estimates
Dependent variable: food_exp
(Usual) 
(HC3 Robust) 

const 
72.96* 
72.96** 
(38.83) 
(19.91) 

income 
11.50** 
11.50** 
(2.508) 
(2.078) 

n 
20 
20 
Replace sortby income with dsortby income to sort the sample by income in descending order. 
R2 0.5389 0.5389
і 109.1 109.1
Standard errors in parentheses * indicates significance at the 10 percent level ** indicates significance at the 5 percent level
A number of commands behave differently when used after a model that employs the —robust option. For instance, the omit and restrict commands will use a Wald test instead of the usual one based on the difference in sum of squared errors.
The confidence intervals can be computed manually using saved results from the regression or from the model window of a model estimated through the GUI. Estimate the model using ols from the GUI. Select Analysis > Confidence Intervals for coefficients in the model window to generate confidence intervals based on the HCCME.
When you estimate the model, check the ‘Robust standard errors’ option (see Figure 8.2) and choose the ‘Configure’ button to select one of the options for bias correction using the pulldown menu for crosssectional data as shown earlier in Figure 8.3.
These robust standard errors are obtained from what is often referred to as the heteroskedasticity – consistent covariance matrix estimator (HCCME) that was proposed by Huber and rediscovered by White. In econometrics, the HCCME standard errors may be referred to as White’s standard errors or Huber/White standard errors. This probably accounts for the tab’s name in the dialog box.
Leave a reply