Documentation for Robust Standard Errors
Types of Robust Standard Errors
The OLS Regression add-in allows users to choose from four different types of robust standard errors, which are called HC0, HC1, HC2, and HC3. HC0 is the type of robust standard error we describe in the textbook. We discuss HC0 because it is the simplest version. However, the other methods for computing robust standard errors are superior. HC1 is an easily computed improvement, but HC2 and HC3 are preferred.
HC1
This version of robust standard errors simply corrects for degrees of freedom.
The discussion that follows is aimed at readers who understand matrix algebra and wish to know the technical details.
HC2
We closely follow Davidson and Mackinnon’s discussion of robust standard errors.[1] They point out that the standard formula for the heteroskedasticity-consistent covariance matrix, although consistent, is unreliable in finite samples. The standard formula is
[pic]
Here the central matrix [pic] has diagonal entries equal to [pic],where [pic]is the residual associated with the tth observation.
Davidson and MacKinnon recommend instead defining the tth diagonal element of the central matrix [pic] as
[pic],
where
[pic].
The t subscripts indicate that we are dealing with the tth row of the X matrix.
HC3
In this final alternate version, [pic] is replaced with
[pic].
Reference
Davidson, R. and J. G. MacKinnon (1993). Estimation and Inference in Econometrics. New York: Oxford University Press.
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[1] Davidson, R. and J. G. MacKinnon (1993, p. 553.)
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