 # EC220 - Introduction to econometrics (chapter 7)

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EC220 - Introduction to econometrics (chapter 7)
Christopher Dougherty EC220 - Introduction to econometrics (chapter 7) Slideshow: heteroscedasticity-consistent standard errors Original citation: Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 7). [Teaching Resource] © 2012 The Author This version available at: Available in LSE Learning Resources Online: May 2012 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License. This license allows the user to remix, tweak, and build upon the work even for commercial purposes, as long as the user credits the author and licenses their new creations under the identical terms.

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where Heteroscedasticity causes OLS standard errors to be biased is finite samples. However it can be demonstrated that they are nevertheless consistent, provided that their variances are distributed independently of the regressors. 1

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where Even if this is not the case, it is still possible to obtain consistent estimators. We have seen that the slope coefficient in a simple OLS regression could be decomposed as above. 2

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where We have also seen that the variance of the estimator is given by the expression above if ui is distributed independently of uj for j i. 3

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where White (1980) demonstrates that a consistent estimator of is obtained if the squared residual in observation i is used as an estimator of Taking the square root, one obtains a heteroscedasticity-consistent standard error. 4

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where Thus in a situation where heteroscedasticity is suspected, but there is not enough information to identify its nature, it is possible to overcome the problem of biased standard errors, at least in large samples, and the t tests and F tests are asymptotically valid. 5

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
where Two points, need to be kept in mind, however. One is that, although the White estimator is consistent, it may not perform well in finite samples (MacKinnon and White, 1985). The other is that the OLS estimators remain inefficient. 6

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
. reg manu gdp Source | SS df MS Number of obs = F( 1, 26) = Model | e e Prob > F = Residual | e R-squared = Adj R-squared = Total | e e Root MSE = manu | Coef. Std. Err t P>|t| [95% Conf. Interval] gdp | _cons | . reg manu gdp, robust Regression with robust standard errors Number of obs = F( 1, 26) = Prob > F = R-squared = Root MSE = | Robust gdp | _cons | To illustrate the use of heteroscedasticity-consistent standard errors, the regression of MANU on GDP in the previous sequence is repeated with the ‘robust’ option available in Stata. 7

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
. reg manu gdp Source | SS df MS Number of obs = F( 1, 26) = Model | e e Prob > F = Residual | e R-squared = Adj R-squared = Total | e e Root MSE = manu | Coef. Std. Err t P>|t| [95% Conf. Interval] gdp | _cons | . reg manu gdp, robust Regression with robust standard errors Number of obs = F( 1, 26) = Prob > F = R-squared = Root MSE = | Robust gdp | _cons | The point estimates of the coefficients are exactly the same. They are not affected by the procedure, and so their inefficiency is not alleviated. 8

HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS
. reg manu gdp Source | SS df MS Number of obs = F( 1, 26) = Model | e e Prob > F = Residual | e R-squared = Adj R-squared = Total | e e Root MSE = manu | Coef. Std. Err t P>|t| [95% Conf. Interval] gdp | _cons | . reg manu gdp, robust Regression with robust standard errors Number of obs = F( 1, 26) = Prob > F = R-squared = Root MSE = | Robust gdp | _cons | However the standard error of the coefficient of GDP rises from 0.13 to 0.18, indicating that it is underestimated in the original OLS regression. 9