Empirical
FinanceLecture 4: When OLS is no longer
valid: examples of alternative
estimators used in empirical
finance.
代写留学生论文Module Leader: Dr Stuart Fraser
stuart.fraser@wbs.ac.uk
Room D1.18 (
Social Studies)Warwick Business School 2
Introduction
Last time…
Estimating and testing CAPM and 3-factor model.
Need to carry out misspecification testing (test assumptions of the CLRM).
Today…
Consequences of heteroscedasticityand autocorrelation for OLS estimators.
Look at a solution widely used in empirical finance: Newey-West HAC var-covmatrix.
Consequences of endogenous regressors(correlated with the error term).
Alternative estimators used in empirical finance when regressorsare endogenous: IV/GMMWarwick Business School 3
Consequences of heteroscedasticityand autocorrelation
In the presence of heteroscedasticityor autocorrelation OLS point estimators remain unbiased and consistent (see e.g., Gujarati Chps11+12; Brooks Chp4)
However the standard formula for the variance-covariance matrix…
…is no longer correct.
Therefore whilst OLS pointestimators are unbiased(and consistent) inferencesbased on the above formula (t-, F-tests and confidence intervals) are invalid.
()()12ˆvar−′=XXσβ
An estimator is consistent if its sampling distribution ‘collapses’on the true
parameter value as T→∞Warwick Business School 4
Consequences of heteroscedasticityand autocorrelation
Under het. and/or auto. the correct formula for is: Therefore if a consistentestimator of can be found then we can…Use OLS point estimators (which are unbiased and consistent)Combined with a consistent estimator of…yielding an estimator which is consistent andgives valid inferences. Principle underlying the use of OLS point estimateswith inferences based on a Newey-West HAC var-covmatrix.()βˆ var()()()()εεβ′=Ω′Ω′′=−−EXXXXXX11ˆvar()βˆ var()βˆ varΩis the variance-covariance matrix of the error terms. If the errors are homoscedasticand uncorrelated then this matrix is diagonalIn that case1Appendix see 2Iσ=Ω()()12ˆvar−′=XXσβWarwick Business School 5
Newey-West heteroscedasticityand autocorrelation consistent (HAC) variance-covariance matrix
()()()()ΣΣΣ=+=−−−−−=−−−′+′+′=′′=qjTjtttjtjtjtjtttjTttttTTxxxxwTxxTVXXVTXX11112111ˆˆˆˆˆˆwhereˆˆrˆvaεεεεεβ0,110==−=qjwwqjwXXVTTΩ′ ofestimator consistent a is ˆThis first term corrects the var-covmatrix for heteroscedasticity:(on its own this term is known as a White var-covmatrix) The second term corrects the var-covmatrix for autocorrelation:This estimator truncates the autocorrelations at lags q
Application of Newey-West HAC variance-covariance matrix
So to re-cap:
OLS point estimates with inferences based on Newey-West HAC standard errors (rather than OLS standard errors) is one solution to the problem of het. and/or auto.
However this estimator is not BLUE –there is an estimator with a smaller variance (more efficient): Generalized Least Squares (GLS).
Nonetheless Newey-West HAC var-covmatrices are widely used in empirical finance.
A common instance in which they are used is where the ho本论文由英语论文网提供整理,提供论文代写,英语论文代写,代写论文,代写英语论文,代写留学生论文,代写英文论文,留学生论文代写相关核心关键词搜索。