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Unformatted text preview: Economics 140A Error: Serial Correlation We continue with the remaining classic assumptions that refer to the error and are statistical in meaning. Today we focus on the assumption that the error has zero serial correlation. The assumption of zero serial correlation is closely related to the assumption of homoskedasticity in that, violation of either assumption allows one to construct a more e¢ cient estimator by weighting the observations unequally. Recall that if the error is heteroskedastic, then the observations are not equally accurate and should be weighted according to their accuracy. If the error is serially correlated, then knowledge of one value of the error term contains information about the other values of the error term and so can be used to improve estimation. In the classic model we assume that each observation does not provide infor- mation about the unknown error for any other observation; E ( U s U t ) = 0 if s and t index di/erent observations. If the assumption is satis&ed, the covariance (and so, the correlation) between any two observations is zero. As the observations are often related through time, that is they are serial in nature, the assumption is often said to imply that the error is serially uncorrelated. If the assumption is violated, so that E ( U s U t ) = & 2 s;t ; then the error is said to be serially correlated. Why might the error be serially correlated? One natural cause would be an omitted variable. (Studenmund refers to this as impure serial correlation.) If we have incorrectly excluded X t;K from the regression, then the regression error is U t + ¡ K X t;K . If X t;K is serially correlated, then so too is the error. The example brings to light why many state that error serial correlation is largely a problem of data in which the regressors are serially correlated. The solution here is to include the omitted variable, which also eliminates serial correlation. Yet serial correlation may arise for other reasons. For example, if the mis- measurement of the dependent variable arises from the introduction of a poorly measured component (as happened when computers were &rst introduced into the price index), the measurement error may be serially correlated. Incorrect func- tional form can also lead to serial correlation in the error. Suppose the population model is a curve from the origin and the estimated model is a line. For low values of the regressor, the population curve lies below the estimated line and the errors will tend to be negative. For high values of the regressor, the population curve lies above the estimated line and the errors will tend to be positive. If the regressors are grouped by size, as would be the case if the value of the regressor grew over time, then the error is serially correlated. As this example makes clear, serial correlation may arise from model misspeci&cation, and yet not be easily cured by adding in another variable....
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08