Transcription of Lecture 8: Serial Correlation - Columbia
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Lecture 8: Serial Correlation - Columbia
Lecture 8: Serial CorrelationProf. Sharyn O Halloran Sustainable Development U9611 Econometrics IIMidterm Review Most people did very well Good use of graphics Good writeups of results A few technical issues gave people trouble F-tests Predictions from linear regression Transforming variables A do-file will be available on Courseworksto check your answersReview of independence assumption Model: yi= b0+ b1xi+ ei(i = 1, 2, .., n) eiis independent of ejfor all distinct indices i, j Consequences of non-independence: SE s, tests, and CIs will be incorrect; LS isn t the best way to estimate sMain Violations Cluster effects (ex: mice litter mates) Serial effects (for data collected over time or space)Spatial AutocorrelationMap of Over- and Under-Gerrymanders Clearly, the value for a given state is correlated with neighbors This is a hot topic in econometrics these Series Analysis More usual is Correlation over time, or Serial Correlation : this is time seriesanalysis So residuals in one period ( t) are correlated with residuals in previous periods ( t-1, t-2, etc.)
(Note ). The estimate of the first serial correlation coefficient (α) is r 1 = c 1/c 0 Note: this is (almost) the sample correlation of residuals e 2, e 3, ...,e n with the “lag 1” residuals e 1, e 2, ..., e n-1 Estimating the first serial correlation coefficient from residuals of a single series ∑ ∑ = = = − = n t t n t c etet c e 2 ...
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