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# 321_09_slides12 - Heteroscedasticity Chapter 8 Econ 321...

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Heteroscedasticity Chapter 8 Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1

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Outline What is heteroscedasticity Consequences Detection (Tests) Solutions for correcting it Form of heteroscedasticity is known Form of heteroscedasticity is unknown 2 Econ 321-Stéphanie Lluis
Introduction MLR assumption: the error terms u i are homoscedastic They all have the same variance. So var(u i ) = 2 a constant Suppose the variance varies across observations Then we have heteroscedasticity. So var(u i ) = ( i ) 2 which varies with each observation 3 Econ 321-Stéphanie Lluis

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Firm Size-Wage Example Average wages rise with the size of firm. Suppose wages look like this: 1,310 4,538 250 1,081 4,241 100-249 930 4,146 50-99 805 4,104 20-49 728 4,013 10-19 851 3,787 5-9 744 3,396 1-4 s.d. Wage Firm Size 4 Econ 321-Stéphanie Lluis
Firm Size-Wage Example Can we expect the variance of wages to be constant? The variance increases as firm size increases. So larger firms pay more on average, but there is more variability in wages within large firms than within small firms. 5 Econ 321-Stéphanie Lluis

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Savings Example Savings increases with income, so does the variability of savings or spending As incomes grow, people have more discretionary income, so more scope for choice about how to dispose of it. 6 Econ 321-Stéphanie Lluis
Simple Regression Model when Heteroscedasticity Econ 321-Stéphanie Lluis 7

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Overall Heteroscedasticity is more likely in cross sectional than time-series data. 8 Econ 321-Stéphanie Lluis
Consequences of Heteroscedasticity If we have heteroscedasticity , what happens to our estimator? Still linear Still unbiased Not the most efficient - it does not have minimum variance. So it is not BLUE. 9 Econ 321-Stéphanie Lluis (X)

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If we use usual variance formulas, they will be biased This is because the estimator is not an unbiased estimator of 2 So F tests and t tests are unreliable Consequences of Heteroscedasticity 10 Econ 321-Stéphanie Lluis
Examine residuals Assume no heteroscedasticity and run OLS and then look at estimated residuals In a 2-variable model Plot squared residuals against the independent variable. 11

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## This note was uploaded on 07/11/2011 for the course ECON 321 taught by Professor Louis during the Fall '09 term at Waterloo.

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321_09_slides12 - Heteroscedasticity Chapter 8 Econ 321...

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