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class16-06 - Econ 444 Monday November 20 class 16 Econ 444...

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Econ 444, Monday November 20, class 16 Econ 444, Monday November 20, class 16 Robert de Jong 1 1 Department of Economics Ohio State University Robert de Jong Econ 444, Monday November 20, class 16

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Econ 444, Monday November 20, class 16 Monday November 20 1 Heteroskedasticity - repeat of last Wednesday 2 Autocorrelation 3 Probit model and fixed effect model Robert de Jong Econ 444, Monday November 20, class 16
Econ 444, Monday November 20, class 16 Heteroskedasticity is the failure of model assumption 5 The model assumptions: 1 The regression model is linear in the coefficients, is correctly specified, and has an additive error term. 2 The error term has a zero population term. 3 All explanatory variables are uncorrelated with the error term. 4 Observations of the error term are uncorrelated with each other (no serial correlation). 5 The error term has a constant variance (no heteroskedasticity). 6 No explanatory variable is a perfect linear combination of any other explanatory variable(s) (no perfect multicollinearity). 7 The error term is normally distributed (this assumption is optional but usually is invoked). Robert de Jong Econ 444, Monday November 20, class 16

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Econ 444, Monday November 20, class 16 Heteroskedasticity can take various forms Example: expenditure on housing vs. income Example: crop yield vs. world price over 24 years, technical innovation after 12 years Example: sales of VCRs in the 1970-1992 period explained from price level and income Consequence of heteroskedasticity: 1 The coefficients will still remain correct. 2 t -values, standard errors and tests will be incorrect Compare to omitted variable or endogeneity: coefficients AND standard errors and tests will be incorrect Robert de Jong Econ 444, Monday November 20, class 16
Econ 444, Monday November 20, class 16 Testing: use the White test 1 Obtain residuals 2 Run a regression of the squared residuals on the regressors and on squares and cross-products. Example for two regressors: ( e i ) 2 = α 0 + α 1 X 1 i + α 2 X 2 i + α 3 X 1 i X 2 i + α 3 X 2 1 i + α 4 X 2 2 i + u i 3 Calculate nR 2 and compare to critical value from chi-square table with appropriate number of degrees of freedom l 4 l equals the number of variables in the above regression, not counting the constant (here: 5) Robert de Jong Econ 444, Monday November 20, class 16

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Econ 444, Monday November 20, class 16 Problems with White test: 1 not “automatic" - i.e. we get no p -value that can be compared to 0.05 2 number of terms can be large if number of regressors is large Robert de Jong Econ 444, Monday November 20, class 16
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class16-06 - Econ 444 Monday November 20 class 16 Econ 444...

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