OLS_Assumptions08B

OLS_Assumptions08B - Assumptions of Ordinary Least Squares...

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1 Assumptions of Ordinary Least Squares Regression (Part 1) ESM 206 Jan 17, 2008
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2 Assumptions of OLS regression 1. Model is linear in parameters 2. The data are a random sample of the population 1. The errors are statistically independent from one another 3. The expected value of the errors is always zero 4. The independent variables are not too strongly collinear 5. The independent variables are measured precisely 6. The residuals have constant variance 7. The errors are normally distributed If assumptions 1-5 are satisfied, then OLS estimator is unbiased If assumption 6 is also satisfied, then OLS estimator has minimum variance of all unbiased estimators. If assumption 7 is also satisfied, then we can do hypothesis testing using t and F tests How can we test these assumptions? If assumptions are violated, what does this do to our conclusions? how do we fix the problem?
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3 1. Model not linear in parameters Problem: Can’t fit the model! Diagnosis: Look at the model Solutions: 1. Re-frame the model 2. Use nonlinear least squares (NLS) regression
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4 2. Errors not independent Problem: parameter estimates are biased Diagnosis (1): look for correlation between residuals and another variable (not in the model) I.e., residuals are dominated by another variable, Z, which is not random with respect to the other independent variables Solution (1): add the variable to the model Diagnosis (2): look at autocorrelation function of residuals to find patterns in time Space I.e., observations that are nearby in time or space have residuals that are more similar than average Solution (2): fit model using generalized least squares (GLS)
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5 0.4 0.6 0.8 1.0 300 350 400 450 Price Consumption 1960 1970 1980 1990 -50 0 50 Year residuals.RegModel.10
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OLS_Assumptions08B - Assumptions of Ordinary Least Squares...

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