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Lecture 21 2010

# Lecture 21 2010 - ε change in Y 2 C Non-Linear Models 1...

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1 V. Extensions of Multiple Regression A. Dummy Variables B. Scaling Variables C. Non-Linear Models 1. Basic Idea for Estimation . 2. Models that don’t require logs 3. Models that require log transform . B. Scaling Variables 1. Scaling the Dependent and Independent Variables : The effects of scaling by a known constant are perfectly predictable: Suppose we multiply Y by ‘a’ and X by ‘b’ ( ) * 1 1 2 2 2 ( ) ˆ ˆ ( ) i i i i i i b x a Y x Y b a a b x b x b β = = = Scaling variables by constants has no real consequences. 2. Indexes – the case of an unknown scale. The independent variable, and possibly the dependent variable, may be “indexes.” Examples: Consumer Price Indexes. You have no idea about the “base year” value. Indexes – pure numbers, no “units.” Solution – calculate elasticities , pure numbers. A 1% change in X causes an

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Unformatted text preview: ε % change in Y. 2 C. Non-Linear Models 1. Basic idea : Make the model look linear in the parameters. Then estimate using OLS. 2. Models that don’t require a log transform . Quadratic form: Examples: Interpretation: C. Non-Linear Models Inverse form: Y = β + 1 (1/X) + u Example: Interpretation: C. Non-Linear Models 3. Models that require a log transform . • Cobb-Douglas : log-log models. • Transform using natural logarithm. • Interpretation: 3 3. Models that require a log transform . • Semi-Log models : log-linear • Transform using natural logarithm. • Parameters: 1 1 2 2 exp X X u Y β + + + = 3. Models that require a log transform . • Semi-Log models : linear-log. 1 2 1 2 exp exp Y u AX X = • Transform using natural logarithm. • Parameters:...
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Lecture 21 2010 - ε change in Y 2 C Non-Linear Models 1...

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