lect19_2010

# lect19_2010 - 1 / 28 Introduction to Econometrics Econ 322...

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Unformatted text preview: 1 / 28 Introduction to Econometrics Econ 322 Section 1 Fall, 2010 Lecture 19: Non-linear models (cont) November 8, 2010 Topics Covered triangleright Topics Covered Logarithmic functions of Y and/or X Three Important Cases I. Linear-Log Model II. Log-Linear Model Log-Log Model Comparison of Log-linear and Log-Log Summary: Logarithmic transformations Interactions between Variables Interactions between two binary variables Our Earnings Example Interactions between Binary and Continuous Variables Interactions between two continuous Variables 2 / 28 1. logarithmic functions 2. modelling interactions between variable Logarithmic functions of Y and/or X Topics Covered triangleright Logarithmic functions of Y and/or X Three Important Cases I. Linear-Log Model II. Log-Linear Model Log-Log Model Comparison of Log-linear and Log-Log Summary: Logarithmic transformations Interactions between Variables Interactions between two binary variables Our Earnings Example Interactions between Binary and Continuous Variables Interactions between two continuous Variables 3 / 28 square Let ln(X) = the natural logarithm of X square Logarithmic transforms permit modeling relations in percentage terms (like elasticities), rather than linearly. square Heres why: square (calculus: dln ( x ) dx = 1 x ) square Numerically: ln (1 . 01) = . 00995 = . 01; ln (1 . 10) = . 0953 = . 10 (sort of) Three Important Cases Topics Covered Logarithmic functions of Y and/or X triangleright Three Important Cases I. Linear-Log Model II. Log-Linear Model Log-Log Model Comparison of Log-linear and Log-Log Summary: Logarithmic transformations Interactions between Variables Interactions between two binary variables Our Earnings Example Interactions between Binary and Continuous Variables Interactions between two continuous Variables 4 / 28 Case Population Regression Function I. Linear-Log y i = + 1 log( x i ) + epsilon1 i II. Log-Linear log( y i ) = + 1 x i + epsilon1 i III. Log-Log log( y i ) = + 1 log( x i ) + epsilon1 i square The interpretation of the slope coefficient differs in each case. square The interpretation is found by applying the general before and after rule: figure out the change in Y for a given change in X. I. Linear-Log Model Topics Covered Logarithmic functions of Y and/or X Three Important Cases triangleright I. Linear-Log Model II. Log-Linear Model Log-Log Model Comparison of Log-linear and Log-Log Summary: Logarithmic transformations Interactions between Variables Interactions between two binary variables Our Earnings Example Interactions between Binary and Continuous Variables Interactions between two continuous Variables 5 / 28 square interpretation of 1 consider what happens when we change X by a small amount 1. before: 2. after: difference is y = 1 [log( x + x )- log( x )] = 1 x x ....
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## lect19_2010 - 1 / 28 Introduction to Econometrics Econ 322...

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