lect19_2010

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

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

Page1 / 28

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online