Econ 281 Non-Linear Regression Functions

Econ 281 Non-Linear Regression Functions - Non-Linear...

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Non-Linear Regression Functions Introduction to Econometrics Econ 281 Spring Quarter 2007
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 The Population Regression Function Remember the population regression function So far we assumed it is linear Now we want to look at NON-LINEAR population regression functions () ( ) i i i x m x X Y E = = |
Background image of page 2
3 Non-Linear Population Regression Function The population regression function could be Non-linear in the independent variables Non-linear in the betas Non-linear in both We are only dealing with the first case where the independent variables appear as X 2 , 1/X, X 1 *X 2 , ln(X) etc. Why use non-linear functions?
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 TestScore Income relation looks nonlinear
Background image of page 4
5 Non-Linear Population Regression Function We have already encountered an example when we estimated the following wage regression In this model, what is the effect of experience on the wage? This means that the effect of experience on the wage depends on the level of experience 2 3 2 1 0 Exp Exp Edu wage + + + = ββ 23 2 wage Exp Exp δ =+
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 Non-Linear Functions of a Single Independent Variable Assume we have a regression with only one independent variable We will deal with to forms of non-linear variables Polynomials Logarithm
Background image of page 6
7 Logarithmic functions of Y and/or X ln( X ) = the natural logarithm of X Logarithmic transforms permit modeling relations in “percentage” terms ln( x + Δ x ) – ln( x ) = Numerically : ln(1.01) = .00995 .01; ln(1.10) = .0953 .10 (sort of) ln 1 x x Δ + x x Δ
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 Logarithms We can distinguish 3 cases Case I: Linear dependent Variable with log of independent variable Linear-Log Case II: Log of dependent Variable with linear independent variable Log-Linear Case III: Log of both independent and dependent variable Log-Log
Background image of page 8
9 Linear-Log Case Looks like this What does measure? measures the effect of a percentage change in X on Y 01 ln YX u β = +⋅ + 1 1 % YY Y X XX X Δ ΔΔ == = Δ Δ Δ 1
Background image of page 9

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

View Full DocumentRight Arrow Icon
10 Log-Linear Case Looks like this What does measure? Measures the percentage change in Y due to a unit change in X 01 ln YX u β = +⋅ + 1 1 % Y YY Y XX X Δ ΔΔ == = Δ
Background image of page 10
11 Log-Log Case Looks like this What does measure? Measures the elasticity of Y with respect to X 01 ln YX u β = +⋅ + 1 1 % % Y YY Y X XX X Δ ΔΔ == = Δ
Background image of page 11

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

View Full DocumentRight Arrow Icon
12 Examples of Non-Linear Regressions Let’s look at some examples We saw that the relationship between test scores and income is not linear Let’s look how different regression specifications fit the data
Background image of page 12
13 Quadratic Regression Function n TestScore = 607.3 + 3.85 Income i – 0.0423( Income i ) 2 (2.9) (0.27) (0.0048)
Background image of page 13

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

View Full DocumentRight Arrow Icon
14 The linear-log and cubic regression functions
Background image of page 14
15 The log-linear and log-log specifications: Note vertical axis Neither seems to fit as well as the cubic or linear-log
Background image of page 15

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

View Full DocumentRight Arrow Icon
16 Summary: Log-Transforms Three cases, differing in whether Y and/or X is transformed by taking logarithms.
Background image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/25/2010 for the course ECON 281 taught by Professor Habermalz during the Winter '08 term at Northwestern.

Page1 / 44

Econ 281 Non-Linear Regression Functions - Non-Linear...

This preview shows document pages 1 - 17. Sign up to view the full document.

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