lect17_2010

lect17_2010 - 1 19 Introduction to Econometrics Econ 322...

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Unformatted text preview: 1 / 19 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 17: Non-linear models November 1, 2010 Topics Covered triangleright Topics Covered Non-Linear Regression: Introduction Test Scores and Class Size Non-Linear Regression Models The General Nonlinear Pop. Regression Function Interpretation of Model Nonlinear Functions of a Single Independent Variable Polynomials in X Test Score Example Quadratic Regression Results Quadratic Regression Results (cont) Marginal Effects Effect of Adding the Cubic term Summary: polynomial regression functions 2 / 19 1. nonlinear regression model 2. polynomial regression model Non-Linear Regression: Introduction Topics Covered triangleright Non-Linear Regression: Introduction Test Scores and Class Size Non-Linear Regression Models The General Nonlinear Pop. Regression Function Interpretation of Model Nonlinear Functions of a Single Independent Variable Polynomials in X Test Score Example Quadratic Regression Results Quadratic Regression Results (cont) Marginal Effects Effect of Adding the Cubic term Summary: polynomial regression functions 3 / 19 square Everything so far has been linear in the X’s square The approximation that the regression function is linear might be good for some variables, but not for others. square The multiple regression framework can be extended to handle regression functions that are nonlinear in one or more X. square the linear regression model assumes that the effect of a change in X on Y is always constant square economic theory suggests that this can sometimes be an incorrect assumption Introduction (cont) Topics Covered triangleright Non-Linear Regression: Introduction Test Scores and Class Size Non-Linear Regression Models The General Nonlinear Pop. Regression Function Interpretation of Model Nonlinear Functions of a Single Independent Variable Polynomials in X Test Score Example Quadratic Regression Results Quadratic Regression Results (cont) Marginal Effects Effect of Adding the Cubic term Summary: polynomial regression functions 4 / 19 square For example – consider the effect of an extra dollar of income on consumption of M&M’s – do you think that the impact on demand for M&M’s for a 1 dollar increase in income is the same when income is $200/week compared to $4000 per week? – probably not– law of diminishing marginal utility – at some point we will get sick of eating M&M’s – so we would expect the marginal effect of income of demand for M&M’s to decline with income square same goes for our earnings example – we would expect that the impact of age on hourly earnings to change over the life of an individual – theory suggests that the increase in hourly earnings decreases with age Test Scores and Class Size Topics Covered Non-Linear Regression: Introduction triangleright Test Scores and Class Size Non-Linear Regression Models The General Nonlinear Pop. Regression Function Interpretation of Model Nonlinear Functions of a Single Independent Variable Polynomials in X...
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lect17_2010 - 1 19 Introduction to Econometrics Econ 322...

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