Nonlinear Relationships

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Presentation transcript:

Nonlinear Relationships ECON 4550 Econometrics Memorial University of Newfoundland Nonlinear Relationships Chapter 7 Adapted from Vera Tabakova’s

Chapter 7: Nonlinear Relationships 7.1 Polynomials 7.2 Dummy Variables 7.3 Applying Dummy Variables 7.4 Interactions Between Continuous Variables 7.5 Log-Linear Models (not covered in class) Principles of Econometrics, 3rd Edition

Figure 7.1 (a) Total cost curve and (b) total product curve 7.1 Polynomials 7.1.1 Cost and Product Curves Figure 7.1 (a) Total cost curve and (b) total product curve Principles of Econometrics, 3rd Edition

Figure 7.2 Average and marginal (a) cost curves and (b) product curves 7.1 Polynomials Figure 7.2 Average and marginal (a) cost curves and (b) product curves Principles of Econometrics, 3rd Edition

7.1 Polynomials (7.1) (7.2) (7.3) (7.4) Principles of Econometrics, 3rd Edition

7.1.2 A Wage Equation (7.5) (7.6) Principles of Econometrics, 3rd Edition

7.1.2 A Wage Equation Principles of Econometrics, 3rd Edition

7.1.2 A Wage Equation At the sample median of age (18 years old) the estimated marginal effect is: The turning point of the relationship is given by Principles of Econometrics, 3rd Edition

7.2 Dummy Variables (7.7) (7.8) Principles of Econometrics, 3rd Edition

7.2.1 Intercept Dummy Variables (7.9) (7.10) Principles of Econometrics, 3rd Edition

7.2.1 Intercept Dummy Variables Figure 7.3 An intercept dummy variable Principles of Econometrics, 3rd Edition

7.2.1a Choosing The Reference Group But would this Second version Work? Principles of Econometrics, 3rd Edition

7.2.2 Slope Dummy Variables (7.11) Principles of Econometrics, 3rd Edition

7.2.2 Slope Dummy Variables Figure 7.4 (a) A slope dummy variable. (b) A slope and intercept dummy variable Principles of Econometrics, 3rd Edition

7.2.2 Slope Dummy Variables (7.12) Principles of Econometrics, 3rd Edition

7.2.3 An Example: The University Effect on House Prices Principles of Econometrics, 3rd Edition

7.2.3 An Example: The University Effect on House Prices (7.13) Principles of Econometrics, 3rd Edition

7.2.3 An Example: The University Effect on House Prices Principles of Econometrics, 3rd Edition

7.2.3 An Example: The University Effect on House Prices For university area: For non-university area: Principles of Econometrics, 3rd Edition

7.2.3 An Example: The University Effect on House Prices Based on these regression results, we estimate the location premium, for lots near the university, to be $27,453 the price per square foot to be $89.12 for houses near the university, and $76.12 for houses in other areas. that houses depreciate $190.10 per year that a pool increases the value of a home by $4377.20 that a fireplace increases the value of a home by $1649.20 Principles of Econometrics, 3rd Edition

7.3 Applying dummy variables 7.3.1 Interactions Between Qualitative Factors (7.14) Principles of Econometrics, 3rd Edition

7.3.1 Interactions Between Qualitative Factors Principles of Econometrics, 3rd Edition

7.3.1 Interactions Between Qualitative Factors Principles of Econometrics, 3rd Edition

7.3.2 Qualitative Factors with Several Categories (7.15) Principles of Econometrics, 3rd Edition

7.3.2 Qualitative Factors with Several Categories Principles of Econometrics, 3rd Edition

7.3.3 Testing the Equivalence of Two Regressions Principles of Econometrics, 3rd Edition

7.3.3 Testing the Equivalence of Two Regressions (7.16) Principles of Econometrics, 3rd Edition

7.3.3 Testing the Equivalence of Two Regressions Principles of Econometrics, 3rd Edition

7.3.3 Testing the Equivalence of Two Regressions Principles of Econometrics, 3rd Edition

7.3.3 Testing the Equivalence of Two Regressions Remark: The usual F-test of a joint hypothesis relies on the assumptions MR1-MR6 of the linear regression model. Of particular relevance for testing the equivalence of two regressions is assumption MR3, that the variance of the error term is the same for all observations. If we are considering possibly different slopes and intercepts for parts of the data, it might also be true that the error variances are different in the two parts of the data. In such a case the usual F-test is not valid. Principles of Econometrics, 3rd Edition

7.3.4 Controlling for Time 7.3.4a Seasonal Dummies 7.3.4b Annual Dummies 7.3.4c Regime Effects Principles of Econometrics, 3rd Edition

7.4 Interactions Between Continuous Variables Principles of Econometrics, 3rd Edition

7.4 Interactions Between Continuous Variables (7.17) Principles of Econometrics, 3rd Edition

7.4 Interactions Between Continuous Variables (7.18) Principles of Econometrics, 3rd Edition

7.4 Interactions Between Continuous Variables Principles of Econometrics, 3rd Edition

Keywords annual dummy variables reference group binary variable regional dummy variable Chow test seasonal dummy variables collinearity slope dummy variable dichotomous variable dummy variable dummy variable trap exact collinearity hedonic model interaction variable intercept dummy variable log-linear models nonlinear relationship polynomial Principles of Econometrics, 3rd Edition

Chapter 7 Appendix Appendix 7 Details of log-linear model interpretation Principles of Econometrics, 3rd Edition

Appendix 7 Details of log-linear model interpretation Principles of Econometrics, 3rd Edition

Appendix 7 Details of log-linear model interpretation Principles of Econometrics, 3rd Edition

Appendix 7 Details of log-linear model interpretation Principles of Econometrics, 3rd Edition