1. Nonlinear Relationships
ECON 6002
Econometrics
Memorial University of Newfoundland
Nonlinear Relationships
Chapter 7
Adapted from Vera Tabakova’s

2. 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
Principles of Econometrics, 3rd Edition

3. 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

4. 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

5. 7.1 Polynomials
(7.1)
(7.2)
(7.3)
(7.4)
Principles of Econometrics, 3rd Edition

6. 7.1.2 A Wage Equation
(7.5)
(7.6)
Principles of Econometrics, 3rd Edition

7. 7.1.2 A Wage Equation
Principles of Econometrics, 3rd Edition

8. 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

9. 7.2 Dummy Variables
(7.7)
(7.8)
Principles of Econometrics, 3rd Edition

10. 7.2.1 Intercept Dummy Variables
(7.9)
(7.10)
Principles of Econometrics, 3rd Edition

11. 7.2.1 Intercept Dummy Variables
Figure 7.3 An intercept dummy variable
Principles of Econometrics, 3rd Edition

12. 7.2.1a Choosing The Reference Group
But would this
Second version
Work?
Principles of Econometrics, 3rd Edition

13. 7.2.2 Slope Dummy Variables (7.11)
Principles of Econometrics, 3rd Edition

14. 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

15. 7.2.2 Slope Dummy Variables (7.12)
Principles of Econometrics, 3rd Edition

16. 7.2.3 An Example: The University Effect on House Prices
Principles of Econometrics, 3rd Edition

17. 7.2.3 An Example: The University Effect on House Prices
(7.13)
Principles of Econometrics, 3rd Edition

18. 7.2.3 An Example: The University Effect on House Prices
Principles of Econometrics, 3rd Edition

19. 7.2.3 An Example: The University Effect on House Prices
For university area:
For non-university area:
Principles of Econometrics, 3rd Edition

20. 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 $ per year
that a pool increases the value of a home by $
that a fireplace increases the value of a home by $
Principles of Econometrics, 3rd Edition

21. 7.3 Applying dummy variables
7.3.1 Interactions Between Qualitative Factors
(7.14)
Principles of Econometrics, 3rd Edition

22. 7.3.1 Interactions Between Qualitative Factors
Principles of Econometrics, 3rd Edition

23. 7.3.1 Interactions Between Qualitative Factors
Principles of Econometrics, 3rd Edition

24. 7.3.2 Qualitative Factors with Several Categories
(7.15)
Principles of Econometrics, 3rd Edition

25. 7.3.2 Qualitative Factors with Several Categories
Principles of Econometrics, 3rd Edition

26. 7.3.3 Testing the Equivalence of Two Regressions
Principles of Econometrics, 3rd Edition

27. 7.3.3 Testing the Equivalence of Two Regressions
(7.16)
Principles of Econometrics, 3rd Edition

28. 7.3.3 Testing the Equivalence of Two Regressions
Principles of Econometrics, 3rd Edition

29. 7.3.3 Testing the Equivalence of Two Regressions
Principles of Econometrics, 3rd Edition

30. 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

31. 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

32. 7.4 Interactions Between Continuous Variables
Principles of Econometrics, 3rd Edition

33. 7.4 Interactions Between Continuous Variables
(7.17)
Principles of Econometrics, 3rd Edition

34. 7.4 Interactions Between Continuous Variables
(7.18)
Principles of Econometrics, 3rd Edition

35. 7.4 Interactions Between Continuous Variables
Principles of Econometrics, 3rd Edition

36. 7.5 Log-Linear models 7.5.1 Dummy Variables (7.19)
Principles of Econometrics, 3rd Edition

37. 7.5.1a A Rough Calculation
Principles of Econometrics, 3rd Edition

38. 7.5.1b An Exact Calculation
Principles of Econometrics, 3rd Edition

39. 7.5.2 Interaction and Quadratic Terms
(7.20)
Principles of Econometrics, 3rd Edition

40. 7.5.2 Interaction and Quadratic Terms
Principles of Econometrics, 3rd Edition

41. 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

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

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

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

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