Marietta College

1. Marietta College Spring 2011 Econ 420: Applied Regression Analysis Dr. Jacqueline Khorassani Week 10

2. Thursday, March 15 Exam 2: Tuesday, March 22 Exam 3: Monday, April 25, 12- 2:30PM Return Asst 14

3. Collect Asst 15 • Recall our height-weight regression • Estimate the regression that has gender and height as its independent variables • Is the coefficient of gender likely to be biased? Why or why not? • Suppose that we suspect the coefficient of gender to be biased downward. Suggest an omitted variable that is likely to be the cause of this bias. Discuss your reasoning.

4. Midterm grade configuration • Total possible points = 380 100 points on Exam 1 280 points on Assts • If you received more than 90% of 380  A • If you received more than 80% of 380  B • …..

5. Upper level Econ classes Next Year Spring 2012 Econ 340 (Sports Econ) Econ 349 (Micro II) Econ 414 (Int’l Trade) Econ 420 (Applied Regression Analysis) Fall 2011 Econ 301 (Money & Banking) Econ 350 (Environmental Econ) Econ 360 (Law & Econ) Econ 421 (Empirical Research) Major in econ = 33 to 34 hours Minor in econ = 18 hours

6. Chapter 7 • What accounts for the value of estimated intercept? Factors affecting the estimated intercept • True beta • Mean of error term • Affected by omitted variables (or other specification errors)

7. Should we exclude intercept ? • No • Why not? • Which assumption may be violated? (Page 94) • Assumption II mean of error = zero • If not, intercept captures it • If don’t include intercept  violated assumption II • OLS will not yield a BLUE • Graph • When you suppress constant, you are forcing the intercept to be zero • May not get the best fit

8. Hand out of useful rules • Do they ring a bell?? • Linear regression equation Slope = ? dY/dX = β1 = constant Elasticity of Y with respect to X = ? % dY / %dX Is it constant? (dY/Y)/(dX/X)= ? (dY/dX) * (X/Y) Elasticity varies based on values of X and Y

9. Double log Models • Let’s do some econ • What is the price elasticity of demand, E? Percentage change in quantity demanded divided by percentage change in price E = (dQd/ Qd) / (d P/ P)

10. Suppose • Theory suggests that E is constant at all levels of price • Your goal is to estimate the price elasticity of demand (E) • Will a linear function work? • No, because it allows for elasticity to vary • You can use a double log function • lnQd = β0 + β1ln P + є • What does β1 measure? • β1 =d (lnQd) / d (ln P) which is approximately equal to E • β1 = E = (d Qd/ Qd) / (dP/ P) • Do you expect β1 to be positive or negative? • Negative • What if β1 = -3; what does it mean?

11. Note • The double-log model is appropriate if you believe that the elasticity of Qd w.r.t. P is a constant: • A given % change in P is associated with a constant % change in Qd .

12. Let’s go back to our height weight example • Suppose the theory suggests that the elasticity of weight with respect to height is constant • Let’s use Eviews to estimate the elasticity of weight with respect to height

13. How can we estimate the model using EViews? • Transform the model to a linear model Open your workfile Then click on quick Generate series Type lnh = log (h) Do it again for w Then run the regression lnw c lnh g

14. Dependent Variable: LNW Method: Least Squares Date: 03/15/11 Time: 09:47 Sample: 1 17 Included observations: 17 Variable Coefficient Std. Error t-Statistic Prob.   C -6.338596 5.723760 -1.107418 0.2868 LNH 2.659653 1.374604 1.934851 0.0735 G 0.109758 0.172338 0.636879 0.5345 R-squared 0.663009     Mean dependent var 4.995731 Adjusted R-squared 0.614867     S.D. dependent var 0.261955 S.E. of regression 0.162567     Akaike info criterion -0.636671 Sum squared resid 0.369991     Schwarz criterion -0.489633 Log likelihood 8.411704     Hannan-Quinn criter. -0.622055 F-statistic 13.77206     Durbin-Watson stat 2.056212 Prob(F-statistic) 0.000494

15. Graphs • Ln (weight) as a function ln (height)? Slope = E = 2.7 • Weight as a function of height? Slope = ???

16. ln w = β0 + …..+ β2ln h + є • β2 = d (ln w) /d (ln h) • β2 = (dw/w) / (dh/h) • β2 = (dw/w) * (h/dh) • β2 = (dw/dh) * (h/w) • Slope = dw/dh = β2(w/h) • Slope = dw/dh = 2.7 (w/h)

17. dw/dh= 2.7(w/h) • When w is zero, slope is ? • As w goes up, what is the slope?

18. Let’s look at the graph of double log functions

19. Asst 16: Due Thursday in class • Use Chick (Chapter 6) data set • Variables are defined on Page 172 • Assuming that the elasticity of per capita chicken consumption with respect to the price of chicken is constant, estimates Y as a function of PC, PB and YD. • Is the demand for chicken elastic or inelastic? Why? • Attach your work.

20. Semi Log Models Suppose a theory suggests that, holding everything else constant, for each additional inch in height, a person’s weight changes by a constant and positive percentage. ln weight= β0+ β1height +…. d (ln weight)/ d (height) = β1 Do you expect β1 to be positive or negative? Positive Estimate β1 using our data set

21. Thursday, March 17 • Exam 2: Tuesday, March 22 Covers PP 93-220 Closed book and notes Data set: DRUGS (Chapter 5, PP 157- 158) available online at http://pearsonhighered.com/studenmund/

22. Return and discuss Asst 15 • Recall our height-weight regression model. • Estimate the regression model that has gender and height as its independent variables. • Is the coefficient of gender likely to be biased? Why or why not? • Suppose that we suspect the coefficient of gender to be biased downward. Suggest an omitted variable that is likely to be the cause of this bias. Discuss your reasoning.

23. Key Wi^ = - 417.72 + 8.28 Hi – 3.06 Gi Holding height constant, on average a male weighs 3.06 pounds less than a female! We Suspect a downward (negative) bias Why suspect? Why aren’t we sure? Nate? If you said there is a bias, you lost 0.5 points

24. E(βG^) = βG+ βomitted* r omitted, G Bias = βomitted* r omitted, G <0 Either • Βomitted <0and r omitted, G >0 Or 2) Βomitted >0and r omitted, G <0 Candidates omitted variable? • Linda said? • Others said? • Jackie says: Can the omitted variable be age?

25. Collect and discuss Asst 16 • Use Chick (Chapter 6) data set • Variables are defined on Page 172 • Assuming that the elasticity of per capita chicken consumption with respect to the price of chicken is constant, estimates Y as a function of PC, PB and YD. • Is the demand for chicken elastic or inelastic? Why? • Attach your work.

26. Elasticity Do the appropriate test to see if the coefficient significant at 5%? Dependent Variable: LNY Method: Least Squares Date: 03/16/11 Time: 15:49 Sample: 1974 2002 Included observations: 29 Variable Coefficient Std. Error t-Statistic Prob.   C 2.055126 0.292408 7.028284 0.0000 LNPB -0.033464 0.090345 -0.370403 0.7142 LNPC -0.1028250.027901 -3.685405 0.0011 LNYD 0.540969 0.044874 12.05533 0.0000 R-squared 0.984550      Mean dependent var 4.139678 Adjusted R-squared 0.982696      S.D. dependent var 0.278389 S.E. of regression 0.036620      Akaike info criterion -3.648980 Sum squared resid 0.033526      Schwarz criterion -3.460387 Log likelihood 56.91021      Hannan-Quinn criter. -3.589915 F-statistic 531.0463      Durbin-Watson stat 0.674244 Prob(F-statistic) 0.000000

27. Do you recall producer’s total revenue (or consumer’s total expenditures) curve from econ 211? • How does it look? • The theory suggests that as Q (quantity of output) increases, TR (producer’s total revenue) increases at a declining rate and And, eventually it decreases

28. Total Revenue Curve TR TR Quantity of output fig

29. Would this equation capture the theoretical shape of TR curve? • TR = B0 + B1Q + error • d TR/d Q = ? • d TR/d Q = B1 • No, B1 can be either positive or negative but not both. • Graph

30. How about this model? • TR = B0 + B1Q2 + error • d TR /d Q = ? • d TR /d Q = 2B1Q • No, Q is either 0 or positive. So, depending on the sign of B1, the slope is either positive, zero, or negative but not all

31. How about this one? • TR = B0 + B1Q + B2 Q2 + є • d TR/d Q = ? • d TR/d Q = B1 + 2 B2 Q • When Q is zero slope is ? • We expect B1 to be ? • And we expect B2 to be ? • At high levels of Q, the negative component of the slope(2B2Q) will be greater than the positive component of the slope (B1)

32. Another Example • Recall the Woody’s Restaurant problem (PP77-78) • Suppose the theory suggests that there exists a positive but declining relationship between the income and the number of customers. • Y= B0 + B1 I + B2I2 + B3P + B4N+ error • d Y/d I = B1+ 2 B2I • We expect B1>0 and B2 <0 • How do we set the null and alternative hypotheses to test the theory?

33. Open the data set Woody in Chapter 3 • Quick • Generate series • isquare= i*i • Now run the regression Y c iisquare p n

34. Dependent Variable: Y Method: Least Squares Date: 03/17/11 Time: 10:38 Sample: 1 33 Included observations: 33 Variable Coefficient Std. Error t-Statistic Prob.   C 42745.84 44034.73 0.970730 0.3400 I 6.959679 4.061301 1.713657 0.0976 ISQUARE -0.000125 8.90E-05 -1.408781 0.1699 N -9885.677 2099.168 -4.709330 0.0001 P 0.380099 0.073722 5.155867 0.0000 Did you find evidence for your hypothesized relationship between income and number of customers at 10 percent level of significance (α = 10%)?