Source: Damodar Gujarati, "The Behaviour of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971," The Economic Journal, vol. 82, March 1972, p. 202.
Damodar Gujarati, "The Behaviour of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971," The Economic Journal, vol. 82, March 1972, pp. 195-202.
326 PART ONE: SINGLE-EQUATION REGRESSION MODELS
where UN = unemployment rate, % V = job vacancy rate, % D = 1, for period beginning in 1966-IV
= 0, for period before 1966-IV t = time, measured in quarters
Note: In the fourth quarter of 1966, the then Labor government liberalized the National Insurance Act by replacing the flat-rate system of short-term unemployment benefits by a mixed system of flat-rate and (previous) earnings-related benefits, which increased the level of unemployment benefits.
a. What are your prior expectations about the relationship between the unemployment and vacancy rates?
b. Holding the job vacancy rate constant, what is the average unemployment rate in the period beginning in the fourth quarter of 1966? Is it statistically different from the period before 1966 fourth quarter? How do you know?
c. Are the slopes in the pre- and post-1966 fourth quarter statistically different? How do you know?
d. Is it safe to conclude from this study that generous unemployment benefits lead to higher unemployment rates? Does this make economic sense?
9.4. From annual data for 1972-1979, William Nordhaus estimated the following model to explain the OPEC's oil price behavior (standard errors in parentheses).*
where y = difference between current and previous year's price (dollars per barrel)
x1 = difference between current year's spot price and OPEC's price in the previous year x2 = 1 for 1974 and 0 otherwise Interpret this result and show the results graphically. What do these results suggest about OPEC's monopoly power?
9.5. Consider the following model
Yi = « + a2 Di + P Xi + u where Y = annual salary of a college professor X = years of teaching experience D = dummy for gender
Consider three ways of defining the dummy variable.
Interpret the preceding regression model for each dummy assignment. Is one method preferable to another? Justify your answer.
"Oil and Economic Performance in Industrial Countries," Brookings Papers on Economic Activity, 1980, pp. 341-388.
CHAPTER NINE: DUMMY VARIABLE REGRESSION MODELS 327
9.6. Refer to regression (9.7.3). How would you test the hypothesis that the coefficients of D2 and D3 are the same? And that the coefficients of D2 and D4 are the same? If the coefficient of D3 is statistically different from that of D2 and the coefficient of D4 is different from that of D2, does that mean that the coefficients D3 and D4 are also different?
Hint: var (A ± B) = var (A) + var (B) ± 2 cov (A, B)
9.7. Refer to the U.S. savings-income example discussed in the chapter.
a. How would you obtain the standard errors of the regression coefficients given in (9.5.5) and (9.5.6), which were obtained from the pooled regression (9.5.4)?
b. To obtain numerical answers, what additional information, if any, is required?
9.8. In his study on the labor hours spent by the FDIC (Federal Deposit Insurance Corporation) on 91 bank examinations, R.J. Miller estimated the following function*:
íñy = 2.41 + 0.3674 ln Xi + 0.2217 ln X2 + 0.0803 ln X3 (0.0477) (0.0628) (0.0287)
-0.1755Di + 0.2799D2 + 0.5634D3 - 0.2572D4 (0.2905) (0.1044) (0.1657) (0.0787)
where Y = FDIC examiner labor hours X1 = total assets of bank X2 = total number of offices in bank X3 = ratio of classified loans to total loans for bank D1 = 1 if management rating was "good" D2 = 1 if management rating was "fair" D3 = 1 if management rating was "satisfactory" D4 = 1 if examination was conducted jointly with the state
The figures in parentheses are the estimated standard errors.
a. Interpret these results.
b. Is there any problem in interpreting the dummy variables in this model since Y is in the log form?
c. How would you interpret the dummy coefficients?
9.9. To assess the effect of the Fed's policy of deregulating interest rates beginning in July 1979, Sidney Langer, a student of mine, estimated the following model for the quarterly period of 1975-III to 1983-II.1
Yt = 8.5871 - 0.1328Pt - 0.7102Unt - 0.2389Mt se (1.9563) (0.0992) (0.1909) (0.0727)
+ 0.6592Yt-1 + 2.5831Dumt R2 = 0.9156 (0.1036) (0.7549)
"Examination of Man-Hour Cost for Independent, Joint, and Divided Examination Programs," Journal of Bank Research, vol. 11, 1980, pp. 28-35. Note: The notations have been altered to conform with our notations.
^Sidney Langer, "Interest Rate Deregulation and Short-Term Interest Rates," unpublished term paper.
328 PART ONE: SINGLE-EQUATION REGRESSION MODELS
where Y = 3-month Treasury bill rate P = expected rate of inflation Un = seasonally adjusted unemployment rate M = changes in the monetary base Dum = dummy, taking value of 1 for observations beginning July 1, 1979
a. Interpret these results.
b. What has been the effect of rate deregulation? Do the results make economic sense?
c. The coefficients of Pt, Unt, and Mt are negative. Can you offer an economic rationale?
9.10. Refer to the piecewise regression discussed in the text. Suppose there not only is a change in the slope coefficient at X* but also the regression line jumps, as shown in Figure 9.7. How would you modify (9.8.1) to take into account the jump in the regression line at X*?
9.11. Determinants of price per ounce of cola. Cathy Schaefer, a student of mine, estimated the following regression from cross-sectional data of 77 observations*:
where Pi = price per ounce of cola D1i = 001 if discount store = 010 if chain store = 100 if convenience store D2i = 10 if branded good
= 01 if unbranded good D3i = 0001 if 67.6 ounce (2 liter) bottle
= 0010 if 28-33.8 ounce bottles (Note: 33.8 oz = 1 liter) = 0100 if 16-ounce bottle = 1000 if 12-ounce can
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