In a study of turnover in the labor market, James F. Ragan, Jr., obtained the following results for the U.S. economy for the period of 1950-I to 1979-IV.* (Figures in the parentheses are the estimated t statistics.)
l^n Yt = 4.47 - 0.34 ln X2t + 1.22 ln X3t + 1.22 ln X4t+ 0.80 ln X5t - 0.0055 X6t
(4.28) (-5.31) (3.64) (3.10) (1.10) (-3.09)
R¯ 2 = 0.5370
Note: We will discuss the t statistics in the next chapter.
where Y = quit rate in manufacturing, de?ned as number of people leav- ing jobs voluntarily per 100 employees
X2 = an instrumental or proxy variable for adult male unemploy- ment rate
X3 = percentage of employees younger than 25
X4 = Nt-1 / Nt-4 = ratio of manufacturing employment in quarter (t - 1) to that in quarter (t - 4)
X5 = percentage of women employees
X6 = time trend (1950-I = 1)
a. Interpret the foregoing results.
b. Is the observed negative relationship between the logs of Y and X2 jus- ti?able a priori?
c. Why is the coef?cient of ln X3 positive?
d. Since the trend coef?cient is negative, there is a secular decline of what percent in the quit rate and why is there such a decline?
e. Is the R¯ 2 "too" low?
f. Can you estimate the standard errors of the regression coef?cients from the given data? Why or why not?