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.)

ln Ŷ_t = 4.47 – 0.34 lnX_2t + 1.22 X_2t + 1.22 ln X_4t

          (4.28)      (-5.31)       (3.64)        (3.10)

        + 0.80 ln X_5t -    0.0055 X_6t        R̅² = 0.5370

         (1.10)                      (-3.09)

where

Y = quit rate in manufacturing, defined as number of people leaving jobs voluntarily per 100 employees

X₂ = an instrumental or proxy variable for adult male unemployment rate
X₃ = percentage of employees younger than 25
X₄ = N_t−1/N_t−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 justifiable a priori?

c. Why is the coefficient of ln X₃ positive?

d. Since the trend coefficient is negative, there is a secular decline of what percent in the quit rate and why is there such a decline?

e. Is the R̅² “too” low?

f. Can you estimate the standard errors of the regression coefficients from the given data? Why or why not?