A researcher has data on the average annual rate of growth of employment, e, and the average annual rate of growth of GDP, x, both measured as percentages, for a sample of 27 developing countries and 23 developed ones for the period 1985−1995 He defines a dummy variable D that is equal to 1 for the developing countries and 0 for the others. Hypothesizing that the impact of GDP growth on employment growth is lower in the developed countries than in the developing ones, he defines a slope dummy variable xD as the product of x and D and fits the regression (standard errors in parentheses):
eˆ = −1.45 (0.36) + 0.119 (0.10) x + 0.78 (0.10) xD
R2 = 0.61, RSS = 50.23
He also runs simple regressions of e on x for the whole sample, for the developed countries only, and for the developing countries only, with the following results:
1Whole Sample eˆ = −0.56 (0.53) + 0.24 (0.16) x
R2 = 0.04, RSS = 121.61
Developed countries eˆ = −2.74 (0.53) + 0.50 (0.15) x
R2 = 0.35, RSS = 18.63
Developing countries eˆ = −0.85 (0.42) + 0.78 (0.15) x
R2 = 0.51, RSS = 25.23 a
a. Explain mathematically and graphically the role of the dummy variable xD in this model.
b. The researcher could have included D as well as xD as an explanatory variable in the model. Explain mathematically and graphically how it would have affected the model.
c. Suppose that the researcher had included D as well as xD. What would the coefficients of the regression have been?