In their study of the demand for international reserves (i.e., foreign reserve currency such as the dollar or International Monetary Fund [IMF] drawing rights), Mohsen Bahami-Oskooee and Margaret Malixi obtained the following regression results for a sample of 28 less developed countries (LDC):
In(R/P) = 0.1223 + 0.4079 In(Y/P) + 0.5040 In σBP - 0.0918 In σEX
t = (2.5128) (17.6377) (15.2437) (- 2.7449)
R2 = 0.8268
F = 1151
n = 1120
where R = the level of nominal reserves in U.S. dollars
P = U.S. implicit price deflator for GNP
Y = the nominal GNP in U.S. dollars
σBP = the variability measure of balance of payments
σEX = the variability measure of exchange rates
The figures in parentheses are t ratios. This regression was based on quarterly data from 1976 to 1985 (40 quarters) for each of the 28 countries, giving a total sample size of 1120.
a. A priori, what are the expected signs of the various coefficients? Are the results in accord with these expectations?
b. What is the interpretation of the various partial slope coefficients?
c. Test the statistical significance of each estimated partial regression coefficient (i.e., the null hypothesis is that individually each true or population regression coefficient is equal to zero).
d. How would you test the hypothesis that all partial slope coefficients are simultaneously zero?