Question

1. In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment as a percent of GDP. Standard errors are in parentheses below the coefficients.

log(gdp) = 2.85 + 0.547log(bankcredit) + 0.296FDI

                  (0.13)    (0.022) (0.017)

2. Holding the level of FDI constant, if bank credit increases by 1%, gdp increases by ___________.
3. Holding the level of bank credit constant, if FDI increases by 1 percentage point, gdp increases by ____________.
4. Construct a 95% confidence interval & a 99% confidence interval around each coefficient. Which is larger & why?
5. SSR = 564.08, SST = 769.07, n = 80. Calculate the model F statistic & adjusted R².

Answer 1

Solution:

Notice that we are given a log-linear (or a log-log regression model), which depicts all changes in percentage terms. That is, interpretation for such models can be understood in percentage terms directly.

b) The coefficient estimate which shows how the bank credit impacts GDP is 0.547. Holding FDI constant, if bank credit increases by 1%, GDP increases by 0.547%.

c) Similar to above part, the coefficient estimate which shows how the FDI impacts GDP is 0.296. Holding bank credit constant, if FDI increases by 1 percentage point, GDP increases by 0.296 percentage.

d) Confidence intervals: degrees of freedom = n - k - 1, where k is number of regressors, so df = 80 - 2 - 1 = 77

critical t-value at 95% = t_0.05/2,df = t_0.025,77 = 1.991

critical t-value at 99% = t_0.01/2,df = t_0.005,77 = 2.642

CI = coefficient estimate (+/-) t-value*standard error of coeff.

So, 95% confidence interval around:

i) Intercept: CI = 2.85 (+/-) 1.991*0.13 = (2.591, 3.109)

ii) Bank credit: CI = 0.547 (+/-) 1.991*0.022 = (0.503, 0.591)

iii) FDI: CI = 0.296 (+/-) 1.991*0.017 = (0.262, 0.330)

And, 99% confidence interval around:

i) Intercept: CI = 2.85 (+/-) 2.642*0.13 = (2.507, 3.193)

ii) Bank credit: CI = 0.547 (+/-) 2.642*0.022 = (0.489, 0.605)

iii) FDI: CI = 0.296 (+/-) 2.642*0.017 = (0.251, 0.341)

It is easily noticeable that for all coefficients, 99% CI is larger. It makes sense as to claim that the true parameter value lying within a particular range with more confidence (or more number of times in sample), wee require a bigger range, such that more variations can be incorporated and the confidence level become more. (for more number of times the true parameter value to lie within a range, we require a bigger range).

e) SSR = 564.08, SST = 769.07, n = 80

So, R² = SSR/SST = 564.08/769.07 = 0.733

F-statistic = [R²/(k-1)]/[(1 - R²)/(n-k)]

F-statistic = [0.733/(2-1)]/[(1-0.733)/(80-2)]

F-statistic = 0.733/0.00342 = 214.33

Adjusted R² = 1 - (1 - R²)*(n-1/n-k-1)

Adjusted R² = 1 - (1 - 0.733)*(80 - 1)/(80 - 2 - 1)

Adjusted R² = 1 - 0.274 = 0.726