[10 + 20 + 15] The monetarists maintain that national income is determined large

Question

[10 + 20 + 15] The monetarists maintain that national income is determined largely by the quantity of money. To test this, consider the following model: GDP_t = beta_1 + beta_2M_t + epsilon_t, where GDP = gross domestic product, M = money supply, t = time, and epsilon_t ~ IIDN (0, sigma^2). We have the following Australian data for 13 years, 1967-1979. Using this data we get the following OLS results: GDP_t = - 15.193(2.757) + 8.128(0.311) M_t, (1) where the standard errors are in parentheses. (a) Test the hypothesis H_0: beta_2 = 0 against H: beta_2 notequalto 0 and interpret the outcome. Use t_.025(11) = 2.201. (b) Find R^2, the coefficient of determination for this regression. What does it say about the relationship between GDP and M? (c) If we measure GDP in terms of $10 billion, how will the results in equation (1) change?

Explanation / Answer

We can solve this question using excel.

First enter data into excel.

Click on Data -------> Data Analysis --------> Regression ------->

Input

Input Y Range : select GDP values.

Input X Range :select values of money supply.

Output Range : select any empty cell.

---------> ok.

We get output

a) We have given critical value t crit = 2.201

We have got t test statistic value = 26.12777 corresponding to slope.

So test statistic value > critical value so we fail to reject null hypothesis.

Conclusion : Money supply is significant regressor.

b) R^2 = 0.9841   ( Using output)

Correlation coefficient = r = 0.9920

So the is positive relationship between GDP and M.

c) If we measure GDP in terms of $10 billion

We get GDP = -15.193 + 8.128*10 = 66.087

SUMMARY OUTPUT Regression Statistics Multiple R 0.992039 R Square 0.984142 Adjusted R Square 0.9827 Standard Error 3.547408 Observations 13 ANOVA df SS MS F Significance F Regression 1 8590.672 8590.672 682.6606 2.99E-11 Residual 11 138.4251 12.5841 Total 12 8729.097 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -15.1933 2.756521 -5.51175 0.000183 -21.2603 -9.1262 -21.2603 -9.1262 M 8.128368 0.311101 26.12777 2.99E-11 7.44364 8.813096 7.44364 8.813096

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