Answer the following questions. a) Inspect the following parameter estimation and Wald test results. Determine whether there is unidirectional, bilateral or independence causality between money supply (M) and interest rate (R). Write the model specification used and state the tested hypothesis. Make decision at 5% significance level. Regression 1: Dependent Variable: M Sample (adjusted): 3 40 Included observations: 38 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 1476.871 992.8921 1.487444 0.1464 R(-1) -231.3066 45.95685 -5.033125 0.0000 R(-2) 153.5037 49.32190 3.112284 0.0038 M(-1) 1.017241 0.154422 6.587395 0.0000 M(-2) -0.023561 0.151906 -0.155100 0.8777 Wald Test: Test Statistic Value df Probability F-statistic 12.92655 (2, 33) 0.0001 Chi-square 25.85310 2 0.0000 Null Hypothesis: C(2)=C(3)=0 Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. C(2) -231.3066 45.95685 C(3) 153.5037 49.32190 Restrictions are linear in coefficients.
The Correct Answer and Explanation is:
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Answer:
Causality Type: Unidirectional causality from interest rate (R) to money supply (M).
Model Specification:
The regression estimated is:Mt=α+β1Rt−1+β2Rt−2+γ1Mt−1+γ2Mt−2+εtM_t = \alpha + \beta_1 R_{t-1} + \beta_2 R_{t-2} + \gamma_1 M_{t-1} + \gamma_2 M_{t-2} + \varepsilon_tMt=α+β1Rt−1+β2Rt−2+γ1Mt−1+γ2Mt−2+εt
Where:
- MtM_tMt: Money supply at time t
- Rt−1,Rt−2R_{t-1}, R_{t-2}Rt−1,Rt−2: Lagged interest rates
- Mt−1,Mt−2M_{t-1}, M_{t-2}Mt−1,Mt−2: Lagged money supply
Tested Hypothesis (Wald Test):
- Null Hypothesis (H₀): β1=β2=0\beta_1 = \beta_2 = 0β1=β2=0
(Lagged values of interest rate do not Granger-cause money supply) - Alternative Hypothesis (H₁): At least one of β1,β2≠0\beta_1, \beta_2 \neq 0β1,β2=0
Decision Rule:
- Significance Level: 5%
- p-value of the Wald test = 0.0000, which is less than 0.05
- Reject the null hypothesis
Interpretation:
The regression and Wald test indicate that past values of the interest rate (R(-1) and R(-2)) significantly explain variations in the money supply (M), as seen from their significant coefficients (p-values: 0.0000 and 0.0038 respectively). The Wald test confirms this: the joint significance test of R(-1) and R(-2) yields a Chi-square statistic of 25.85310 with a p-value of 0.0000, leading us to reject the null hypothesis that interest rates have no effect on money supply.
Thus, interest rate Granger-causes money supply, meaning changes in interest rates contain useful information for predicting future changes in money supply.
Since we only have one regression (M as dependent variable), we cannot yet conclude bilateral causality. To check whether money supply also causes interest rate (i.e., if R is affected by lagged M), a second regression with R as dependent variable and similar Wald tests would be required. Without that, we only have evidence for unidirectional causality from R → M.
Conclusion:
At the 5% significance level, there is unidirectional causality from interest rate to money supply, based on the given regression and Wald test.
