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Consumption & Long-run interest rate
For our econometric model analysis, we start with the regression (2) model for the consumption as the dependent variable and the long run interest rate as one of the independent variables as seen in the following regression:
In order for us to run the regression and test for causality, we have to first make sure that the data we have can be applicable, so we apply a number of tests and configurations in order to make our data useful and make sure that the regression was run properly and the right and reliable results were obtained.
Stationarity
First we have to test whether our data is stationary or non-stationary, running the Augmented Dickey-Fuller test for unit root for each data set does this and the following results were obtained:
For the Consumption data we found out that the data obtained was non-stationary at the level with test statistic values -0.0075, while the critical value at the 5% level was – 2.8838, with the null-hypothesis indicating that there is a unit root in consumption, thus we do not reject the null-hypothesis meaning that the data is non-stationary at the level. We ran the same root test but at the first difference level and we obtained that the calculated test statistic was equal to –8.9795, while the critical value at the 5% level was at -2.8838, this means that we reject the null-hypothesis, meaning that the data is stationary.
For the QE data set, we ran the unit root test and obtained the following data for the level unit root, a calculated value of -0.0949 and a critical value of -2.8838, again by comparing the absolute values we do not reject the null-hypothesis meaning that there is a unit root at the level; after running the unit root test at the first difference we find a calculated value of -7.4822, and a critical value of -2.8838, meaning that the data is stationary at the first level, by rejecting the null-hypothesis. The same was applied on the long run interest rate and we found out that the interest rate data was stationary at the first difference level as well (calculated value of -1.4429 and a critical value of – 2.8838 for the unit root level, while at the first difference we obtained -9.2569 as a calculated value, while -2.8838 as a critical value).
In order to validate our results even more, we decided to apply another test, which is KPSS, where the null hypothesis is the opposite meaning that the null-hypothesis indicates that there is stationarity, the following results were obtained:
For Consumption we applied the test on the level difference, and the obtained LMstatistic was 1.3876, and the critical value at the 5% level was 0.4630, this indicates that we reject the null-hypothesis meaning that the data is non-stationary. We ran the test again but at the first difference level, and the values obtained we, LM-statistic 0.1333, and the critical value at the 5% level is 0.4630, this means that we do not reject the null-hypothesis meaning that the data is stationary. As for QE, when the test was applied on the level constant, the data obtained were, LM-statistic 1.3636, and the 5% value 0.4630, thus we reject the null-hypothesis, meaning that the data is nonstationary.
We ran the test again on the first difference level, and the obtained values were, LM-statistic 0.1572, and the 5% critical value 0.4630, thus we do not reject the null-hypothesis and the data is stationary. The same test was run for the long run interest rate and the values obtained were, the LM-statistic was 1.1890, and the critical value at the 5% level was 0.4630, meaning that we reject the null-hypothesis, thus the data is non-stationary. After running the test again on the first difference level, we obtained the following values, the LM-statistic was 0.0617, the critical value at the 5% level was 0.4630, this means that we do not reject the null-hypothesis and the data is stationary. After test our data for all the variables using both tests, we now know that the data we have at hand is at the first degree of integration.
1 Introduction
2 Theory and practise .
3 Methodology and econometric analysis
4 Conclusion and final remarks
5. References
6. Appendix
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Unconventional Monetary Policy in the United States
