Model 1- Static Regression
Our first model has the log of consumption as the dependent variable and the log of income as the independent variable and used 29 observations. The intercept is 0.1171 and that’s our best prediction for consumption in case income is zero. The slope reveals that for a $1 billion increase in income, consumption would go up by 0.8247 billion and from the elasticity we observe that for a 1% increase in income there will be an 82% increase in consumption, so as one would expect a higher level of income would lead to a higher consumption level. The estimated variance is 0.00047696 and the standard error is 0.01288. Using the t-statistic of a which is 1.96 we accept the null that the
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The estimated variance is 0.00040841 and the standard error is 0.01062 Using the t-statistic of a which is 5.34 we reject the null that the intercept is zero and the t-statistic for b is 114.84 and it allows us to reject the null about the slope. The Fvalue of 13187.9 allows us to assume a strong relationship between consumption and income. The DW statistic is 1.0280, and checking at the 5% significance points of d1 and du for DW test, we find that for one independent variable our DW statistic is between 0 and d1, that’s the region of rejection, this tells us that we reject the Null Hypothesis and that there is a no significant autocorrelation in the residuals, and that there’s a positive autocorrelation. The coefficient of the lagged consumption is less than one and this can be interpreted as follows. If consumption in the previous year had been $1 billion higher, then consumption this year would be $0.963 billions higher.So the growth of consumption today is less than the growth of consumption yesterday. Or you can interpret it in reference to lambda, It implies that the speed of adjustment is (1-0.9636) =0.037, meaning that 0.037 of the difference between desired and actual consumption is eliminated in one year.