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i)In order for an estimator to be Consistent it would be required to have a large amount of observations. An estimator ? approaches its true value ?^ when observations approach infinity. In our case the estimator is calculated by using data on the lending rates of the USA and Canada. These values are highly tracked and a large database of them should be available therefore we can assume that the estimators would be consistent.
ii) since the Lending rates are measured in terms of percentage points, a one-point increase in the USA lending rate would refer to an increase of 0.3 percentage points in the Canadian lending rate in the current year (yt). In the following year (t+1) y^ would still be affected by this change as it would increase by 0.2percentage points.
iii) The presence of serial correlation can be tested by the Durbin Watson test and by plotting the residuals of each lag against them. Serial correlation essentially refers to errors of one period t carrying their effect to future periods like it was shown in the previous question. However, the Durbin Watson test showcases correct coefficients, but the standard errors are wrong, as the residuals are assumed to have 0 correlation between them. In such a case HAC/Newey-West test can be used which has a Heteroskedasticity and Autocorrelation consistent variance.
iv) if this model shows that it has Heteroskedastic errors this would mean that the estimated lending rate errors are not significant anymore since they would not be the Best Linear Unbiased Estimators (BLUE) and their variance is not accurate or low enough compared to other estimators. In other words, the estimators of the lending rates would still be correct, but their errors would be wrongly estimated as they would be assumed to be constant which would mean that we cannot reject or accept the null hypothesis of their significance.
When it comes to serial correlation this would mean that changes in the lending rates of one period will affect future periods, thus their effects carry over. In our model this is shown as the coefficient of the USA lending rate in period t-1 has a 0.2 positive effect in the current t period.
v) If our model shows signs of Serial correlation in the Durbin Watson test then it is best to use an ARIMA (Autoregressive Integrated moving average model) in order to help quantify this serial correlation. An ARIMA model is used to measure the effect past events have on future therefore our conclusions can be corrected when these effects are quantified. In the case of heteroskedasticity, it would be advisable to use the HAC/Newey West test as it is robust with Heteroskedasticity and it will still provide a reliable output.
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