Exercise for an Estimator to Be Consistent
Assignment ID Number AFFGEHU83939HD Type of Document Essay Writing Format APA/MLA/Harvard Academic Level Masters/University References/Sources 4 References
Having a large number of observations would be essential for an estimator to be consistent. When the number of observations approaches infinity, an estimator approaches its true value. In our case, the estimator is based on data from the United States and Canada’s lending rates. We can expect that the estimators will be consistent because these variables are closely recorded and a huge database of them should be available.
ii) Because lending rates are expressed in percentage points, a one-point increase in the US lending rate corresponds to a 0.3-percentage-point increase in the Canadian lending rate this year (yt). This modification would still effect y the following year (t+1), as it would grow by 0.2 percentage points.
iii) The Durbin Watson test and plotting the residuals of each lag against them can be used to determine whether there is serial correlation. As shown in the previous question, serial correlation relates to errors from one period having an influence on subsequent periods. The Durbin Watson test, on the other hand, shows proper coefficients but incorrect standard errors since the residuals are believed to have no association. The HAC/Newey-West test, which has a Heteroskedasticity and Autocorrelation consistent variance, can be employed in this scenario.
iv) If this model has heteroskedastic errors, the estimated lending rate errors are no longer important because they are not the Best Linear Unbiased Estimators (BLUE) and their variance is not accurate or low enough in comparison to other estimators. In other words, the loan rate estimators would still be right, but their errors would be incorrectly calculated because they would be expected to be constant, preventing us from rejecting or accepting the null hypothesis of their importance.
When it comes to serial correlation, this means that changes in one period’s loan rates have an effect on subsequent periods, and so their effects are carried over. The coefficient of the US loan rate in period t-1 has a 0.2 positive influence in the current t period, according to our model.
v) If our model displays symptoms of serial correlation in the Durbin Watson test, we should apply an ARIMA (Autoregressive Integrated Moving Average Model) to quantify it. The effect of previous events on future occurrences is measured using an ARIMA model, thus our conclusions can be modified once these effects are defined. In the case of heteroskedasticity, the HAC/Newey West test is recommended since it is robust to heteroskedasticity and still provides a trustworthy result.
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