The following model postulates that the demand for money is a function of expected interest rate:...

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The following model postulates that the demand for money is a function of expected interest rate: Y; = Bo + Bi X; + u; where Y = demand for money (real cash balances) X* = expected rate of interest u = error term. Since the expectational variable X" is not directly observable, we propose the following hy- pothesis about how expectations are formed: X; - X-1 = r(X;- X;-1) where 0 <y<1. It implies that expectations are revised each period by a fraction y of the gap between the current value of the variable and its previous expected value. (a) Transform the given model into an autoregressive model of Y; with the explanatory vari- ables X, and Y,-1. Y; = ao + a, X; + a2Y-1+ Ut If we apply OLS to the model obtained in (a), are the estimators consistent? If not, explain the reason why. (10pts) (b) How can we obtain consistent estimators? The following model postulates that the demand for money is a function of expected interest rate: Y; = Bo + Bi X; + u; where Y = demand for money (real cash balances) X* = expected rate of interest u = error term. Since the expectational variable X" is not directly observable, we propose the following hy- pothesis about how expectations are formed: X; - X-1 = r(X;- X;-1) where 0 <y<1. It implies that expectations are revised each period by a fraction y of the gap between the current value of the variable and its previous expected value. (a) Transform the given model into an autoregressive model of Y; with the explanatory vari- ables X, and Y,-1. Y; = ao + a, X; + a2Y-1+ Ut If we apply OLS to the model obtained in (a), are the estimators consistent? If not, explain the reason why. (10pts) (b) How can we obtain consistent estimators?