Question 1 (a) Consider the following wage-price market. We ao + pt + zut + t Pt = Bo + BWe + Brt + B3m + Ezt Where: t-current time period. w rate of change in money wage. u-unemployment rate in percentage. Pt rate of change in prices (inflation). r=rate of change in cost of capital. m-money supply. Et and Ezt are error terms. wage equation price equation Suppose the equation of interest, one which is to be estimated, is the wage equation. (i) Can the equation be estimated by ordinary least squares (OLS) method? Explain. [5 marks] (ii) Of the possible estimation methods, explain and illustrate how the most suitable estimation method can be used to estimate the the wage equation. [10 marks] (b) The M matrix, M = [In - X(X'X)-X'], gives a vector of residuals in the OLS regression of y on the set of regressors, X. The hat matrix (denoted by H) and given by X(X'X)-X', gives the fitted values, , in the OLS estimation. Suppose the PRF is y = XB+ u Given the OLS residuals equation can be expressed as y = y + ; where is estimator of y (are predicted values) and are residuals, show that OLS estimation procedure partitions the vector into two parts such that y = Hy + My. [10 marks] (c) Explain the role of the errors/residuals in the estimation and evaluation process of a regression equation. [5 marks] Question 2 (a) Given two time series variables, Y, and X. Assume that the time series properties of Y, can be represented in terms of a random walk model, without drift while Xt can be represented by a stationary autoregressive model of order 1 - i.e., AR(1). Using suitable equations, show how a shock to the disturbance term will affect each of these variables. [10 marks] (b) The ordinary least squares (OLS) estimator of the variance of the disturbance term of a regression model is 8 = ara n-(K+1) Demonstrate that 2 is an unbiased estimator of o. 1 [10 marks] (c) In the matrix approach, state which set of Gauss-Markov assumptions is needed for (i) the derivation of OLS estimators (ii) the statistical properties of OLS estimation. [3 marks] [2 marks]