Temple University

Department of Economics

Economics 8009

Using the data set consumption.txt which has the variables consumption, C_{t}, and disposable income, Y_{t}, construct the variables c_{t} = ln(C_{t}), , y_{t} = ln(Y_{t}), and

. You will so Wald, Likelihood Ratio and Lagrange Multiplier tests in this homework. Most statistical software packages will do these at the touch of a button. However, you are to do them long hand. That is, write out the formulae and do the calculations by hand.

1. Estimate the coefficients of and report the results.

2. Suppose that the disturbance, u_{t}, in the model in question 1 is . Write the log-likelihood function for the model.

3. Construct the Wald statistic for a test of the hypothesis that .

4. Construct the Lagrange Multiplier test statistic for the hypothesis that .

5. Construct the Likelihood Ratio test statistic for the hypothesis that