Temple University

Department of Economics

Economics 615

Hypothesis Testing

1. (P) Consider T observations on a Bernoulli random variable with mass function
2. Where One can use several different test statistics for the test of hypothesis:

a. Derive the likelihood ratio test statistic.

b. Derive the Wald test statistic.

c. Derive the lagrange multiplier test statistic.

3. (B) For the period 1947-1971 there are data in the file klem.txt on the quantities for gross output quantity (QY), capital input (QK), labor input (QL), energy input (QE), and material input (QM), as well as the corresponding nominal prices. You will also find the quantity of value added output (QV) and its nominal price.
4. 2.a. Plot the quantities. Plot the nominal prices. What is happening to the series?

2.b. Deflate the input prices by the price of output and plot the resulting series. Which series are increasing/constant/decreasing? Comment.

2.c. Create the input-output coefficients KY=QK/QY, LY=QL/QY, EY=QE/QY, MY=QM/QY. Plot these series. Was production becoming more or less labor/capital/energy intensive?

2.d. Verify the accounting relationship between gross output and value added.

2.e. Fit the data to the regression models

and