Temple University

Department of Economics

Economics 615

Heteroscedasticity and Autocorrelation

In his pioneering study of the demand for electricity ("Some Calculations of Electricity Consumption in Great Britain", Journal of the Royal Statistical Society (A), no. 114, part III, pp. 351-371) H. Houthakker collected data for 42 towns in the U.K. for 1937-1938. The data is in the file ukelec.txt. The variables are
CUST - # of customers in thousands in the town
INC - average income of customers in the town (pounds sterling/year)
MC4 - marginal cost of electricity in 1933-34
MC6 - marginal cost of electricity in 1935-36

MC8 - marginal cost of electricity in 1937-38 (all 3 MC's are pence/KWH)

GAS6 - marginal price of gas in 1935-36

GAS8 - marginal price of gas in 1937-38 (both GAS are in pence/therm)

KWH - per capita electricity consumption in the town

CAP - a measure of electrical appliance consumption capacity in KW

EXPEN - average total expenditure on electricity (pounds sterling)

(Note: 1 pound = 20 shillings and 1 shilling = 12 pence)
As a first step you will need to create the new variable PRecip=1/MC6.
Consider the electricity demand model

  1. Using the data from ukelec.txt, construct the OLS estimates of the parameters of this model. Comment on the t-statistics.
  2. Construct White's heteroscedasticity robust standard errors. How do they compare with those reported in part a.?
  3. Do two different test for heteroscedasticity.
  4. Correct for heteroscedasticity. (Hint: This problem is not unlike the test scores problem in the lecture notes.)
  5. From your heteroscedasticity corrected results compute the income, own and cross price elasticities of demand at the observation corresponding to the median consumption of electricity. Are your estimates plausible?

Monetary theory suggests that the demand for money (M) depends on a scale variable such as GDP, and an opportunity cost of holding money such as the interest rate (INT). Use the MathCAD file reading.mcdto read data from the file BRD.txt. These two files are found in theself extracting file for this homework.

a. Deflate money and GDP by the Price index in BRD.txt. Create the opportunity cost of holding money as R=1+(INT/100). Take the log of real Money, real GDP and the opportunity cost of holding money.

  1. Estimate the parameters of by OLS using the real, logged data, of course.
  2. Use the Durbin Watson test for first order serial correlation.
  3. Use the LM test for higher orders of serial correlation.
  4. Decide on an appropriate degree of serial correlation and correct for it.
  5. Using the residuals from the OLS regression of part a., estimate the parameters of . One can use as a test statistic for the hypothesis that . For large values of the test statistic one rejects the null. This is known as a test for first order autoregressive conditional heteroscedasticity.