ECON 413 – Assignment #6

Due: April 10^th in class

If you need more room, write on back

1) Studenmund p. 339 #11 a), c) and on c) take your answer to part a) into account.

2) Studenmund p. 378#5 a); b) use the White test for heteroskedasticity; if it rejects the null, present White corrected standard error results; c) suppose that the variance of the equation error is proportional to income^2 (squared) – estimate an equation that corrects for heteroskedasticity given this model of the heteroskedasticity and test for heteroskedasticity with the White test and report your results; d) suppose that the variance of the equation error is proportional to income (not squared). Estimate an equation that corrects for heteroskedasticity given this model of the heteroskedasticity (noting that you will have THREE variables now because you ALWAYS use an intercept) and test for heteroskedasticity with the White test and report your results; e) using all three estimates, discuss an estimate for the Marginal Propensity to Consume, giving approximate 95% confidence intervals. Do the corrections seem more correct? Explain.

3) Studenmund p. 386#15 – a) test with both the serial LM and DW; b) Use an AR(1) term for the GLS procedure; c) ; d) use the White test; e) meaning test the equation in b); f) note that this is not an exact answer. Remember that if you have heteroskedasticity, your standard errors are fraudulent.

4) Open house.xls: the dataset contains data on 88 houses. The variables from the dataset are in the following order.

PRICE = the housing price in dollars.

ASSESS = the assessed value of house in dollars.

BDRMS = the number of bedrooms in the house.

LOTSIZE = the size of the lot in square feet.

SQFT = the size of the house in square feet.

COLONIAL = 1 if the house is colonial style, 0 otherwise.

LNPRICE = log of the housing price.

LNASSESS = log of the assessed value.

LNLOTSZ = log of the lot size.

LNSQFT = log of the size of the house.

a) Restrict the sample to observations where price is positive.

b) Regress PRICE on LOTSIZE, SQFT, and BDRMS. Save the residuals from this regression.

a. Does heteroskedasticity seem theoretically likely for this regression? Explain.

b. Plot the residuals against LOTSIZE. Does there appear to be a relationship between the variance of the residuals and LOTSIZE? Based on this alone, do you think that this model suffers from heteroskedasticity?

c. Use the Goldfeld-Quandt test to test the null hypothesis of homoskedasticity, using SQFT as the proportionality factor.

d. Use the Park test to test the null hypothesis of homoskedasticity, using SQFT as the proportionality factor.

e. Use the White test to test the null hypothesis of homoskedasticity.

f. What is the underlying functional form of the variance of the error term assumed for the Goldfeld-Quandt and Park tests? Do you think that this is a good assumption for this model? What is the underlying functional form of the variance of the error term assumed for the White test?

c) Given your answers above, it does not seem reasonable to use Weighted Least Squares based on the proportionality factor, SQFT, to correct for heteroskedasticity. Why?

d) A logical reformulation of the regression equation that might rid the model of heteroskedasticity is to use LNPRICE as the dependent variable and LNLOTSZ, LNSQFT, and BDRMS as the independent variables. One benefit of using the logarithmic functional form is that heteroskedasticity is often reduced. Run OLS on this new model, and test for heteroskedasticity using the White test. Did this reformulation succeed in reducing the occurrence of heteroskedasticity? What can you say about the coefficients in the log equation?