What restrictions on the coefficients of eqna give equation

Question

Q1) This question is concerned with the value of houses in towns surrounding Boston. It uses data of Harrison, D., and D.L. Rubinfeld (1978), "Hedonic Prices and the Demand for Clean Air," Journal of Environmental Economics and Management, 5, 81-102. The output appears in the table below. The variables are defined as follows:

VALUE = median value of owner-occupied homes in thousands of dollars

CRIME = per capita crime rate

NITOX = nitric oxide concentration (parts per million)

ROOMS = average number of rooms per dwelling

AGE = proportion of owner-occupied units built prior to 1940

DIET = weighted distances to five Boston employment centers

ACCESS = index of accessibility to radial highways

TAX = full-value property-tax rate per $10,000

PTRATIO = pupil-teacher ratio by town

Dependent Variable: VALUE Included observations: 506

Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	28.4067	5.3659	5.2939	0.0000
CRIME	-0.1834	0.0365	-5.0275	0.0000
NITOX	-22.8109	4.1607	-5.4824	0.0000
ROOMS	6.3715	0.3924	16.2378	0.0000
AGE	-0.0478	0.0141	-3.3861	0.0008
DIST	-1.3353	0.2001	-6.6714	0.0000
ACCESS	0.2723	0.0723	3.7673	0.0002
TAX	-0.0126	0.0038	-3.3399	0.0009
PTRATIO	-1.1768	0.1394	-8.4409	0.0000

a) Report briefly on how each of the variables influences the value of a home.

 b) Test the hypothesis that increasing the number of rooms by one increases the value of a house by $ 7,000.

Q2. Consider the wage equation

Ln (WAGE) = β₁ + β₂EDUC + β₃EDUC² + β₄EXPER + β₅EXPER² + β₆(EDUC * EXPER) + β₇HRSWK + e

where the explanatory variables are the years of education, years of experience and hours worked per week. Estimation results for this equation, and for modified versions of it obtained by dropping some of the variables, are displayed in the table below. These results are from 1,000 observations in the file cps4c_small.dat

a) What restrictions on the coefficients of Eqn(A) give equation (C)? Use an F-test to test these restrictions.

b) What question would you be trying to answer by performing this test?

Q3. A sample of 200 Chicago households was taken to investigate how far American households tend to travel when they take vacation.  Measuring distance in miles per year, the following model was estimated

MILES = β₁ + β₂INCOME + β₃AGE + β₄KIDS + e   

The variables are self-explanatory except perhaps for AGE, the average age of the adult members of the household. The data are in the file vacation.dat

a) The equation was estimated by least squares and the residuals are plotted against age and income as shown in the figure above. What do these graphs suggest to you? Be specific.

b) Ordering the observations according to descending values of INCOME, and applying least squares to the first 100 observations, and again to the second 100 observations, yields the sums of squared errors

SSE₁ = 2.9471*10⁷;           SSE₂ = 1.0479*10⁷

Use the Goldfeld-Quandt test to test for heteroskedastic errors. Include specification of the null and alternative hypothesis.

Q4. Identify 2 possible solutions to the problem of heteroskedasticity.

Q5. What are the consequences of having high (but not perfect) collinearity among the explanatory variables in a regression equation? Are OLS estimators BLUE? Carefully explain.

Q6. Identify 2 solutions to the problem of collinearity or multicollinearity.

Q7. Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question we consider an where monthly change in the number of new one-family houses sold in the U.S. depends on last month's change in the 30-year conventional mortgage rate. Let HOMES be the number of new houses sold (in thousands) and IRATE be the mortgage rate. Their monthly changes are denoted by DHOMES = HOMES_t - HOMES_t-1 and DIRATE = IRATE_t - IRATE_t-1. Using data from January 1992 to March 2010 (stored in the file hoes.dat), we obtain the following least squares regression estimates:

(DHOMES)^{^} = - 2.077 - 53.51DIRATE_t-1      obs = 218

(se)        (3.498) (16.98)

a) Let ehat denote the residuals from the above equation. Use the following estimated equation to conduct two separate tests for first-order autoregressive errors.

e^{^}t = - 0.1835 - 3.210DIRATE_t-1 - 0.3306e^{^}_t    R² = 0.1077 obs = 218

(se)                        (16.087)                (0.0649)

Q8. What are the consequences of using OLS in the presence of serial correlation? Are the estimators BLUE? (Be complete in your answer.)

Attachment:- Tables.rar