Assignment 11 Economics 31 Fall 1999

Non Standard Regression Analysis

Reading: Mirer Chpt. 15,17, Beals Chpt. 7,13,14

(For further aid see A.H.Stuendmund, Using Econometrics, and Johnson, Johnson and Buse, Econometrics Basic and Applied)

1. See attached table and fill in missing blanks (courtesy of Studenmund)

PS11table

2. For each of the above problems in regression analysis, explain which of
the classical assumptions were violated, and how.

3. True or False (Johnson, Johnson, Buse) ? If False, why?

A) Multicollinearity between independent variables means that the OLS
estimators of regression coefficients are biased

B) Researchers should try to purge their regression models and data of all
traces of multicollinearity before reporting their results

4. Consider the following results: Y=182-16X₁+2X₂

The t value for X₁=2, for X₂=1

R²=.47 , n=57, r₁₂=.75

Theory suggests the signs on both coefficients should be negative. Are the
following approaches reasonable? Why or why not? (JJB)

A) Collect new data on X₁,X₂,and Y.

B) Reject H₀: B₁=0 and do not reject H₀: B₂=0 and
go on with work.

C) Do not Reject H₀: B₁=0 because multicollinearity makes a
t-test unreliable.

D) Reject H₀: B₂=0 because multicollinearity makes the
confidence intervals too wide.

E) Add some X₃ that will clear up the collinearity that exists between
X₁ and X₂.

F) Find a different specific variable to represent the generic variable
between X₁ and X₂.

5. Suppose that a researcher is trying to estimate the following
consumption function, where consumption is hypothesized to depend on
current income (Y_t) habit or past income (Y_t-1), and
expectations or change in income deltaY=(Y_t-Y_t-1)(JJB):
E_t=b₀+ b₁ Y_t +b₂Y_t-1+b₃(deltaY)+e_t.
Show that without further information it is impossible to estimate
b₁,b₂, and b₃.

6. Assume that the following production function is to be estimated from
annual data on a firm (JJB):
Q=B₀ + B₁L₁+B₂L₂+B₃K

L₁= acres of land
L₂= dollars of labor
K= dollars of capital equipment

Suppose that the firm always budgets $30,000 a year for labor and capital

(i.e. L₂+K=30,000)

a) Is there a multicolinearity problem?

b) Can the coefficients be estimated?

7. (Studenmund). Which of the following pairs of variables is likely to
include a ''redundant'' variable?

A) the price of refridgerators and the price of washing machines in a
durable-goods demand function

B) The number of acres harvested and the amount of seed used in an
agricultural supply function

C) long-term interest rates and the money supply in an investment function

8. Model A: Y=B₀+B₁X₁+B₂X₂+U
Model B: Y=b₀+b₁X₁+e

A researcher estimates Model B, when the correct model is Model A (JJB)

a) Is E(b₁)=B₁?
b) Under what condition might b₁=B₁?

Suppose instead a researcher estimates Model A, when the correct model is
model B.

c)Is E(b₁)=B₁ ?
d)What is B₂?
e)What possible harm is there in including X₂?

9. The following regression model is heteroscetastic: (1) Y=B₀+B₁X₁+B₂X₂+U where Y=dollars spent by consumers

on food in a city in a week, X₁= dollars of income earned by consumers
in a city during a week, and X₂=population of a city (JJB). A
researcher uses OLS to estimate (1) by the following equation, assuming
that E(U²)=sigma² . Y=b₀+b₁X₁+b₂X₂+e

a) Is E(b₀)=B₀?Is E(b₁)=B₁?Is E(b₂)=B₂? E(S²)=sigma²?
b) Assuming that b₀ ,b₁ and b₂ are unbiased estimators of the
parameters in 1, can S_bi be used to test hypothesis?

10. Autocorr/heterosketasticity (JJB).

A) Which type of mispecified
disturbance term is more likely to occur in time-series data? In cross
sectional data?

B)Is the variance of the disturbance term more likely to be positively or
negatively correlated with the independent variables?

C)Is autocorrelation more likely to be positive or negative?

11. (JJB) A) What is the difference between error in equations and error in
variables?

B) Suppose that the dependent variable is measured with error and tha tthe
measurement error has mean zero, a positive but constant variance, is
uncorrelated with the population disturbance term, and is uncorrelated with
the independent variable. What effects does such measurement error have on
the empirical results? How serious are these effects?

C) Suppose that the independent variable is measured with error and that
the measurement error has mean zero, a positive but constant variance, is
uncorrelated with the population disturbance term, and is uncorrelated with
the independent variable. What effects does such measurement error have on
the empirical results? How serious are these effects?

12.Without looking at your book or notes, explain in your own words,
heterosketasticity, autocorrelation, simultaneous equation bias, and
multicollinearity.

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