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. 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?

6. (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?

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

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