Finance theory says that each intercept parameter estimate ( E 0 ) should be zero (remember in Stata, this is labeled as “constant”). Using your results from part 1 (e) from HW2, statistically test...

3. a.
i. Left shoe and Right shoe are linear function of each other. For every left shoe that a student wears,
there will be a co
esponding right shoe. This violates Assumption VI.
ii. Consumption and Disposable income of last 30 years of USA may not violate Assumption VI because
consumption may not always be a linear function of disposable income. Hence, there may not be a
perfect multicollinearity.
iii. Xi and 2Xi violate Assumption VI. They are both linear function of each other.
iv.Xi and X2 i do not violate Assumption VI because these both variables have a quadratic relationship
amongst themselves.
–
A. I would pick unbiased non-minimum variance estimate over a biased minimum variance one. It is
important that an estimate is centered around the true mean of the distribution even if its variance is
not least since a distribution with biased mean and minimum variance will yield inco
ect estimates.
Also, by central limit theorem the variance of the distribution of the estimates will reduce as number of
observations increases.
B. We may change the answer in part a if there are very few observations (say less than 30). In that
event, we would prefer minimum variance over biasness to prevent inclusion of outliers.
C. One of the way which I can think of is to conduct a hypothesis testing using a t-test statistic and check
which of the estimates show up in the confidence interval that is constructed using the estimates and
the standard e
or.
c.
We have the below regression results –
a. C – Everything else held constant, every one percentage change in non-white labor force the labor
force participation rate changes by 0.002%.
D – This is dummy variable. Everything else held constant , labor force participation declines by 0.80
units if the city is located in South.
. To detect multicollinearity we must perform diagnostic checks such as finding if regressors are
co
elated among themselves. Another test is to look at the Variance Inflation factor. Or, having a
coefficient whose sign is what is confirmed by theory. In the above regression, the sign of estimated
coefficient of S is negative which looks counter-intuitive. This can be taken as an evidence for
multicollinearity in the model.
c. No, we wouldn’t imply that the estimates are biased. This is because different sample from a
distribution will yield different estimate. For unbiasedness property to be satisfied, it must be the case
that the expected value of all the estimates from the distribution is equal to the true parameter. One of
the ways to know the bias would be to do repeated sampling and produce a distribution of the unknown
parameter whose mean must lie around the center of the distribution. Once the mean is known, we may
produce a confidence interval around the true mean. The estimate can be said to be biased if it doesn’t
lie in the 95% confidence interval around the true parameter.
d. I agree. If the sign is not per expectations then one must perform the diagnostic checks to rule out
any violation of the OLS assumptions that could result in non-BLUE estimate. In the above case, the
problem multicollinearity could lead to high standard e
ors and also result in unstable parameter
estimates.
4.
a.
We specify null hypothesis for first case –
We first set the critical value which is at 14...