# University of Pittsburgh Standard Deviation Problem Set

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(4) Demonstrate the following statistic follows a (Student) t-distribution,
a
se(a)
Econometric Methods (AF6208)
Dr. Steven X.. Wei
where the first term of the numerator is the OLS estimator of a and the denominator is the estimated standard deviation of a
and a is the true value. [You can check any reference in your textbook, slides, internet, and other reference books. Comments:
Through the exercise, you should understand the unconditional analysis is actually a special case of conditional analysis! This
exercise sets up a link between a conditional analysis and an unconditional analysis! It is also a good exercise for your
understanding the intuition and mathematics behind a simple linear regression model. To some extent, you understand that there
Q3. Consider a special case of simple linear regression model,
Yi = a + u;
i = 1, 2,…,n
?
where u; ~N(0, o?).
(1) Using the FOC to work out the OLS estimate of a, and then construct the OLS estimate of o?? [Pay special attention to the
divisor” of the estimate to make sure that your estimate of o is unbiased).
(2) Demonstrate mathematically that a , the OLS estimator of a, is unbiased, and then calculate its variance and estimated standard
deviation, i.e., Var( a ) and Sel a ).
(4) Demonstrate the following statistic follows a (Student) t-distribution,
>
a
a
se(a)
(3) Through the analysis, you should understand that in your thesis, missing a control variable is in fact a serious problem in principle.
Investigate how the missing variable problem is dealt with or mitigated in research (or more clearly in published research papers).