practice_test1_solutions_v3

practice_test1_solutions_v3 - Professor Francesca Molinari...

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Unformatted text preview: Professor Francesca Molinari Spring 2010 TAs Simon Kwok and Tae-Hoon Lim Economics 320 Introduction to Econometrics Draft of Suggested Solutions to Practice Questions for Test 1 Part 1. a) A sequence of random variables X n converges to X if lim n !1 P ( j X n &amp; X j &lt; &quot; ) = 1 for &quot; &gt; : or lim n !1 P ( j X n &amp; X j &gt; &quot; ) = 0 for &quot; &gt; : X n p ! X if the probability that X n is very close to X is very high (is one in the limit). b) The least squares estimator minimizes the sum of squared residuals, P b U 2 i where b U i = Y i &amp; b Y i : c) A con&amp;dence interval is the set of null values for a parameter that are not rejected by a T-stat at a given signi&amp;cance level; e.g. b &amp; 1 se ( b &amp; 1 ) CV &amp;= 2 d) An estimator is unbiased if its mean is equal to the parameter value it is estimating, e.g. E ( b &amp; 1 ) = &amp; 1 : This says that the average, in repeated samples, of the estimator is equal(close) to the para- meter. e) OLS is the best linear unbiased estimator (BLUE): Among linear ( P c i Y i ; c i not a function of the Y s ), unbiased estimators of a regression model, OLS has the smallest variance....
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practice_test1_solutions_v3 - Professor Francesca Molinari...

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