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Unformatted text preview: Introduction to Econometrics Professor Alexei Onatski Problem Set 5 October 21 Problem 1) [ Stock and Watson5.4 ] (a) 3.13 + 1.47 16 = $20.39 per hour (b) The wage is expected to increase from $14.51 to $17.45 or by $2.94 per hour. (c) The increase in wages for college education is 1 4. Thus, the counselors assertion is that 1 = 10/4 = 2.50. The t-statistic for this null hypothesis is 1.47 2.50 14.71, 0.07 t = which has a p-value of 0.00. Thus, the counselors assertion can be rejected at the 1% significance level. A 95% confidence for 1 4 is 4 (1.47 1.97 0.07) or $5.33 Gain $6.43. Problem 2) [ Stock and Watson5.13 ] (a) Yes. The Gauss-Markov Theorem (Key Concept 5.5) says if (Y i , X i ) satisfy the assumptions in Key Concept 4.3 and if errors are homoskedastic then the OLS estimator is the Best Linear conditionally Unbiased Estimator. (b) Yes See (a). (c) They would be unchanged. The Gauss-Markov Theorem does not require that the errors be normally distributed; it only requires homoskedasticity. (d) (a) is unchanged; (b) is no longer true as the errors are not conditionally homoskedastic. If the errors are heteroskedastic, GLS estimators have a smaller variance than the OLS estimators. Problem 3 ) a ) Consider the model: Y i = & + & 1 X i + u i ; (1) where X i is a binary variable. Assume that heteroskedasticity is known and has the following form: & V ar ( u i j X i = 1) = 4 V ar ( u i j X i = & 1) = 1 (2) From previous exercises (see problems 5 : 10 and 5 : 11 from the book), we know that the OLS estimator for this model will give us the following estimates: ( b & OLS + b & OLS 1 = Y m b & OLS & b & OLS 1 = Y w !...
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This note was uploaded on 12/20/2009 for the course ECON 1300 taught by Professor Natski during the Fall '09 term at Columbia.
- Fall '09