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4818-Exam3a

# 4818-Exam3a - Student Name Economics 4818 Introduction to...

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Unformatted text preview: Student Name: Economics 4818 - Introduction to Econometrics - Fall 2007 Final Exam - Answers SHOW ALL WORK! Evaluation: Problems: 3, 4C, 5C and 5F are worth 4 points. All other questions are worth 3 points. 1. Answer the following questions: A) What is the consequence of specifying a model with a varable in log form, if in the population model, the variable is in level form? This is a case of Functional Form Misspeci&cation, which causes the OLS estimators to be biased. B) Suppose the true income-consumption model is cons = & + & 1 inc + & 2 inc 2 + u . What is the consequence, if we estimate the model without the quadratic term inc 2 ? This is another case of Functional Form Misspeci&cation, which causes the OLS estimators to be biased. It is also a case of omitted variable. C) Why does the simple regression model y = & + & 1 x + u typically fail to uncover the ceteris paribus e/ect of x on y ? There are typically unobserved factors of y , which are correlated with x , and enter into the error term, causing the OLS estimators to be biased. D) Is a regression with a low R 2 useless? Explain. What does a low R 2 imply about the speci&ed regression model? Not necessarily. However, the low R 2 implies that the included regressors do not explain much of the variation in y. That is, there are important omitted factors. E) What would be the likely sign of the bias of the coe¢ cient on IQ if we omitt edu from the model: log ( wage ) = & + & 1 IQ + & 2 edu + & 3 tenure + u ? Bias & f & 1 ¡ = & 2 & e ¡ 1 ¡ & 2 is expected to be > e ¡ 1 = Corr ( IQ;edu ) is expected to be > Bias & f & 1 ¡ is expected to be > F) What is the e/ect of increasing the sample size on se & c & j ¡ ? Explain. 1 Increasing the sample size decreases the error variance V ar ( u ) = & 2 and so se & c ¡ j ¡ = r b & 2 SST j ( 1 & R 2 j ) will decrease, where b & 2 is the estimator of & 2 . G) What is the e/ect of increasing the sample size on bias & c ¡ j ¡ ? Explain. The bias in c ¡ j remains as the sample size increases. 2. Suppose you have estimated the following linear probability model explaining 401(k) eligibility in terms of of income, age, and gender: \ e 401 k = & : 506 + : 0124 inc & : 000062 inc 2 + : 0265 age & : 00031 age 2 & : 0035 male ( : 081) ( : 0006) ( : 000005) ( : 0039) ( : 00005) ( : 0121) n = 9 ; 275 ; R 2 = : 094 where e 401 k is a binary variable for eligibility in a 401(k) plan ( e 401 k = 1 if eligble for 401(k), and = 0 otherwise), inc denotes family annual income (in \$1 ; 000 ), age denotes the individual&s age (in years), and male is a binary variable for gender ( male = 1 if male individual, and = 0 otherwise)....
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4818-Exam3a - Student Name Economics 4818 Introduction to...

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