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ps5solutions_v4

# ps5solutions_v4 - Solutions to Homework 5 Econ 3200...

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Solutions to Homework 5 Econ 3200 - Introduction to Econometrics Spring 2010 Cornell University Prof. Molinari Part I ° 20 points (4 points each) 1. OLS Estimator: It is the estimator that minimizes the sum of squared residuals in a linear regression model. It is unbiased and has the smallest variance among all the linear unbiased estimators. 2. Total Sum of Squares: SST = P n i =1 ° Y i ° ° Y ± 2 : This is a measure of the sample variation in the observed values of the dependent variable in a linear regression model. 3. Multicollinearity: It is a phenomenon of high (but not perfect) correlation between two or more independent variables in a multiple linear regression model. This leads to imprecise (high variance) estimate of parameters. 4. Interpreting the slope coe¢ cient of a log-level regression: The slope parameter ° j correspond- ing to X j tells us the expected percentage change in Y associated with a one unit increase in X j , keeping all other X i °s ( i 6 = j ) constant (i.e. ceteris paribus). In particular, a one unit increase in X j gives a 100 ± ° j percent change in Y on average, ceteris paribus. 5. Variance-Covariance Matrix: Given a vector of random variables °! Z = ( Z 1 ; : : : ; Z k ) 0 , its variance-covariance matrix V ar ( °! Z ) is a ( k ² k ) square matrix where the ( i; i ) entry is V ar ( Z i ) , i = 1 ; : : : ; k , and the ( i; j ) element is Cov ( Z i ; Z j ) for i 6 = j , i; j = 1 ; : : : ; k . 1

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Part II ° 80 points (40 points each) 1. Long question 1. (a) One year increase in education increases wage by 7.2% on average. One more year of experience is associated with a 2% increase in wage. An increase in wage in response to an increase in education and experience makes sense. The estimates suggest that
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ps5solutions_v4 - Solutions to Homework 5 Econ 3200...

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