FinalProblems2A

# FinalProblems2A - Final Practice Problems Answer Key...

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Final Practice Problems Answer Key - Econometrics 120A dss.ucsd.edu/ a2santos/Econ120a.htm 1. The following is a fictional joint probability distribution for GDP growth in the US and China. US GDP growth is entered in the left most column, and Chinese GDP growth in the top most row. US/China -2% 3% 10% -1% 0.1 0 0 2% 0.2 0.2 0.2 5% 0 0.1 0.2 (a) What is the probability that Chinese GDP growth is 3%? What is the probability that Chinese GDP growth is 10%? Let C denote Chinese GDP growth and U US GDP growth. Then adding up to find the marginals we get P ( C = 3%) = 0 . 3 and P ( C = 10%) = 0 . 4. (b) Conditional on Chinese GDP growth being 10%, what is the probability that US GDP growth is 5%? Using P ( U = 5% | C = 10%) = P ( U = 5% , C = 10%) /P ( C = 10%) = 0 . 2 / 0 . 4 = 0 . 5. (c) Are the US and Chinese GDP growth independent? Since P ( U = 5%) = 0 . 3, we have P ( U = 5% , C = 10%) = 0 . 2 6 = 0 . 3 × 0 . 4 6 = P ( U = 5%) × P ( C = 10%). Therefore US and GDP growth are not independent. (d) Notice that P (US GDP growth = 5%) = 0.3. Looking at your answer to b), an economist argues that high Chinese GDP growth causes US GDP growth to be high. Are the numbers in this table enough to support his conclusion? No, while in the table it is clear that US and Chinese GDP growth are positively related, this is no indication of causality. 2. Suppose the US unemployment rate follows a normal distribution with mean 4% and standard devi- ation 5%. (a) What is the probability of observing an unemployment rate larger than 7%? Let X be the unemployment rate. Then: P ( X 7) = P X - 4 5 7 - 4 5 = P ( Z 0 . 6) = 0 . 274 (b) What is the probability that the unemployment rate is between 1% of its mean? (i.e. between 3% and 5%?) Again, with X the unemployment rate: P (3 X 5) = P 3 - 4 5 Z 5 - 4 5 = P ( - 0 . 2 Z 0 . 2) = 1 - 2 × P ( Z 0 . 2) = 0 . 158 1

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