Economics 310 Menzie D. Chinn Fall 2004 Social Sciences 7418 University of Wisconsin-Madison Problem Set 4 This problem set is due in lecture on Wednesday, December 1st. No late problem sets will be accepted. Be sure to show your work (that is, do not use a spreadsheet or statistical program to generate your answers), and to write your name, ID number, as well as the name of your Teaching Assistant, on your problem set. Numbered problems refer to the textbook problems. • 8.16 • 8.20 • 8.30 • 8.50 • 8.56 • 8.62 • 8.72 • 8.80 • 8.82 • 9.2 • 9.22 • 9.28 • 9.36 • 9.44 • 9.60 • 9.70 • Problem X.1 During the late 1990s, there was a belief that Europe lagged behind the United States in productivity growth, especially over the 1995q1-2000q4 period (shaded area in the graph below). -.02-.01.00.01.02.03.04.05.0682 84 86 88 90 92 94 96 98 00D(LPRODUS90,0,4) D(LPRODEU90,0,4)US (4 qtr growth rate)Eurozone(4 qtr growth rate) Figure 1: US and Eurozone 4 quarter growth rates. Here are some statistics below on quarter-on-quarter annualized growth rates and differences in growth rates between the two economies.2012345-0.02 0.00 0.02 0.04 0.06 0.08Series: D(LPRODUS90)*4Sample 1995:1 2000:4Observations 24Mean 0.026989Median 0.023134Maximum 0.088328Minimum -0.016824Std. Dev. 0.025717Skewness 0.575041Kurtosis 3.120793Jarque-Bera 1.337277Probability 0.512406 Figure 2: Histogram for United States qoq annualized GDP growth 01234567-0.04 -0.02 0.00 0.02 0.04 0.06 0.08Series: D(LPRODEU90)*4Sample 1995:1 2000:4Observations 24Mean 0.012612Median 0.008859Maximum 0.089501Minimum -0.036604Std. Dev. 0.025384Skewness 0.843972Kurtosis 4.866237Jarque-Bera 6.331998Probability 0.042172 Figure 3: Histogram for Eurozone qoq annualized GDP growth 012345-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Series: DIFSample 1995:1 2000:4Observations 24Mean 0.014377Median 0.013389Maximum 0.061469Minimum -0.055100Std. Dev. 0.032564Skewness -0.357949Kurtosis 2.343087Jarque-Bera 0.944045Probability 0.623739 Figure 4: Histogram for DIF = (d(lprodus90)-d(lprodeu90))*4 X.1.a. Conduct a test for difference in means between the US and Eurozone, assuming independent sampling, and setting the probability of Type I error equal to 2.5%.3 X.1.b. Conduct a test for difference in means between the US and Eurozone assuming paired sampling, and once again setting the probability of Type I error equal to 2.5%. X.1.c. Which testing procedure is more appropriate? Why? • Problem X.2 Consider the following data pertaining to annualized quarter-on-quarter growth rates of real US GDP (in 1996 chained dollars) over the last 25 years. -.10-.05.00.05.1080 82 84 86 88 90 92 94 96 98 00 02 04D(LGDP96C)*4 Figure 5: US qoq annualized GDP growth rate, 1979q1-2004q3 X.2.a. Suppose one wanted to test the hypothesis that the variability of US GDP growth was greater than 2.5%. Write out the hypothesis test, given the following information. 024681012-0.05 0.00 0.05Series: D(LGDP96C)*4Sample 1979:3 2004:4Observations 101Mean 0.029616Median 0.032474Maximum 0.089218Minimum -0.081572Std. Dev. 0.029318Skewness -0.971839Kurtosis 5.257074Jarque-Bera 37.33745Probability 0.000000 Figure 6: Histogram for United States qoq annualized GDP growth, 1979q3-2004q3.4X.2.b. Conduct the hypothesis test, using the data provided. What is your conclusion, setting α = 0.05? X.2.c. What assumptions do you need to impose in order to arrive at your conclusion? • X.3. There is a widespread view that the US macroeconomy has been more “stable” since 1984. X.3.a. Write out a hypothesis test that the economy has been more stable in the post-1984 era. X.3.b. Conduct the appropriate test, using the statistics provided below, and setting Type I error equal to 1%. 048121620-0.10 -0.05 -0.00 0.05 0.10 0.15Series: D(LGDP96C)*4Sample 1953:1 1984:4Observations 127Mean 0.032815Median 0.031627Maximum 0.154627Minimum -0.110207Std. Dev. 0.045075Skewness -0.371950Kurtosis 3.224857Jarque-Bera 3.195890Probability 0.202312 Figure 7: Histogram for United States qoq annualized GDP growth, 1953q1-1984q4 0246810-0.02 0.00 0.02 0.04 0.06Series: D(LGDP96C)*4Sample 1985:1 2004:4Observations 79Mean 0.030981Median 0.032474Maximum 0.071446Minimum -0.030350Std. Dev. 0.020221Skewness -0.426968Kurtosis 3.492274Jarque-Bera 3.197991Probability 0.202099 Figure 8: Histogram for United States qoq annualized GDP growth, 1985q1-2004q3
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