322Quiz02Fall11 - Instructor : H.H. Kim 1 Econometrics Quiz...

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Unformatted text preview: Instructor : H.H. Kim 1 Econometrics Quiz 02 Name: ______________________ 1) You have obtained a sub‐sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression yielded the following result: = 239.16 + 5.20×Age , R2 = 0.05, SER = 287.21., (20.24) (0.57) where Earn and Age are measured in dollars and years respectively. (a) Interpret the results. (b) Why should age matter in the determination of earnings? Do the results suggest that there is a guarantee for earnings to rise for everyone as they become older? Do you think that the relationship between age and earnings is linear? (c) The average age in this sample is 37.5 years. What is annual income in the sample? (d) Is the relationship between Age and Earn statistically significant? (e) Construct a 95% confidence interval for both the slop and the intercept. pe 2 Fall 2011 Rutgers University 2) Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the “Current Population Survey” (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 7,602 randomly selected U.S. households are surveyed each month. The sample is chosen by randomly selecting addresses from a database comprised of addresses from the most recent decennial census augmented with data on new housing units constructed after the last census. These data are from the March 2005 survey. Series in Data Set: AGE: Age of the sample observation AHE: Average Hourly Earnings in 2004 The following table shows the result of the regression of AHE on AGE from E‐views. Calculate appropriate value for (a) intercept and (b) R2 Dependent Variable: AHE Method: Least Squares Variable C AGE R‐squared Coefficient Std. Error t‐Statistic Prob. (a) 0.669706 3.872250 0.0001 0.304082 0.022440 13.55095 0.0000 (b) Mean dependent var 11.62818 Adjusted R‐squared 0.023463 S.D. dependent var 5.558322 S.E. of regression 5.492727 Akaike info criterion 6.244990 Sum squared resid 229292.4 Schwarz criterion 6.246815 Log likelihood 183.6283 Durbin‐Watson stat 1.699449 Prob(F‐statistic) 6.245616 F‐statistic ‐23735.21 Hannan‐Quinn criter. 0.000000 Total Sum Square 234832.57 Instructor : H.H. Kim 3 Econometrics Answer: (a) A person who is one year older increases her weekly earnings by $5.20. There is no meaning attached to the intercept. The regression explains 5 percent of the variation in earnings. The regression R2 indicates that five percent of the variation in earnings is explained by the model. The typical error is $287.21. (b) In general, age‐earnings profiles take on an inverted U‐shape. Hence it is not linear and the r linear approximation may not be good at all. Age may be a proxy for ʺexperience,ʺ which in itself can approximate ʺon the job training.ʺ Hence the positive effect between age and earnings. The results do not suggest that there is a guarantee for earnings to rise for everyone as they become older since the regression R2 does not equal 1. Instead the result holds ʺon average.ʺ (c) Since = ‐ ⇒ = + . Substituting the estimates for the slope and the intercept then results in average weekly earnings of $434.16 or annual average earnings of $22,576.32. (d) The t‐statistic on the slope is 9.12, which is above the critical value from the standard normal distribution for any reasonable level of significance. (e) The confidence interval for the slope is (4.08,6.32). The confidence interval for the intercept is (199.49,278.83). Answer (a) 2.593268 = t‐stat x SE β β , = 3.872250 x 0.669706 ‐ 0 (b) 0.023592 = 1‐ SSR/TSS = 1‐ 229292.4/234832.57 ...
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