The following table contains data on the joint distribution of age ?(Age?) and a

Question

The following table contains data on the joint distribution of age ?(Age?) and average hourly earnings ?(AHE?) for 25 to 34? year-old full-time workers with an educational level that exceeds a high school diploma in 2012. Download the data from the table by clicking the download table icon . A detailed description of the variables used in the dataset is available here . Use a statistical package of your choice to answer the following questions.

Use the law of iterated expectations to compute the mean of AHE?;

Age and Hourly Earnings Age Hourly Earnings (AHE) 25 26 27 28 29 30 31 32 33 34 5 0.001431 0.001943 0.001636 0.001943 0.001022 0.001022 0.001125 0.001227 0.000511 0.001125 6 0.001431 0.000613 0.001534 0.001431 0.001125 0.001227 0.001431 0.000409 0.001329 0.000409 7 0.001431 0.001943 0.000818 0.001534 0.00092 0.001738 0.001022 0.00092 0.000613 0.001125 8 0.002351 0.001534 0.001738 0.001022 0.001329 0.000818 0.001329 0.00184 0.001227 0.001329 9 0.002351 0.002965 0.002045 0.002351 0.002249 0.001943 0.001636 0.001227 0.001636 0.001227 10 0.004192 0.004805 0.003681 0.004294 0.003681 0.004192 0.003578 0.002965 0.00276 0.002147 11 0.003272 0.003476 0.002863 0.002454 0.002454 0.003067 0.002045 0.002863 0.002965 0.002249 12 0.00685 0.006134 0.005623 0.004396 0.005828 0.005521 0.004805 0.00501 0.00501 0.004601 13 0.003885 0.003681 0.005112 0.003885 0.003578 0.003987 0.003067 0.003272 0.003681 0.003374 14 0.005828 0.004907 0.007054 0.006134 0.004703 0.006646 0.006748 0.005828 0.004907 0.005419 15 0.003476 0.003169 0.00409 0.003578 0.003987 0.005112 0.003987 0.00501 0.002351 0.003578 16 0.002658 0.003272 0.004192 0.003067 0.004805 0.003272 0.004396 0.003681 0.003169 0.002147 17 0.004703 0.00501 0.006441 0.006339 0.005828 0.004703 0.005828 0.007054 0.004805 0.005214 18 0.002658 0.003169 0.003578 0.002965 0.003169 0.003681 0.003681 0.003476 0.003681 0.003783 19 0.003681 0.00409 0.005214 0.004805 0.006032 0.006646 0.006339 0.005828 0.00685 0.004601 20 0.002965 0.002863 0.003067 0.00276 0.003681 0.003885 0.004192 0.00501 0.005419 0.003374 22 0.003885 0.004601 0.005419 0.006543 0.007054 0.007975 0.006646 0.007975 0.007361 0.007054 24 0.00409 0.005725 0.006748 0.009508 0.007668 0.007872 0.011349 0.007566 0.009713 0.008997 26 0.003169 0.003169 0.00501 0.003476 0.004499 0.005419 0.004499 0.005316 0.004601 0.005828 28 0.002965 0.002658 0.003681 0.004601 0.004805 0.00685 0.005725 0.006543 0.006237 0.007872 30 0.001943 0.002249 0.00409 0.003476 0.005214 0.005316 0.005725 0.006032 0.006032 0.006237 35 0.002556 0.002658 0.004907 0.006952 0.006237 0.007054 0.006237 0.008281 0.010326 0.00685 40 0.001329 0.002249 0.001636 0.002863 0.003067 0.004294 0.004396 0.006134 0.004703 0.005214 45 0.001022 0.000511 0.001431 0.001534 0.001738 0.003272 0.003885 0.003783 0.005214 0.004601 50 0.000511 0.000511 0.001227 0.001227 0.001227 0.001738 0.00276 0.002249 0.002556 0.003067 55 0.000102 0.000818 0.000613 0.000818 0.000511 0.001022 0.000818 0.001125 0.001534 0.001738 60 0.000204 0.000613 0.000307 0.000511 0.000716 0.000818 0.001125 0.00092 0.001738 0.001329 65 0.000102 0.000204 0.000102 0.000102 0.000511 0.000204 0.000409 0.000204 0.000716 0.000818 70 0.000307 0.000204 0.000818 0.000716 0.000613 0.001227 0.002147 0.001636 0.001738 0.003169

Explanation / Answer

The marginal distribution would be simply the vertical summation over various ages.

So Marginal distribution of age 25= 0.075398

Age 26= 0.0797461

Age 27= 0.0946735

Age 28=0.0952867

Age 29=0.0982517

Age 30=0.1052039

Age31=0.1109293

Age32=0.1133830

Age 33=0.1133832

Age 34=0.1159583

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