solution to problem set1

# solution to problem set1 - Eco 572 Research methods in...

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Eco 572: Research methods in Demography Solutions to Problem Set 1 [1] World Population (a) The U.S. Census Bureau ( ) estimates the world population at the time this problem set was due, 3/1/06, as 6,500,609,361. (For an up-to-the-second answer see ). The same page shows the population going from 6,451,058,790 to 6,525,486,603 between 7/1/05 and 7/1/06, for an annual growth rate of . scalar r = log(6525486603/6451058790) . display r .01147125 (Can you figure out how they interpolate between these numbers to get monthly figures or run the population clock?) (b) The time it takes to reach 12 billion from now is . scalar p0 = 6500609361 . scalar t = log(12000000000/p0)/r . display t 53.438856 and the date is . scalar d = date("3/1/2006","mdy") + t * 365.25 . display month(d) "/" day(d) "/" year(d) 8/8/2059 (c) To postpone reaching 12 billion until 12/31/2100 we would need an average rate of . scalar y = (date("12/31/2100","mdy")-date("3/1/2006","mdy"))/365.25 . scalar ar = log(12000000000/p0)/y . display ar .00646406 If the growth rate was to decline linearly from its present value of r, it would have to be . display 2 * ar - r .00145687 (1 of 13) [2/11/2008 2:13:53 PM]

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Eco 572: Research methods in Demography by the time we reach 12 billion to meet the average. In other words, we would need to reach almost zero population growth by the end of the century. [2] Standardization I cut and pasted the data, put quotes around the age group labels, and then read it into Stata: . clear . input str5 ageg urbann urbanuse ruraln ruraluse ageg urbann urbanuse ruraln ruraluse 1. "15-19" 298 37 1451 88 2. "20-24" 332 116 1020 281 3. "25-29" 267 132 926 370 4. "30-34" 185 103 714 299 5. "35-39" 162 73 782 343 6. "40-44" 69 37 556 213 7. "45-49" 68 17 452 119 8. end The calculations are a lot easier if we stack rural below urban (which you can do by hand or using a reshape command) as you can then follow the handout using tabstat . (a) I reshape, compute the prevalence rates, and average them using the actual n's to get crude rates. . quietly reshape long @n @use, i(ageg) j(tpr) string . gen prev = use/n . tabstat prev [fw=n], by(tpr) Summary for variables: prev by categories of: tpr tpr | mean ------+---------- rural | .2902898 urban | .3729182 ------+---------- Total | .3059599 ----------------- The urban prevalence rate is much higher than the rural one, 37.3 versus 29.0%. To get standardized rates I get the urban and rural compositions, average them, and use that as weight . egen comp = pc(n), by(tpr) . egen avgcomp = mean(comp), by(ageg) . tabstat prev [aw=avgcomp], by(tpr) Summary for variables: prev by categories of: tpr (2 of 13) [2/11/2008 2:13:53 PM]
Eco 572: Research methods in Demography tpr | mean ------+---------- rural | .2932567 urban | .3690886 ------+---------- Total | .3311726 ----------------- The rural sample is younger than the urban, but that accounts for only a small part of the difference, as the standardized rates are 36.9 and 29.3%. We can also use the overall age ditribution . egen totcomp = sum(comp), by (ageg) . tabstat prev [w=totcomp], by(tpr) (analytic weights assumed) Summary for variables: prev by categories of: tpr tpr | mean ------+---------- rural | .2932567 urban | .3690886 ------+---------- Total | .3311726 ----------------- (b) I now compute the average prevalence rates and average these using the observed numbers of women to see how much difference the rates make . egen avgprev = mean(prev), by(ageg) . tabstat avgprev [fw=n], by(tpr) Summary for variables: avgprev

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