Assumption 1Review1. Forward/backward survival estimates of migration2. Projection of stable characteristics (e.g., race educational attainment, literacy)3. Source of CSRs4. Purpose and mechanics of pop projections5. Applications of life table tools6. Forward survival and the open ended age category7. New stuff – projections involving time-varying characteristics1Forward/backward survival estimates of migrationQ: Use forward (and backward) survival methods to calculate age-specific (and total) net migration to/from North regionAge National population North region1996 Census 2000 Census 1996 Census 2000 Census0- 419625 17358 4509 40595-920231 18369 4614 408610-1420249 19197 4165 421515-1916472 17910 3990 435320- 2412108 14787 3095 380425- 299744 11034 2474 275130- 347459 8964 1871 221435- 397043 7137 1655 178840- 445639 6513 1265 151545- 494743 5259 911 116450- 543479 4221 718 80755- 592568 3066 450 59460- 641971 2211 381 38765+2927 3321 434 5222Example from PS #8North regionAge1996Census2000Census CSRsprojectedsurvivors(forward)Difference=NMprojected #(backward)Difference=NM0- 44509 4059 4365 -1445-94614 4086 0.9360000 4220 -134 4442 -17210-144165 4215 0.9488903 4378 -163 4921 75615-193990 4353 0.8844881 3684 669 4237 24720- 243095 3804 0.8977052 3582 222 3019 -7625- 292474 2751 0.9112983 2820 -69 2407 -6730- 341871 2214 0.9199507 2276 -62 1869 -235- 391655 1788 0.9568307 1790 -2 1638 -1740- 441265 1515 0.9247480 1530 -15 1248 -1745- 49911 1164 0.9326122 1180 -16 907 -450- 54718 807 0.8899431 811 -4 674 -4455- 59450 594 0.8812877 633 -39 449 -160- 64381 387 0.8609813 387 0 770 -4565+434 522 0.6780319 553 -31 356 414Takeaverage 3853Projection of stable characteristics Using the methods described in the paper by Hermalin and Christenson and the datafrom Mexico below, answer the following:a. What is the projected proportion of Mexicans age 55-64 that will be literate in 2000, 2010, and 2020?b. What is the projected proportion of Mexicans age 65+ that will be literate in 2000, 2010, and 2020?(for convenience, let’s assume that literacy is a fixed characteristic – i.e., the number of illiterate adults who learn to read and write is negligibly small) 1980 1980 1990 1990Age Total Population Literate population Total Population Literate population15-19 7,656,539 7,114,592 9,664,403 9,268,72220-246,154,527 5,584,296 7,829,163 7,395,70325-29 4,804,392 4,219,010 6,404,512 5,929,46830-343,838,059 3,274,644 5,387,619 4,921,65435-39 3,406,934 2,750,979 4,579,116 4,019,22440-442,745,198 2,155,515 3,497,770 2,955,58345-49 2,315,629 1,746,528 2,971,860 2,376,58450-541,863,963 1,356,333 2,393,791 1,854,18555-59 1,465,903 1,049,483 1,894,484 1,407,97860-641,115,146 732,683 1,611,317 1,119,08865+ 2,561,120 1,491,607 3,376,841 2,105,8781980 1980 1990 1990Age Total Literate Total Literate % literate 90 % literate 00 % literate 10 % literate4Population population Population population 2015-19 7,656,539 7,114,592 9,664,403 9,268,722 0.9590620-24 6,154,527 5,584,296 7,829,163 7,395,703 0.9446425-29 4,804,392 4,219,010 6,404,512 5,929,468 0.92583 0.9590630-34 3,838,059 3,274,644 5,387,619 4,921,654 0.91351 0.9446435-39 3,406,934 2,750,979 4,579,116 4,019,224 0.87773 0.92583 0.9590640-44 2,745,198 2,155,515 3,497,770 2,955,583 0.84499 0.91351 0.9446445-49 2,315,629 1,746,528 2,971,860 2,376,584 0.79970 0.87773 0.92583 0.9590650-54 1,863,963 1,356,333 2,393,791 1,854,185 0.77458 0.84499 0.91351 0.9446455-59 1,465,903 1,049,483 1,894,484 1,407,978 0.74320 0.79970 0.87773 0.9258360-64 1,115,146 732,683 1,611,317 1,119,088 0.69452 0.77458 0.84499 0.9135165+ 2,561,120 1,491,607 3,376,841 2,105,878 0.62362 0.67313 0.73052 0.79671CSR proj pop 2000 proj pop 2010 proj pop 2020# literate 2000# literate 2010# literate 202025-290.836476115 8084042 775306430-340.875391236 6853581 647413435-390.953110404 6104207 7704985 5651438 738952740-440.911338257 4909943 6245931 4485291 590012645-490.872297497 3994351 5324684 6721039 3505959 4929734 644586650-540.871992111 3050028 4281432 5446403 2577245 3911139 514486455-590.818129329 2431366 3267896 4356280 1944353 2868328 403316060-640.86445761 2069331 2636620 3701116 1602864 2227919 338101365+0.656695842 4519802 5923724 7767556 3042435 4327397 6188468% literate 55-64 0.7881484 0.8631100 0.9201699% literate 65+ 0.6731346 0.7305197 0.79670725Source of SRs1. Life tables or successive censues?2. Largely determined by data availability3. Census coverage is also an issuea. Census based CSRs reflect both mortality and cross-census differentials in coverageb. Life tables (theoretically) reflect only mortalityc. If census coverage differentials are large, life table CSRs will over/understate number of survivors4. Also depends on comfort with assumption of no cohort differences in age-specific mortality – may not hold if cohorts are very distinct w/re health circumstances6Cohort component method of population projectionConsider a small piece of the larger calculationSR 15-19/20-24 ASFR*1000 # migrantsAssumption 10.95 20 200Assumption 2 0.99 10 50Assumption 30.90 25 300Survivors 20-24 Surviving migrantsProjected pop 20-24Projected pop 15-19# births950 195 1145 1000 100990 50 1040 950 49900 285 1185 1100 1317Steps in generating output using cohort component method (RAW – most complicated case)8A: [Base population age x →x+5] x SR = projected survivors age x+5 → x+10B: [# net immigrants age x – x+5] x [(1+SR)/2] = projected surviving immigrants age x+5 → x+10C: A+B = projected population age x+5 → x+10D: [{(Base population age x →x+5)+ (Projected population age x →x+5)}/2] x(ASFRx-x+5 x 5) = projected # births to women age x →x+5E: D x SR for infants (0-4) = projected # surviving births (i.e., pop age 0-4)Life Table Applications Example – inventory and profitsA grocery store gets a shipment of 100 cartons of milk every Saturday morning (milk keeps for a week and then has to be discarded). The probability of milk being sold across the week follows this pattern:Day Probability of being soldSat 0.30Sun 0.40Mon 0.15Tues 0.20Wed 0.25Thurs 0.30Fri 0.40Each carton of milk costs the grocer $1.50 and he sells it for $2.00. It costs an average of 3 cents per day to keep one carton of milk. The grocer gets no refund on cartons that remain unsold. What is profit on a week’s shipment of milk?9Milk exampleday Qx lx dx Lx Tx exSat 0.30 100 30 145.0 450.5 4.505Sun 0.40 70 28 112.0 305.5 4.364Mon 0.15 42 6 51.0 193.5 4.607Tues 0.20 36 7 46.5 142.5 3.958Wed 0.25 29 7 39.5