Avalable onlne at www.nternatonalejournals.com ISSN 0976 1411 Internatonal ejournals Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 MODELING AND PREDICTING URBAN MALE POPULATION OF BANGLADESH: EVIDENCE FROM CENSUS DATA Authors: 1 Md. Rafqul Islam and A.B.M.Rabul Alam Beg 1 Md. Rafqul Islam Department of Populaton Scence and Human Resource Development Unversty of Rajshah, Rajshah-605, Bangladesh. E-mal: rafque_pops@yahoo.com A.B.M.Rabul Alam Beg James Cook Unversty Australa. E-mal: rabul.beg@jcu.edu.au Correspondng Author: Md. Rafqul Islam Abstract. Ths paper predcts the urban male populaton of Bangladesh usng geometrc growth rate method. The predctons are computed n three stages. In the frst stage, the urban male populaton for the years 1981 and 1991 was predcted usng the smoothed data for those years. The frst stage predctons were obtaned by usng generalzed negatve exponental model estmated by nonlnear least squares method. Whle the urban male populaton for the year 001 was predcted by a lnear model. Usng the cross valdaton predctve power (CVPP) and R ths artcle constructed shrnkage coeffcent whch determnes the adequacy of the frst stage predcted values. These predcted values are then used n the second stage to estmate the geometrc growth rate for dfferent age groups. Fnally, consderng year 001 urban male populaton as the base perod and usng the estmated geometrc growth rate of the second stage the predctons of the urban male populatons are computed for 00 through to 031. Key words: Urban populaton, lnear forecast model, negatve exponental forecast model, nonlnear least square estmaton, geometrc growth rate, cross valdty predctve power (CVPP), R, shrnkage Runnng Head Lne: Modelng and Predctng Urban Male Populaton of Bangladesh
87 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 1. Introducton Bangladesh s a poor country manly depends on foregn ad. People of Bangladesh always struggle for survval. Rural people are generally hard htted fnancally than the urban Bangladesh. There s a trend of people movng from rural area to urban Bangladesh for better lfe. Populaton n urban area s growng snce the ndependence n 1971. It s to be noted that the male populaton of Bangladesh are the man drvng force of ncome generaton. The heavy nflux of people n the urban areas s a burden to the Bangladesh government. Thus, the Bangladesh government needs frm polcy to accommodate ts fast growng urban populaton by provdng shelter, educaton, health, clean water and etc. The objectve of ths paper s to provde effcent predcton of urban male populaton at dfferent age groups usng a three stage procedures for the government s nfrastructural polcy decsons. Snce the pattern of age structure of populaton may change from varous demographc varables and from country to country. Islam et al. (003) found that the age structure of Bangladesh follows a modfed negatve exponental model. Whle the age structure for the populaton of both sexes of Bangladesh follows a generalzed negatve exponental model (Islam, 005). Islam and Beg (009) predcted the populaton of Dhaka Dstrct of Bangladesh usng cubc polynomal durng 00-031. A study by Bangladesh Bureau of Statstcs (BBS, 1994) used logstc functon to project lfe expectancy at brth up to year 006. But the objectve of ths paper s to predct the urban male populaton. Therefore, followng Islam et al. (003), Islam (005) and Islam and Beg (009), ths paper uses the most recent data and the geometrc growth rate approach n three stages to predct the urban male populaton of Bangladesh for the years 00 through to 031. Ths paper also estmates the number of years needed to double the urban male populaton for dfferent age groups usng the predcted values of 1991 and 001. So far none of the prevous studes of Bangladesh consdered ths knd of analyss. Ths paper s organzed as follows. Secton presents the data and the data sources. The models and the methodologcal ssues and varous tests are descrbed n secton 3. Emprcal results and dscusson of the results are reported n secton 4. Fnally secton 5 concludes the paper.. Data and Data Sources To fulfll the objectve of ths paper the secondary qunquennal age data on urban male populaton of Bangladesh have been taken from varous ssues (BBS 1984, 1994, 003) of Bangladesh census starng from 1981. Note that the census happens n Bangladesh n every ten years and the last census took place n 001. Usng the last three census data ths paper forms the predctons for the years 00 through to 031. The age group consdered n ths study are (0-4, 5-9, 10-14, 15-19,, 65-69, 70 and above). The populaton values are n thousand. The data are shown n Table-1
Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 88 Table 1. Observed urban male populaton (n thousands) by age group of Bangladesh for the census years 1981, 1991, and 001. Age group Census year 1981 1991 001 0-4 955 1438 1588 5-9 935 154 166 10-14 947 1360 188 15-19 744 1038 1684 0-4 741 1115 1594 5-9 709 1104 1508 30-34 58 859 151 35-39 450 806 117 40-44 360 597 909 45-49 59 418 655 50-54 33 39 514 55-59 130 195 84 60-64 153 1 301 65-69 65 10 155 70 and 161 04 319 above Total 7370 11301 15433 3. Models and the Methodologcal Issues If the populaton due to ages s presented n the graph paper, then t s found that thre are some short of dstortons exst n the data aggregate. For that reason, data needs to be adjusted. Therefore, the data have been smoothed out to elmnate any abnormaltes from the data. The technque used s 453H twce of Velleman (1980). Ths s the default n the Mntab package - verson 1.1. The smoothed seres are then used to predct the urban male populaton of Bangladesh usng negatve exponental for the years 1981 and 1991 data and the lnear model for the year 001 data. The smoothed seres for the years 1981, 1991, and 001 for dfferent age groups are gven below.
89 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 Table. Smoothed urban male populaton Age Census year group 1981 1991 001 0-4 955 1467 1595 5-9 934 1437 1645 10-14 881 1341 1674 15-19 805 117 1667 0-4 735 1118 1607 5-9 659 107 1480 30-34 554 910 1304 35-39 446 760 1106 40-44 353 595 897 45-49 75 438 684 50-54 06 31 483 55-59 158 8 339 60-64 140 189 81 65-69 138 181 74 70 and 138 181 74 above Total 7377 11401 15310 The models Both the orgnal and smoothed age structure of urban male populaton dsplay negatve exponental patterns n terms of dfferent age groups for the years 1981 and 1991. Therefore, ths study employs a generalzed negatve exponental model to the data for predcton purpose. Whle a lnear predcton model fts the observed data well for the year 001. The models consdered for the frst stage predctons are the followng. ax b (generalzed negatve exponental) y = c + e ( + ) + u (1) j (Polynomal) = α + α x + η () Wth y 0 p = 1 n () produces a lnear model. p j= 1 Where wth reference to the present research, j represents the urban male populaton of the -th age group, x s the md value of the -the age group, j =1,., p s the order of the polynomal, c, a, b,α 0, α1,..., α p are parameters, and y
Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 u and η are normal random varables wth mean zero and constant varance of model (1) and model () respectvely. The models are estmated by usng nonlnear least squares and ordnary least squares methods avalable n STATISTICA. Note that the ordnary least squares s appled to estmatng the polynomal model (). Geometrc growth rate method Geometrc growth rate s estmated by usng the followng equaton. 90 ˆ ˆ 5 P = P + r (3) m m+ 5 m m+ 5 m m+ t t1 t {1 } t1 Where, m to m ˆ m m+ 5 P t 1 Pˆ m t + s the predcted ntal populaton at tme t for the age group m+5 5 ; s the predcted termnal populaton at tme t for the age group m m+5 m to m + 5 ; r s the ntercensal annual growth rate of the age group m to m + 5 ; and (t t 1 ) s the tme nterval between ntercensal perod. m m+5 The r s computed for dfferent age group from (3) as follows. 1 ˆ m m+ 5 m m + 5 1 P r = Antlog log t e 1 ˆ 5 m m+ 1 t t Pt 1 (4) s 1991 and 001 are consdered as the ntal and the termnal urban predcted male populatons respectvely n estmatng the age specfc growth rate by equaton (4). For predcton purpose, year 001 census s treated as the base male populaton. The ntercensal annual growth rate durng 1991-001 s used n ths study assumng fertlty and mortalty reman unchanged durng the forecast perod. Estmaton of the ntercensal annul geometrc growth rate for dfferent age groups s computed based on the frst-stage predcted data for 1991 and 001. Model evaluaton crtera used are the usual regresson t-test, and R. For model valdaton ths paper uses cross valdaton predctve power (CVPP) denoted, computed by ( n 1)( n )( n + 1) ρ cv = 1 (1 R n( n k 1)( n k ) ρ cv ), where n s the number of classes, k s the number of regressors n the model, and R s the coeffcent of determnaton n the frst stage of estmaton. The shrnkage of the model s equal to the absolute value of λ = ( ρ cv R ), Steven (1996). The shrnkage crteron asserts that the better predctons are obtaned f λ approaches zero.
Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 4. Emprcal Results and Dscusson of the Results Ths study used both the smoothed and the orgnal seres to ft generalzed negatve exponental model for the years 1981 and 1991 for all age groups. Whle a lnear model s ftted to the smoothed and the orgnal data for the year 001 only. Ths study found that the smoothed data has the better predctons. Consequently ths current study has used the smoothed seres n the frst stage of predcton. The estmated models are gven below. 91 1981: y = 916.170 + exp( 0.0099x + 7.599) t rato : ( 9.45486) ( 11.0564) (168.5038) R = 0.97454 λ = 0.00636 1991: y = 88.9 + exp( 0.0059x + 8.415) t rato: ( 3.10) ( 16.40506) (319.009) R = 0.97737 λ = 0.00564 001: y = 1961.4 5.086x t rato : (84.36) ( 1.95) R = 0.971 λ = 0.01779 All of the estmated coeffcents are statstcally sgnfcant at the conventonal level for all of the above estmated models. The R of each model s hgh. Moreover, the above models provde good predctons based on the shrnkage crteron λ. Therefore, these models can be adopted for predcton. The predcted values for the years 1991 and 001 are then used to estmate the geometrc growth rates for each age group. Whch n turns these rates are used to predct the urban male populaton of Bangladesh for the years 00 through to 031 consderng orgnal 001 census as the base. Ths study has also estmated the number of years requred to double the populaton at dfferent age groups, whch s provded n the followng Table 3.
9 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 Table 3. Estmated geometrc growth rate and the number of years requred to double the urban male populaton at each age group. Age group The estmated geometrc growth rate Approxmate number of s requred to double the urban male populaton 0-4 0.00 36 5-9 0.01 33 10-14 0.03 30 15-19 0.05 8 0-4 0.07 6 5-9 0.09 4 30-34 0.03 35-39 0.034 1 40-44 0.037 19 45-49 0.040 18 50-54 0.043 16 55-59 0.048 15 60-64 0.054 13 65-69 0.066 11 70-above 0.105 7 Ths table ndcates that the aged male populaton wll grow at a faster rate than the younger. The man reason for ths may be due to the fact that there s a growng tendency of late marrage among males and also there s a tendency of the females to be nvolved n the payroll. Usng ths estmated growth rate and 001 census as the base ths paper predcts the urban male populaton whch s gven below n the Table 4. Table 4. Predcted urban male populaton (n thousands) for the years 00 through to 031 Age Group 00 003 004 005 006 0-4 619.05 1650.656 168.905 1715.784 1749.306 5-9 1697.598 1733.958 1771.097 1809.031 1847.778 10-14 195.90 1970.865 016.858 063.95 11.091 15-19 176.609 1770.96 1815.089 1861.015 1908.103 0-4 1637.564 168.318 178.95 1775.59 184.053 5-9 155.394 1598.095 1645.141 1693.573 1743.430 30-34 190.607 1331.467 1373.61 1417.110 1461.976 35-39 1165.360 105.05 146.040 188.45 133.307 40-44 94.3066 976.8335 101.66 1049.79 1088.19 45-49 680.930 707.8907 735.9166 765.05 795.3413 50-54 536.1559 559.669 583.3740 608.503 634.7505 55-59 97.567 311.6976 36.5435 34.0964 358.390 60-64 317.369 334.5393 35.6854 371.8158 391.9839 65-69 165.96 176.686 187.9735 00.4556 13.7666 70 and above 35.531 389.5691 430.508 475.7496 55.745
93 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 Age Group 007 008 009 010 011 0-4 1783.48 1818.36 1853.851 1890.070 196.996 5-9 1887.354 197.779 1969.069 011.44 054.3 10-14 161.380 11.80 63.436 316.58 370.31 15-19 1956.383 005.884 056.637 108.675 16.030 0-4 1873.904 195.117 1977.730 031.781 087.309 5-9 1794.755 1847.591 1901.98 1957.975 015.616 30-34 1508.6 1556.013 1605.77 1656.100 1708.53 35-39 1377.655 144.546 1473.033 153.171 1575.015 40-44 118.064 1169.398 11.45 156.663 130.708 45-49 86.895 859.5643 893.595 98.9734 965.75 50-54 66.1113 690.6516 70.40 751.4757 783.8680 55-59 375.4600 393.348 41.0774 431.704 45.659 60-64 413.459 435.661 459.94 484.054 510.4697 65-69 7.9615 43.0990 59.416 76.456 94.8139 70 and above 580.9948 64.0505 709.54 784.0848 866.488 Age Group 01 013 014 015 016 0-4 1964.644 003.08 04.161 08.059 1.737 5-9 098.3 143.65 189.171 36.060 83.953 10-14 45.67 48.34 540.161 599.440 660.103 15-19 16.734 7.83 330.331 389.93 449.748 0-4 144.354 0.959 63.165 35.016 388.558 5-9 074.953 136.038 198.91 63.655 330.95 30-34 176.64 1818.48 1876.000 1935.394 1996.668 35-39 168.64 1684.057 1741.378 1800.649 1861.937 40-44 1350.441 1399.9 1451.16 1504.390 1559.51 45-49 1003.987 1043.736 1085.058 118.017 117.676 50-54 817.6566 85.9016 889.6658 98.0147 968.0167 55-59 473.8069 496.3739 50.0158 544.7837 570.731 60-64 538.1586 567.3494 598.136 630.5671 664.7704 65-69 314.3907 335.674 357.5303 381.717 406.5895 70 and above 957.5399 1058.166 1169.367 19.53 148.054 Age Group 017 018 019 00 01 0-4 164.09 06.491 49.600 93.550 338.360 5-9 33.87 38.838 433.875 486.005 539.5 10-14 7.181 785.708 850.717 917.44 985.33 15-19 511.733 575.85 640.446 707.56 775.756 0-4 453.837 50.899 589.795 660.573 733.86 5-9 398.897 469.518 54.18 617.058 694.10 30-34 059.883 15.098 19.379 61.790 333.398 35-39 195.31 1990.844 058.606 18.675 01.19 40-44 1616.654 1675.890 1737.96 1800.95 1866.941 45-49 119.103 167.368 1317.544 1369.707 143.935 50-54 1009.743 1053.68 1098.669 1146.07 1195.46 55-59 597.9146 66.397 656.73 687.488 70.70 60-64 700.889 738.8433 778.9197 81.1699 865.7119 65-69 433.5885 46.3804 493.084 55.867 560.7436 70 and above 1578.15 1743.968 197.38 19.768 353.58
94 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 Age 0 03 04 05 06 Group 0-4 384.045 430.6 478.109 56.55 575.886 5-9 593.639 649.191 705.933 763.890 83.089 10-14 3054.991 316.85 3199.4 373.90 3350.304 15-19 845.989 917.999 991.831 3067.53 3145.147 0-4 807.985 884.77 963.565 3044.559 317.766 5-9 773.414 855.061 939.111 305.635 3114.707 30-34 407.73 483.487 56.114 643.31 76.915 35-39 76.049 353.519 433.65 516.459 60.111 40-44 1935.347 006.60 079.771 155.976 34.97 45-49 1480.310 1538.916 1599.843 1663.18 179.09 50-54 146.955 1300.705 1356.77 1415.55 1476.59 55-59 754.5307 790.4683 88.1176 867.5601 908.881 60-64 91.6699 96.1750 1014.365 1069.387 117.39 65-69 597.9790 637.6870 680.0318 75.1884 773.3435 70 and above 600.915 874.41 3176.89 3510.080 3878.947 Age 07 08 09 030 3031 Group 0-4 66.11 677.519 79.831 783.164 837.539 5-9 883.555 945.317 3008.401 307.837 3138.65 10-14 348.490 3508.500 3590.377 3674.165 3759.908 15-19 34.77 3306.30 3389.978 3475.75 3563.697 0-4 313.46 3301.063 3391.80 3483.963 3579.179 5-9 306.401 3300.795 3397.967 3498.000 3600.978 30-34 813.49 90.317 994.04 3089.000 3186.798 35-39 690.679 78.6 876.96 974.885 3076.141 40-44 316.864 401.756 489.758 580.985 675.555 45-49 1797.483 1868.647 194.68 019.538 099.494 50-54 1539.893 1606.70 1675.508 1747.731 183.067 55-59 95.170 997.51 1045.03 1094.806 1146.951 60-64 1188.545 153.014 130.980 139.63 1468.17 65-69 84.696 879.459 937.859 1000.136 1066.549 70 and above 486.579 4737.048 534.855 5784.977 639.909 The rate at whch the urban male populaton s growng s a concern to the government of Bangladesh. Bangladesh Government, therefore, requres polces to provde maxmum welfare to ts frst growng urban populaton. That s the government needs strategc plannng to provde good health care, accommodaton, roads and hghways, educatonal nsttutons, and jobs to satsfy the mnmum need of the people of Bangladesh.
95 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 5. Conclusons Ths study observed that the age pattern of urban male populaton of Bangladesh follows generalzed negatve exponental model for the census years 1981 and 1991. But the lnearty s mantaned for the data of the census year 001. The smoothed seres are then used to estmate the geometrc growth rate for each age group of urban males followng Malthusan law of populaton growth. It s observed that the older urban males are growng faster to double the populaton than the younger. The projected growth of urban males s an early warnng to the government of Bangladesh to take the matter serously to accommodate ts urban ctzens wth maxmum welfare. Although ths paper has used the generalzed exponental and lnear models for frst stage populaton predcton there are, however a number of models e.g. logstc, Gompertz, Makeham models can also be appled for such predctons. But these models performed poorly n ths study. Therefore, these models were omtted from the analyss. The research can be further explored to nvestgate the dstrct wse growth of urban male populaton of Bangladesh. Specfcally, the heavly populated dstrcts e.g. Chttagong, Rajshah, and Khulna are n our next research agenda. References BBS (1984). Bangladesh populaton census 1981, Natonal Seres, Government of the People s Republc of Bangladesh, Dhaka. BBS (1994). Bangladesh populaton census 1991, Vol. 1, Natonal Seres, Government of the People s Republc of Bangladesh, Dhaka. BBS. (003). Bangladesh populaton census 001, Natonal report, Government of the People s Republc of Bangladesh, Dhaka. Islam, Md. Rafqul (003). Modelng of demographc parameters of Bangladesh-an emprcal forecastng, unpublshed Ph.D. Thess, Rajshah Unversty. Islam, Md. Rafqul, Islam, Md. Nurul, Al, Md. Ayub & Mostofa, Md. Golam. (003). Constructon of male lfe table from female wdowed nformaton of Bangladesh, Internatonal Journal of Statstcal Scences, Vol., Dept. of Statstcs, Unversty of Rajshah, Bangladesh, Page 69-8. Islam, Md. Rafqul. (005). Constructon of female lfe table from male wdowed nformaton of Bangladesh, Pakstan Journal of Statstcs, Vol. 1(3),Page 75-84. Islam, Md. Rafqul and A.B.M. Rabul Alam Beg. Modelng and Predctng Populaton of Dhaka Dstrct of Bangladesh, Internatonal J. of Mathematcs and Computaton, Vol. 4, No. S09, pp. 69-80, September-009. Stevens, J. (1996). Appled multvarate statstcs for the socal scences, Thrd Edton, Lawrence Erlbaum Assocates, Inc., Publshers, New Jersey. Velleman, P. F. (1980). Defnton and comparson of robust nonlnear data smoothng algorthms, Journal of the Amercan Statstcal Assocaton, Volume 75. Number 371, 609-615.