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1 Avalable onlne at ISSN Internatonal ejournals Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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

2 87 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 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 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 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

3 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 and above Total 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.

4 89 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) Table. Smoothed urban male populaton Age Census year group and above Total 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 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

5 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 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 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.

6 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 : y = exp( x ) t rato : ( ) ( ) ( ) R = λ = : y = exp( x ) t rato: ( 3.10) ( ) ( ) R = λ = : y = x t rato : (84.36) ( 1.95) R = λ = 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.

7 9 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 above 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 and above

8 93 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) Age Group and above Age Group and above Age Group and above

9 94 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) Age Group and above Age Group and above 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.

10 95 Md. Rafqul Islam, A.B.M.Rabul Alam Beg Internatonal ejournal of Mathematcs and Engneerng 7 (010) 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 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 Islam, Md. Rafqul. (005). Constructon of female lfe table from male wdowed nformaton of Bangladesh, Pakstan Journal of Statstcs, Vol. 1(3),Page 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 , 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,