View of Forecasting Age specific fertility rate in Thailand Using Natural Cubic Spline Function

Turkish Journal of Computer and Mathematics Education Vol.12 No. 8 (2021), 2601-2603

2601 Research Article

Forecasting Age specific fertility rate in Thailand Using Natural Cubic Spline Function

a,b_{Department of Mathematics and Computer Science, Faculty of Science and Technology,}

Prince of Songkla University, Pattani, Thailand.

a_{Centre of Excellence in Mathematics, Commission on Higher Education,}

Ratchathewi, Bangkok, Thailand.

c_{Division of Statistics, Faculty of Science, Maejo University, Chiang Mai, Thailand.}

*Corresponding author, Email address: apiradee.s@psu.ac.th

Article History: Received: 10 January 2021; Revised: 12 February 2021; Accepted: 27 March 2021; Published online: 20 April 2021

Abstract: Thailand has decreased the total fertility rate over the five three decades and continues to fall. The significant changes

occurring in age specific fertility rate (ASFR). In this study aims to investigate ASFR trends and forecast the ASFR of Thailand from 2020 to 2050. The ASFRs were downloaded from the US Census Bureau’s website by separated by 7 age groups from 15 to 49 years between 1990 and 2019. Natural Cubic Spline Function were used to investigate ASFR patterns from years 2010-2019 of each age group and were used to forecast the ASFRs in 2020 to 2050. From forecasted the results show ASFRs in Thailand of age group 25-29, 30-34, and 35-39 years have slightly increased trends whereas ASFRs in the young and old age group were down relatively constant. In summary, the fertility change in Thailand will occur dramatically entering an aging society within next 10 years from 2020

Keywords: age-specific fertility rates, natural cubic spline Function, fertility patterns

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Projections of fertility, mortality, and migration are the three main factors affecting the future size predictions and population compositions. Among these factors, fertility prediction plays a vital role due to its importance in determining and control population growth and dynamics [1]. It is a major factor for biological substitution and maintenance of mankind development [2] and it has a big impact on the socioeconomic condition of a country [3]. Hence, in forecasting of population, fertility remains a key factor. The most index usually used to predict fertility and measure population growth is the total fertility rate (TFR) and age specific fertility rate [4] but the TFR it does not provide information on the age group number of birth [5]. On the other hand, the age-specific fertility rate (ASFR) is a measure of the annual number of births by women of specific age group (15-49) per 1,000 women. Thus, should consider a model that can describe the fertility illustrate more accurately and precisely as it will allow the fertility forecasts to be reasonable. [6]

The World Fertility Report, Southeast Asia fertility has decreased remarkably over past five decades, from 2.5 births per woman in 1990 to 1.8 in 2019 and remain constant projected in 2050 [7]. Almost a half of the world’s population lives in countries with below replacement fertility or fertility rate below 2.1 births per woman on of them is Southeast Asia. It is obvious that family size is likely smaller, especially in countries having substantial industrial and urban growth. The fertility is the main engine of population change [8] and this fertility decline drives a slowing rate of world’s population growth. However, fertility rate of Thailand fell gradually from 5.4 children per woman in 1971 to 1.5 children per woman in 2020 and faced such problem that mention above.

The ASFR in age group 20-24 has been and remains the highest in Thailand since 1990 until 2000 while age group 45-29 occur lowest [9]. There has been a reduction in ASFR for all age group. This reduction is attributed to different reasons. The most consistent reasons are transitions to lower fertility which are driven by two direct causes: a rise in marriage ages, thus reducing teenage childbearing; and increased family size limitation by contraception and abortion. There is enough evidence of continuous declining in the TFRs of South Asia countries [10].

The significant of having a child differs based on a woman’s age. Therefore, forecasting ASFR is useful for indicating which age groups have more effect on population change and this contribution helps better understanding not only fertility transition over decades but also changing patterns in the annual number of births by specific-aged-woman in these countries.

2. Materials and Methods A. Data source

Data on age-specific fertility rate (ASFR) in Thailand estimates were retrieved from the website of the United States Census Bureau. The ASFR data covered a period of 30 years from 1990 to 2019. Basically, the age pattern

Nasriyah Arbu, Apiradee Lim, Cherdchai Me-ead

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of reproductive women was distributed into 7 age groups from ages 15 to 49 years with 5-years intervals at: 15-19, 20-24, 25-29, 30-34, 35-39, 40-44 and 45-49 years.

B. Statistical analysis

(1) Cubic Spline

The natural Cubic Spline functions have been suggested in demographic research for interpolating age-specific

data as they have desirable smoothness optimality properties [11]. This is because spline functions [12] are piecewise p, with respect to fitting and forecasting [13]. They minimize the integrated squared second derivative and provide plausible linear forecasts that can be controlled by a judicious placement of the knots. The final integrated spline log-linear models developed in this study were constructed as following equations:

𝑌𝑡 = 𝑆(𝑡) + 𝑧𝑡 (1)

where t is time, 𝑌𝑡 is an observation at time t, S(t) is a spline function, 𝑧𝑡 is the random error. 3. Result

The time series data of ASFR were preliminarily explored values of each age group. For statistical modeling, these yearly data of ASFR were first assessed the stability of variance and the necessity of data transformation by fitting simple linear regression model to the entire ASFR with years, age-groups and countries. As illustrated in Fig.3, the normal quantile-quantile (Q-Q) plots of the model’s studentized residuals illustrate normally distributed after using the 9th root transformation to stabilize the variance the 30-year data.

Figure 1: Comparison normal Q-Q plots of the model’s studentized residuals between before data transformation (a) and after the 9th-root transformation (b) in age-specific fertility rates.

Figure 2 shows the results of ASFR forecasting in each reproductive age group of Thailand. The solid-colored lines illustrate the trend of ASFR in each age group between 1990 and 2019. The dotted colored lines are forecasts given by projecting these natural cubic spline function values from the year 2020 to 2050 in each age group and country.

Figure 2: The forecasting trend of ASFR in each age group

The patterns of 30-year ASFR in Figure 2 show high volatility of fertility transitions. There was a slight decline of all ASFRs during the period, 1990-2009. However, fertility rates in the most recent decade (2010-2019) of all age group showed stable declining trends which make most forecasts of the ASFR reliable. The forecasts with dotted lines indicate declining trends of ASFR in most age groups 30-34, 35-39 and 40-44.

Forecasting Age specific fertility rate in Thailand Using Natural Cubic Spline Function

4. Discussion and Conclusion

We have proposed an approach to forecasting the age specific fertility rate. In Thailand it uses a natural cubic spline function for projecting which this method produces a full predictive distribution of future fertility rate. This forecast is broadly in developing countries. It can be seen that fertility is decreasing steadily. Due to countries have a relatively high standard of living, the population are well-educated and are in a high economic status compared to other regions of the world [14]. They have high income under a very complex economic system. A cautious note should be taken in having a baby as it requires very high responsibilities. Women have their own career and are not dependent on men anymore. Therefore, it is not necessary to seek a spouse to support themselves. This has led to fewer marriages and an increase in single-person households [15]. These factors tend to have an influence on the decreasing fertility trends. However, this situation causes problems in these countries. The problems include 1) a shortage of labor, law number of labor, has an impact on economic and social development 2) an increase in the number of elderly will burden members of the family and 3) an increase of immigration between regions causes a social distance and controversies among immigrants.

5. Acknowledgement

We are grateful to Emeritus Professor Dr. Don McNeil from Macquarie University, Sydney, Australia, and Assoc. Prof. Dr.Apiradee Sae-lim my advisor for initiative and guidance on forecasting techniques used in this statistical modeling. Moreover, we wish to thankful to supported by the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.

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