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- 1. Amy Ko Ko 1 Barbara Kuzmak STAT 4893W 4/19/2015 Forecasting the population and Estimating the Population Trend 1. Background There have been a lot of research articles that suggest the prediction for each country¡¯s population by 2050. The projections recently issued by the United Nations suggest that ¡°world population by 2050 could reach 8.9 billion, but in alternative scenarios could be as high as 10.6 billion or as low as 7.4 billion¡±(United Nation Population Fund, 2004). The table below shows the population of most populated countries in 2010 based on the UN population fund data.(UN population Fund 2004) Table 1 The top 10 mostpopulated countries in 2010 (UN population Fund 2004) Current Ranking Country Population (mils) 1 China 1275.2 2 India 1016.9 3 USA 285.0 4 Indonesia 211.6 5 Brazil 171.8 6 Russian Federation 145.6
- 2. 7 Pakistan 142.7 8 Bangladesh 138.0 9 Japan 127.0 10 Nigeria 114.7 The table below is the population prediction for 2050 from United Nation Population Fund. Table 2 the top 10 mostpopulated countries in 2050(UN population fund) Ranking Country Population (mils) 1 India 1531.4 2 China 1395.2 3 USA 408.7 4 Pakistan 348.7 5 Indonesia 293.8 6 Nigeria 258.5 7 Bangladesh 254.6 8 Brazil 233.1 9 Ethiopia 171.0 10 Congo,DR 151.6 Comparing the two tables, we can observe that India¡¯s population will surpass China¡¯s population within 50 years. One of the most reasonable aspects behind this prediction would be the fertility rate. There has been ¡°one-child policy¡± in China since in order to
- 3. Ko 3 control the population. ¡°In 1979, the Chinese government embarked on an ambitious program of market reform following the economic stagnation of the Cultural Revolution. At the time, China was home to a quarter of the world's people, who were occupying just 7 percent of world's arable land. Two thirds of the population was under the age of 30 years, and the baby boomers of the 1950s and 1960s were entering their reproductive years. The government saw strict population containment as essential to economic reform and to an improvement in living standards.2 So the one-child family policy was introduced.¡±(Hesketh &Zhu, 2015) The graph below is the fertility rate in China from 1970 to 2014 based on the UN data. Figure1 the fertility rate from 1960 to 2005 inChina It shows that the fertility rate has been dropped from 4.7 to 1.7 for 40 years. It implies that the growth rate of the Chinese population is likely to be decreased or stagnated. Also, Japan, the 9th most populated country in the world, is eliminated in the top 10 most 0 1 2 3 4 5 6 Year 1970 1975 1980 1985 1990 1995 2000 2005 Fertility rate Fertility rate
- 4. Ko 4 populated countries in 2050 population prediction. Likewise, this can be attributed to low fertility rate constantly ranging between 1 and 2 since 1975 based on the UN data. 2. Objective This research aims to project the population for every decade from 2010 to 2050 and show the rank of the top ten most populated countries. Time series analysis method is applied as a prediction method. The two main causes of population growth are fertility rate and migration trend. In earlier part of this paper, it demonstrated how much the fertility rate in China has been decreased. Thus it would be essential to achieve the fertility rate data for more accurate forecasting. After the prediction of the population until 2050 for each decade, it is followed with the GDP prediction for the top ten most populated countries Although the United Nation already presented the population prediction with using professional methods, I would aim to apply my knowledge and technical skills that I have gained in time series analysis class. 3.Analysis Method There have been many research papers that used time series analysis method to predict growth rate and population. ¡°Time Series Test of Endogenous Growth Models¡±(Jones 1995) which is one of the most cited Economics article applied the log
- 5. Ko 5 transformation on the data to achieve the stationary series. Jones chose an augmented Dicky Fuller(ADF) method for forecasting the GDP per capita from 1929 to 1987. On the other hand, "On the Appropriate Transformation Technique and Model Selection in Forecasting Economic Time Series: An Application to Botswana GDP Data,"(Shangodoyin et.al 2010) applied AR(1) model to predict the GDP in Botswana. Authors of the article used AIC and SIC and model residuals to judge which model is the most precise. I have learned ARIMA model and GARCH model during the Time Series Analysis class for this semester. ARIMA model stands for Autoregressive Moving Average Models. The model is a generalization of an autoregressive moving average (ARMA) model. ¡°Classical linear regression is often insufficient for explaining all of the interesting dynamic in time series. The introduction of correlation as a phenomenon that may be generated through lagged linear relations leads to proposing the autoregressive(AR) and autogressive moving average models. Adding nonstationary models to the mix leads to the ARIMA models.¡±(Shumway &Stoffer 2011) GARCH model stands for Generalized ARCH model. ¡°ARCH is an acronym meaning AutoRegressive Conditional Heteroscedasticity. In ARCH models the conditional variance has a structure very similar to the structure of the conditional expectation in an AR model.¡± (Ruppert 2011) For example, an AR(1) process has a nonconstant conditional mean but a constant conditional variance, while an ARCH(1) process is just the opposite. ¡°A deficiency of ARCH(q) models is that the conditional standard deviation
- 6. process has high-frequency oscillations with high volatility coming in short bursts. However, GARCH models permit a wider range of behavior, in particular, more persistent volatility. Because past values of the ¦Òt process are fed back into the present value, the conditional standard deviation can exhibit more persistent periods of high or low volatility than seen in an ARCH process. ¡°(Rupert 2011) From the literature review about time series analysis method, it is crucial to choose the best model that generates the lowest AIC and BIC and the best model is different from data. The starting point of the analysis is achieving population data of the top 20 most populated countries from 1950 to 2050 listed in the UN Population Fund research paper. So, the research is based on the population data from 17 countries.
- 7. These plots are time series plots for 17 selected countries from 1950 to 2010. Congo, Democratic of Republic, Ethiopia and Nigeria show similar patterns with exponential function graph. It implies that these countries have rapid growth rates than other countries. In contrast, the growth rate of Japan and Russia show decreasing patterns and it implies that the growth rates of the two countries are under downfall. In short, this observation may imply that it is important to select the best model for each country rather than selecting and applying the single model for whole 17 countries. According to ¡°Growth Forecasts Using Time Series and Growth models¡±, it is said that ¡°it¡¯s difficult to choose the ¡°best¡± model for forecasting real GDP per capita¡±(Aart 1999). When it comes to selecting the most appropriate ARMA models for each country, I took the first difference on the log-transformed data and used the ACF and the PACF
- 8. Ko 8 graphs. Consequently, the ARMA models for all the countries are either AR (1) model or AR (2) model. For selecting the most suitable GARCH model, it turned out that the AIC values of GARCH (2,1) are closer to zero for most countries besides Mexico that GARCH (1,1) performs better. Then I calculated the error of predicted values for GARCH(2,1) and and the AR model. The result is the AR model generated the lower error value so I chose ARIMA models for my prediction. The next step was judging each country on ARIMA model order. The judgment was made based on the behavior of autocorrelation function (ACF) and partial ACF (PACF). If PACF shows there is a cut off after lag(p), it¡¯s AR(p) model. If ACF shows there is a cut of after lag(q), it¡¯s MA(q) model. The table below shows each model for 17 countries. Table 3 each model for 17 countries AR(1) AR(2) MA(2) Brazil, China, Indonesia, Japan, Mexico, Nigeria, Philippines, Russia, Turkey, Vietnam USA, Bangladesh, Congo DR, Egypt, Ethiopia, India Pakistan 5. Result Here¡¯s the ranking for 2020 population
- 9. Table 4 Estimated the top 10 mostpopulated countries in2020 Current Ranking Country Population (thousands) 1 China 1,357,250 2 India 1,349,486 3 USA 338,972.1 4 Indonesia 240,168.9 5 Pakistan 203,699 6 Brazil 194,800.5 7 Bangladesh 161,916 8 Nigeria 151714 9 Russia 143,374.9 10 Japan 127,182.8 Comparing to the population in 2010, there are some changes. Although China manages to keep the number one most populated country in the world in 2020, the gap between India and China gets much narrower than in 2010. In 2010, Brazil and Russia were in higher rank than Pakistan but the circumstance is altered in 2020 that Pakistan¡¯s population is expected to surpass Brazil and Russia within 10 years. As it is shown in time series plot, the ranks of Russia and Japan dropped compared to 2010. Here is the rank for 2030. Table 5 estimated the top 10 mostpopulated countries in 2030 Current Ranking Country Population (thousands)
- 10. 1 India 1,467,972 2 China 1,354,696 3 USA 363,675.5 4 Indonesia 239,664.8 5 Pakistan 234,249 6 Brazil 194,393.4 7 Bangladesh 161,627.4 8 Nigeria 149,711.3 9 Russia 143,134.8 10 Ethiopia 128,273.96 Based on this analysis, it is expected that India¡¯s population will outnumber China¡¯s population and settle down as the most populated country in the world. There has not been many chances in rank compared to 2020. However, Japan will not be in one of the 10 most populated countries within 15 years. Instead, Ethiopia will show the first appearance on the list. Here is the rank for 2040. Table 6 estimated top 10 populated countries in 2040 Current Ranking Country Population (thousands) 1 India 1,555,249 2 China 1,352,158
- 11. 3 USA 385,668.9 4 Pakistan 264,799 5 Indonesia 239,163.7 6 Brazil 193,988.6 7 Bangladesh 150,317.5 8 Nigeria 148,004.3 9 Ethiopia 144,599.3 10 Russia 142,897.7 In 2040 forecasting, we can observe that the population gap between China and India will be larger compared to 2030. Within 15 years, Pakistan¡¯s population will surpass Indonesia. Likewise, it is expected that the population of Ethiopia will surpass the population of Russia. Here¡¯s the rank for 2050. Table 7 the top 10 mostpopulated countries in 2050 Current Ranking Country Population (thousands) 1 India 1,607,982 2 China 1,349,636 3 USA 404,353.2 4 Pakistan 295,349 5 Indonesia 238,665.5 6 Brazil 193,586.2
- 12. 7 Ethiopia 154,891.81 8 Nigeria 146,549.3 9 Russia 142,663.4 10 Congo, DR 134,223.19 Compared to 2040 analysis, it is easy to notice that Congo, Democratic of Republic will make on the list for the first time. In the earlier part or the paper, Congo,DR showed rapid growth pattern in time series plot which resembles the exponential function. In a longer term, there is a high possibility that the population of Congo, Democratic of Republic will be larger than the population of Russia. Overall, the analysis shows the similar pattern with the United Nation report although there are some numerical differences in the number of population. Both of them show that India¡¯s population will outnumber Chinese population within 35 years at the most. Especially, it is exactly the same ranking with the report from the rank 1 to the rank 5 and the rank 10. My time series analysis estimates higher growth rate for Ethiopia and Russia than the UN report but lower growth rate for Bangladesh from 2040 to 2050. 4.Conclusion I performed the population forecasting based on the 17 most populated countries data from 1950 to 2010. I used AR(1),AR(2) or MA(2) model based on the ACF and PACF pattern for each country population data. Then I showed the estimated population in 2020, 2030, 2040 and 2050 and then compared my analysis on 2050 to the report from
- 13. Ko 13 UN population fund. The analysis shows that India¡¯s population will exceed China¡¯s population within 15 years and the population gap between India and China will larger since India becomes the most populated country in the world. The Unites States will be likely to maintain the third most populated country in the world from 2010. Due to the low growth rate, Japan will likely to be disappeared from the list within 15 years. In 2050, it is estimated that there will be more African countries on the list than in 2010 as Ethiopia, Nigeria and Congo, DR has high population growth rates while Asia will retain its status as the most populated continent in the world. Consequently, the analysis shows similar pattern with the United Nation Population report overall. However, the prediction with my time series method showed relatively more positive outlook on the population growth rates of Russia and Ethiopia than the result of UN population report. On the other hand, the prediction with my time series analysis method estimated lower growth rate for Bangladesh. Generally, using ARIMA model is a simple and relatively accurate time series analysis method with knowledge of interpreting the behavior of ACF and PACF. As long as the data can achieve stationarity, ARIMA model has a versatile application on forecasting.
- 14. Reference Aart. Kraay George Monokroussos(1999); Growth Forecasts Using Time Series and Growth Models. World Bank. Development Research Group. Macroeconomics and Growth.Washington, DC : World Bank, Development Research Group, Macroeconomics and Growth. Charles I. Jones(1995). Time Series Test of Endogenous Growth Models. The Quarterly Journal of Economics, Vol. 110, No. 2 (May, 1995), pp. 495-525 Hesketh, T., Lu, L., & Xing, Zhu. W. (2015). The effect of China's one-child family policy after 25 years. New England Journal of Medicine, 353(11), 1171-1176. Ruppert, D., 2011. GARCH Models. In Ruppert, D. (ed) Statistics and Data Analysis for Financial Engineering. Springer T., New York, NY: Springer New York. Shangodoyin, D. K.; Setlhare, K.; Moseki, K. K.; and Sediakgotla, K. (2010) "On the Appropriate Transformation Technique and Model Selection in Forecasting Economic Time Series: An Application to Botswana GDP Data," Journal of Modern Applied Statistical Methods: Vol. 9: Iss. 1, Article 28. Shumway, Robert &Stoffer, David , 2011. The Time Series Analysis and Its Applications Springer T., New York, NY: Springer New York. World Population to 2300 Department of Economic and Social Affairs Population Division, 2004