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Population Projections of Pakistan Using Traditional and Time Series Models.

Byline: Muhammad Zakria, Faqir Muhammad and Salah-ud-din


The major innovative of this study is to project the population of Pakistan for vision 2030. Different Population growth and time series models have been used to project the population of Pakistan. The projected population by traditional growth model (Modified exponential model) is close to the projection by time series ARIMA (1, 2, 0) model. The MAPE of these models are 1.0578% and 0.485797% respectively. The projection by ARIMA (1, 2, 0) is more close to the projected population of Pakistan by at least four other bureaus i.e. Population Reference Bureau (2007), United States Census Bureau (2008), Pakistan Reality (2008) & Population of Pakistan (2008). These organizations predicted that the population of Pakistan in the year 2025 will be approximately 229 million. This projection may be helpful for the future planning of the country and facilitate the projects of the Government and Non Government Organizations.

Keywords: Population census, Projections, Traditional growth models and ARIMA.


Population of any country plays a significant role in the planning as well as the decision making for the socio economic and demographic development. Now-a-days, the major issue of the developing countries like Pakistan, is the tremendous growth in population. According to National Institute of Population Studies [NIPS] (2006), Pakistan was ranked 14th among the most populous countries of the world with population of 33 million in 1950 whereas, it was ranked 6th populous country of the world with population of 156.26 million in 2006. Moreover, it would be the 5th populous country of the world in 2050 with population of 295 million (PRB, 2007). The only reason is the high growth rate of population of Pakistan as compared to the other countries of the world. Although the growth rate of Pakistan has decreased from 2.69% to 1.86% during 1998 to 2006 respectively. Even then the size of the population of Pakistan is very large.

According to the population growth rate (2008), there are 156 countries out of 229 in the world that have less growth rate as compared to Pakistan. The reality is that Pakistan witnessed a very high growth rate in its early decades after gaining independence. The population of Pakistan drastically increased from 34 million to 158 million during 1951 to 2007. The growth rate of population of Pakistan must be decreased in order to control the population of our country as compared to the other countries of the world. The reduction in growth rate is indispensable to maintain a balance between the population and the available resources of the country. So far, five population censuses have been conducted. In 1951, the first census was held which recorded a population of 34 million while the 2nd second census reported 43 million population thus exhibiting an average annual growth rate of 2.45% (Anonymous 1967).

The 3rd population census was delayed by one year till 1972 because of India-Pakistan war. In this census, Population was reported 65 million and 52.31% increase had been observed as compared to that of 1961 population census of Pakistan with an average annual growth rate of 3.67%. This was the highest growth rate in the history of Pakistan. It became the main cause of the drastic increase in population especially during the second census (Anonymous, 1972).

The 4th population census was held in 1981 and population was reported 84 million with an average annual growth rate of 3.06% (Anonymous, 1984). The 5th Population census was delayed by 7 years and held in 1998 because of the volatile and disturbing political issues of province Sind. Population and growth rate of this census were 132 million and 2.69% respectively (Anonymous, 2001). The above mentioned figures indicate that up-to March 1998; the population of Pakistan was quadrupled from the year 1951 to 1998. NIPS (2006) reported 156.26 million population and 1.86% growth rate of Pakistan respectively. Iqbal (2007) also reported 158 million and 1.83%, the population and annual average growth rate of Pakistan respectively. Relationship between Literacy, Education and Demographic (2009) advocated the relationship between women's education level and population growth. The Educated women have less number of children than the uneducated women.

An extra year of schooling reduces female fertility by as much as 5 to 10 percent. Education, particularly of girls and women, helps to control excessive population growth by promoting the concepts of family planning, collective health and well-being. An educated family makes informed choices with respect to having a child as well as for maintaining the health of the whole family. With the passage of time, the literacy rate is being increased especially in the females and to some extent; the fertility also depends on them. Nobody can deny this fact that there is a negative relationship between education and the growth rate especially the female education. Most of the educated community prefers small family size. That is why; the growth rate of population is decreased as compared to the past. Looking at the current trend of the growth rate, it is expected that in future the growth rate will either decrease or at least remain the same.

If the current growth trend continues, the population will grow with same age and sex distribution. Due to such drastic increase in the population of Pakistan and limited available resources of the country and infeasible future planning and management policies, all the past Governments of Pakistan had been in trouble since its independence. That is why, since 1947, Pakistan could never have managed its future planning properly. Consequently, the citizens of Pakistan have been deprived of the basic necessities of life e.g., quality water, food, health, education, employment, electricity, gas, transportation and manufacturing goods etc. It is only because of the irregular conduct of population census and inadequate forecasting of the population of Pakistan. It is observed that without regular census and adequate forecasting of the population, the solution of population problems as well as the stability of the elected democratic Governments of Pakistan is impossible.

Moreover, Pakistan can neither stand in the row of the developed countries during the 21st century nor take the right decisions about its current and future planning.

The only key to success is the optimum forecasting of the population of Pakistan in order to take right decisions regarding future planning and to honour the commitments at the national and the international levels. A large number of national and international scientists and agencies projected the population of Pakistan and its territories for different years. NIPS (2006) projected the population of Pakistan for different years which are 161.86 million, 175.65 million, 189.42 million and 202.11 million for the years 2010, 2015, 2020, 2025 respectively. These Figures are less than the estimates reported by all other national as well as international agencies.

According to the World Population Prospects [WPP] (2006), the population of Pakistan will be 173.351 million, 190.659 million, 208.315 million and 224.956 million for the years 2010, 2015, 2020 and 2025 respectively. Jan, Ishfaq & Shuhrat (2007) projected the population of NWFP province of Pakistan by Modified Exponential model and reported that it would be 61.12 million in 2053 whereas, it was 21 million in 2008. It would be about 2.75 times more than the population of 2008. Such a tremendous increase in only 45 years is an alarming bell for the scientists as well as for the Government of Pakistan.

The choice of a parsimonious model depends on the nature and population trend, the model may be the linear and nonlinear including the first and higher degree regression models, simple exponential and Modified Exponential, Gompertz and Logistic growth models. Using such models, population of different countries is projected by different scientists (Shryock & Seigel, 1973; Agrawal, 2000; Jan, et al. 2007). Srinivasan (1998) used the component method to project the Population. According to one school of thought, the forecasting with respect to vision 2030 in human population is preferable as the growth rate of population does not remain constant for too long a period ahead. Beauregard (1990) revealed that forecasting for 2 to 4 years is assumed to be short term and for more years a long term forecasting. This study aims to project the population of Pakistan for the next 25 years from 2007 to 2032 using some traditional growth models and time series models.


The data set for this study is spread over the 57 years from 1951 to 2007 with regular interval of one year. Most of the data is taken from (Kemal, Irfan & Mahmood, 2003; Iqbal, 2007) and population census reports of Pakistan (Anonymous, 1967, 1972, 1984, 2001). Goodness of fit of the models is assessed on the basis of Mean Absolute Percentage Error (MAPE). All statistical analyses are done using the computer software Minitb- 14 and SPSS- 16. The Population is projected on the yearly basis from 2008 to 2032. The Mathematical forms of used models are as under:

Logistic Growth curve: The curve is of the form


y = ----------

1 + ABt



Where Y is the response variable, A and B are the parameters of logistic model (SPSS-16, 2007). This curve is not recommended for too long a period forecasting and the population that is decreasing (Shryock et al., 1973).

Gompertz Curve: The logistic curve closely resembles the half normal curve whereas the Gompertz curve is not normal but a skewed one. The curve is of the form

The Gompertz curve is exactly the same as that of the Modified exponential curve except that it is the increase in the logarithms of the y values which are decreased by a constant proportion (Shryock et al., 1973).

Modified Exponential Curve: The form of the modified exponential curve is

Y = K + AB t

Which yields an ascending asymptotic curve, the value of B lies between 0 and 1 whereas A assumes the negative values (Shryock et al., 1973).

Exponential Growth Model: Exponential growth model can be characterized by a constant percentage increase in the value of population over time

Where P equals the initial population of Pakistan at time t = 0, B is the percentage rate of growth and t is the time measured in the appropriate unit of one or five years and e is the base of the natural system of logarithms (Shryock et al., 1973).

Autoregressive Integrated Moving Average (ARIMA): Verbeek (2005) gave the following general form of ARMA (p, q) model

ARIMA (p, q) is the combination of autoregressive and moving average specification which consists of AR part of order p and MA part of order q. Where is the population at time t and is treated as response variable, is the population at lagged one and so on whereas is a white noise process at time t and the residual at lag one.

Goodness of fit criteria

Mean Absolute Percentage Error (MAPE)

It is an evaluation statistics which is used to assess the goodness of fit of different models in national and sub national population projections. This statistics is expressed in percentage. The concept of MAPE seems to be very simple but is of great importance in selecting a parsimonious model than the other statistics e.g. Coefficient of relative variation (CRV) and mean error (ME). A model with smaller MAPE is preferred to the other models.

The Mathematical form of the MAPE is as under

Where are the actual, fitted and number of observation of the (dependent variable) population respectively?

Results and Discussion

The reported and projected population by traditional and time series models are given in Table 1 for the years 2012, 2017, 2022, 2027, 2032. Box Cox transformation was applied to the data for the stationary purposes which gave the value of = 0.220734 1 along with its interval (-0.405 1015, 0.8465697). Since the interval contains the value zero it recommended that the log transformation is appropriate choice to make our series stationary before differencing of the series for the application of ARIMA models (Box & Jenkins, 1976).

The fitted population for the year 2007 is 162.23 million and 158.08 million using Modified exponential and ARIMA (1, 2, 0) models respectively. These estimates are not only close to each other but also close (NIPS, 2006; Iqbal, 2007) and also less than the other three traditional models given in the Table 1. Similarly, the projected population for the year 2027 is 250.68 million and 230.68 million by Modified exponential model and ARIMA (1, 2, 0) respectively. The projected population by Modified exponential growth model is higher than the projected population by ARIMA (1, 2, 0) model. If the current growth rate continues, the projected population would also be approximately 250 million using compound growth model as that of the Modified exponential model. Consequently, the population would be doubled during the next 37 years. On the other hand, NIPS (2006) reported 1.86% growth rate of Pakistan which is about 83% lower than the growth rate 2.69% of 1998.

Although the growth rate is decreased, still it is very high as compared to many other countries of the world. The decrease in growth rate might be due to the increase in the female literacy rate. In future, it seems that there may be more decrease in the growth rate because of the increased literacy rate. The projected population by logistic model is 364.16 million which is more than double as compared to the population of 2007 during the next 25 years. It might be the overestimation of the population. It indicates that the growth rate in future will be greater than 3, which seems to be impossible and contradictory to the real situation. The logic behind this fact is that in 1998 census, the

Government of Pakistan's expectations about growth rate was around 3% but after the computation, it was announced 2.69% which was far more than (NIPS, 2006). If the current population growth rate continues, the projected population by ARIMA (1, 2, 0) might be 254 million in 2032. It seems too much increase in population that is unaffordable for a third world country like Pakistan. This figure is also inconsistent with the other researcher's projections. The projection by ARIMA (1, 2, 0) is satisfactory up to 2027. The real challenge is to decrease the growth rate or to limit the population size and to increase our resources to fulfil the ever increasing needs of our population in future. The decrease in growth rate is an easiest route to limit the population and this target might be achieved by only increasing the literacy rate in the female chunk of the population.

The Mean Absolute Percentage errors are also given in Table 1. MAPE for ARIMA (1, 2, 0) is 0.49% which is minimum whereas MAPE (4.28%) is maximum for Logistic model. The remaining MAPEs are between these limits. On the basis of this selection criterion, ARIMA model can be preferred to the other growth models for population projection of Pakistan. Jan, et al. (2007) used seven traditional growth models to project the population of NWFP province of Pakistan from 2003 to 2053. Jan, et al. (2007) reported 61.12 million population of NWFP province of Pakistan in 2053 and recommended the Modified exponential growth model. The reason might be the trend differences between the population of Pakistan and its province NWFP. Jan also used the same evaluation statistics for goodness of fit of the model. Figure 1 presents the trend of the reported population of Pakistan during the years 1972-2007.

The line graph does not show any clear cut clue about the linear or quadratic trend of the population but it seems to be a nonlinear trend of the population of Pakistan. Moreover, univariate time series model may also be tried to project the population of Pakistan.

Conclusion and Recommendations

The projected population for the years 2032 with logistic, Gompertz, Exponential, Modified exponential and ARIMA model is 364.16 million, 356.46 million 341.93 million, 277.98 million and 254.09 million respectively. The projection by exponential method is slightly less than the Gompertz and the logistic but higher than the Modified exponential model. The Modified exponential growth model projected the population 277.97 million and 250.68 million for the years 2032 and 2027 respectively which is the least one, as compared to the other three traditional models. On the other hand, The ARIMA (1, 2, 0) projected 230.68 million population for the years 2027 which is more close to the other national and international scientist's forecast (NIPS, 2006; WPP, 2006).

Logistic model has 4.28% MAPE, which is highest among all the five models whereas the ARIMA (1, 2, 0) has 0.49% MAPE which is minimum. MAPE of other models are between these two limits. So the ARIMA (1, 2, 0) might be declared the parsimonious model. According to the parsimonious model ARIMA (1, 2, 0), there will be 74.29% increase in the Population of Pakistan till 2027 as compared to the 1998 population census and 45.74% increase in the population of Pakistan as compared to (Iqbal, 2007).

The government of Pakistan and NGOs should start a mass-scale advertising campaign to highlight the significance of the female education. The private and the government educational institutions of the less developed cities, villages as well as the remote and for flung areas of our country must fall within the most targeted zones. In this way, the rustic population may also be involved positively in this awareness drive. The education of IT and science and technology must be given priority in order to utilize the maximum potentials of our youth. It is the need of modern era. Since the private educational institutes are out of reach of common man, subsidized education must be provided to everyone at government educational institutes.


The authors would like to thank the population census organization for providing the population census data, the editor and referees who suggested very helpful comments to improve the presentation.


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Table 1: Population projection of Pakistan using different growth models

###Projected Population (in millions)



###(in millions)###Logistic###Gompertz###Growth###Growth###(1,2,0)














Statistical Evaluation Techniques (Beauregard, 1990)

Mean Absolute %###4.28 %###3.48 %###3.71 %###1.06 %###0.49 %

Error (MAPE)###

Coefficient of


variation (CRV)

Muhammad Zakria and Faqir Muhammad Department of Mathematics and Statistics Allama Iqbal Open University, Islamabad, Pakistan and Salah-ud-din Department of Statistics University of Peshawar, Peshawar, Pakistan
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Publication:The Journal of Humanities and Social Sciences
Article Type:Report
Geographic Code:9PAKI
Date:Dec 31, 2009
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