Population

The kenyan population size over the years is shown to be increasing steadily.

	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
Statistic	6076758	10539894	20622560	24214503	35635271	56215221

Gross Domestic Product(GDP)

GDP and its related GDP per capita are measures of economic growth of a county. The relationship between economic and population growth has been studied in various literature on demographic studies. (Tsen and Furuoka, 2005)22 See the full paper Tsen and Fukuroka(2005) argued that there exists an equilibrium positive relationship between the economic growth as measured by GDP/capita and population growth. Several other researches such as (Dao, 2012)33 See the full paper Population and Economic Growth in Developing Countries found that there exists a linear dependence between GDP per capita and population growth. In Kenya, (Thuku, Paul, and Almadi, 2013)44 See the full paper Thuku, Paul, and Almadi(2013) studied the relationship between economic growth and population growth and established that there exists a positive linear relationship between the two. Thus adding it as a variable in population studies seems only relevant.

(%) changes for GDP, and Per Capital GDP

Fertility rates

Fertility rates explore the level of reproduction in a given society. The fertility rate at a given age is the number of children born alive to women of that age during the year as a proportion of the average annual population of women of the same age.

Annual Fertility rates

(%) changes in annual fertility rates

A higher fertility rate has a positive correlation with population growth in the long run, keeping other factors constant. Factors such as literacy rates have been shown to be negatively related to fertility rates, and research in both developed and developing nations show that fertility rates have been on a decrease with increasing literacy rates, improved health care services such as family planning, and poverty has been shown to have positive correlation with fertility rates.55 The links to several research papers and articles have been attached to the topics [Education] and [Poverty rates] below.

For the Kenyan Fertility data, there seems to be declining fertility rates overally. It is also evident that the population growth changes are declinig after the year 1990, to a steady plateau in [2000-2006]. The population size increases throughout. Thus a decrease in fertility rates is accompanied by a decrese in population growth rates.

Mortality rates

Mortality rates of a country are the annual numbe of deaths per 1000 total population.

(%) changes annual mortality rates

A higher mortality rate has a negative relationship with population growth if all other factor such as fertility rates, and migration rates are kept constant.66 An article on a study conducted on Life expectancy and mortality rates can be found here.

The overall mortality rates decrease, all along the years, implying that the country has experienced decreased mortality rates possibly due to improvement of living conditions, life expectancy, affordable health care, and other factors which play an important role in reducing population mortality rates.

Migration rates

This is the net effect of immigration and emmigration on a country’s population. The net migration rate which is commonly calculated as:

Number of Immigrants - Number of Emmigrants

This implies that the NMR77 Abbreviation for: [Net Migration Rate], is positive when the number of immigrants is higher than emmigrants, and is negative when the emmigrants number is higher than immigrants numbers.

(%) changes annual net migration rates

This is calculated for persons including both citizens and non-citizens. Including migration rates in demographic and population modelling studies is important as shown88 The article linked is: Does migration lead to increased population on a study done on UK, which indicates that migration was a major component of population growth.

The net migration rates during the years [1990-1995] were the highest historically, as well as an increase during the years [2010-2013] is witnessed possibly due to the fact that: during the wars in South Sudan in the year 2013, majority of south Sudanese fleeing war came to seek refuge in Kenya which could be interestng to monitor in Kenyan population numbers99 Link to article: Kenya Refugee Response

Human Development Index(HDI)

According to Wikipedia1010 Link to the Wikipedia article on Human Development Index Wikipedia/HDI, The Human Development index is a composite statistic comprising the life expectancy, education and per Capita income. A higher HDI generally implies that the conditions in a given country are better i.e. high standards of living, decent education and healthcare.

Historical Human Development Index

(%) changes in Historical Human Development Index

This will in turn impact the population growth of a country by attracting more immigrants. Several research studies have been conducted on impacts of population growth on HDI, as opposed to the converse relationship.

From the above chart, it is evident that there is a positive relationship between the % changes in HDI, and the population growth rate, which was to be expected since the HDI is a measure of how good the living conditions in a country are, and we expect that the better the living conditions, the higher the population grows.

Labour Force Participation Rate

This is an estimate of an economy’s work force1111 More on definitions: investopedia.com. A higher Labour force participation rate implies that there is a higher population.

Labour force participation rate for ages 15-24

(%) changes in Labour force participation rate for ages 15-24

This is because a rising population is accompanied by a higher labour participation rate. This would in turn lead to reduction in real wages, although that relationship is beyond the scope of this study.

For the above plot, we seek to establish the relationship between the labour force participation rate 5 years ago, and the population size now, since effects of labour force participation rates are usually not felt immediately by population e.g. an increase in female labour force participation rate is usually associated with a decrease in population growth rates, although the results might not have immediate effects on population growth. The relationship is a negative one whereby, an increase in labour force participation rate leads to decreased population

Unemployment rate

It is well established in several studies and analyses that high population growth in turn has an inverse relationship with economic variables such as unemployment rates.

Unemployment rates (%) in kenya

(%) changes Unemployment rates

It has been observed that higher populations tend to have higher unemployment rates as well, because an increase in labor force in turn leads to an increased competition ffor the available resources a nation has and thus leading to unemployment.1212 Links to articlesArticle 1 Article 2]

There has been a decrease in unemployment rates in the early 2000-2010, however there is an evident sharp spike in unemployment rates during the year 2020-2022, due to the COVID-19 pandemic. The relationship between unemployment rates and per capita GDP is a negative relationship whereby, an increase in standards of living(as measured using GDP per capita) is associated with a decrease in unemployment rate. This however doesnt suggest a cause-and-effect relationship. The relationship between unemployment rates and population growth is a positive relationship, since an increase in unemployment rates is associated with an increase in population growth. Various studies suggest this is a cause-and-effect relationship, since unemployment would lead to inability to afford birth-control and family-planning options.

Education spending

Education spending has a positive impact on literacy rates of a country, since it is through the increased allocation of a country’s spending to education that schools reach the vast majority of a country. Mark Montgomery, an economics professor notes that the higher the education level goes up, the lower the fertility rates. The relationship is an inverse one as he notes. Thus education leads to lower birth rates, and this slows down population growth in the long run.

The education spending rate(% of GDP)

In kenya, several key education milestones achieved were:1313 More information on educational achievements in kenya under the reign of Mwai Kibaki can be found at: this link

• The government under Mwai Kibaki introduced the Free Primary Education(FPE) in January 2003, where the government would cover the cost of tuition for the students. This was meant to enable disadvantages children have access to education. This is evident in the spike seen on the graphs.

• In his second term, the president Mwai Kibaki, rolled out the Free Day Secondary Education in 2008, to offer tuition free Day secondary education in order to enhance retention rate among learners.

These key achievements must have come at an increased education spending rate by the government. The population increase in later years 2015-2020 did not lead to an increase in government spending on Education, possibly because the increased population implies an increased tax income for the government to be able to provide affordable education.

Health care spending

Increased health care spending implies making more affordable health care services within the reach of the common mwananchi, constructing more hospitals and dispensaries in marginalized areas.

The healthcare spending rate (% of GDP)

Increased health care spending is a major driver of population growth, this is because good health care leads to lower infant mortality rates, and maternal mortality rates, as well as it prolongs the longevity of the elderly, who could not earlier on afford health care services.

The healthcare spending rate (% of GDP) and mortality rates

The healthcare spending rte (% of GDP) and life expectancy

The elderly and infants are among the population with highest demand for health care services, thus, improving health care services goes a long way in increasing life expectancy in a nation.1414 For further studies NIH research covers this in the context of first-world nation, although the sme conclusions apply to developing nations: Implications of Population Change

In kenya(2013), under the reign of Uhuru Keyatta, the Linda Mama programme on Free maternity was introduced in 2013. The Kenyan UHC program began in 2018 as a pilot program (Ministry of Health of Kenya 2018)1515 The official statement from ministry of health in kenyaUHC Program, which is evident in the increase in cost of healthcare funding from the year 2017-2018.

From the plot above, the relationship between the population growth rates and healthcare funding is a positive one, where increased population would lead the government to expand their health care services in order to cater for the growing population. Increased health care funding would lead to affordable healthcare services to citizens, which would have an effect of increasing population in later years, due to better standards of living.

Infant and maternal mortality rate

According to NIH (National Library of Medicine)1616 The NIH research article on child survival bias can be found at: How does infant mortality affect birth rates?, reduction of infant mortality(children under 5 years old), leads to reduction of fertility, with some delay.

Annual Infant Mortality Rate

Annual Maternal Mortality Rate(Per 100K Live Births)

More formally, the Child survival hypothesis, states that “if child mortality is reduced, then eventually fertility reduction follows, with the net effect of lower growth of population”. This could be interesting to confirm with the Kenyan population growth data.

Increased health care spending by the government has a negative relationship with maternal and infant mortality rates, whereby: an increased spending in health care services leads to a decrease in maternal and infant mortality. This is because by increasing government funding to health care sector, more funds are utilized in public ediucation on maternity, building more clinics, dispensaries and hospitals in order to reach more citizens. This will have a positive impact of lowering maternal and infant mortality.

The per capita GDP, which is a common measure for living standards in a country, is usually assumed to have an inverse relationship with mortality rates for infants and mothers, since increased living stadards usually imply increased access to essential services such as health care, however from the look of the above charts, there seems to be a positive linear relationship, whereby an increase in (%) change in per capita GDP, leads to increased changes in infant and maternal mortality, however, the relationship is not significant due to prescence of outliers in the per capita dataset.

The relationship between the maternal and infant mortality rates to the population growth rate is a negative relationship whereby: an increase in infant and maternal mortality rates leads to decreased population growth rates, although the effects are not observable instantly. This relationship does not come out clearly in the context of infant mortality rates, but is seen more evidently in maternal mortality rates against the population growth rate chart.

Suicide rates

Studies on suicide rates and socio-economic variables1717 The most notable one being the research article by NIH on Suicide in the world: Toward a population increase theory of suicide, one of which was conducted on global economy suicide rates and population growth indicators suggest that suicide rates are positively correlated with modernization, further the study suggests that suicide rates are negatively correlated with population growth indicators, but positively correlated with quality of life indicators.

Poverty rates

A research done on population growth and poverty in developing nations pointed out that many aspects of poverty actually increase fertility rates, high infant mortality possibly due to lack of access to decent health care, and little-to-no education among women and female children.

This also goes in same thinking with the notion that1818 The research article can be read in full at UNFPA article suggests that poverty rates is influenced by, and also influences population growth.1919 The research article by NIH can be found at Population growth and poverty in the developing world

The above plots show that an increase in GDP per Capita, leads to a decrease in poverty rates, which is expected, since when standards of living improve in a country, then it implies more people are crossing above the poverty line. The graphs also illustrate that increased poverty rates lead to increased fertility rates, which is in-line with the research findings by NIH above.

Electricity access

The percentage of citizens with electricity access annually.

Research done on electricity access and population growth indicates that there is a significant positive impact of electricity access to the life expectancy, quality of living and the socio-economic well being of communities.2020 The research paper further tackles this The effects of energy use on infant mortality rates in Africa

The relationship between electricity access and Although the relationship between electricity access and life expectancy is a positive linear relationship, whereby, an increase in % of population with electricity access is associated with increased life epxectancy. Although this relationship might seem far-fetched, increased electrcitiy access is essential for education and health care services to reach the citizens in all the nation, and it is through these services that life expectancy increases.

Crime rates

Increased crime rates activities and especially in urban areas could trivially be explained using interesting researches such as on universe252121 This interesting study on The explosive Growth and Demise of a Mouse Population.

The chart of crime rates per 100K population in kenya, annually.

However, crime rates have been shown to be significantly affected by unemployment rates, whereby high unemployment rates lead to higher crime rates, and vice versa. Increased population especially in urban areas have been studies to have highe crime rates as compared to less populated areas, since in high population environments, there is competition for resources, such as jobs, and this would lead to unemployment, which further leads to increased crime rates.

From the above plots, the relationship between crime rates and unemployment rates is a positive one as expected, where increasing unemployment rates is associated with higher crime rates.

CO2 Emissions

Research conducted on effect of CO_2 emissions on infant mortality rates in Africa during the duration 1999-2014 suggest that there is a significant relationshiop between a rise in CO_2 emissions and infant mortality.2222 The study can be found at: The effects of energy use on infant mortality rates in Africa.

The chart of crime rates per 100K population in kenya, annually.

The study also shows that high degrees of pollution as measured using energy indicators such as CO2 emissions have significant positive correlation with increased mortality rates which further impact population growth.

It is evident that the relationship between the emissions of CO_2 (metric tons per capita) has a positive relationship with infant and general population mortality rates, where an increase in CO_2 emissions leads to an increase in mortality rates, both for infants and general population, as concluded in the research paper above.

Modelling Population size using demographic models

In this section we explore the three major models used in demographic studies, which are:

• Arithmetic growth models: This model assumes that the growth is linear, and that the population growth is constant per unit of time
• Geometric growth models: This model assumes that population grows like a geometric progression, i.e. population grows at a constant proportion, or percentage of current population
• Exponential growth models: This model assumes that population size grows exponentially, i.e. that future population equals current population with some exponential growth factor.

Based on the chart on population growth in Kenya, it would be safe to assume that the population of Kenya has exhibited a stable geometric growth, and thus modelling the population size using a geometric model is more favourable as compared to the arithmetic model. However, it is interesting to note that for one year changes, the three mathematical models give an approximate equal answer, but for longer time frames(>1), the models will give different estimates for rate of growth and Population forecasts.

Population as a stochastic process

A stochastic process is a model for a time-dependent random phenomenon. Modelling population or population growth as a stochastic process is useful, since population data is a time indexed random variable, and there are a lot of tools within the field of stochastic process which could be used to model population size, and changes in order to better describe the population dynamics. In this section we will not directly model population, rather we will model population changes annually, since it is much easier to study and construct models for the increments of a process rather than the process itself.

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In this section we will fit several models for stochastic processes, starting with a martingale process which could be the simplest stochastic process model. A martingale is simply a stochastic process where the most optimal estimate for the future state of the process is the process’ current state. Under this model, we will determine next year’s forecast using the previous year’s increment, making this process the simplest one. The motivation for using such a model, where we assume that population increments each year will be 0, is that since population increment is affected by various factors which add to the population e.g fertility rates, immigration rates, and other factors which subtract from the population such as mortality rates and emigration rates, then their net effect is 0, and that population does not change at all.

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This section will cover MA(q) models2323 Moving average models, where we will experiment with Simple and Weighted moving average models, both in an expanding window fashion as well as a rolling window fashion, in order to better determine which model is better suited to our population data.

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In this section, AR(p) models2424 Auto-regressive models are implemented to model the population changes. An AR(p) model is given by the following:

\[P_t = \beta_0 + \beta_1 * P_{t-1}+ \beta_2 * P_{t-2} +...+ \beta_p * P_{t-p} + \epsilon_t\]

where:

\(P_t\) : The estimate of the population increment at time t.

\(P_{t-i}\) : The population increments in the year \(t-i\).

\(\beta_i\) : The coefficient of the model for the \(i^{th}\) year.

\(\epsilon_t\) : The random error component, which simply accounts for unexplaind variation of the estimate \(P_t\).

The model fitted in this section is an AR(1) model which implies, that the population change now, is a function of the recent year population change plus some constant and random shock. The AR(p) models are fitted with-intercept, and the analysis employs both both an expanding window AR(p) process as well as a rolling window type.

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This section covers modelling population increments using a poisson model.2525 The Poisson distribution is a common discrete distribution used for counting processes and other processes, with the unique characteristic that the distribution’s mean and variance are equal, and that it is strictly defined for positive integer only. We make a strong assumption that over the period, Kenya has not had a population decrease and will not have one in the near future, since it is a developing nation, thus we use the poisson distribution to model population changes.. The poisson distribution is a discrete distribution for positive-valued integers which is given by the following probability mass function: \[f(X;\lambda) = \frac{e^{- \lambda} \lambda^x}{x!}, \hspace{1 mm}x = 0,1,2,...\] whereby for our analysis, \(x\) is the population increments.

The poisson distribution is fitted to the population increments both in an expanding window and a rolling window: a 5-year and a 10-year window. An estimate for the population sizes over the years is calculated and compared to the actual population.

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Modelling population using a linear model

Year	Expected Geometric	Martingale	Expanding WMA	Rolling SMA(5)	Rolling WMA(5)	AR(1)	AR(1)-weighted	Expanding Poisson	Rolling(5) Poisson	Rolling(10) Poisson	Estimated LM	Actual Population
1960	8116820	8109533	8084924	8090606	8096759	8114645	8118911	8073274	8086198	NA	NA	8120080
1961	8374251	8366537	8337773	8346564	8353041	8371062	8375264	8324412	8341975	8324412	8377680	8377696
1962	8643485	8635312	8602042	8614190	8621034	8639223	8643356	8586872	8609369	8586872	8649849	8647011
1963	8924984	8916326	8878276	8894060	8901289	8919695	8923756	8861198	8888975	8865639	8934495	8928511
1964	9219175	9210011	9166952	9186670	9194273	9212892	9216877	9147876	9181302	9156924	9232154	9222692
1965	9526566	9516873	9468565	9492505	9500461	9519256	9523162	9447401	9486855	9461284	9540878	9530173
1966	9847905	9837654	9783747	9812191	9820498	9839415	9843239	9760400	9806264	9779397	9863641	9851444
1967	10183545	10172715	10112982	10146193	10154853	10173984	10177721	10087361	10140004	10111788	10201002	10187478
1968	10534974	10523512	10457293	10495571	10504648	10523805	10527454	10429285	10489108	10459500	10553956	10539894
1969	10904501	10892310	10818404	10862170	10871838	10890982	10894534	10787846	10855374	10824269	10924236	10910675
1970	11294500	11281456	11198412	11248271	11258787	11278142	11281588	11165091	11241035	11208217	11311974	11301394
1971	11706105	11692113	11598939	11655638	11667214	11687222	11690549	11562625	11647844	11613009	11720631	11713048
1972	12139697	12124702	12020966	12085368	12098005	12118811	12122008	11981442	12076860	12039681	12151244	12146068
1973	12595096	12579088	12464865	12537786	12551258	12572762	12575824	12421945	12528505	12488647	12604298	12600797
1974	13072550	13055526	12930921	13012977	13026990	13048853	13051776	12884450	13003016	12960232	13080150	13077341
1975	13571907	13553885	13419179	13510674	13524989	13547102	13549885	13369031	13500248	13454507	13575764	13575907
1976	14093481	14074473	13929801	14030809	14045299	14067479	14070120	13875872	14020112	13971653	14094309	14096263
1977	14636564	14616619	14462487	14572906	14587473	14609853	14612351	14404705	14562074	14511362	14635553	14638890
1978	15202405	15181517	15017715	15137454	15152094	15174266	15176623	14956006	15126530	15074112	15199994	15205374
1979	15793779	15771858	15597141	15726289	15741218	15763017	15765229	15531396	15715258	15661546	15789285	15797776
1980	16413258	16390178	16202918	16341863	16357449	16379271	16381329	16132983	16330605	16275765	16403481	16417197
1981	17060905	17036618	16836164	16985455	17001982	17024605	17026496	16761878	16973839	16917789	17045643	17063876
1982	17736028	17710555	17497075	17657398	17674801	17698298	17700013	17418299	17645204	17587738	17716141	17736326
1983	18435276	18408776	18184025	18355813	18373560	18398001	18399540	18100687	18343003	18283896	18413205	18431761
1984	19154464	19127196	18894032	19077038	19094311	19119203	19120574	18806155	19063906	19003187	19134067	19146400
1985	19888747	19861039	19623092	19816124	19832070	19856822	19858044	19530801	19803237	19741454	19865028	19877083
1986	20635651	20607766	20367886	20569060	20583073	20606706	20607803	20271378	20556967	20495241	20611889	20622560
1987	21395996	21368037	21127129	21334296	21346383	21368224	21369217	21026610	21323453	21263164	21373161	21382112
1988	22169639	22141664	21900101	22111269	22121874	22142567	22143465	21795770	22101818	22044461	22148261	22153676
1989	22953082	22925240	22684669	22898059	22907573	22928203	22929010	22576752	22889901	22836838	22934850	22935092
1990	23744071	23716508	23478606	23692830	23701333	23721629	23722358	23367356	23685647	23637793	23726627	23724579
1991	24541242	24514066	24280092	24494078	24501403	24520966	24521631	24165774	24487608	24445197	24525691	24521703
1992	25345610	25318827	25088721	25301531	25307736	25326160	25326772	24971579	25295806	25258476	25331348	25326078
1993	26156839	26130453	25904136	26114871	26120293	26138170	26138733	25784395	26109997	26077187	26143419	26136216
1994	26972269	26946354	26724823	26932724	26937546	26955558	26956074	26602715	26928566	26899842	26960109	26950513
1995	27790180	27764810	27549151	27753597	27757772	27775617	27776096	27424916	27749985	27724945	27776300	27768296
1996	28610894	28586079	28376462	28577039	28580455	28597558	28598010	28250330	28573830	28552104	28594644	28589451
1997	29434889	29410606	29206680	29403000	29405747	29422199	29422628	29078857	29400263	29381484	29415007	29415659
1998	30265744	30241867	30041595	30233575	30236175	30251778	30252185	29912231	30231318	30215031	30239122	30250488
1999	31109010	31085317	30884951	31073342	31076641	31091659	31092033	30754107	31071223	31056704	31070635	31098757
2000	31970813	31947026	31741772	31928405	31933382	31948548	31948866	31609410	31925847	31911946	31933684	31964557
2001	32854461	32830357	32616309	32803809	32811232	32827785	32828016	32482312	32800231	32785417	32814282	32848564
2002	33757019	33732571	33509248	33700386	33710157	33729320	33729437	33373501	33695275	33678017	33713076	33751739
2003	34679747	34654914	34421574	34618955	34630450	34650698	34650698	34283950	34612120	34590833	34631102	34678779
2004	35631281	35605819	35358140	35564437	35577431	35596903	35596778	35218439	35555965	35529024	35573130	35635271
2005	36618144	36591763	36324710	36542573	36557534	36577255	36576976	36182650	36532734	36498821	36560928	36624895
2006	37642002	37614519	37325054	37556962	37574599	37596326	37595856	37180315	37545918	37504384	37583082	37649033
2007	38701809	38673171	38360560	38609126	38629427	38653590	38652905	38212823	38596445	38547281	38641027	38705932
2008	39792501	39762831	39429368	39696770	39718594	39744997	39744088	39278373	39682160	39625612	39732984	39791981
2009	40908503	40878030	40527709	40814621	40836380	40863801	40862679	40373277	40798688	40735283	40855264	40901792
2010	42042556	42011603	41649990	41955096	41975248	42002756	42001446	41492046	41938960	41870092	41991804	42030676
2011	43190717	43159560	42791355	43111832	43129325	43155398	43153933	42629907	43096576	43024486	43147764	43178274
2012	44357206	44325872	43951435	44284122	44299071	44322065	44320477	43786495	44270503	44197702	44322804	44343467
2013	45540103	45508660	45129073	45470974	45484045	45505969	45504259	44960671	45459206	45388458	45515710	45519981
2014	46727710	46696495	46317803	46665581	46676895	46700075	46698251	46146063	46655655	46589821	46720068	46700055
2015	47910722	47880129	47509638	47859707	47868460	47891467	47889571	47334794	47851400	47792898	47917127	47878336
2016	49086346	49056617	48699092	49047868	49052951	49073308	49071388	48521437	49041093	48991341	49111633	49051534
2017	50253480	50224732	49882811	50226186	50227371	50244713	50242805	49702666	50221677	50181228	50300166	50221142
2018	51418639	51390750	51062370	51396677	51395297	51409239	51407364	50880013	51394953	51364061	51484356	51392565
2019	52591312	52563988	52243363	52567081	52565350	52577073	52575221	52058973	52567414	52545895	52669698	52573973
2020	53782539	53755381	53434217	53748756	53749055	53760295	53758431	53247845	53749638	53735972	53869140	53771296
2021	54995887	54968619	54641036	54949888	54953891	54967602	54965673	54452646	54949836	54941250	55084376	54985698
2022	56227527	56200100	55865012	56172530	56180230	56197916	56195884	55674556	56170258	56163427	56316308	56215221

The mean squared error plot for the various population processes is shown below:

The tracking error for the population processes is shown below: