RMIT INTERNATIONAL UNIVERSITY VIETNAM INDIVIDUAL CASE STUDY age dependency ratio data set 4

Part 3: Confidence Intervals a The Confidence Level CL applied for the calculation of world average of age dependency ratio is 95% and hence, the Level of significance α will be 0.05..

RMIT INTERNATIONAL UNIVERSITY VIETNAM

INDIVIDUAL CASE STUDY Age Dependency Ratio_Data set 4

STUDENT

Part 1: Introduction

The 17 Sustainable Development Goals is a set of implementations that aims for peace and

prosperity of humanity and Earth (United Nations n.d.) SDG 3 is the Good Health and

Well-being Goal, which strives to ensure healthy lives and promote well-Well-being for all at all ages Since

one of the sub-goals concerns with ‘increases life expectancy’, Age Dependency Ratio (ADR) is

unarguably one of the most effective indicators for the progression of the plan

ADR is the number of individuals that tend to

be reliant on others for their daily living (under 15+65 age and above) per 100 individuals who has adequate capabilities of handling these support (between 15 to 64 age) (WHO n.d.)

This demographic indicator measures the burden non-working people brings upon a nation’s potential workers (United Nations

2006) The higher the ADR, the greater the burden

the economically active population and overall

economy has to sustain in terms of public finances

(pensions and health care services) Therefore,

ADR reveals how a country’s social and economic

development can be affected due to the shift in

population age structure and thus, pointing out new

trends in social support demands (Amadeo 2020)

Figure 1 illustrates the Global ADR from 2009-2019 (The World Bank) Global ADR

experienced steady but insignificant decline (0.81% in total) from 2009-2015 However, it slowly

rose again in the next 4 years, from 54.001% to 54.481%, gaining back approximately half the

decline it witnessed during 2009-2015 and thus, forming a U-shape line One of the main reasons

behind the formation of the U-line was that there has been an increase in life expectancy of

OECD countries in recent years (OECD 2017) ADR is affected by mortality rates, fertility rates

and net migrations and thus, the prolonged life expectancy undoubtedly played a major part in

the growth of Global ADR (OECD 2017) Improved life expectancy provides elders with

additional years to pursue new opportunities and spend more time with their families (WHO

2018) However, Global ADR increased in the context of fertility rates substantially declined is

Year

World population by age group (%)

Figure 2: World population by age group (%) (Source: United Nations 2019)

Figure 1: Global Age Dependency Ratio (%) from 2009-2019

(Source: The World Bank)

53.4

53.6

53.8

54

54.2

54.4

54.6

54.8

55

Global Age Dependency Ratio

(% of working-age population)

Year

raising concerns Looking at Figure 2, the proportion of children in the population (blue) consistently shrunk and ended up at 26% in 2019, while the elderly population (green) has been expanding, implying that the current Global ADR is largely occupied by old-age-dependency ratio rather than youth-dependency ratio Moreover, all OECD countries reported a transition from high mortality and high fertility to low mortality and low fertility (OECD 2017) Rising longevity is undoubtedly a good thing, but old-workers’ physical and cognitive abilities will reduce overtime and thus, can’t compensate for the fall in labor productivity caused by the steady decline in fertility rates, which will diminish the future growth of labor force and significantly affect the economy (IMF 2019)

Abovementioned, ADR’s evolution depends on mortality and fertility rates Hence, it is important to monitor the ADR in achieving the SDG 3 because the indicator will analyze whether old-dependency ratio or youth-dependency ratio is taking over to strategically approach the situation For instance, more investments in long-term care and pensions or in schooling and child-care will depend on which ADR is currently leading (United Nations 2006)

Gross National Income (GNI) is the total domestic and foreign income generated by a nation’s residents and businesses (WHO n.d.) Age dependency and GNI negatively influence each other

as economic output is bound to fall if fewer workers participate in the economy (IMF 2019) To some extent (excluding unemployment rate), a lower ADR implies that a larger proportion of the population is contributing to the economy and income-raising work, which is then accumulated toward GNI (Gable and Lofgren 2014) Moreover, given that the economic independents population tend to have higher saving rates, an increase in this proportion will accelerate the GDP growth and thus, GNI will also rise In conclusion, GNI of a nation is dependent on its ADR

Part 2: Descriptive Statistics and Probability

1 Probability

Contingency Table according to country categories with High- or Low-ADR

Low Age Dependency Ratio

(LADR)

High Age Dependency Ratio

a) Income and Age Dependency ratio are statistically independent events when the probability

of one event is not affected by the other event Hence, Middle-Income (MI) and High ADR (HADR) is put into comparison to recognize the events

The probability of Middle-Income countries: P (MI) = 16

35 The probability of Middle-Income countries with High ADR: P (MI | HADR) =

P (MI ∩ HADR)

12

After calculation, it turns out that P (MI) ≠ P (MI | HADR) ( 16

12 ) Because P (MI) is different from P (MI | HADR), we can conclude that that the change in ADR level does affect the condition of Income event and thus, they are statistically dependent

b) Conditional Probability will be applied to consider the likelihood of having high ADR for each country category

The probability of Low-Income countries having High ADR: P (HADR | LI) = 0

The probability of Middle-Income countries having High ADR: P (HADR | MI) = 1

16 = 6.25%

The probability of High-Income countries having High ADR: P (HADR | HI) = 1 = 100% The calculation clearly indicates that most of the time High-Income countries are expected to have High ADR with the likelihood of 100% In contrast, for both Middle-Income and Low-Income countries, the chances are low as the probabilities are 6.25% and 0% respectively

2 Descriptive Statistic

Outliers Calculation

Measures of Central Tendency for ADR, old (% of working-age population)

Initially, there is an Outlier in the ADR for Middle-Income dataset Hence, Median is the most appropriate measure to use in this case because extreme values will affect the value of Mean

It is obvious that High-Income has the highest median out of the three categories, at 28.51%, followed by Middle-Income at 8.4% and Low-Income at 5.1% Through Median, it is implied that 50% of the countries in all income categories witness the ADR above the median and the other remaining values lie below the median For instance, there is a total of 11 countries in the High-Income category with the median of 28.51%, implying that 5 or 6 countries will have the ADR below 28.51% and the rest belongs to the upper group, with ADR higher than 28.51% Contrary to High-Income, Middle-Income and Low-Income categories witness much lower Median value, about 1/3 and 1/5 of High-Income countries respectively

Regarding the given condition to classify countries into High- or Low-ADR, countries with ADR above 20% is sorted as having High-ADR Hence, relating back to the High-Income category, its median is 28.51%, which far exceed the given condition Hence, this finding further fortifies our conclusion in the previous part, that it is unlikely for Low- and Middle-Income countries to have High ADR, while for High-Income countries, High ADR is a common and obvious element

Part 3: Confidence Intervals

a) The Confidence Level (CL) applied for the calculation of world average of age dependency ratio is 95% and hence, the Level of significance ( α ) will be 0.05 Since the population

standard deviation ( σ ) is unknown, sample standard deviation (s) and t-table will be

applied

Statistics Summary Table

Average of ADR, old (% of working-age population)

t-value ( α

Applying the formula:

μ = ´ X ± t × √s n = 14.33 ± 2.032 × 9.95

√35 = [10.91; 17.75]

With 95% Level of confidence, we can conclude that the world average age dependency ratio, old (%) is between 10.91% and 17.75%

b) No assumptions about the population distribution are required to be made when calculating Confidence Intervals in this case as the sample size is n=35 > 30 Hence, the Central Limit Theorem (CLT) is applicable and thus, sampling distribution of mean is normally distributed

c) Impact on the Confidence Interval results when the world standard deviation is known Since world standard deviation of age dependency is known and the sample size n=35 > 30, sampling distribution of mean will always be normally distributed Hence, the sample mean (

´X ) becomes the confidence interval’s center and other values would spread around in

accordance to the standard deviation Theoretically, sample standard deviation has greater variability compared to population standard deviation (Taylor 2019) The formula for Confidence

Interval ( σ known) is applied to examine the change:

μ = ´X ± z( σ

√n) From the formula, the results of Confidence Interval ( μ ) will depend on the chosen CL (

Zα ), population standard deviation ( σ ) and sample size (n) As ´X and n value remains the same, it now narrowed down the dependent of μ to 2 variables z and σ only Firstly, when σ exists, z-table will be utilized instead of t-table and thus, result in a

different value For the previous case, at the CL of 95%, z-value would be ± 1.96, implying a

smaller Confidence Interval range compared to when t-value is used ( ± 2.032) Moreover, by comparing the two formula of σ and s with the same sample size n , σ will always have

smaller value than s due to its higher denominator

σ=√ ∑(X i −μ)2

n , s=√ ∑( X i − ´X )2

n−1

In conclusion, if world standard deviation is known, Confidence Interval width outcomes will be reduced and thus, the data will experience higher spread and closer to the sample mean Hence, with the same CL, we will get smaller and more accurate intervals with population standard deviation than sample standard deviation as sample standard deviation might be varied as sample change

Part 4: Hypothesis Testing

a) By comparing the world average age dependency ratio reported in 2014 and the confidence intervals of 2015, I think that the mean of age dependency ratio will remain unchanged in the future Hence, I will conduct a Hypothesis testing to prove my claim

t-value ( α

 The chosen Level of confidence is α = 0.05.

 Since the sample size n=35 > 30, CLT is applicable and thus sampling distribution of mean becomes normally distributed

 {H0; μ=12.9

H1; μ ≠ 12.9

→ By looking at the sign of H1 , we can say that this is a Two-tailed test

 Because the population standard deviation ( σ ) is unknown, t-table will be used.

 For α = 0.05, the critical values will be ± 2.032.

 Test statistic

t = ´X−μ

s/√n = 14.33 12.9−

9.95/√35 = 0.85

 Because -2.031 < t = 0.85 < 2.032, the test statistic does not fall into in the Rejection Region

Hence, we do not reject H0

 As H0 is not rejected, hence with 95% Level of confidence we can conclude that the world average age dependency ratio will remain the same at 12.9% in the future

(Claim)

α=0.025

α=0.025

0.85 2.032 0

-2.032

 Since we did not reject the Null Hypothesis ( H0 ), we might have committed Type II error.

We said that the world age dependency ratio will remain at 12.9% in the future, the same as

in 2014, but actually the percentage might be different than 12.9%

 Type II error can be minimized by:

o Increasing the significance level ( α ) and thus, critical value will be reduced which

then widen the Rejection region for more precise testing

o Decrease the population standard deviation ( σ ) However, σ is unknown in this

case

o Increasing the sample size (n) and σ will decrease.

b) Impact on the Hypothesis testing if sample size is doubled

In identifying the possible impacts of doubling the sample size (n) can have on the Hypothesis testing results, the formula for sample standard deviation (s) will be examined:

s=√ ∑( X i − ´X )2

n−1

Initially, sample standard deviation (s) and sample size (n) are inversely related Therefore, when

n is doubled, s is bound to decreased proportionally to √n−1 Moreover, the sample mean (

´X ) and sample standard deviation will shift closer to the actual population mean Thus, less

variables will occur and sampling distribution will be more consistent

With the incline in the value of n, the degree of freedom (d.f = n-1) will also increase accordingly and affect the critical value Higher d.f will cause a reduction in critical value considering the case of significance level remain unchanged and thus, widen the Rejection region Meanwhile, the test statistic t=´X−μ

s/√n is positively influenced since n is inversely proportional to t Specifically, the increase in n will cause an increase in test statistic t while reducing the critical value and non-rejection region Therefore, the possibility of test statistic falls within the rejection region is increased, which will eliminate inevitable approximate results Regarding the Hypothesis test result in the previous part, it can be clearly recognized that between the test statistic and rejection regions exists a huge gap The closer the original test statistic to the rejection region, the higher the chance it will fall into the rejection region after the increase in sample size took place In my opinion, even after the change had happened, specifically the test statistic shifted to the right while the rejection regions moved closer to the center, it is unlikely that the test statistic will fall within the rejection region as there is a huge

distance from t=0.85 to critical value ± 2.032 Hence, the statistical decision will remain the

same after the change

A larger sample size would also lessen the probability of committing Type II error in which we failed to reject the false null hypothesis and thus, the power of the test is consolidated By all means, the accuracy of the Hypothesis test will be undoubtedly increased

Part 5: Overall conclusion

Based on the above theoretic research and analysis of the given data, these are the main findings

of this report

Firstly, Income and ADR are statistically dependent events as the probability of one event can be affected by the other event Simply put, the change in income will affect the ADR level and vice versa Therefore, it is important to monitor the ADR level of one country to improve the GNI and ensure healthier living standard in achieving the SDG 3 Moreover, since P (HADR | HI) > P (HADR | MI) > P (HADR | LI) (100% > 6.25% > 0%), it seems that the higher the income category, the higher chance one country will experience High ADR

Secondly, High-Income countries tend to have the highest ADR through the observation of Median The Median of High-Income countries’ ADR is the highest compared to the other two and far exceed the required condition to be classified as ‘High ADR’ Hence, it is implied that regardless of the position of the values, which is above or below Median, the likelihood of the value being greater than the given condition is high By all means, if one country falls into the High-Income category, it will most likely have High ADR also

Based on the calculation of ADR, old (% of working-age population) taken from all three categories, we can conclude that with 95% Confidence Level, the world average age dependency ratio, old (%) in 2015 will fall with 10.91% and 17.75% Furthermore, by conducting a Hypothesis test, the world average age dependency ratio in the future will remain unchanged at 12.9% compared to 2014

In my opinion, ADR is an important measure that every country needs to monitor to ensure the growth of the economy Abovementioned, ADR can greatly affect the Income level of a nation as

it will determine the current and future labor force For instance, if one country has high ADR and that ADR is largely comprised of youth-dependency ratio, it implies that the country’s workforce might be scarce now, but it will later thrive in the future as the young generation will age and join the working-age population According to IMF (2019), the world is witnessing steady decline in fertility rates while the life expectancy is increasing overtime Accordingly, the number of potential workers is predicted to fall and will greatly affect the economy Regarding the above Hypothesis test result, even though the claim of world average age dependency ratio will remain unchanged in the future was not rejected, there was insufficient evidence to state

whether old-age dependency ratio or youth-dependency ratio will occupy for the bigger proportion of the total percentage Hence, precautious measures toward the declining fertility rates need to be taken immediately to ensure a sufficient labor force for the future

Reference

Amadeo, K 2020, ‘What Is the Dependency Ratio’, the balance, 30 November, viewed 11 December 2020, <https://www.thebalance.com/dependency-ratio-definition-solvency-4172447>

Gable, S & Lofgren, H 2014, ‘Country Development Diagnostics Post-2015: Uganda’, research

<https://www.researchgate.net/publication/285589757_Country_Development_Diagnostics_Post -2015_Uganda#pf46>

IMF 2019, ‘Macroeconomics of Aging and Policy Implications’, international monetary fund, 5

Jun, viewed 11 December 2020, <https://www.imf.org/external/np/g20/pdf/2019/060519a.pdf>

OECD 2017, ‘Old-age dependency ratio’, Pensions at a Glance: OECD and G20 Indicators, viewed 11 December 2020, < https://www.oecd-ilibrary.org/docserver/pension_glance-2017-22-en.pdf?

expires=1607677933&id=id&accname=guest&checksum=049F8128CC42F3C9465E083CE2FE A06F>