(TIỂU LUẬN) RMIT INTERNATIONAL UNIVERSITY VIETNAM INDIVIDUAL CASE STUDY age dependency ratio data set 4

RMIT INTERNATIONAL UNIVERSITY VIETNAM INDIVIDUAL CASE STUDY Age Dependency Ratio_Data set COURSE CODE ECON1193 COURSE NAME BUSINESS STATISTICS STUDENT LECTURER GREENI M PAGE COUNTS PAGES Part 1: Introduction Global Age Dependency Ratio (% of working-age population) 55 54.8 54.6 54.4 54.2 54 53.8 53.6 53.4 09 10 11 12 13 14 15 16 17 18 19 20 20 20 20 20 20 20 20 20 20 20 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 Percentage in total population (%) Age Dependency Ratio (%) 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 is the Good Health and Wellbeing Goal, which strives to ensure healthy lives and promote 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 World population by age group (%) Year 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: Global Age Dependency Ratio (%) from 2009-2019 (Source: The World Bank) Year Figure 2: World population by age group (%) (Source: United Nations 2019) Figure 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 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 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 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 Probability Contingency Table according to country categories with High- or Low-ADR Low Age Dependency Ratio High Age Dependency Ratio (LADR) (HADR) Low-Income (LI) Middle-Income (MI) 15 High-Income (HI) 11 Total 23 12 Total 16 11 35 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) = P (HADR) 12 After calculation, it turns out that P (MI) ≠ P (MI | HADR) ( 16 35 ≠ 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) = The probability of Middle-Income countries having High ADR: P (HADR | MI) = = 0% 16 = 6.25% The probability of High-Income countries having High ADR: P (HADR | HI) = = 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 LowIncome countries, the chances are low as the probabilities are 6.25% and 0% respectively Descriptive Statistic Q1 Q3 IQR (Q3-Q1) Lower bound (Q1-1.5*IQR) Upper bound (Q3+1.5*IQR) Outliers Calculation Low-Income Middle-Income 5.07 7.32 5.25 10.82 0.18 3.5 4.8 2.07 5.5 16.1 High Income 24.6 30.3 5.74 15.95 38.91 Measures of Central Tendency for ADR, old (% of working-age population) Low-Income Middle-Income High-Income Mean (%) 5.31 9.93 27.3 Median (%) 5.1 8.4 28.51 Mode None None None 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 or 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) 0.05 Level of significance ( α ¿ Sample size (n) 35 Sample standard deviation (s) (%) 9.95 14.33 Sample mean ( X´ ) (%) Degree of freedom (n-1) 34 α ± 2.032 t-value ( , n-1) Applying the formula: μ = X´ ± t → 10.91 ≤ × μ s √n = 14.33 ≤ 17.75 ± 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 ( √σn ) From the formula, the results of Confidence Interval ( μ ) will depend on the chosen CL ( ´ and n value Zα ), population standard deviation ( σ ) and sample size (n) As X remains the same, it now narrowed down the dependent of μ to 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 , s= ∑ ( X i− X´ )2 n 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 Level of significance ( α ¿ Sample size (n) Sample standard deviation (s) (%) Sample mean ( X´ ) (%) Population mean ( μ ) (%) Degree of freedom (n-1) α t-value ( , n-1)   0.05 35 9.95 14.33 12.9 34 ± 2.032 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 H ; μ=12.9 (Claim) H ; μ ≠ 12.9 {  H , we can say that this is a Two-tailed test → By looking at the sign of    t= 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 ´X−μ s /√ n = 14.33 −12.9 9.95/ √ 35 = 0.85 α =0.025 -2.032   α=0.025 0.85 2.032 Because -2.031 < t = 0.85 < 2.032, the test statistic does not fall into in the Rejection Region Hence, we not reject H As H 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   Since we did not reject the Null Hypothesis ( H ), 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 ´ X−μ is positively influenced since n is inversely region Meanwhile, the test statistic t= s / √n 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 same after the change ± 2.032 Hence, the statistical decision will remain the 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 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, Gable, S & Lofgren, H 2014, ‘Country Development Diagnostics Post-2015: Uganda’, research gate, viewed 12 December 2020, IMF 2019, ‘Macroeconomics of Aging and Policy Implications’, international monetary fund, Jun, viewed 11 December 2020, OECD 2017, ‘Old-age dependency ratio’, Pensions at a Glance: OECD and G20 Indicators, viewed 11 December 2020, 10 Taylor, C 2019, ‘Differences between Population and Sample Standard Deviations’, thought co., 23 January, viewed 12 December 2020, The World Bank n.d., ‘Age dependency ratio (% of working-age population)’, world bank, viewed 11 December 2020, United Nations n.d., ‘Transforming our world: the 2030 Agenda for Sustainable Development’, united nations, viewed December 2020, United Nations 2006, ‘Dependency Ratio’, World Population Prospects: The 2006 Revision, vol 1, viewed 11 December 2020, WHO 2018, ‘Ageing and health’, world health organization, February, viewed 11 December 2020, WHO n.d., ‘Gross Nation Income (GNI), per capita, current US$ (Atlas Method)’, world health data platform, viewed 11 December 2020, WHO n.d., ‘Dependency Ratio’, world health data platform, viewed December 2020, 11 ... Global Age Dependency Ratio (% of working -age population) 55 54. 8 54. 6 54. 4 54. 2 54 53.8 53.6 53 .4 09 10 11 12 13 14 15 16 17 18 19 20 20 20 20 20 20 20 20 20 20 20 ADR is the number of individuals... sample change Part 4: Hypothesis Testing a) By comparing the world average age dependency ratio reported in 20 14 and the confidence intervals of 2015, I think that the mean of age dependency ratio... or Low-ADR Low Age Dependency Ratio High Age Dependency Ratio (LADR) (HADR) Low-Income (LI) Middle-Income (MI) 15 High-Income (HI) 11 Total 23 12 Total 16 11 35 a) Income and Age Dependency ratio