Essays on forecasting life expectancy and fiscal sustainability 2

ESSAY FORECASTING LIFE EXPECTANCY 1.1. INTRODUCTION Spurred by the well-established Lee-Carter (LC) approach (1992), there have been renewed interests in mortality forecasting, see Booth (2006). Sophisticated models and methods for forecasting life expectancy, such as the LC model, can have significant impacts and contributions towards macroeconomics research. Accurate demographic forecasts are important as they yield important insights to issues relating to economic growth, life-cycle consumption, retirement annuity, defined contribution plans and fiscal sustainability. See Heijdra and Romp (2009), Lau (2009) and Alho et al. (2008), among others. The LC method is based on a linear fit to an additive model of age-specific death rates, with a fixed-age component and a time-varying component assuming homoskedastic Gaussian error structure. It is computationally simple, yet reasonably accurate in capturing trends and variations in mortality rates. Though significantly deviated from previous methods, the LC model and its extensions have been applied successfully to forecast life expectancy in developed countries, including the USA and the G7 countries. See Lee and Miller (2002), Booth et al. (2002) and Booth (2006). The LC method and many other mortality models have commonly assumed the variance of error terms to be constant over time i.e. a homoskedastic error 1|Page structure is adopted. This assumption may not be satisfactory; since for time series data, it is often observed that volatility clustering are present, where large changes are followed by large changes and small changes followed by small changes, an evidence of heteroskedasticity. In the presence of time-varying volatility in mortality data, the classical LC model will be inadequate. Although the importance of time-varying volatility has been accounted for in various macroeconomic time series data, to the best of our knowledge, there is no study of volatility clustering in the LC model. This essay aims to fill this current gap, and seek evidence of such time-variation in volatility using the welldocumented autoregressive conditional heteroskedasticity (ARCH)/generalized ARCH (GARCH) models introduced respectively by Engle (1982) and Bollerslev (1986). The countries included in this study are Japan, Australia, Hong Kong, Taiwan, U.S. and U.K. In addition to time-varying volatility, the presence of time-varying correlations between the male and female mortality series of each country are also of practical value and importance. While extending the LC method with univariate GARCH model captures volatility clustering for individual series, volatility comovements between related series will require the use of Multivariate GARCH (MGARCH) models. To the best of our knowledge, there has also been no study of time-varying correlation dynamics of mortality series using MGARCH-type models. We adopt 2|Page the use of such models with the LC approach to simultaneously examine the presence of time-varying volatility and correlations in mortality forecasting. We will adopt the use of both the Constant Conditional Correlation (CCC-) GARCH model of Bollerslev (1990) and time-varying Conditional Correlation (VC-) GARCH model of Tse and Tsui (2002). We then seek to compare the withinsample forecast performance of the classical LC model with the proposed model extensions in this paper in forecasting life expectancy at birth and at age 65. This essay is structured as follows: Section 1.2 offers a literature review. Section 1.3 describes the LC-GARCH model while section 1.4 summarizes the data used and presents the estimation results. In section 1.5, we offer an overview of the MGARCH models, and Section 1.6 describes the LC method extended with CCC-GARCH and VC-GARCH models. Estimation results are then reported in section 1.7. In section 1.8, we show that using the LC model with VC-GARCH structure offers the largest improvement in within samples forecasts of life expectancy at birth and at age 65. Concluding remarks are offered in the final section. 3|Page 1.2. LITERATURE REVIEW While there are many approaches to forecast mortality rates, the LC method is still one of the leading statistical models in the demographic literature for mortality trend fitting and life expectancy projections since its development in 1992. Proposed by Lee and Carter, it was initially used for projecting age-specific mortality rates in the United States but has since been adopted by many other countries as the basic mortality model for population projections. See applications in, for example, Canada (Lee and Nault, 1993), Japan (Wilmoth, 1996) and the seven most economically developed nations (G7) (Tuljapurkar et al., 2000). The LC model was designed to examine the long-term patterns in the natural logarithm of central death rates using a single index of mortality. It essentially describes the logarithmically transformed age-specific central rate of death as a sum of an age-specific component that is independent of time, and the product of a time-varying parameter (also known as the mortality index that summarizes the general level of mortality) and an additional age-specific component that represents how rapidly or slowly mortality at each age varies when the mortality index changes. The advantages of the parsimonious LC model lie in its simplicity. This is because once data is fitted to the model and the model parameter values are estimated, they are held fixed as constants and only the mortality index needs to be 4|Page forecasted. The LC model also adopts an extrapolative method where forecasts are carried out using time series methods and historical information. With the use of logarithms, it also allows mortality rates to decrease exponentially without the need for restrictions. Like many other models, the LC model has its set of limitations as well. As it is based on extrapolation methods, its forecast accuracy fares unfavorably when historical data fails to hold in the future and/or structural changes occur. It also does not account for any changes in social economic factors, such as medical advancement, lifestyle changes etc. Furthermore, the LC model assumes a constant variance for the residual term; which can potentially be another limitation since it constrains the model's ability to capture the volatility of series if changes across periods are far from being constant. While many extensions to the LC model have likewise assumed a constant variance for the residual term, the presence of time-variation in volatility has been detected in mortality series and some studies have questioned the assumption of using constant variances. Among them, Renshaw & Haberman (2003a, b) used heteroskedastic Poisson error structures in their mortality forecast, where ordinary least-squares regression is replaced with Poisson regression for the death counts. Cossette et al (2007) suggested the use of a Binomial regression model where the annual number of deaths is assumed to follow a Binomial distribution and the death probability is expressed as a function of the force of mortality. Delwarde, Denuit 5|Page and Partrat (2007) also proposed the use of Negative Binomial Distribution to account for the presence of heterogeneity in mortality. The use of ARCH and GARCH models (Engle, 1982; Bollerslev, 1986) has been proven to be capable in capturing the existence of non-constant variances in many applications. Nonetheless, among these extensions, the use of ARCH/GARCH models in demography forecasting is limited. While Keilman and Pham (2004) incorporated ARCH-type structure with the use of ARIMA models in their forecasts of fertility, mortality and net migration for 18 countries in the European Economic Area, their study did not attempt to incorporate the use of ARCH/GARCH models with the LC model. This is our first objective in this essay. Univariate ARCH/GARCH models face two restrictions; firstly it does not accommodate the asymmetric effects of positive and negative shocks and secondly, it assumes independence between conditional volatilities across different groups. In financial series, it has been established that volatility in the returns of financial variables exhibit an asymmetric character where negative shocks contribute more to volatility than positive shocks of the same magnitude (see for instance, Nelson, 1991 and Glosten, Jagannathan and Runkle, 1993). It is not known if such asymmetric effects are also present in mortality data and this is the second objective of this essay which seeks to address the limitation of using univariate ARCH/GARCH models. Hence, further to extending the LC model with 6|Page ARCH/GARCH type models, we will also examine the presence of asymmetric effects in mortality series using the LC model extended with EGARCH. Other variations of the LC method included the recent works of Girosi and King (2008), who adopted the Baynesian approach and Markov Chain Monte Carlo estimation to improve on mortality forecasting. They developed a general Baynesian hierarchical framework for forecasting different demographic variables and incorporated exogenously measured covariates as proxies for systematic causes of death. Their methodology have not only generalized the LC model to an analysis involving several principal components; it also uses additional information about regularities along the dimensions of age, sex, country and death causes to improve on forecasting results. The framework, however, only models a single population in isolation, and also requires a lot of extensive information which may not be easily available in many countries. The use of multivariate GARCH models allows one to account for the presence of co-movements across related series, which makes it possible to model separate series jointly and incorporate their interactions. In the financial sector, the dependence in co-movements across asset returns is important since the comovements or covariance of assets in a portfolio provides critical information for asset pricing. Using MGARCH models allow us to extract such covariance information and improve the analysis for asset pricing models, hedging, portfolio selection and Value-at-Risk forecasts. Studies have found the variances of financial time series to be interacting, see for instance, Cifarelli and Paladino 7|Page (2005) who studied the linkages in equity markets. MGARCH models have been used to examine the volatility and correlation transmissions and spillover effects in contagion studies as well, see Tse and Tsui (2002). MGARCH models estimate a conditional covariance matrix comprising time-varying conditional volatilities and correlations. It has been proven in many financial applications that modeling the dynamics of the covariance matrix using a multivariate approach yields better results than working with separate univariate models for each individual series. The importance of accounting for co- movements using MGARCH models is similarly valid for other markets. In the area of mortality, the presence of co-movements between the male and female population is potentially large. The MGARCH literature include several types of models including VEC model by Bollerslev, Engle and Wooldridge (1988), Baba-Engle-Kraft-Kroner (BEKK) model by Engle and Kroner (1995), CCC-GARCH model by Bollerslev (1990) and time-varying conditional correlation GARCH models (VC-GARCH and DCC-GARCH models by Tse and Tsui (2002) and Engle (2002) respectively. In the area of demography, the extension of the LC model with MGARCH models has not been attempted in the literature and this is the third gap which we seek to address in this essay. Such an extension will allow us to examine the presence of co-movements between the mortality series of male and female populations. 8|Page 1.3. EMPIRICAL MODEL 1.3.1. LC Model The LC Model is widely used in mortality forecasting and life expectancy forecasting. It was introduced in 1992 and has been used by the United States Social Security Administration, the US Census Bureau, and the United Nations. The structure proposed by Lee and Carter (1992) is as follows: 1.1 1.2 where is the central death rate for an individual aged at time t; is the additive age-specific constant displaying the average shape across age of the mortality schedule; describes the relative sensitivity of the mortality at age changes in the general level; to is the error term which reflects any age-specific historical influences not captured in the model and is a time-specific index of the general level of mortality. is modeled to follow the random walk model with drift1 as described in (1.2) with a constant drift μ and distributed Normal is assumed to be independent, identically For different values of , the fitted model defines a set of central death rates, which can then be used to derive a life table conveniently. Lee and Carter (1992) claimed that other ARIMA models might be preferable for different set of data, but the random walk model with drift is mostly used in practice. 9|Page When changes linearly with time, mortality at each age changes at a constant exponential rate accompanied by the age-specific constants varying by age. As equation (1.1) is over-parameterized, mean of over time while the sums of and is taken to be the arithmetic are normalized to one and zero respectively, so as to ensure a unique solution. Furthermore, given that all the parameters on the right-hand side of equation (1.1) are unobservable, the LC model requires a two-stage estimation procedure. In stage one, the Singular Value Decomposition (SVD) estimation procedure is applied to the matrix of to obtain estimates of and . Following stage one, the time series of in equation (1.2) is re-estimated in stage two by solving the following 1.3 where is the total number of deaths in time t, and an individual aged x in time t. The re-estimation of is the exposure to risk of in stage two ensures that the mortality schedules fitted will reconcile with the actual total number of deaths and the population age distributions. 10 | P a g e need. To contain government overall total spending, we could consider gradually extending the means-testing mechanism to other areas as well, such as education, training subsidies through the skills development fund etc. There are other important areas associated with an ageing population that warrants concerns as they might have direct and indirect fiscal implications. Among them are, a shift in healthcare utilization from end-of-life care to prevention and chronic care, which can have important implications in terms of healthcare resources and future infrastructural planning; changing patterns of population's savings and expenditures; lower labor productivity and labor supply issues, etc. Population ageing may lower the aggregate labor force participation rates since the older cohort tends to work less and the desire for better quality of life may further contribute to reducing the average hours of work. There is thus a continuous need to improve the health status of the population to allow for longer working years, build in more incentives to encourage businesses to continue to employ older employees, training in skills for older workers for their continued participation in the work force, increase workplace quality in order to raise labor force participation and productivity, focus on lifelong learning and encouraging workers to remain in the labor force longer, more flexible work arrangements especially for mothers to re-enter the workforce, as well as encouraging skilled migration to address skills shortages and raising productivity. 223 | P a g e There is still much scope to improve the work and family life balance in Singapore so as to raise our existing low fertility rate. Although our earlier results showed that lower fertility can actually offer some fiscal relief to the government and hence lower the fiscal pressures of ageing, this effect is only so in short to medium-term since our analysis covered a period of twenty years. Population ageing is contributed by both longer life expectancy and lower fertility rates and it is possible to slow down the speed of population ageing in the long run by increasing fertility rates. Over the long term, an increase in fertility rate will expand the working age cohort and tax base, reduce the old dependency ratio and thereby delaying the fiscal pressures brought about by population ageing. Overall, minimizing the adverse fiscal effects of population ageing will also require implementation of long-term supply side strategies or growth-enhancing measures to raise the future sustainable economic growth of Singapore. These include, for instance, policies to foster innovation and productivity growth, increasing competition, and continuous investment in human capital (life-long learning) and Research & Development. In Singapore, the policy stance and philosophy adopted is always for each individual to be responsible for themselves, followed by family's support and any aid from the government is only a last resort. Going forward, the direction will still be for individuals to be able to remain independent and continue to be self-reliant for as long as possible. 224 | P a g e Before ending this section, it is worth mentioning some limitations of this study. First of all, by not explicitly modeling factors which might affect expenditures over time, the projections in this study could have underestimated the future fiscal burden. Similarly, our adopted methodology to model the impact of demographic factors has also ignored the possible improvements in the health status of elderly over time, which might help contain expenditure pressures. With compression of morbidity, the elderly can continue to contribute to the workforce and delay the effects of population ageing. As pointed out by Bloom et al (2008), policymakers need not be overly pessimistic or alarmed with population ageing effects, since behavioral changes towards healthier diets and lifestyle improvements, coupled with medical advancements are some of the promising avenues to offset and lower the economic burden of ageing. 225 | P a g e 3.9. Concluding Remarks One of the most critical demographic issues today is population ageing, initially experienced by developed countries but now affecting developing nations as well. Mid to long-term fiscal projections are important to assess public finance sustainability; and this importance has been intensified due to the challenges posed by population ageing. Singapore is one of the fastest aging countries in Asia; in this essay, we have used a method of age specific benefit and tax projection framework to examine the impact of demographic changes on the fiscal stance of Singapore. Demographic projections over the next 20 years show a significant increase in the elderly share of the population as fertility rates are projected to remain low while life expectancy increases. Given that the incidence of government spending is not evenly distributed across age groups and largely falls on the young and elderly, spending pressures are likely to emerge in key categories such as health and elderly benefits. Population ageing will reduce the growth of government revenue as the large (baby-boom) age cohort move out of their peak earning years into retirement while declining births reduces the size of working age group. This essay show that under the case of “pure demographic effects”, the budget position for Singapore government will inevitably deteriorate and the fiscal support ratio will fall under all fertility scenarios. The fiscal support ratio is also expected to decline faster if the growth rate of fertility numbers increases. 226 | P a g e The calibration results in this study also show that if we face an increase in immigrant population going forward, the rate of decline in the fiscal support ratio will be moderated. Similarly, an extension of the retirement age to 70 years old is expected to improve the fiscal budget position and fiscal support ratios. The same conclusion holds if we can increase the female labor force participation rates. Lastly, the calibrations also point that allowing for an annual increase in labor productivity will help to moderate the projected decline in the fiscal support ratio, while a reduction will aggravate the decline. As earlier mentioned, given that the objective of this essay is not on generational effects, we did not incorporate generational accounting to measure the burden of current fiscal policies on future generations,. Hence, we did not assess the generational balance for Singapore and are not able to identify a set of policy reforms needed to ensure that the future generations will face the same lifetime net tax rates as current cohort, as a result of population ageing. This could be an area where future studies can look into. Going forward, the issue of fiscal sustainability will continue to be a topic of growing interest and one of the principle challenges facing all policymakers. It is important to bear in mind that fiscal sustainability does not only imply budget balance, it also entails keeping the tax burden at reasonable levels and ensuring that non-age related expenditures are not crowded-out by increased spending on health care and other elderly-related costs. Equally important, fiscal sustainability should 227 | P a g e not be achieved at the expenses of reduced government spending on programmes that primarily benefit the young. 228 | P a g e REFERENCES Ashley, R., and Guerard, J. (1983), “Applications of Time Series Analysis to Texas Financial Forecasting,” Interfaces, 13, 46-55. Auerbach, A. J., Kotlikoff, L. J., and Leibfritz, W., eds. (1999), “Generational Accounting Around the World,” Chicago, Illinois: The Chicago University Press. Auerbach, A. J., Young, J. C. (2003), “Generational Accounting in Korea,” NBER Working Paper no. 9983. Baguestani, H. and McNown, R. (1992), “Forecasting the Federal Budget with Time Series Models,” Journal of Forecasting, 11, 127-139. Bezdek, V., Dybczak, K., and Krejdl, A. (2003), “Fiscal Implications of Population Aging,” Czech Journal of Economics and Finance, 53, 562-591. Bloom, D. E., Canning, D., and Fink, G. (2008), “Population Ageing and Economic Growth,” Commission on Growth and Development, Working Paper No. 32. Box, George E. P. and Jenkins, G. M. (1976), “Time Series Analysis: Forecasting and Control,” Revised Edition, Oakland, CA: Holden-Day. 229 | P a g e Cardarelli, R., Sefton, J., and Kotlikoff, L. J. (2000), “Generational Accounting in the UK,” Economic Journal, 110 (467), 547-74. Chand, S., and Jaeger, A. (1996), “Aging Populations and Public Pension Schemes,” Occasional Papers No. 147, IMF. Centers for Medicare and Medicaid Services (2006), “Personal Health Care Expenditures by Age: 1987-1999,” Washington, D.C.: U.S. Department of Health and Human Services. http://www.cms.hhs.gov/National HealthExpendData/downloads/agetables.pdf. Chia, N. C., and Tsui, A. K. C. (2003). “Life Annuities of Compulsory Savings and Income Adequacy of the Elderly in Singapore," Journal of Pension Economics and Finance, 2(1), 41-65. Creedy, J., Scobie, G. (2005), “Population Ageing and Social Expenditure in New Zealand,” Australian Economic Review, 38 (1), 19 - 39. Cutler, D. M., Elmendorf, D. W., and Zeckhauser, R. J. (1993), “Demographic Composition and the Public Bundle”, Public Finance, 178-198; reprinted in Wolfe, B., ed. (1994), “On the Role of Public Policy in Demographic Change”. Dang, T. T., Antolin, P., and Oxley, H. (2001), “Fiscal Implications of Aging: Projections of Age-Related Spending,” Geneva: OECD. 230 | P a g e Dekle, R. (2003), “The Deteriorating Fiscal Situation and an Aging Population,” 71-88; in Blomstrom, M., Corbett, J., Hayashi, F., and Kashyap, A., eds., “Structural Impediments to Growth in Japan,” National Bureau of Economic Research, University of Chicago press. http://www.nber.org/chapters/c9573 Duncan, G., Gorr, W., and Szczypula, J. (1993), “Bayesian Forecasting for Seemingly Unrelated Time Series: Application to Local Government Revenue Forecasting," Management Science, 39 (3), 275-293. Feyzioglu, T., Skaarup, M., and Syed, M. (2008). “Addressing Korea's Long-Term Fiscal Challenges," Occasional Papers No. 27, IMF. Frank, H. A., and Gianakis, G. A. (1990), “Raising the Bridge Using Time Series Forecasting Models,” Public Productivity & Management Review, 14 (2), 171-188. Fullerton, Jr. T. M. (1989), “A Composite Approach to Forecasting State Government Revenues: Case Study of the Idaho Sales Tax," International Journal of Forecasting, 5, 373-380. Gruber, J. and Wise, D. (2001), “An International Perspective on Policies for an Aging Society,” National Bureau of Economic Research Working Paper No. 8103. 231 | P a g e Guest, R. S., and McDonald, I. M. (2000), “Population Ageing and Projections of Government Social Outlays in Australia,” The Australian Economic Review, 33, 1. Heller, P. S., and Hauner, D. (2005), “Characterizing the Expenditure Uncertainties of Industrial Countries in the 21st Century,” Occasional Papers No.91, IMF. Heller, P. S., Hemming, R., Kohnert, P., and staff team from Fiscal Affairs Department (1986), “Aging and Social Expenditure in the Major Industrial Countries, 1980-2025,” Occasional Papers No. 47, IMF. Hofmann, M., Kempkes, G., and Seitz, H. (2008), “Demographic Change and Public Sector Budgets in a Federal System,” paper prepared for research project Governance of federal systems: theoretical approaches and empirical evidence, No. 540/2-2. Hondroyiannis, G. and Papapetrou, E. (2000), “Do Demographic Changes Affect Fiscal Developments?" Public Finance Review, 28, 468-488. Jackson, H. and Matier, C. (2003), “Public Finance Implications of Population Aging: An Update,” Department of Finance Working Paper No. 3. Khan A. (1995), “Forecasting the Federal Budget with Time-Series Analysis, Public Budgeting,” Accounting and Financial Management, (1), 1-20. 232 | P a g e King, P. and Jackson, H. (2000), “Public Finance Implications of Population Aging,” Department of Finance Working Paper, No. 8. Lee, R. D. and Carter, L. (1992), “Modelling and Forecasting U.S. Mortality,” Journal of the American Statistical Association, 87 (419), 659-671, and "Rejoinder" same issue, 674-675. Lee, R. D. and Edwards, R. D. (2001), “The Fiscal Impact of Population Change,” presented in a conference organized by the Boston Federal Reserve Bank. OECD (1988), “Aging Populations,” The Social Policy Implications, Paris. OECD (1998), Meeting of the Employment Labour and Social Affairs Committee at Ministerial Level on Social Policy, background documents. “The Caring World: An Analysis,” Tables and Charts, Paris, 23-24 June 1998. http://www.oecd.org OECD (1996), “Aging in OECD Countries: A Critical Policy Challenge.” Paris. OECD (2001), “Aging and Income, Financial Resources and Retirement,” Paris. Sanz, I. and Velazquez, F. J. (2007), “The Role of Aging in the Growth of Government and Social Welfare Spending in the OECD,” European Journal of Political Economy, 23, 917-931. 233 | P a g e Takayama, N., Kitamura, Y., and Yoshida, H. (1998), “Generational Accounting in Japan,” Institute for Monetary and Economic Studies (IMES) Discussion Paper Series No. 98-E-1, Bank of Japan. Tse, Y. K., and Tsui, A. K. C. (2002), “A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations,” Journal of Business and Economic Statistics, 20, 351-362. United Nations, http://hdr.undp.org/en/ Singapore, Central Provident Fund (CPF), http://www.cpf.gov.sg Singapore, Ministry of Community Development, Youth and Sports (MCYS), http://www.mcys.gov.sg Singapore, Ministry of Education (MOE), http://www.moe.gov.sg Singapore, Ministry of Finance (MOF), http://www.mof.gov.sg Singapore, Ministry of Health (MOH), http://www.moh.gov.sg Singapore, Department of Statistics (DOS), http://www.singstats.gov.sg 234 | P a g e Tse, Y. K., and Tsui, A. K. C. (2002), “A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations,” Journal of Business and Economic Statistics, 20, 351-362. 235 | P a g e Appendix 3A Figure 3.44. FY2008 Budget Distribution 236 | P a g e Appendix 3B Table 3.9. Average Benefits Received in FY08 – Females Education Health Baby Bonus MCYS (Less Baby Bonus) National Development Information, Communication and Arts Environment and Water Resources Home Affairs Transport Trade & Industry Manpower Defence Foreign Affairs Finance Law Organs of State Average Benefit for each Age 755.87 574.37 71.57 107.03 34.34 51.86 151.89 208.68 163.21 38.75 2965.66 1-4 755.87 577.34 279.12 417.44 133.92 202.27 592.40 813.90 636.56 151.15 2965.66 5-9 1,417.80 755.87 583.44 401.42 600.35 192.59 290.90 851.96 1170.51 915.48 217.37 2965.66 505.25 505.25 505.25 10-14 15-19 20-24 5,556.38 12,631.00 14,204.45 755.87 164.84 164.84 0 458.07 477.33 414.38 685.08 713.88 619.73 219.78 229.01 198.81 331.96 345.91 300.29 972.21 1013.08 879.47 1335.72 1391.87 1208.31 1044.69 1088.61 945.03 248.06 258.48 224.39 2965.66 2965.66 2965.66 505.25 505.25 505.25 25-29 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 164.84 505.10 755.42 242.34 366.04 1072.03 1472.86 1151.95 273.52 2965.66 30-34 164.84 558.06 834.61 267.75 404.42 1184.42 1627.27 1272.71 302.20 2965.66 164.84 582.50 871.17 279.47 422.13 1236.29 1698.54 1328.45 315.43 2965.66 164.84 586.57 877.26 281.43 425.08 1244.93 1710.42 1337.74 317.64 2965.66 164.84 582.13 870.61 279.29 421.86 1235.50 1697.46 1327.61 315.23 2965.66 164.84 531.39 794.74 254.95 385.09 1127.83 1549.53 1211.91 287.76 2965.66 164.84 424.00 634.13 203.43 307.27 899.90 1236.38 966.99 229.61 2965.66 164.84 288.47 431.43 138.40 209.05 612.25 841.17 657.89 156.21 2965.66 4888.59 224.41 335.62 107.67 162.62 476.28 654.36 511.79 121.52 2965.66 4888.59 162.20 242.58 77.82 117.54 344.24 472.96 369.91 87.83 2965.66 75-79 4888.59 123.68 184.98 59.34 89.63 262.50 360.66 282.07 66.98 2965.66 80-84 4888.59 76.65 114.64 36.78 55.55 162.69 223.52 174.82 41.51 2965.66 85 & over 4888.59 65.54 98.03 31.45 47.50 139.11 191.13 149.48 35.49 2965.66 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 6638.98 9041.34 11879.08 16089.21 22795.42 23641.10 10485.49 11097.67 11380.22 11427.31 11375.94 10789.44 9547.96 7981.12 11964.26 11245.05 10799.83 10256.15 10127.72 Table 3.10. Average Benefits Received in FY08 – Males Education Health Baby Bonus MCYS (Less Baby Bonus) National Development Environment and Water Resources Information, Communication and Arts Home Affairs Transport Trade & Industry Manpower Defence Foreign Affairs Finance Law Organs of State Average Benefit for each Age 1-4 819.94 574.37 77.46 115.85 56.13 37.16 164.40 225.87 176.65 41.95 2965.66 819.94 577.34 296.99 444.17 215.22 142.49 630.33 866.01 677.32 160.82 2965.66 5-9 1409.98 819.94 583.44 435.28 650.99 315.44 208.84 923.84 1269.26 992.71 235.71 2965.66 505.25 505.25 505.25 10-14 5522.47 819.94 491.58 735.19 356.24 235.85 1043.32 1433.43 1121.10 266.20 2965.66 15-19 12606.52 143.75 506.32 757.23 366.92 242.92 1074.60 1476.40 1154.71 274.18 2965.66 20-24 14250.87 143.75 428.86 641.39 310.79 205.76 910.20 1250.53 978.06 232.23 2965.66 505.25 505.25 505.25 25-29 55-59 60-64 65-69 143.75 479.11 716.54 347.20 229.87 1016.86 1397.07 1092.67 259.45 2965.66 30-34 143.75 525.59 786.05 380.88 252.17 1115.50 1532.59 1198.66 284.62 2965.66 35-39 143.75 566.39 847.08 410.46 271.75 1202.11 1651.58 1291.73 306.71 2965.66 40-44 143.75 600.78 898.51 435.37 288.24 1275.09 1751.84 1370.14 325.33 2965.66 45-49 143.75 607.58 908.68 440.30 291.51 1289.52 1771.68 1385.65 329.02 2965.66 50-54 143.75 550.52 823.35 398.96 264.13 1168.43 1605.31 1255.53 298.12 2965.66 143.75 434.15 649.30 314.62 208.30 921.43 1265.95 990.12 235.10 2965.66 143.75 284.52 425.52 206.19 136.51 603.86 829.65 648.88 154.07 2965.66 6830.70 206.30 308.54 149.51 98.98 437.86 601.58 470.50 111.72 2965.66 70-74 6830.70 141.69 211.91 102.68 67.98 300.73 413.17 323.15 76.73 2965.66 75-79 6830.70 96.73 144.67 70.10 46.41 205.30 282.06 220.60 52.38 2965.66 80-84 6830.70 49.88 74.59 36.14 23.93 105.86 145.44 113.75 27.01 2965.66 85 & over 6830.70 32.87 49.16 23.82 15.77 69.77 95.86 74.97 17.80 2965.66 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 505.25 6265.93 8806.77 11821.59 16001.48 22579.70 23328.59 9658.68 10195.95 10667.71 11065.21 11143.84 10484.25 9138.87 7409.10 13191.84 12444.89 11925.09 11383.44 11186.88 237 | P a g e Appendix 3C Table 3.11. Average Taxes Paid in FY08 – Females INCOME TAX Corporate and Personal Income Taxes Statutory Boards' Contribution ASSETS TAXES Property Tax Estate Duty Custom & Excise Taxes Motor Vehicle Taxes Goods & Services Tax Betting DUTY Tax STAMP Stamp Duty Water conservation tax Other Taxes Fees & Charges 1-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 588.18 588.18 588.18 588.18 37.79 588.18 2882.87 588.18 7254.07 588.18 6597.87 588.18 5533.79 588.18 0 0 0 9.46 758.85 0 0 0 37.84 758.85 0 0 0 48.42 758.85 0 0 0 48.99 758.85 1317.35 34.75 819.71 114.91 657.35 206.11 48.76 758.85 889.63 1139.05 458.92 819.71 1517.57 657.35 526.36 47.33 758.85 889.63 1013.49 914.01 819.71 3022.48 657.35 455.12 45.54 758.85 889.63 1198.92 866.95 819.71 2866.86 657.35 449.00 46.19 758.85 889.63 1188.02 781.69 819.71 2584.92 657.35 479.04 47.38 758.85 889.63 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85 & over 4521.22 588.18 3249.88 588.18 2009.82 588.18 770.88 588.18 256.45 588.18 51.14 588.18 20.90 588.18 588.18 588.18 588.18 1245.11 680.12 819.71 2249.04 657.35 474.68 47.32 758.85 889.63 961.03 496.92 819.71 1643.25 657.35 497.49 47.08 758.85 889.63 1260.28 341.44 819.71 1129.08 657.35 502.21 46.57 758.85 889.63 1304.26 169.55 819.71 560.68 657.35 503.55 45.81 758.85 889.63 0 70.15 819.71 231.99 657.35 521.13 44.92 758.85 889.63 0 32.58 107.73 657.35 444.64 43.48 758.85 889.63 0 27.74 91.74 657.35 464.44 43.03 758.85 889.63 0 0 657.35 436.53 43.31 758.85 687.18 0 0 439.93 44.14 758.85 635.48 0 0 406.83 45.27 758.85 1356.50 1384.88 1395.46 1396.02 5473.40 10285.84 16418.43 15739.54 14328.57 12931.21 10609.39 9003.12 7068.47 4838.38 3573.59 3541.87 2484.23 2518.29 2434.61 Average Tax paid for each Age Group Table 3.12. Average Taxes Paid in FY08 – Males INCOME TAX Corporate and Personal Income Taxes Statutory Boards' Contribution ASSETS TAXES Property Tax Estate Duty Custom & Excise Taxes Motor Vehicle Taxes Goods & Services Tax Betting Taxes Stamp Duty Water conservation tax Other Taxes Fees & Charges 0-4 5-9 10-14 588.18 588.18 588.18 588.18 0 0 0 9.46 758.85 0 0 0 37.84 758.85 0 0 0 48.42 758.85 0 0 0 48.99 758.85 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85 & over 56.15 588.18 2256.19 588.18 9797.01 588.18 13950.58 588.18 15303.16 588.18 13620.90 588.18 10657.26 588.18 8031.38 588.18 4231.11 588.18 2355.52 588.18 773.68 588.18 371.24 588.18 588.18 588.18 588.18 0 43.09 819.71 142.51 657.35 194.31 48.76 758.85 889.63 1274.26 363.85 819.71 1203.18 657.35 508.59 47.33 758.85 889.63 1202.16 1116.22 819.71 3691.15 657.35 479.81 45.54 758.85 889.63 1077.28 1496.74 819.71 4949.48 657.35 476.74 46.19 758.85 889.63 1234.36 1632.93 819.71 5399.84 657.35 492.66 47.38 758.85 889.63 1161.19 1450.10 819.71 4795.26 657.35 463.46 47.32 758.85 889.63 1194.26 1143.24 819.71 3780.52 657.35 476.65 47.08 758.85 889.63 928.65 894.46 819.71 2957.82 657.35 484.76 46.57 758.85 889.63 1232.18 514.89 819.71 1702.66 657.35 491.79 45.81 758.85 889.63 1323.82 377.61 819.71 1248.71 657.35 528.37 44.92 758.85 889.63 0 200.47 662.93 657.35 483.66 43.48 758.85 889.63 0 163.58 540.94 657.35 531.64 43.03 758.85 889.63 0 0 657.35 558.17 43.31 758.85 614.58 0 0 676.13 44.14 758.85 737.34 0 0 811.18 45.27 758.85 Average Tax paid for each Age 1356.50 1384.88 1395.46 1396.02 4198.56 9367.13 20045.62 25710.74 27824.08 25251.97 21012.74 17057.36 11932.17 9592.70 5058.25 4544.45 2605.87 2681.89 2940.82 238 | P a g e [...]... -10 - 12 6 4 2 19 82 19 92 0 1971 -2 20 02 1981 1991 20 01 -4 -6 -8 USA-Females 6 UK-Females 4 4 2 0 -21 946 2 0 -21 9 42 Taiwan-Males 8 19 52 19 62 19 72 19 82 19 92 20 02 1956 1966 1976 1986 1996 20 06 1986 1996 20 06 -4 -6 -4 -8 -6 -8 -10 - 12 -10 -14 - 12 -16 USA-Males 3 8 6 4 2 1 19 42 -1 -3 -5 UK-Males 12 10 19 52 19 62 19 72 19 82 19 92 20 02 0 -21 946 -4 -6 1956 1966 1976 -8 -10 23 | P a g e 1.4.3 Estimation Results... F M -2. 85 -1.64 (0.44) (0.50) 0.08 -0.35 (0.10) (0.13) 0.31 2. 26 (0 .27 ) (0.47) 1. 32 -1.44 (0.30) (0.55) 0.44 0.70 (0.31) (0.37) -78.3 - 72. 3 -21 4.3 -100 .2 F -1.51 (0.31) -0.13 (0. 12) 0. 92 (0 .22 ) 1.03 (0.30) -0 .29 (0. 12) M -1.00 (0 .22 ) 0. 12 (0. 12) 0.65 (0 .24 ) 0.87 (0 .22 ) -0.16 (0.11) F -2. 62 (0. 32) -0.49 (0.07) 0.87 (0 .23 ) 1 .21 (0.19) 0.35 (0.17) M -2. 19 (0.38) -0 .28 (0.16) 1.13 (0.31) 0. 82 (0. 32) 0.10... 1996 20 06 -5 0 -21 946 -4 -6 1956 1966 1976 1986 1996 20 06 1996 20 06 -8 -10 -10 Japan-Males 3 Australia-Males 10 8 1 6 -11956 -3 1966 1976 1986 1996 20 06 4 2 -5 0 -21 946 -7 -4 -9 -11 1956 1966 1976 1986 -6 -8 -10 22 | P a g e Hong Kong-Females Taiwan-Females 6 2 4 0 -21 9 72 19 82 19 92 20 02 2 -4 0 1971 -2 -6 -8 -10 1981 1991 20 01 -4 - 12 -6 -14 -8 -16 Hong Kong-Males 12 10 8 6 4 2 0 -21 9 72 -4 -6 -8 -10 - 12. .. (0.85) (0 .28 ) -0.03 -0.16 -0.04 -0 .20 -2. 92 -0 .27 (0.80) (0. 12) (0.07) (0.14) (0.19) (0.06) 1.49 1.40 2. 92 2.53 2. 11 3. 62 (0.30) (0 .26 ) (0.19) (0 .21 ) (0. 32) (0. 62) 0.95 0.68 -0.49 -0.41 0.78 -1.84 (0 .25 ) (0 .29 ) (0.19) (0 .21 ) (0 .25 ) (0.75) 0 .26 -0.17 -0.04 -0.01 0.34 -0.55 (0.18) (0.19) (0.16) (0.17) (0 .23 ) (0.38) 28 | P a g e LogLikelihood Country Gender μ φ δ0 ξ1 γ1 LogLikelihood - 127 .0 - 122 .7 -22 7.5 Taiwan... 1.8 2. 2 2. 2 2. 0 1.8 1.8 JB test 3.4 3.4 5.6 6.8 2. 2 2. 4 Unit root test Augmented DF PP 0.3 -4.7 -2. 9 -1.8 1.0 -0.9 2. 2 -3.0 -0.5 -3.3 -0.4 -4.6 Country Gender Descriptive Statistics Mean Median Maximum Minimum Std deviation Skewness Kurtosis Taiwan USA UK F M F M F M 2. 9 6.6 40.4 -41.6 22 .4 -0 .2 2.1 1.9 1.1 32. 7 -28 .3 16.0 -0.03 2. 4 -15.8 -14.3 55.7 -67 .2 33 .2 0.3 2. 0 -6.7 -0.4 36.8 - 52. 6 25 .6 -0 .2 1.9... -2. 19 -1.57 -4.11 -3.03 (0.40) (0.45) (0.45) (0.33) (0.86) (0.68) φ -0.07 -0.17 -0 .21 -0 .26 -0.36 -0 .28 (0.18) (0.15) (0.13) (0.09) (0. 12) (0.13) α0 3.76 3.74 12. 74 9.51 9.53 7.81 (1. 12) (1.10) (2. 80) (2. 11) (2. 68) (2. 14) α1 0.54 0.47 0.35 0.35 0.57 0.49 (0 .27 ) (0 .24 ) (0.18) (0.16) (0 .27 ) (0 .25 ) LogLikelihood Diagnostic checks Q(4) Q2(4) - 123 .5 - 120 .8 -24 4.6 -22 9.6 -101.5 -98.14 0.14 3 .20 4.49 3. 42. .. sex for Australia (1945 -20 07), Japan (1955 -20 07), Hong Kong (1971 -20 08), Taiwan (1970 -20 08), U.K (1945 -20 06) and U.S (1941 -20 06) There are a total of 111 (0, 1, 2 110+) ages for each of the countries, with the exception of Hong Kong where only 101 ages (0, 1, 2 100+) are available And except for Hong Kong which is obtained from the Census and Statistics Department of Hong Kong2, the rest are culled... CCC-GARCH model, the conditional covariance matrix decomposed into conditional variances and correlations is The conditional correlation matrix represented by R is a constant and is independent of time The conditional covariance matrix is expressed as 1.11 1. 12 where R is the constant unconditional correlation matrix with for all i = N is a diagonal matrix containing the conditional volatility output... result, the conditional covariances are proportional to the product of the corresponding conditional volatility This simplification has significantly reduced the number of parameters to be estimated For the CCC-GARCH, VC-GARCH and DCC-GARCH models, the conditional variances and correlations are modeled instead of the conditional covariance matrix The conditional variance and conditional correlation matrix... -3.44 -3.19 -3.06 -1.36 -2. 92 -3.13 Maximum 11.9 1.91 9.71 8.60 2. 54 9.95 Minimum -9 .21 -10.4 -9.57 -7.95 -14.8 -11.6 Std deviation 3.60 2. 91 4.14 3.70 4 .21 4 .22 Skewness 1.63 -0.55 0.64 0.58 -0.73 0.67 Kurtosis 7.86 2. 98 3.06 3.06 3 .21 4. 02 JB test 74 .2 2.60 4 .22 3.47 3.39 4.38 Unit root test Augmented DF PP -5.95 -5. 92 -6.31 -7.05 -9.47 -9.74 -7.39 -8. 82 -6 .24 -15.3 -7.61 -8. 72 Country Gender Descriptive . to economic growth, life- cycle consumption, retirement annuity, defined contribution plans and fiscal sustainability. See Heijdra and Romp (20 09), Lau (20 09) and Alho et al. (20 08), among others Engle and Kroner (1995), CCC-GARCH model by Bollerslev (1990) and time-varying conditional correlation GARCH models (VC-GARCH and DCC-GARCH models by Tse and Tsui (20 02) and Engle (20 02) respectively 2. 9 6.6 40.4 -41.6 22 .4 -0 .2 2. 1 1.8 1.9 1.1 32. 7 -28 .3 16.0 -0.03 2. 4 0.7 -15.8 -14.3 55.7 -67 .2 33 .2 0.3 2. 0 3.7 -6.7 -0.4 36.8 - 52. 6 25 .6