Essays on forecasting life expectancy and fiscal sustainability 1

ESSAYS ON FORECASTING LIFE EXPECTANCY AND FISCAL SUSTAINABILITY TAN SIOK HONG (BACHELOR OF ARTS, NUS; BACHELOR OF SOCIAL SCIENCES (HONS.), NUS; MASTERS OF SOCIAL SCIENCES (APPLIED ECONOMICS), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2011 ACKNOWLEDGEMENTS I would first like to express my deepest gratitude to my supervisor, Associate Professor Chia Ngee Choon, for her willingness to supervise me, her unlimited patience, motivation and constant encouragement. This thesis would not be possible without her valuable guidance, generous suggestions and support. I am equally grateful to my co-supervisor, Associate Professor Tsui Ka Cheng, Albert. I have benefited greatly from his constructive ideas and generous coaching, especially the technical aspects of my research. His interest in research work and encouragement has kept me interested and motivated throughout. I would also like to extend appreciation to other Faculty staff who have previously taught and helped me, not forgetting the staff of the Economics Department and my friends in NUS for their support and advice. Last but not the least, I am greatly indebted to my family and loved ones. This had been a long journey and I am very fortunate to receive their constant encouragement and support while I pursue my dream. ii TABLE OF CONTENTS Acknowledgements ii Table of Contents iii Overview List of Tables v viii List of Figures x Essay 1: Forecasting Life Expectancy 1.1. Introduction 1.2. Literature Review 1.3. Empirical Model 1.4. Data and Estimation Results of LC-GARCH Models 16 1.5. Multivariate Conditional Volatility Models 30 1.6. Lee-Carter Model with Time-Varying Correlations 41 1.7. Estimation Results of LC-VC-GARCH Model 43 1.8. Forecast Comparisons 54 1.9. Concluding Remarks 62 References 65 Appendix 1A 75 Essay 2: Forecasting Real GDP Growth Rates Using Mortality Index 79 2.1. Introduction 79 iii 2.2. Literature Review 85 2.3. Data and Variables 91 2.4. VC-MGARCH Model 102 2.5. Estimation Results 106 2.6. Discussion 113 2.7. EGARCH-in-Mean Forecasting Model 118 2.8. Concluding Remarks 127 References 128 Essay 3: Fiscal Impacts of Population Ageing in Singapore 139 3.1. Introduction 139 3.2. Literature Review 143 3.3. Lee & Edwards (2001) Model 150 3.4. Population Ageing and Budgetary System in Singapore 156 3.5. Age Specific Benefit and Taxes 170 3.6. Projecting Demographic Changes in Singapore 186 3.7. Projected Fiscal Pressures for Singapore 200 3.8. Discussion 220 3.9. Concluding Remarks 226 References 229 Appendix 3A 236 Appendix 3B 237 Appendix 3C 238 iv OVERVIEW This thesis covers three broad objectives. Firstly, we extend an existing popular mortality model to improve forecasts of mortality and life expectancy rates. Secondly, we use the improved demographic projections as inputs and show that it is capable of enhancing the performance of term spread in generating forecasts of GDP growth rates. Lastly, as mortality changes directly affect fiscal sustainability, we use the improved demographic projections to examine the fiscal impacts of population ageing in Singapore. The first essay is focused on improving forecasts of life expectancy rates. The Lee-Carter (LC) model is a popular model but being a simple model, it assumes homoskedasticity. We believe that there is scope to value-add to the existing literature by relaxing this assumption. Essay one first extends the classical LC model with GARCH-type structures to allow for volatility clustering in its time-varying component. This allows us to model the presence of conditional volatility in mortality rates. Next, the model is further extended with time-varying multivariate GARCH models to account for, not just conditional volatility, but also the presence of conditional correlations between the male and female mortality series. The idea is that male and female populations within each country are exposed to the same underlying demographic history, medical and other conditions, resulting in a certain degree of correlations between their mortality data series. In essay one, we show that modeling both the presence of conditional volatility and correlations offer the greatest improvements to forecasts of life expectancy at birth and at retirement age. v In the second essay, we are interested to examine if including the use of demographic projections can enhance the usefulness of the term spread in forecasting GDP growth rates. Term spread has been commonly used to forecast real GDP growth rates but evidences of its forecasting ability have been mixed across countries and overtime. There are also signs that its forecasting ability has declined over the years. In essay two, we seek to examine both the relevance of term spread as well as the contributions of mortality indexes in forecasting real GDP growth rates. We first use multivariate GARCH models to investigate the evidence of conditional correlations between real GDP growth rates, term spreads and mortality indexes, which has not been attempted in the literature. Next, we show that including the use of conditional volatility of male mortality indexes, together with term spreads, helps to improve forecasts of real GDP growth rates. This finding supports that the improved demographic forecasts in essay one using LC method extended with multivariate GARCH model has important and useful implications towards macroeconomic forecasting. In the last essay, we are primarily interested in the study of the fiscal impacts of population ageing in Singapore. Demographic changes produce direct and significant effects on fiscal sustainability and with a rapidly ageing population in Singapore, the demographic shift caused by a shrinking working age group and smaller income tax base is expected to impose increasingly important fiscal implications. In order to derive an accurate assessment of future fiscal burdens brought about by demographic pressures, it is important to have accurate projections of future population changes. Using the methodology of stochastic vi demographic projections obtained from the LC method extended with time-varying multivariate GARCH model in essay one, we first project how the population ageing problem is expected to worsen in Singapore and how it will impact the government fiscal position over the next twenty years. The baseline results show that the fiscal support ratio for Singapore will fall and the cost of providing existing benefit policies will inevitably increase as population ages. In addition to the case of pure demographic effects, we also included several calibration analysis to account for an increase in immigration figures, an extension of retirement age, an increase in female labor force participation rates, and an increase in labor force productivity rates. The calibration results supports that the rate of decline in the fiscal support ratio under the baseline scenario will be moderated with higher immigrant inflow, extended retirement age, larger female labor force and higher labor force participation rates. vii LIST OF TABLES Essay 1: Forecasting Life Expectancy 1.1 Descriptive Statistics and Unit Root Tests for Time-Varying Mortality Index 1.2 Descriptive Statistics & Unit Root Tests for Time-Varying Mortality Index after First Differencing 1.3 Estimated Parameters of LC-Univariate GARCH Model 1.4 Estimated Parameters of LC-EGARCH Model 1.5 Estimated Parameters for LC-CCC-GARCH Model 1.6 Estimated Parameters for LC-VC-GARCH Model 1.7 Forecast Error Comparison: Life expectancy at Age 1.8 Forecast Error Comparison: Life expectancy at Age 65 1.9 Actual & Forecasted e0 under LC-VC-GARCH, LC-GARCH & LC- Random Walk with Drift Models 1.10 Actual & Forecasted e65 under LC-VC-GARCH, LC-GARCH & LC-Random Walk with Drift Models Essay 2: Forecasting Real GDP Growth Rates Using Mortality Index 2.1 Variables and Period of Data Used 2.2 Descriptive Statistics 2.3 Pearson Product-Moment Correlations by Country 2.4 Estimation Results for VC-MGARCH Model 2.5 Model I: Parameter Estimates and Diagnostic Tests viii 2.6 Model II: Parameter Estimates & Diagnostic Tests 2.7 Forecast Results of Annual Real GDP Growth Rates 2.8 Forecast Error Measurements Essay 3: Fiscal Impacts of Population Ageing in Singapore 3.1 Share of Singapore Residents, Non-Residents and Average Growth Rates 3.2 Age Composition for Total Population, 1980 & 2009 3.3 Number of Working-Age Population to Sustain Each Elderly, 1980-2008 3.4 FY2008 Revised Operating & Development Expenditure 3.5 Categorization of Benefits (Age-Specific, Public & Social Goods and Services) 3.6 FY2008 Revised Revenue Receipts 3.7 Parameter Estimates for LC-VC-GARCH Models 3.8 Summary of Fiscal Support Ratios for Baseline Case 3.9 Average Benefits Received in FY08 – Females 3.10 Average Benefits Received in FY08 – Males 3.11 Average Taxes Paid in FY08 – Females 3.12 Average Taxes Paid in FY08 – Males ix LIST OF FIGURES Essay 1: Forecasting Life Expectancy 1.1 Plots of Time-Varying Mortality Index 1.2 Plots of Time-Varying Mortality Index After First Differencing 1.3 Plots of Conditional Volatility Under LC-Univariate GARCH Models 1.4 Plots of Conditional Volatility Under LC-VC-GARCH Models 1.5 Plots of Time-Varying Correlations 1.6 Actual and Forecast Values for Life Expectancy at Birth 1.7 Actual and Forecast Values for Life Expectancy at Age 65 Essay 2: Forecasting Real GDP Growth Rates Using Mortality Index 2.1 Annual Real GDP Growth Rates 2.2 Annual Term Spreads & Recessions 2.3 Annual Mortality Indexes for Males and Females 2.4 Time Paths of Conditional Correlations 2.5 Conditional Volatility with Recession Periods Essay 3: Fiscal Impacts of Population Ageing in Singapore 3.1 Population Ageing Caused by Lower Fertility Rates - Lower Benefits & Lower Taxes 3.2 Population Ageing Caused by Lower Fertility Rates - Lower Benefits & Higher Taxes x 3.3 Time-Line of Demographic Changes 3.4 Age Pyramid for Singapore, Males and Females 3.5 Total Fertility Rates, 1960-2008 3.6 Crude Death Rates, 1960-2008 3.7 Age-Specific Death Rates, 1997 & 2008 3.8 Life Expectancies at Birth and Age 65 3.9 Young, Old and Total Dependency Ratios 3.10 Operating Revenue, Expenditure Outlay and Budget Position, 1999-2008 3.11 Budget Surpluses/Deficits, 1996-2008 3.12 Expected Growth in Elderly Healthcare Consumption 3.13 Average Benefit by Age in FY2008 - Females 3.14 Average Benefit by Age in FY2008 - Males 3.15 Average Tax Payments by Age in FY2008 - Females 3.16 Average Tax Payments by Age in FY2008 - Males 3.17 Plots of Conditional Volatility Under LC-VC-GARCH Models 3.18 Plot of Time-Varying Correlations between Male & Female Population Series 3.19 Age Pyramid, Actual 2009 & Projected 2029 3.20 Old Age Support Ratio, Actual 2009 & Projected 2029 3.21 Projected Female Population Structure, 2009-2029 3.22 Projected Male Population Structure, 2009-2029 3.23 Projected Changes in Female Dependency Ratios, 2009-2029 3.24 Projected Changes in Male Dependency Ratios, 2009-2029 3.25 Projected Changes in Total Dependency Ratios, 2009-2029 xi 3.26 Projected Government Revenue and Expenditure, 2010-2029 3.27 Projected Budget Surplus/Deficit, 2010-2029 3.28 Projected Fiscal Support Ratio, 2010-2029 3.29 Required Change in b(t) for Budget Balance 3.30 Required Change in d(t) for Budget Balance 3.31 Projected Dependency Ratios with 5% Yearly Increase in Immigrants 3.32 Projected Budget Surplus/Deficit with 5% Yearly Increase in Immigrants 3.33 Projected Fiscal Support Ratios with 5% Yearly Increase in Immigrants 3.34 Projected Fiscal Support Ratios with 10% Yearly Increase in Immigrants 3.35 Projected Dependency Ratios with Retirement Age Raised to 70 3.36 Projected Budget Surplus/Deficit with Retirement Age Raised to 70 3.37 Projected Fiscal Support Ratio with Retirement Age Raised to 70 3.38 Projected Budget Surplus/Deficit with 1% Yearly Increase in FLFPR 3.39 Projected Fiscal Support Ratio with 1% Yearly Increase in FLFPR 3.40 Projected Budget Surplus/Deficit with Yearly Reductions in Labor Productivity 3.41 Projected Fiscal Support Ratios with Yearly Reductions in Labor Productivity 3.42 Projected Budget Surplus/Deficit with Yearly Increase in Labor Productivity 3.43 Projected Fiscal Support Ratio with Yearly Increase in Labor Productivity 3.44 FY2008 Budget Distribution xii [...]... Singapore, Males and Females 3.5 Total Fertility Rates, 19 60-2008 3.6 Crude Death Rates, 19 60-2008 3.7 Age-Specific Death Rates, 19 97 & 2008 3.8 Life Expectancies at Birth and Age 65 3.9 Young, Old and Total Dependency Ratios 3 .10 Operating Revenue, Expenditure Outlay and Budget Position, 19 99-2008 3 .11 Budget Surpluses/Deficits, 19 96-2008 3 .12 Expected Growth in Elderly Healthcare Consumption 3 .13 Average... 3 .14 Average Benefit by Age in FY2008 - Males 3 .15 Average Tax Payments by Age in FY2008 - Females 3 .16 Average Tax Payments by Age in FY2008 - Males 3 .17 Plots of Conditional Volatility Under LC-VC-GARCH Models 3 .18 Plot of Time-Varying Correlations between Male & Female Population Series 3 .19 Age Pyramid, Actual 2009 & Projected 2029 3.20 Old Age Support Ratio, Actual 2009 & Projected 2029 3. 21 Projected... Retirement Age Raised to 70 3.37 Projected Fiscal Support Ratio with Retirement Age Raised to 70 3.38 Projected Budget Surplus/Deficit with 1% Yearly Increase in FLFPR 3.39 Projected Fiscal Support Ratio with 1% Yearly Increase in FLFPR 3.40 Projected Budget Surplus/Deficit with Yearly Reductions in Labor Productivity 3. 41 Projected Fiscal Support Ratios with Yearly Reductions in Labor Productivity 3.42 Projected... Population Structure, 2009-2029 3.22 Projected Male Population Structure, 2009-2029 3.23 Projected Changes in Female Dependency Ratios, 2009-2029 3.24 Projected Changes in Male Dependency Ratios, 2009-2029 3.25 Projected Changes in Total Dependency Ratios, 2009-2029 xi 3.26 Projected Government Revenue and Expenditure, 2 010 -2029 3.27 Projected Budget Surplus/Deficit, 2 010 -2029 3.28 Projected Fiscal. .. Support Ratio, 2 010 -2029 3.29 Required Change in b(t) for Budget Balance 3.30 Required Change in d(t) for Budget Balance 3. 31 Projected Dependency Ratios with 5% Yearly Increase in Immigrants 3.32 Projected Budget Surplus/Deficit with 5% Yearly Increase in Immigrants 3.33 Projected Fiscal Support Ratios with 5% Yearly Increase in Immigrants 3.34 Projected Fiscal Support Ratios with 10 % Yearly Increase... Support Ratios with Yearly Reductions in Labor Productivity 3.42 Projected Budget Surplus/Deficit with Yearly Increase in Labor Productivity 3.43 Projected Fiscal Support Ratio with Yearly Increase in Labor Productivity 3.44 FY2008 Budget Distribution xii . Essay 1: Forecasting Life Expectancy 1 1. 1. Introduction 1 1. 2. Literature Review 4 1. 3. Empirical Model 9 1. 4. Data and Estimation Results of LC-GARCH Models 16 1. 5. Multivariate Conditional. 10 2 2.5. Estimation Results 10 6 2.6. Discussion 11 3 2.7. EGARCH-in-Mean Forecasting Model 11 8 2.8. Concluding Remarks 12 7 References 12 8 Essay 3: Fiscal Impacts of Population. 13 9 3 .1. Introduction 13 9 3.2. Literature Review 14 3 3.3. Lee & Edwards (20 01) Model 15 0 3.4. Population Ageing and Budgetary System in Singapore 15 6 3.5. Age Specific Benefit and