ISBN: 3540222685
TITLE: Social Security, Demographics and Risk
AUTHOR: C. Borgmann
TOC:

List of Symbols XIII
List of Abbreviations XIV
1 Introduction 1
2 Fundamental Results on Social Security in a Deterministic Economy 5
2.1 PAYG versus Funded Social Security under Certainty 6
2.1.1 The Framework 6
2.1.2 The Budget Constraint Under a Funded System 6
2.1.3 The Budget Constraint Under PAYG Social Security 7
2.2 The Equivalence of Public Debt and Social Security 8
2.2.1 An Economy with Public Debt 8
2.2.2 Equivalence in a Microeconomic Context 9
2.2.3 Equivalence in a Macroeconomic Context 10
2.3 The Present Value of the Perpetual Implicit Tax of PAYG Social Security 12
2.3.1 A Simple Proof 12
2.3.2 Policy Implications of the Equality of the Perpetual Implicit Tax and Benefit Payments 13
2.3.3 Dynamic Efficiency, Inefficiency, Social Security, Bubbles, and Land 15
2.3.4 On the Discussion of Switching Regimes 16
2.4 The Typology of Social Security and Further Issues 17
2.4.1 The Indexation of Benefits: Wage Indexation and Demographic Indexation 18
2.4.2 Social Security and Incentives to Retire Early 19
2.4.3 Bismarckian versus Beveridgean Social Security 23
2.5 Summary 25
3 Social Security and Demographic Transition 31
3.1 Demographic Trends Around the World 31
3.1.1 Fertility and Life-Expectancy: 1950  2050 32
3.1.2 Changes in the Population Size and the Age Structure 34
3.1.3 The Old-Age Dependency Ratio: 19502050 40
3.2 Implications of Demographic Transition 42
3.2.1 Aging and Fiscal Sustainability 42
3.2.2 Aging, Factor Prices, Capital Flows, and Pension Reform: A Survey 44
4 Old-Age Provision and Uncertainty: An Introduction to Issues of Risk and Risk Sharing 51
4.1 A Primer on Intergenerational Risk Sharing and Social Security 51
4.2 Old-Age Income and Sources of Aggregate Risk 54
4.2.1 Productivity Risk and Valuation Risks 54
4.2.2 Demographic Risk 56
4.2.3 Political Risk 59
4.3 Overview 59
5 Labor Income Risk, Demographic Risk, and the Design of (Wage-Indexed) Social Security 63
5.1 A Simple Overlapping Generations Model with Stochastic Labor Income and Stochastic Population Growth 64
5.2 PAYG Pension Programs in a Small Open Economy with Stochastic Labor Income and Population Growth 66
5.2.1 Defined Contribution Income Indexation 66
5.2.2 Defined Benefit Income Indexation 68
5.3 Defined Contribution and Defined Benefits in a Closed Economy 71
5.3.1 Life-Cycle Resources under Defined Contribution and Defined Benefit 71
5.3.2 Variance of Life-Cycle Resources under Defined Contribution 72
5.3.3 Defined Benefit versus Defined Contribution 73
5.4 Between Defined Contribution and Defined Benefit: Optimal Demographic Indexation 75
5.4.1 Optimal Demographic Indexation in a Small Open Economy 75
5.4.2 Optimal Demographic Indexation in a Closed Economy 77
5.5 Further Issues 79
5.5.1 Uncertain Life-Expectation 79
5.5.2 Ex-Ante versus Ex-Post Risk Sharing 81
5.6 Summary 82
6 Demographics and Political Risks of Benefit Rule Changes:
A Case Study for Germany 85
6.1 A Chronicle of the German Benefit Formula 87
6.1.1 The History of the German Gesetzliche Rentenversicherung 87
6.1.2 The Benefit Formula: A General Description 88
6.1.3 The Benefit Formula from 1957 to 2001: A Moving History 90
6.1.4 Disability, Incapability, Unemployment and Part-Time Work: One Thousand and One Ways to Retire Even Earlier than Early 94
6.2 The Volatility of Individual Social Security Wealth: A Cohort Analysis of the Generosity of the Benefit Rule 99
6.2.1 A Measure of Relative Generosity 100
6.2.2 The Impact of Benefit Rule Changes on Relative Generosity for Selective Cohorts 102
6.2.3 Discussion and Caveats 108
6.3 Demographics and Population Projections 109
6.3.1 Demographic Developments of the Past Decades 109
6.3.2 On the Precision of Past Population Projections 111
6.4 Demographic Development and Benefit Rule Changes 113
6.4.1 TimeSeries Analysis of Relative Generosity 114
6.4.2 Estimating a Policy Function of Generosity: Does Germany Have an Implicit Demographic Factor? 115
6.5 Future Changes: What Does It Take To Make the GRV Sustainable? 118
6.5.1 Applying Generational Accounting to the Public Pension Scheme 119
6.5.2 Soft Transition  An Alternative Indicator of Sustainablility 122
6.5.3 Quantifying Sustainability Under Status Quo: Results 123
6.6 Summary 125
7 Social Security, Portfolio Choice, and Financial Markets 127
7.1 Social Security and Optimal Portfolio Diversification 127
7.1.1 Portfolio Choice in the Presence of Social Security 128
7.1.2 A Portfolio Approach to Designing Social Security 134
7.1.3 More Diversification: Real Estate and International Assets 139
7.1.4 Strategic Asset Allocation and Portfolio Choices Over the Life-Cycle 143
7.2 Social Security and Financial Instruments 146
7.2.1 Annuities and Inflation-Indexed Annuities 147
7.2.2 Exploiting the Equity Premium versus Costs of Minimum Benefit Guarantees 149
7.2.3 Potential New Financial Instruments: Innovative Government Debt Management and Macro-Markets 151
8 Conclusion 153
Appendices 155
A Mathematical Appendix 155
A.1 Derivation of the Variance of y^DC_t 155
A.2 Derivation of the Variance of y^DB_t in a Small Open Economy 155
A.3 Derivation of the Variance of y^DB_t with Macroeconomic Feedback 156
A.4 Proof that E[y_t] is Strictly Increasing in rho 157
A.5 Derivation of the Variance Under the General Demographic Indexation Policy in a Closed Economy 157
A.6 The Effect of Changing the Statistical Calculation of the Benefit Formula 158
Appendix: Tables 161
B.1 Regions and Country-Groups 161
B.2 Further Information on the GRV 162
B.3 Tables for Efficient Portfolio Frontier 164
References 165
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