"Pensionomics" puts forward a portfolio perspective on the combination of funded and unfunded pension arrangements. In a second-best type argument it is formally shown that a Pay-As-You-Go pension system can substitute the tradability of human capital: if risk-averse investors were able to directly invest into the present value of future labour income, they would allocate their pension portfolios in both human and physical capital. While this ideal form of diversification can not be implemented due to the imperfection of capital markets, one can design a typical Pay-As-You-Go system in such a way that it allows for the same intertemporal consumption allocations as the first-best solution. This replication works regardless of the demographic development. Therefore, PAYGO should play a key role in optimising the risk-return combinations for old-age savings.
Part 1 The Problem
1 Global Aging and Pensionomics 3
1.1 Global Aging 4
1.2 Pension Problem 12
1.3 Objective and Synopsis 16
2 Methodical Foundation 19
2.1 Outline and Requirements 19
2.2 Theoretical Background 23
2.2.1 Neoclassical Paradigm 23
2.2.2 Portfolio Approach 27
2.2.3 Asset Pricing 31
2.2.4 Production and q-Theory 35
2.2.5 Growth Theory 37
2.2.6 Public Finance 44
2.3 Summary and Survey of Approach 46
Part 11 The Model
3 Tradable Human Capital 53
3.1 Population and Overview 53
3.1.1 Overlapping Generations Framework 53
3.1.2 Outline of Model 56
3.2 Consumption and Capital Technologies 57
3.2.1 Macroeconomic Production Function 57
3.2.2 Capital Adjustment Technology 59
3.2.3 Price of Real Capital and Q-Ratio 61
3.2.4 Real Capital's Rental and Return 62
3.2.5 Extreme Cases 63
3.2.6 Illustrative Example Economy 65
3.3 Financial Markets Description 66
3.3.1 Real Capital Security 66
3.3.2 Human Capital Security 68
3.3.3 Riskless Security 71
3.3.4 Capital Market and Summary 72
3.3.5 Full Depreciation 73
3.3.6 Illustrative Example Economy 75
3.4 Optimization by Agents 76
3.4.1 Utility Assumptions 76
3.4.2 Budget Constraints 79
3.4.3 Optimal Policies 81
3.4.4 Stochastic Discount Factor 85
3.4.5 Summary of Policies 88
3.4.6 Illustrative Example Economy 88
3.5 Capital Market Equilibrium 90
3.5.1 Aggregating Assumptions 90
3.5.2 Deriving Equilibrium 92
3.5.3 Market Portfolio Weights 96
3.5.4 Returns and Interest Rate 98
3.5.5 SDF Approach 100
3.5.6 Full Depreciation 102
3.5.7 Illustrative Example Economy 104
3.6 General Equilibrium 107
3.6.1 Consumption by Cohorts 107
3.6.2 Investment-Output Ratio 110
3.6.3 Goods Market Equilibrium 114
3.6.4 Full Depreciation 116
3.6.5 Illustrative Example Economy 117
3.7 Summary for Tradable Human Capital 118
4 Replication with PAYGO 121
4.1 Incomplete Markets and Overview 121
4.1.1 First- versus Second-best 121
4.1.2 Outline of Replication 124
4.2 Mimicking Economy 126
4.2.1 Maintained Setting 126
4.2.2 Public Sector 129
4.2.3 Agents' Utility and Budget Constraints 132
4.2.4 Summary of Mimicking Economy 134
4.2.5 Full Depreciation and Numerical Example 134
4.3 Solving the Mimicking Economy 138
4.3.1 Failure of Standard Approaches 139
4.3.2 Aggregation and Capital Market Participation 142
4.3.3 Alternative Characterization 144
4.3.4 Sustainability and Integration 146
4.3.5 Full Depreciation and Numerical Example 149
4.4 Replicating Tradability 150
4.4.1 Replication Set-up 150
4.4.2 Solving the Replication 152
4.4.3 Analyzing the Solution 155
4.4.4 Full Depreciation 159
4.4.5 Case of Merton [1983] 163
4.4.6 Illustrative Example Economy 165
4.5 Summary of Replication 167
Part III The Implications
5 Discussion and Assessment 173
5.1 Overview .173
5.2 Analyzing the Framework 176
5.2.1 Asset Pricing and Allocation 176
5.2.2 National Income 181
5.2.3 National Wealth 183
5.2.4 Replication with PAYGO 190
5.2.5 Growth Theory .194
5.2.6 Full Depreciation 198
5.2.7 Illustrative Example Economy 201
5.2.8 Replication of Illustrative Example Economy 203
5.3 Technological Progress 206
5.3.1 Stochastic Growth Theory 207
5.3.2 Factor Incomes in Cobb-Douglas Case 212
5.3.3 Implications for PAYGO 216
5.4 Design of PAYGO Schemes 219
5.4.1 Risk Diversification 219
5.4.2 Earning Points and Indexation 226
5.4.3 Replication Framework and Existing PAYGO Schemes .231
5.5 Summary of Implications 237
6 Conclusion and Further Research 241
6.1 The Model and its Implications 241
6.2 Outlook an Pensionomics 245
Part IV Appendices
A Methodological Foundation 253
A.1 Asset Pricing .253
A.2 Growth Theory .254
B Tradable Human Capital 255
B.1 Optimization by Agents 255
B.1.1 Optimization by Middle-aged 255
B.1.2 Optimization by Young 256
B.1.3 Stochastic Discount Factor 258
B.2 Capital Market Equilibrium 259
B2.1 Deriving Equilibrium 259
B.2.2 Market Portfolio Weights 261
B.3 General Equilibrium 263
B.3.1 Consumption .263
B.3.2 Investment-Output Ratio 264
B.3.3 Full Depreciation 269
C Replication with PAYGO 271
C.1 Replicating Tradability 271
C.1.1 Derivation of (4.4.14) 271
C.1.2 Derivation of Public Sector Parameters 272
C.2 Full Depreciation 274
C.2.1 Replicating Parameters 274
C2.2 Alternative Derivation 276
D Discussion and Assessment 279
D.1 Analyzing the Framework 279
D.2 Technological Progress .280
D.2.1 Stochastic Growth Theory 280
D.2.2 Derivation of Stationary Distribution 281
D.2.3 Cobb-Douglas Case 282
Part V Lists and References
List of Tables 287
List of Figures 289
Symbols and Abbreviations 291
References 295
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