This PhD thesis consists of four papers, whose major aim is to analyse the role of education in an endogenous growth setting. The theoretical framework uses computable OLG models, where the behaviour of individuals is modelled within a lifecycle framework. Firstly, in order to build computable general equilibrium models that are reliable for policy analysis, it is necessary to reproduce all major stylised facts that characterise lifecycle profiles, notably: i) the marked decline in consumption around retirement age; and, ii) in old age, financial wealth data drawn from surveys run down at a slower pace than that implied by usual formulations of the lifecycle theory of consumption. In the first paper, it is argued that a lifecycle framework can reproduce the above-mentioned facts if one assumes: i) uncertainty in the duration of life in a model with imperfect annuity markets; and, ii) existence of a “sufficiently” strong bequest motive. Secondly, it is shown that education choices can play a major role in dampening the negative impact on economic growth of a decline in fertility. In the second paper, it is found that the growth assumption (endogenous versus exogenous) does matter. In an endogenous growth model driven by education, a negative demographic shock represents an “investment opportunity” in education. The rise in education, together with the externalities in human capital formation bring about a permanent increase in labour productivity. Thirdly, in an OLG model with an externality in the education sector, it is important to investigate the set of policies that decentralises the social optimum, depending on some major model assumptions. In the third paper, using calibrations that assume altruism, the results suggest that optimal policies involve basically: a) an education subsidy; and, b) a PAYG pension. Fourthly, given the complementary of education and R&D, it is important to investigate if the adoption of optimal policies to correct a number of externalities causes a leverage effect on growth and welfare. The framework developed in the fourth paper provides for a numerical evaluation of the relative importance of two sources of inefficiency, namely: i) a “market-power” distortion, resulting from the mark-up pricing of intermediate goods; ii) versus the inefficiency in the allocation of resources caused by various “externalities”, affecting the education and R&D sectors. Overall, the results obtained highlight the importance of treating human capital as an endogenous variable.
1. INTRODUCTION 5 2. CHAPTER: THE ROLE OF ALTRUISM AND LIFETIME UNCERTAINTY IN SHAPING LIFECYCLE PROFILES† 15 2.1 Introduction 16 2.2 Some stylised facts about age profiles 20 2.3 An “illustrative” model 24 2.4 The model 25 2.4.1 The death risk and the financial endowment at birth 26 2.4.2 The resource constraints 27 2.4.3 The value function 29 2.4.4 The optimal consumption profile 31 2.4.5 The production function of human capital 34 2.4.6 The optimal profile for human capital 35 2.5 The competitive equilibrium and general equilibrium conditions 37 2.5.1 The competitive equilibrium 37 2.5.2 The general equilibrium conditions 38 2.6 The model’s calibrations 39 2.6.1 General considerations about the calibration process 40 2.6.2 The calibration strategy 40 2.6.3 The relevant ages in the calibrations and the mortality curve 41 2.6.4 Conditions relative to human capital formation 42 2.6.5 Major conditions used in the calibrations 43 2.6.6 Major results of the calibrations 45 2.7 Presentation of age profiles 46 2.7.1 Major characteristics of the simulated age profiles for consumption and financial wealth 50 2.7.2 The age profile for “indebtedness” 53 2.7.3 The liquidity constraint simulation 53 2.8 Conclusions 54 2.9 Annex I: The solution of the “illustrative” two-periods OLG model 55 2.10 Annex II: The individual’s maximisation programme is separable 56 2.11 Annex III: Conditions for the existence of the value function 57 2.12 Annex IV: The allocation of human capital 59 2.13 Appendix: The OLG model with the liquidity constraint 61 2.13.1 Determination of the optimal age profile for human capital 63 2.13.2 Determination of the optimal age profile for consumption 64 2.14 References 65 3 CHAPTER: ENDOGENOUS VERSUS EXOGENOUS GROWTH FACING A FERTILITY SHOCK† 69 3.1 INTRODUCTION 70 3.2 THE OLG FRAMEWORK 74 3.2.1 The insurance market 74 3.2.2 The wealth constraint 75 3.2.3 Human capital 77 3.2.4 The optimisation programme 78 3.2.5 The solution 78 3.3 THE COMPETITIVE EQUILIBRIUM 80 3.4 THE CALIBRATION STRATEGY 81 3.4.1 The relevant ages in the calibrations and the mortality curve 83 3.4.2 Conditions relative to human capital formation 84 3.4.3 Major stylised facts/conditions used in the calibrations 85 3.4.4 Some results of the calibrations for the three scenarios considered 87 3.5 The impact of a permanent fertility shock 88 3.5.1 The set-up for simulations 88 3.5.2 The fertility shock 89 3.5.3 The economy growth rate 91 3.5.4 The labour productivity 93 3.5.5 The intensity of investment in education 94 3.6 Conclusions 96 3.7 References 97 4. CHAPTER: A PAYG PENSION AS A FIRST-BEST OPTIMAL POLICY† 102 4.1 Introduction 103 4.2 The optimisation programme 107 4.3 The government’s budget constraint 111 4.4 The social planner’s problem 112 4.5 Decentralisation of the social optimum in a competitive equilibrium 116 4.6 Calibration and balanced growth results 117 4.6.1 Values 117 4.6.2 Results 121 4.7 A baby boom-baby bust demographic shock 124 4.8 Conclusions 128 4.9 Annex 129 4.10 References 137 5 CHAPTER: “MARKET-POWER” VERSUS “EXTERNALITIES” AS SOURCES OF INEFFICIENCY† 140 5.1 Introduction 141 5.2 An individual’s optimisation programme 144 5.2.1 The optimal private level of education 147 5.2.2 The optimal private level of consumption 150 5.3 The production side of the economy 151 5.3.1 The final goods sector 151 5.3.2 The R&D sector 152 5.3.3 The maximisation programme for final output producers 155 5.3.4 Profit maximisation in the production of intermediate goods 156 5.3.5 Derivation of the balanced equilibrium growth rates 157 5.3.6 Derivation of the free entry condition in the R&D sector 158 5.3.7 Derivation of the optimal private allocation of human capital, and of the growth rate of technology 160 5.4 Derivation of the aggregate value-added and the government budget equations 161 5.5 The social optimum 163 5.6 The decentralisation of the social optimum in a balanced growth equilibrium 164 5.7 Calibration and balanced growth results 165 5.7.1 Calibration of the CSI equilibrium 166 5.7.2 The OGP equilibrium 171 5.7.3 Comparative results for the two equilibria 172 5.7.4 Sensitivity analysis of the social discount rate 173 5.7.5 Sensitivity analysis of the intertemporal elasticity of substitution in consumption 174 5.8 Conclusions 176 5.9 Annex I: Derivation of optimal policies 176 5.10 Annex II: Stationarisation of the model and conditions used to calibrate it 181 5.11 References 187