3sec_simp_13_b - The Three Sector Growth Model part 1 T Roe AP8701 Contents 1 Introduction 3 2 Motivation 4 3 The household 5 4 Firms 6 5

3sec_simp_13_b - The Three Sector Growth Model part 1 T Roe...

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The Three Sector Growth Model: part 1 T. Roe, AP8701 November 18, 2013 Contents 1 Introduction 3 2 Motivation 4 3 The household 5 4 Firms 6 5 Characterization of equilibrium 7 5.1 Intra-temporal . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Reduced forms . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.3 Intra-temporal . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3.1 Steady-state . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3.2 Transition equilibria . . . . . . . . . . . . . . . . . . . 8 6 Comparative statics 10 6.1 No-arbitrage in asset markets . . . . . . . . . . . . . . . . . . 10 6.2 Factor markets . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6.3 Product markets . . . . . . . . . . . . . . . . . . . . . . . . . 11 7 Numerical example 12 7.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 7.2 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 7.2.1 Directions of change . . . . . . . . . . . . . . . . . . . 12 7.2.2 Fundamentals of causation . . . . . . . . . . . . . . . . 13 1
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7.3 Base results (in milliions of 2004 $) . . . . . . . . . . . . . . . 15 8 Three sectors with intermediate factors 17 8.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8.3 Intra-temporal characterization . . . . . . . . . . . . . . . . . 18 8.4 Reduced form equations . . . . . . . . . . . . . . . . . . . . . 19 8.5 Inter-temporal equilibrium . . . . . . . . . . . . . . . . . . . . 20 8.5.1 Long-run . . . . . . . . . . . . . . . . . . . . . . . . . . 20 8.5.2 Transition equilibria . . . . . . . . . . . . . . . . . . . 21 9 Exog. price as a function of time 22 9.1 The household problem . . . . . . . . . . . . . . . . . . . . . . 22 9.2 Steady-state and equations of motion . . . . . . . . . . . . . . 23 9.2.1 Steady-state . . . . . . . . . . . . . . . . . . . . . . . . 23 9.2.2 Transition equilibria . . . . . . . . . . . . . . . . . . . 24 10 Stone-Geary & Exog. price as a function of time 25 10.1 The household problem . . . . . . . . . . . . . . . . . . . . . . 25 10.2 Steady-state and equations of motion . . . . . . . . . . . . . . 27 10.2.1 Steady-state . . . . . . . . . . . . . . . . . . . . . . . . 27 10.2.2 Transition equilibria . . . . . . . . . . . . . . . . . . . 27 2
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THE THREE SECTOR GROWTH MODEL 1 Introduction Reference : ° Roe et al, Chapter 4, pages 79 to 106 ° Codes for the three sector, ° Basic ° With intermediate factors ° With composite capital and ° Complete available in Part 2 The three sector growth model serves as a platform or departure for multi- sector models. Issues that arise with more than three sectors include: sector closure and how to mitigate this, multiple equations of motion (i.e., sev- eral policy functions as opposed to just one policy function and one state variable). 3
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