Dynamics of endogenous economic growth: a case study of the "Romer Model"
Gespeichert in:
1. Verfasser: | |
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Format: | Abschlussarbeit Buch |
Sprache: | English |
Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2003
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Ausgabe: | 1. ed. |
Schriftenreihe: | Contributions to economic analysis
257 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XV, 488 S. graph. Darst. |
ISBN: | 044451225X |
Internformat
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adam_text | Titel: Dynamics of endogenous economic growth
Autor: Schmidt, Gordon W
Jahr: 2003
Contents
Preface ..................................................................... xiii
Chapter 1 Introduction ................................................ 1
1.1 Background ......................................................... 1
1.2 A short history of economic growth theory ........................... 2
1.2.1 Classical, Keynesian, and neoclassical growth theory ........ 3
1.2.2 Early (neoclassical) endogenous growth theory .............. 8
1.2.3 Modern endogenous growth theory ......................... 11
1.3 Structure and summary of the book .................................. 14
1.3.1 Chapter 2: Development of the dynamic system ............. 15
1.3.1.1 Description of the model ......................... 15
1.3.1.2 The dynamic system ............................. 17
1.3.1.3 Calibration and sensitivity ....................... 18
1.3.2 Chapter 3: Dynamic behaviour
of the system: approximations .............................. 19
1.3.2.1 Linearisation of the model ....................... 19
1.3.2.2 Phase-space analysis ............................. 20
1.3.2.3 A Solowian-Romer model ....................... 21
1.3.3 Chapter 4: Numerical integration ........................... 22
1.3.3.1 Application of numerical integration to the Romer
system ........................................... 23
1.3.3.2 Conversion to an initial-value problem ........... 23
1.3.3.3 Finite differences and GEMPACK ............... 24
1.3.3.4 Specification of the solution method .............. 24
1.3.3.5 Numerical results of simulations ................. 25
1.3.4 Chapter 5: Economic welfare and policy issues .............. 26
1.3.4.1 Comparison of the social-optimum and market
solutions ........................................ 27
1.3.4.2 A subsidised-market solution ..................... 28
1.3.4.3 Adjustment of the subsidised-market model to the
social-optimum steady state ...................... 29
1.3.5 Chapter 6: Concluding remarks ............................. 30
Chapter 2 The Romer Model : Development of the Dynamic System ..... 31
2.1 Introduction ......................................................... 31
2.2 Description of the model ............................................. 33
Vlll
2.2.1 General .................................................... 33
2.2.2 Research sector ............................................. 35
2.2.3 Savings and capital accumulation ........................... 36
2.2.4 Final output sector ......................................... 37
2.2.5 Capital goods producing sector ............................. 39
2.2.6 Price of technology ......................................... 43
2.2.7 Allocation of human capital ................................ 44
2.2.8 Consumption ............................................... 45
2.3 The dynamic system ................................................. 47
2.3.1 Transversality conditions ................................... 47
2.3.2 Condensation of the equations .............................. 49
2.3.3 Asymptotic dynamics and the steady-state equilibrium ....... 51
2.4 Calibration and sensitivity ........................................... 56
2.4.1 Calibration of the model .................................... 56
2.4.1.1 Parameter constraints ............................ 58
2.4.1.2 Endogenous variable constraints ................. 61
2.4.1.3 Determining the benchmark parameter set ........ 62
2.4.2 Sensitivity of the steady state to parameter values ........... 64
Appendix 2.1 Production technology and the nature of capital ............. 69
A2.1.1 Production technology ...................................... 69
A2.1.1.1 Specialised capital, increasing returns and
technical change ................................. 69
A2.1.1.2 Marginal products and factor returns ............ 73
A2.1.2 The nature of capital ....................................... 76
Appendix 2.2 Dynamic maximisation problems ............................ 79
A2.2.1 General theory ............................................. 79
A2.2.2 Maximising monopoly profits ............................... 84
A2.2.3 Maximising consumer welfare ............................... 88
Appendix 2.3 Transversality conditions ................................... 89
Appendix 2.4 A second steady state ....................................... 92
Appendix 2.5 Derivation of some supplementary variables ................. 94
Appendix 2.6 Preliminary transitional dynamics ........................... 97
A2.6.1 A 25% rise in the rate of depreciation
of capital 8 ................................................. 98
A2.6.2 A 10% rise in the production cost of capital r|,
and a 20% rise in the quantity of ordinary labour L ......... 100
Chapter 3 Dynamic Behavior of the System: Linearisation,
Phase Space Analysis, and Development
of an Abridged Model ....................................... 103
3.1 Introduction ......................................................... 103
3.2 The linearised Romer model ......................................... 104
IX
3.2.1 Linearisation of the model and its dynamic solution ......... 104
3.2.2 A simulation of the transient dynamics of the
linearised model ............................................ 109
3.2.3 Speed of convergence ....................................... 115
3.3 Phase-space analysis ................................................. 119
3.3.1 Phase surfaces and phase-space regions ...................... 120
3.3.2 The saddle path in phase space .............................. 125
3.3.3 Schematic phase-space analysis .............................. 129
3.4 A Solowian-Romer model .......................................... 133
3.4.1 Development and specification .............................. 133
3.4.2 Numerical integration of the Solowian-Romer system ....... 136
3.4.2.1 An unanticipated and sustained 10%
rise in parameter -y ............................... 138
3.4.2.2 An anticipated and sustained 15%
rise in parameter £ ............................... 141
3.4.2.3 A temporary (five year) fall of 20%
in parameter a ................................... 145
3.4.3 Phase-space of the Solowian-Romer system ................. 148
3.4.4 Phase-space analysis of the Solowian-Romer dynamics ...... 151
3.4.4.1 An unanticipated and sustained 10%
rise in parameter y ............................... 151
3.4.4.2 An anticipated and sustained 15%
rise in parameter £ ............................... 152
3.4.4.3 A temporary (five year) fall of 20%
in parameter a ................................... 154
Appendix 3.1 Linearisation of the Romer model ........................... 156
Appendix 3.2 Solution of a first-order system of linear
differential equations ....................................... 160
A3.2.1 General solution ............................................ 160
A3.2.2 Necessary conditions for equilibrium ........................ 162
A3.2.3 The complete solution ...................................... 166
A3.2.4 The oscillatory effect of complex-valued roots ............... 166
Appendix 3.3 Eigenvalues and eigenvectors of a linear dynamic
system ...................................................... 167
A3.3.1 Eigenvalues of a 3 X 3 matrix ft ............................. 167
A3.3.2 Eigenvectors of a 3 X 3 matrix ft ............................ 177
Appendix 3.4 Anticipated shocks: Analytic determination
with the linearised model ................................... 178
A3.4.1 Algebraic derivation ........................................ 178
A3.4.2 Computations of adjustment paths .......................... 181
A3.4.2.1 A sustained 15% rise in parameter £ ............. 181
A3.4.2.2 A temporary (five year) fall of 20%
in parameter a ................................... 181
Appendix 3.5 Log-linearisation of the Romer model ....................... 187
A3.5.1 Deriving the log-linear coefficients matrix ................... 187
A3.5.2 Speed of convergence in the log-linear model ................ 189
Appendix 3.6 Phase-space surfaces of the Romer model ................... 192
Appendix 3.7 Equivalence of the Solowian-Romer model
and the full Romer model ................................... 204
Appendix 3.8 Log-linearisation of the Solowian-Romer model ............. 212
Chapter 4 Numerical Integration ....................................... 215
4.1 General application to the Romer system ............................. 215
4.2 Conversion to an initial value problem ............................... 220
4.2.1 Time elimination method ................................... 220
4.2.2 Eigenvector-backward integration method ................... 223
4.3 Finite differences and the GEMPACK software ...................... 224
4.3.1 Method of finite differences ................................. 225
4.3.2 GEMPACK and its application to the Romer model ........ 227
4.4 Specification of the solution method .................................. 230
4.4.1 Simulating unanticipated shocks ............................ 231
4.4.2 Simulating anticipated shocks ............................... 232
4.4.3 The solution method: finite differences
and GEMPACK ........................................... 233
4.5 Numerical results of simulations ..................................... 234
4.5.1 An unanticipated rise in the profit share of income .......... 235
4.5.2 An anticipated rise in the productivity of researchers ........ 244
4.5.3 A temporary rise in the ordinary-labour
share of wages .............................................. 255
4.5.4 Comparison of the linearised, Solowian- and
full non-linear Romer model results ......................... 261
4.5.5 An immigration program to raise the level
of human capital ........................................... 262
4.5.6 A sudden, temporary reduction of the capital stock .......... 269
4.5.7 A gradual loss of human capital from research .............. 274
Appendix 4.1 Numerical integration methods for
initial-value problems ....................................... 282
Appendix 4.2 Computing the saddle path of the Romer model as
the solution to an initial value problem .................... 285
A4.2.1 Time-elimination method ................................... 285
A4.2.2 Eigenvector backward-integration method ................... 302
Appendix 4.3 Specification of the finite differences-GEMPACK method
of numerical integration .................................... 313
A4.3.1 General .................................................... 313
A4.3.2 Empirical performances on the Romer model ................ 314
A4.3.3 TABLO input and Command files for GEMPACK .......... 321
Appendix 4.4 Comparison of the computed dynamic behaviours
of the linearised Romer model, the Solowian-Romer
model and the full non-linear Romer model ................. 332
A4.4.1 An unanticipated and sustained 10% rise
in parameter 7 .............................................. 347
A4.4.2 An anticipated and sustained 15% rise
in parameter (, .............................................. 348
A4.4.3 An unanticipated but temporary 20% fall
in parameter a ............................................. 348
Chapter 5 Economic Welfare and Policy Issues ......................... 351
5.1 Sub-optimality of the market solution ................................ 351
5.1.1 Social planning solution to the Romer model ................ 354
5.1.2 Comparison of the social planning
and market solutions ....................................... 358
5.2 Policy implications .................................................. 368
5.2.1 A subsidised-market solution ............................... 369
5.2.1.1 Production-side distortions ....................... 369
5.2.1.2 Externalities in research .......................... 371
5.2.1.3 Subsidised stationary dynamic system ............ 372
5.2.1.4 Steady state of the subsidised-market solution .... 374
5.2.2 Optimum rates of subsidy ................................... 375
5.3 Adjustment to the social-optimum steady state ....................... 379
5.3.1 Unanticipated/single point of time imposition
of the optimum subsidies ................................... 380
5.3.2 Unanticipated imposition of sK; and delayed,
anticipated implementation of sAK ............................. 386
5.3.3 Unanticipated imposition of sAK; and delayed,
anticipated implementation of sK .............................. 391
5.3.4 Dynamic effects of different methods
of implementation .......................................... 396
Appendix 5.1 A social planning solution to the Romer Model ............. 397
A5.1.1 Derivation of the dynamic system and its steady state ....... 397
A5.1.2 Calculation of the speed of convergence
through linearisation ........................................ 403
Appendix 5.2 TABLO input files for the social-optimum
and the subsidised-market Romer systems .................. 405
Appendix 5.3 Limiting levels and shares of human capital ................. 416
Appendix 5.4 Interest rates, capital goods intensities, and technology
prices in the market and optimal steady states ............... 421
A5.4.1 Interest rates ............................................... 421
A5.4.2 Capital goods intensities and the price of technology ........ 422
Appendix 5.5 Alternative subsidisation strategies to attain the
social-optimum steady state ................................. 429
A5.5.1 The production side distortions ............................. 430
A5.5.1.1 Subsidising the rental costs of specialised
capital ........................................... 430
A5.5.1.2 Subsidising the manufacture of final output ....... 431
A5.5.2 The research externality distortion .......................... 432
A5.5.2.1 Subsidising the wages of researchers .............. 432
A5.5.2.2 Subsidising the accumulation of research ........ 434
Appendix 5.6 Dynamic impact of the optimum subsidies .................. 435
A5.6.1 Savings and designs subsidies: (sK, sAK) ...................... 435
A5.6.1.1 Impact of optimum subsidy sK ................... 439
A5.6.1.2 Impact of optimum subsidy sAK .................. 441
A5.6.2 Monopoly correction and designs subsidies:
(sx, sAx) or (sy,say) .......................................... 442
Chapter 6 Concluding Remarks and Policy Implications ................. 447
6.1 Conclusions regarding the dynamics .................................. 447
6.1.1 Technical methods ......................................... 447
6.1.2 Dynamic results ........................................... 449
6.2 Policy implications .................................................. 452
6.2.1 Policy implications from the transitional dynamics ......... 453
6.2.2 Policy implications from the sub-optimality of the model ... 455
6.3 Directions for further research ....................................... 458
Bibliography ................................................................ 463
Author index ............................................................... 473
Subject index ............................................................... 475
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spelling | Schmidt, Gordon W. Verfasser aut Dynamics of endogenous economic growth a case study of the "Romer Model" Gordon W. Schmidt Dynamics of endogenous economic growth theory and related issues 1. ed. Amsterdam [u.a.] Elsevier 2003 XV, 488 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Contributions to economic analysis 257 Zugl.: Melbourne, Monash Univ., Diss., 2001 u.d.T.: Schmidt, Gordon W.: Dynamics of endogenous economic growth theory and related issues Dynamisches Modell (DE-588)4150932-8 gnd rswk-swf Wachstumstheorie (DE-588)4128160-3 gnd rswk-swf Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Endogenes Wirtschaftswachstum (DE-588)4378670-4 s Wachstumstheorie (DE-588)4128160-3 s Dynamisches Modell (DE-588)4150932-8 s DE-188 Contributions to economic analysis 257 (DE-604)BV000001445 257 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022039759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Schmidt, Gordon W. Dynamics of endogenous economic growth a case study of the "Romer Model" Contributions to economic analysis Dynamisches Modell (DE-588)4150932-8 gnd Wachstumstheorie (DE-588)4128160-3 gnd Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd |
subject_GND | (DE-588)4150932-8 (DE-588)4128160-3 (DE-588)4378670-4 (DE-588)4113937-9 |
title | Dynamics of endogenous economic growth a case study of the "Romer Model" |
title_alt | Dynamics of endogenous economic growth theory and related issues |
title_auth | Dynamics of endogenous economic growth a case study of the "Romer Model" |
title_exact_search | Dynamics of endogenous economic growth a case study of the "Romer Model" |
title_full | Dynamics of endogenous economic growth a case study of the "Romer Model" Gordon W. Schmidt |
title_fullStr | Dynamics of endogenous economic growth a case study of the "Romer Model" Gordon W. Schmidt |
title_full_unstemmed | Dynamics of endogenous economic growth a case study of the "Romer Model" Gordon W. Schmidt |
title_short | Dynamics of endogenous economic growth |
title_sort | dynamics of endogenous economic growth a case study of the romer model |
title_sub | a case study of the "Romer Model" |
topic | Dynamisches Modell (DE-588)4150932-8 gnd Wachstumstheorie (DE-588)4128160-3 gnd Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd |
topic_facet | Dynamisches Modell Wachstumstheorie Endogenes Wirtschaftswachstum Hochschulschrift |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022039759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000001445 |
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