Part I An Introduction To Fortran 90 And Numerical Methods |
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1 Fortran 90: A simple programming language |
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3 | (36) |
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1.1 About Fortran in general |
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3 | (3) |
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1.1.1 The history of Fortran |
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3 | (1) |
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4 | (1) |
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1.1.3 The workings of high-level programming languages |
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5 | (1) |
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1.1.4 Fortran compilers for Windows, Mac, and Linux |
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6 | (1) |
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1.2 Imperative Fortran programs |
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6 | (13) |
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1.2.1 The general structure of Fortran programs |
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7 | (1) |
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1.2.2 The declaration of variables |
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7 | (1) |
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1.2.3 The basics of imperative programming |
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8 | (3) |
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1.2.4 Control flow statements |
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11 | (5) |
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1.2.5 The concept of arrays |
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16 | (3) |
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1.3 Subroutines and functions |
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19 | (4) |
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1.4 Modules and global variables |
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23 | (4) |
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1.4.1 Storing code in a module |
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23 | (2) |
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1.4.2 The concept of global variables |
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25 | (2) |
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1.5 Installing the toolbox |
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27 | (1) |
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1.6 Plotting graphs with the toolbox and GNUPIot |
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28 | (6) |
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1.6.1 Two-dimensional plotting |
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28 | (3) |
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1.6.2 Three-dimensional plotting |
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31 | (3) |
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34 | (1) |
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35 | (4) |
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2 Numerical solution methods |
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39 | (74) |
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2.1 Matrices, vectors, and linear equation systems |
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39 | (8) |
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2.1.1 Matrices and vectors in Fortran |
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39 | (1) |
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2.1.2 Solving linear equation systems |
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40 | (7) |
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2.2 Nonlinear equations and equation systems |
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47 | (13) |
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2.2.1 Bisection search in one dimension |
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48 | (3) |
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2.2.2 Newton's method in one dimension |
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51 | (3) |
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2.2.3 Fixed-point iteration methods |
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54 | (2) |
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2.2.4 Multidimensional nonlinear equation systems |
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56 | (4) |
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2.3 Function minimization |
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60 | (8) |
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2.3.1 The Golden-Search method |
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61 | (2) |
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2.3.2 Brent's and Powell's algorithms |
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63 | (4) |
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2.3.3 The problem of local and global minima |
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67 | (1) |
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2.4 Numerical integration |
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68 | (9) |
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2.4.1 Summed Newton-Cotes methods |
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69 | (3) |
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2.4.2 Gaussian quadrature |
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72 | (5) |
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2.5 Random variables, distributions, and simulation |
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77 | (8) |
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2.5.1 Random variables and their distribution |
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77 | (4) |
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2.5.2 Simulating realizations of random variables |
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81 | (4) |
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2.6 Function approximation and interpolation |
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85 | (15) |
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2.6.1 Polynominal interpolation |
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88 | (3) |
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2.6.2 Piecewise polynomial interpolation |
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91 | (4) |
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2.6.3 A two-dimensional interpolation example |
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95 | (5) |
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100 | (5) |
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2.7.1 Graphical solution to linear programs in standard form |
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102 | (1) |
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2.7.2 The simplex algorithm |
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103 | (2) |
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105 | (1) |
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106 | (7) |
Part II Computational Economics For Beginners |
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3 The static general equilibrium model |
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113 | (26) |
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3.1 The basic economy model |
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113 | (10) |
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3.1.1 The command optimum |
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113 | (2) |
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3.1.2 The market solution |
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115 | (4) |
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3.1.3 Variable labour supply |
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119 | (1) |
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3.1.4 Public sector and tax incidence analysis |
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120 | (3) |
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3.2 Extensions of the basic model |
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123 | (11) |
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3.2.1 Imperfect labour markets and unemployment policy |
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123 | (3) |
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3.2.2 Intermediate goods in production |
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126 | (4) |
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3.2.3 Open economies and international trade |
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130 | (4) |
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134 | (1) |
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134 | (5) |
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4 Topics in finance and risk management |
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139 | (66) |
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4.1 Mean-variance portfolio theory |
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139 | (12) |
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4.1.1 Portfolio choice with risky assets |
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139 | (4) |
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4.1.2 Introducing risk-free assets |
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143 | (3) |
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4.1.3 Short-selling constraints |
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146 | (3) |
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4.1.4 Monte Carlo minimization |
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149 | (2) |
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4.2 Option pricing theory |
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151 | (13) |
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4.2.1 The binomial approach by Cox-Ross-Rubinstein |
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152 | (3) |
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4.2.2 The Black-Scholes formula |
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155 | (3) |
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4.2.3 Numerical implementation of both approaches |
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158 | (3) |
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4.2.4 Option pricing with Monte Carlo simulation |
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161 | (3) |
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4.3 Managing credit risk with corporate bonds |
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164 | (20) |
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4.3.1 Modelling credit risk with a single corporate bond |
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164 | (9) |
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4.3.2 Credit risk in a bond portfolio |
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173 | (11) |
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4.4 Mortality risk management |
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184 | (14) |
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4.4.1 Modelling longevity risk |
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184 | (5) |
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4.4.2 Pricing and risk analysis of insurance products |
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189 | (7) |
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4.4.3 Optimization of a mortality portfolio |
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196 | (2) |
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198 | (2) |
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200 | (1) |
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201 | (4) |
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5 The life-cycle model and intertemporal choice |
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205 | (20) |
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205 | (9) |
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5.1.1 Optimal savings in a certain world |
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205 | (2) |
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5.1.2 Uncertain labour income and precautionary savings |
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207 | (5) |
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5.1.3 Uncertain capital and labour income |
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212 | (2) |
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5.2 Where do people save and invest? |
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214 | (7) |
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5.2.1 Uncertain capital income and portfolio choice |
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214 | (4) |
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5.2.2 Uncertain lifespan and annuity choice |
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218 | (3) |
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221 | (1) |
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222 | (3) |
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6 The overlapping generations model |
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225 | (28) |
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6.1 General structure and long-run equilibrium |
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225 | (9) |
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6.1.1 Demographics, behaviour and markets |
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225 | (4) |
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6.1.2 Computation of the long-run equilibrium |
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229 | (3) |
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6.1.3 Long-run analysis of policy reforms |
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232 | (2) |
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6.2 Transitional dynamics and welfare analysis |
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234 | (16) |
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6.2.1 Computation of transitional dynamics |
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235 | (5) |
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6.2.2 Generational welfare and aggregate efficiency |
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240 | (5) |
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6.2.3 Comprehensive analysis of policy reforms |
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245 | (5) |
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250 | (1) |
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250 | (3) |
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7 Extending the OLG model |
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253 | (36) |
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7.1 Accounting for variable labour supply |
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253 | (10) |
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7.1.1 The household decision problem |
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254 | (1) |
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7.1.2 Functional forms and numerical implementation |
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255 | (3) |
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7.1.3 Simulation results and economic interpretations |
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258 | (3) |
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7.1.4 A note on labour-augmenting technological progress |
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261 | (2) |
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7.2 Human capital and the growth process |
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263 | (11) |
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7.2.1 Education investment and externalities |
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264 | (2) |
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7.2.2 Numerical implementation and simulation |
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266 | (4) |
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7.2.3 Human-capital spillovers and endogenous growth |
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270 | (1) |
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7.2.4 Numerical implementation and simulation |
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271 | (3) |
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7.3 Longevity risk and annuitization |
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274 | (8) |
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7.3.1 The households' problem without annuity markets |
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274 | (3) |
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7.3.2 Numerical implementation and simulation |
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277 | (2) |
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7.3.3 Introducing private annuity markets |
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279 | (3) |
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282 | (1) |
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282 | (7) |
Part III Advanced Computational Economics |
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8 Introduction to dynamic programming |
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289 | (34) |
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8.1 Motivation: The cake-eating problem |
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289 | (9) |
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8.1.1 The all-in-one solution |
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290 | (1) |
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8.1.2 The dynamic programming approach |
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291 | (4) |
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8.1.3 An analytical solution |
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295 | (3) |
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8.2 Numerical solution by value function iteration |
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298 | (15) |
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301 | (5) |
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8.2.2 Optimization and interpolation |
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306 | (7) |
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8.3 Numerical solution by policy function iteration |
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313 | (7) |
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8.3.1 Root-finding and interpolation |
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314 | (2) |
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8.3.2 The method of endogenous gridpoints |
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316 | (4) |
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320 | (1) |
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321 | (2) |
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9 Dynamic macro I: Infinite horizon models |
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323 | (83) |
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9.1 The basic neoclassical growth model |
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323 | (18) |
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324 | (5) |
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9.1.2 Numerical implementation |
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329 | (5) |
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9.1.3 A model with a public sector |
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334 | (7) |
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9.2 The stochastic growth model |
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341 | (13) |
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9.2.1 Modelling aggregate uncertainty |
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341 | (3) |
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9.2.2 A numerical implementation using discretized shocks |
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344 | (6) |
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9.2.3 Simulating time paths |
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350 | (2) |
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9.2.4 Speeding up the computational process |
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352 | (2) |
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9.3 The real business-cycle model |
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354 | (20) |
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9.3.1 A dynamic program with endogenous labour supply |
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354 | (2) |
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9.3.2 Numerical implementation with policy function iteration |
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356 | (2) |
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9.3.3 Comparing model results to the data |
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358 | (5) |
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9.3.4 The welfare costs of business-cycle fluctuations |
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363 | (6) |
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9.3.5 Procyclical vs. constant government expenditure |
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369 | (5) |
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9.4 The heterogeneous agent model |
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374 | (27) |
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374 | (3) |
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9.4.2 Solving for market-clearing prices |
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377 | (3) |
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9.4.3 Determining household policy functions |
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380 | (5) |
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9.4.4 Aggregation of individual decisions |
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385 | (5) |
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9.4.5 Model parametrization and simulation |
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390 | (4) |
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9.4.6 The optimum quantity of debt |
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394 | (7) |
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401 | (1) |
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401 | (5) |
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10 Life-cycle choices and risk |
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406 | (99) |
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10.1 Labour supply, savings, and risky earnings |
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406 | (38) |
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10.1.1 The baseline model |
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407 | (15) |
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10.1.2 The role of variable labour supply |
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422 | (7) |
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10.1.3 Female labour-force participation |
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429 | (15) |
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10.2 Portfolio choice and retirement savings |
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444 | (48) |
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10.2.1 A model with stocks and bonds |
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444 | (25) |
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10.2.2 The choice to buy annuities |
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469 | (9) |
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10.2.3 Retirement savings in tax-favoured savings vehicles |
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478 | (14) |
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492 | (1) |
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493 | (12) |
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11 Dynamic macro II: The stochastic OLG model |
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505 | (56) |
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11.1 General structure and long-run equilibrium |
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505 | (20) |
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11.1.1 Demographics, behaviour, and markets |
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506 | (6) |
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11.1.2 Numerical implementation of steady-state equilibrium |
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512 | (4) |
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11.1.3 Model parametrization and calibration |
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516 | (5) |
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11.1.4 The initial equilibrium |
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521 | (2) |
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11.1.5 Long-run analysis of policy reforms |
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523 | (2) |
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11.2 Transitional dynamics and welfare analysis |
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525 | (14) |
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11.2.1 Computation of transitional dynamics |
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525 | (2) |
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11.2.2 Generational welfare and aggregate efficiency |
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527 | (12) |
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11.3 Comprehensive analysis of policy reforms |
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539 | (17) |
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11.3.1 The optimal size of the pension system |
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539 | (5) |
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11.3.2 The optimal progressivity of the labour-income tax |
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544 | (6) |
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11.3.3 Should capital income be taxed? |
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550 | (6) |
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556 | (2) |
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558 | (3) |
Bibliography |
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561 | (6) |
Index |
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