Econometrica 2009 Vol.77 N° 1

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Author(s): Stephen Morris
Year: 2009

Language: English
Pages: 354

0.PDF......Page 1
1.PDF......Page 3
Backward Induction......Page 4
Forward Induction......Page 5
Synopsis......Page 6
An Outside-Option Game......Page 7
A Signaling Game......Page 9
Definition of Forward Induction......Page 12
Definition of Invariance......Page 15
Formulation......Page 16
Statement and Proof the Theorem......Page 19
Reny's Interpretation of Forward Induction......Page 23
Appendix A: Technical Lemma......Page 26
Appendix B: Forward Induction in the Normal Form......Page 27
References......Page 28
Author's Addresses......Page 30
Introduction......Page 31
The Model......Page 33
General Statement......Page 36
Sketch of the Proof......Page 40
General Properties......Page 43
Equilibrium Strategies......Page 45
Related Literature and Concluding Comments......Page 47
Proof of Proposition 1......Page 50
Preliminaries......Page 55
Proof of Proposition 4......Page 58
Proof of Proposition 5......Page 60
Proof of Proposition 6......Page 62
Proof of Proposition 7......Page 63
Equilibrium Delay......Page 64
Author's Addresses......Page 70
Introduction......Page 72
An Example......Page 75
The Model......Page 76
Payoff Characterization......Page 79
Discussion of the Payoff Characterization......Page 83
Contests That Are Not Generic......Page 84
Participation......Page 87
Concluding Remarks......Page 88
Appendix......Page 89
References......Page 92
Author's Addresses......Page 93
Introduction......Page 94
Computationally Bounded Forecasters......Page 96
Definitions......Page 97
Tests More Complex Than the Forecast......Page 99
Forecasts That Factor......Page 101
PSPACE Hardness......Page 102
Conclusion......Page 105
Author's Addresses......Page 106
Introduction......Page 107
Model Invariance and Canonical Form......Page 112
Maximal Invariant Statistic......Page 115
Invariant Prior Distribution......Page 117
Optimality......Page 120
A Closed Form Integrated Likelihood and Correlated Random Effects......Page 122
Connections With the Literature......Page 126
Conclusion......Page 131
References......Page 132
Author's Addresses......Page 133
Introduction......Page 134
Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices......Page 138
Our Approach and Identification of the Baseline Model......Page 141
Identification of the Number of Types......Page 150
Time-Dependent Conditional Choice Probabilities......Page 151
Lagged Dependent Variable and Type-Specific Transition Functions......Page 154
Limited Transition Pattern......Page 163
Concluding Remark......Page 167
Appendix: Proofs......Page 168
References......Page 172
Author's Addresses......Page 174
Introduction......Page 175
Stochastic Discount Factors and Pricing......Page 179
Baseline Process......Page 180
Multiplicative Functionals......Page 182
Stochastic Discount Factors......Page 185
Valuation Functionals and Returns......Page 188
Semigroups......Page 191
Multiplicative Semigroup......Page 192
Semigroups Induced by Cash-Flow Growth......Page 193
Generators......Page 195
Principal Eigenfunctions and Martingales......Page 197
Markov Chain......Page 203
General Analysis......Page 204
Lp Approximation......Page 207
Lyapunov Functions......Page 209
Long-Term Risk......Page 211
Changing Valuation Functionals (M = V)......Page 212
Changing Cash Flows (M=G, M=S, and M=GS)......Page 214
Existence......Page 217
Conclusions......Page 220
Appendix A: Value Function in the Example Economy......Page 221
Appendix B: Approximation......Page 222
Appendix C: Martingales and Absolute Continuity......Page 223
Appendix D: Existence......Page 226
References......Page 231
Author's Addresses......Page 232
Introduction......Page 233
Economies......Page 235
Equilibria......Page 236
Virtual Local Uniqueness......Page 237
Perturbing Indeterminacy Examples......Page 238
Proof of Theorem 5.2......Page 240
Conclusion......Page 243
Appendix: Proof of Theorem 5.1......Page 244
Author's Addresses......Page 245
Introduction......Page 246
Basic Framework......Page 248
Previous Results......Page 250
A New Multisignal Extension of Jewitt's Conditions......Page 253
A Multisignal Extension of the CDFC......Page 256
A Risk Averse Principal......Page 258
Reducing NISP and CISP to Density Flows......Page 260
Local Conditions Sufficient for NISP and CISP......Page 264
Other Extensions......Page 271
Conclusion: Comparison of the Two Approaches......Page 272
Appendix: Proof of Lemma 1......Page 273
References......Page 274
Author's Addresses......Page 275
10.PDF......Page 276
References......Page 277
Author's Addresses......Page 278
Introduction......Page 279
Setup, Notation, and Existing Theory......Page 282
The Bootstrap......Page 283
Second-Order Accuracy of the Bootstrap......Page 285
The i.i.d. Bootstrap Error......Page 288
The Wild Bootstrap Error......Page 289
Third-Order Accuracy of the Bootstrap......Page 291
Monte Carlo Results......Page 293
Conclusions......Page 294
Appendix A: Cumulant Expansions......Page 296
Appendix B: Proofs of Results in Sections 3-5......Page 299
References......Page 300
Author's Addresses......Page 302
Introduction......Page 303
Setting and Basic Concepts......Page 304
Characterization of Revenue Equivalence......Page 305
Discussion......Page 309
References......Page 311
Author's Addresses......Page 312
13.PDF......Page 313
Author's Addresses......Page 314
14.PDF......Page 315
15.PDF......Page 320
Milan, Italy August 26-27, 2008......Page 321
Milan, Italy August 26-27, 2008......Page 328
18.PDF......Page 334
19.PDF......Page 339
20.PDF......Page 348
21.PDF......Page 351