两位诺贝尔经济学获奖者正在合作的下一个经典教科书。还在初步阶段。但还是可以学到即将到来的“主流”经济学。正在为博士论文选材的童鞋们一定可以受启发找到不错的课题。Lars Peter Hansen
University of Chicago and NBER

Thomas J. Sargent
New York University and Hoover Institution

1 Statistical decision theories 1
1.1 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Two theories of decision making . . . . . . . . . . . . . . . . 2
1.3 Bayesian Decision Rules . . . . . . . . . . . . . . . . . . . . 4
1.4 Partial Orderings and Admissibility . . . . . . . . . . . . . . 6
1.5 Max-min Decision Rules . . . . . . . . . . . . . . . . . . . . 8
1.6 Risk versus Uncertainty . . . . . . . . . . . . . . . . . . . . 13
1.7 Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Stochastic Processes 17
2.1 Definitions and an Illustration . . . . . . . . . . . . . . . . . 17
2.2 Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Constructing a Stochastic Process: I . . . . . . . . . . . . . 19
2.4 Stationary Stochastic Processes . . . . . . . . . . . . . . . . 22
2.5 Invariant Events and Conditional Expectations . . . . . . . . 23
2.6 The Law of Large Numbers . . . . . . . . . . . . . . . . . . 26
2.7 Limiting Empirical Measures . . . . . . . . . . . . . . . . . . 28
2.8 Ergodic Decomposition . . . . . . . . . . . . . . . . . . . . . 30
2.9 Constructing a Stochastic Process: II . . . . . . . . . . . . . 40
2.10 Inventing an infinite past . . . . . . . . . . . . . . . . . . . . 41
3 Markov Processes 45
3.1 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3 Eigenfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Ergodic Markov Processes . . . . . . . . . . . . . . . . . . . 49
3.5 Limits of Multi-Period Forecasts . . . . . . . . . . . . . . . . 53
3.6 Finite-State Markov Chains . . . . . . . . . . . . . . . . . . 55
3.7 Vector Autoregression . . . . . . . . . . . . . . . . . . . . . 57
3.8 Estimating a Vector Autoregression . . . . . . . . . . . . . . 59
4 Additive Functionals 61
4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Limited Dependence . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Extracting Martingales . . . . . . . . . . . . . . . . . . . . . 64
4.4 Examples of Additive Functionals . . . . . . . . . . . . . . . 70
4.5 Blanchard and Quah’s model . . . . . . . . . . . . . . . . . 73
4.6 Cointegration . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 Evaluating long-term risk . . . . . . . . . . . . . . . . . . . 84
4.8 A digression on robustness . . . . . . . . . . . . . . . . . . . 89
4.9 Central Limit Theory . . . . . . . . . . . . . . . . . . . . . . 90
4.10 Growth-rate Regimes . . . . . . . . . . . . . . . . . . . . . . 92
4.11 Quadratic Model of Growth . . . . . . . . . . . . . . . . . . 94
4.A Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.B Shapiro and Watson (1988) . . . . . . . . . . . . . . . . . . 98
5 Multiplicative Functionals 101
5.1 Geometric Growth and Decay . . . . . . . . . . . . . . . . . 101
5.2 Special Multiplicative Functionals . . . . . . . . . . . . . . . 102
5.3 Likelihood Ratio Processes . . . . . . . . . . . . . . . . . . . 103
5.4 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.5 Long-run Growth Rate . . . . . . . . . . . . . . . . . . . . . 118
5.6 Applications and Extensions . . . . . . . . . . . . . . . . . . 119
6 Likelihood Processes 121
6.1 Processes with Observed States . . . . . . . . . . . . . . . . 121
6.2 Log-Likelihoods . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3 Score processes . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Limiting Behavior of Likelihood Ratios . . . . . . . . . . . . 130
7 Learning 135
7.1 Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . 135

7.2 Learning about Fixed Parameters . . . . . . . . . . . . . . . 135
7.3 Learning about Discrete States . . . . . . . . . . . . . . . . 140
7.4 Multiple VAR Regimes . . . . . . . . . . . . . . . . . . . . . 141
7.5 Linear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . 143
8 Nonlinear Impulse Response Functions 147
8.1 Modeling an impulse . . . . . . . . . . . . . . . . . . . . . . 147
8.2 Impulse Response for Additive Process . . . . . . . . . . . . 149
8.3 Response for Multiplicative Process . . . . . . . . . . . . . . 150
8.4 Changing a Risk Exposure . . . . . . . . . . . . . . . . . . . 153
8.5 Other elasticities . . . . . . . . . . . . . . . . . . . . . . . . 154
8.6 A Shock Elasticity Process . . . . . . . . . . . . . . . . . . . 155
8.7 Battle plan needed . . . . . . . . . . . . . . . . . . . . . . . 157
8.8 Unfinished Materials and Garbage Cans . . . . . . . . . . . 157
8.9 Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.10 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.11 Change of measure . . . . . . . . . . . . . . . . . . . . . . . 160
8.12 Iterated expectations . . . . . . . . . . . . . . . . . . . . . . 160
8.13 Shifting the exposure date . . . . . . . . . . . . . . . . . . . 163
8.14 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9 Continuation Values 169
9.1 CES Formulation of Recursive Utility . . . . . . . . . . . . . 169
9.2 Stochastic Growth in Consumption . . . . . . . . . . . . . . 171
9.3 A Limit Problem . . . . . . . . . . . . . . . . . . . . . . . . 171
9.4 Log-linear approximation . . . . . . . . . . . . . . . . . . . . 173
9.5 Stochastic Discount Factor Process . . . . . . . . . . . . . . 175
9.6 Equilibrium wealth . . . . . . . . . . . . . . . . . . . . . . . 176
9.7 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.8 Risk adjustment for the example economy . . . . . . . . . . 178
9.9 Small noise approximation . . . . . . . . . . . . . . . . . . . 181
9.10 Preference shocks . . . . . . . . . . . . . . . . . . . . . . . . 184
10 Semiparametric Estimation with Limited Information 185
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
10.2 Underlying Economic Model . . . . . . . . . . . . . . . . . . 185
10.3 Econometrician’s information and the implied orthogonality
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

10.4 An Adjustment Cost Example . . . . . . . . . . . . . . . . . 189
10.5 A Slightly Simpler Estimation Problem . . . . . . . . . . . . 190
10.6 Multidimensional Parameterizations of B . . . . . . . . . . . 193
10.7 Nonparametric Estimation of B . . . . . . . . . . . . . . . . 194
10.8 Back to the Adjustment Cost Model . . . . . . . . . . . . . 195