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内容简介如下！
0 Sneak Peek: Powering Causal Inference with ML and AI 4
Core Material 11
1 Predictive Inference with Linear Regression in Moderately High Di￾mensions 12
1.1 Foundation of Linear Regression . . . . . . . . . . . . . . . . . . . . 13
Regression and the Best Linear Prediction Problem . . . . . . . . . 13
Best Linear Approximation Property . . . . . . . . . . . . . . . . . 14
From Best Linear Predictor to Best Predictor . . . . . . . . . . . . . 14
1.2 Statistical Properties of Least Squares . . . . . . . . . . . . . . . . . 17
The Best Linear Prediction Problem in Finite Samples . . . . . . . . 17
Properties of Sample Linear Regression . . . . . . . . . . . . . . . . 18
Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Overfitting: What Happens When 𝑝/𝑛 Is Not Small . . . . . . . . . 21
Measuring Predictive Ability by Sample Splitting . . . . . . . . . . 22
1.3 Inference about Predictive Effects or Association . . . . . . . . . . . 23
Understanding 𝛽1 via "Partialling-Out" . . . . . . . . . . . . . . . . 24
Adaptive Statistical Inference . . . . . . . . . . . . . . . . . . . . . . 26
1.4 Application: Wage Prediction and Gaps . . . . . . . . . . . . . . . . 27
Prediction of Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Wage Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5 Inference on Predictive Effect when &#119901;/&#119899; < 1 is not small★ . . . . . . 33
1.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.7 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.A Central Limit Theorem★ . . . . . . . . . . . . . . . . . . . . . . . . . 37
Univariate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Multivariate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Causal Inference via Randomized Experiments 42
2.1 Potential Outcomes Framework and Average Treatment Effects . . 43
Random Assignment/Randomized Controlled Trials . . . . . . . . 46
Statistical Inference with Two Sample Means . . . . . . . . . . . . . 48
Pfizer/BioNTech Covid Vaccine RCT . . . . . . . . . . . . . . . . . 49
2.2 Pre-treatment Covariates and Heterogeneity . . . . . . . . . . . . . 50
Regression and Statistical Inference for ATEs . . . . . . . . . . . . . 52
Classical Additive Approach . . . . . . . . . . . . . . . . . . . . . . 53
The Interactive Approach: Always Improves Precision and Discovers
Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Reemployment Bonus RCT . . . . . . . . . . . . . . . . . . . . . . . 56
2.3 Drawing RCTs via Causal Diagrams . . . . . . . . . . . . . . . . . . 57
2.4 The Limitations of RCTs . . . . . . . . . . . . . . . . . . . . . . . . . 58
Externalities, Stability, and Equilibrium Effects . . . . . . . . . . . . 59
Ethical, Practical, and Generalizability Concerns . . . . . . . . . . . 59
2.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.A Approximate Distribution of the Two Sample Means . . . . . . . . 61
2.B Statistical Properties of the Classical Additive Approach★ . . . . . . 62
3 Predictive Inference via Modern High-Dimensional Linear Regression 66
3.1 Linear Regression with High-Dimensional Covariates . . . . . . . . 67
The Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Quick Heuristics for Lasso Properties and Penalty Choice★ . . . . . 73
OLS Post-Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2 Predictive Performance of Lasso and Post-Lasso . . . . . . . . . . . 75
3.3 A Helicopter Tour of Other Penalized Regression Methods for
Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4 Choice of Regression Methods in Practice . . . . . . . . . . . . . . . 84
3.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.A Additional Discussion and Results . . . . . . . . . . . . . . . . . . . 87
Iterative Estimation of &#120590; . . . . . . . . . . . . . . . . . . . . . . . . . 87
Some Lasso Heuristics via Convex Geometry★ . . . . . . . . . . . . 88
Other Variations on Lasso . . . . . . . . . . . . . . . . . . . . . . . . 90
3.B Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.C Laws of Large Numbers for Large Matrices★ . . . . . . . . . . . . . 92
3.D A Sketch of the Lasso Guarantee Under Exact Sparsity★ . . . . . . . 93
4 Statistical Inference on Predictive Effects in High-Dimensional Linear
Regression Models 99
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 Inference with Double Lasso . . . . . . . . . . . . . . . . . . . . . . 100
Inference on One Coefficient . . . . . . . . . . . . . . . . . . . . . . 100
Application to Testing the Convergence Hypothesis . . . . . . . . . 103
4.3 Why Partialling-out Works: Neyman Orthogonality . . . . . . . . . 104
Neyman Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . 104
What Happens if We Don’t Have Neyman Orthogonality? . . . . . 107
4.4 Inference on Many Coefficients . . . . . . . . . . . . . . . . . . . . . 110
Discovering Heterogeneity in the Wage Gap Analysis . . . . . . . . 113
4.5 Other Approaches That Have the Neyman Orthogonality Property 115
Double Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Debiased Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.7 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.A High-Dimensional Central Limit Theorems★ . . . . . . . . . . . . . 119
5 Causal Inference via Conditional Ignorability 124
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2 Potential Outcomes and Ignorability . . . . . . . . . . . . . . . . . . 126
Identification by Conditioning . . . . . . . . . . . . . . . . . . . . . 127
Conditional Ignorability via Causal Diagrams . . . . . . . . . . . . 130
Connections to Linear Regression . . . . . . . . . . . . . . . . . . . 131
5.3 Identification Using Propensity Scores . . . . . . . . . . . . . . . . 132
Stratified RCTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Covariate Balance Checks . . . . . . . . . . . . . . . . . . . . . . . . 134
Connections to Linear Regression . . . . . . . . . . . . . . . . . . . 135
5.4 Conditioning on Propensity Scores★ . . . . . . . . . . . . . . . . . . 135
5.5 Average Treatment Effect for Groups and on the Treated . . . . . . 137
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.A Rosenbaum-Rubin’s Result . . . . . . . . . . . . . . . . . . . . . . . 139
5.B Clever Covariate Regression . . . . . . . . . . . . . . . . . . . . . . 140
5.C Details of ATET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6 Causal Inference via Linear Structural Equations 144
6.1 Structural Equation Modelling and Conditional Exogeneity . . . . 145
A Simple Triangular Structural Equation Model (TSEM) . . . . . . 145
6.2 Drawing the Model: Causal Diagrams, aka DAGs . . . . . . . . . . 148
6.3 When Conditioning Can Go Wrong: Collider Bias, aka Heckman
Selection Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.4 Wage Gap Analysis and Discrimination . . . . . . . . . . . . . . . . 154
6.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.A Details of the Wage Discrimination Analysis . . . . . . . . . . . . . 160
7 Causal Inference via Directed Acyclical Graphs and Nonlinear Struc￾tural Equation Models 164
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.2 General DAG and SEMs via an Example . . . . . . . . . . . . . . . 166
The Impact of 401(k) Eligibility on Financial Wealth . . . . . . . . . 166
The DAG as a Markovian Model . . . . . . . . . . . . . . . . . . . . 167
The DAG as a Structural Equations Model . . . . . . . . . . . . . . 168
Intervention and Counterfactual DAG and SEM . . . . . . . . . . . 168
Conditional Ignorability/Exogeneity . . . . . . . . . . . . . . . . . 170
Wrap-Up and Implications for 401(k) Analysis . . . . . . . . . . . . 172
7.3 Definitions of General DAGs and ASEMs . . . . . . . . . . . . . . . 172
From DAGs to ASEMs . . . . . . . . . . . . . . . . . . . . . . . . . . 173
D-Separation and Testable Restrictions . . . . . . . . . . . . . . . . 174
7.4 Counterfactuals and Identification by Conditioning . . . . . . . . . 177
Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Ignorability by D-Separation in Counterfactual DAGs . . . . . . . . 178
Ignorability by Backdoor Blocking in Factual DAG . . . . . . . . . . 181
7.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.6 Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.7 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.A Review of Conditional Independence . . . . . . . . . . . . . . . . . 185
7.B Theoretical Details of d-Separation★ . . . . . . . . . . . . . . . . . . 185
7.C Faithfulness and Causal Discovery . . . . . . . . . . . . . . . . . . . 187
8 Predictive Inference via Modern Nonlinear Regression 192
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2 Regression Trees and Random Forests . . . . . . . . . . . . . . . . . 193
Introduction to Regression Trees . . . . . . . . . . . . . . . . . . . . 193
Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Boosted Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.3 Neural Nets / Deep Learning . . . . . . . . . . . . . . . . . . . . . 200
Basic Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Deep Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.4 Prediction Quality of Modern Nonlinear Regression Methods . . . 207
Learning Guarantees of Trees and Forests . . . . . . . . . . . . . . . 207
Learning Guarantees of DNNs . . . . . . . . . . . . . . . . . . . . . 210
The Push for More Theory . . . . . . . . . . . . . . . . . . . . . . . 212
Trust but Verify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A Simple Case Study using Wage Data . . . . . . . . . . . . . . . . 213
8.5 Combining Predictions - Aggregation - Ensemble Learning . . . . . 215
Auto ML Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.6 When Do Neural Networks Win? . . . . . . . . . . . . . . . . . . . 217
8.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
8.8 Additional resources . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.9 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.A Variable Importance via Permutations . . . . . . . . . . . . . . . . . 220
9 Statistical Inference on Predictive and Causal Effects in Modern Non￾linear Regression Models 225
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
9.2 DML Inference in the Partially Linear Regression Model . . . . . . 227
Discussion of DML Construction . . . . . . . . . . . . . . . . . . . . 232
The Effect of Gun Ownership on Gun-Homicide Rates . . . . . . . 236
Revisiting the Price Elasticity for Toy Cars . . . . . . . . . . . . . . 240
9.3 DML Inference in the Interactive Regression Model . . . . . . . . . 242
DML Inference on APEs and ATEs . . . . . . . . . . . . . . . . . . . 242
DML Inference for GATEs and ATETs . . . . . . . . . . . . . . . . . 245
The Effect of 401(k) Eligibility on Net Financial Assets . . . . . . . . 247
9.4 Generic Debiased (or Double) Machine Learning . . . . . . . . . . 251
Key Ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Neyman Orthogonal Scores for Regression Problems . . . . . . . . 254
The DML Inference Method . . . . . . . . . . . . . . . . . . . . . . 255
Properties of the General DML Estimator . . . . . . . . . . . . . . . 257
9.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
9.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
9.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
9.A Bias Bounds with Proxy Treatments . . . . . . . . . . . . . . . . . . 263
9.B Illustrative Neyman Orthogonality Calcuations . . . . . . . . . . . 264
10 Feature Engineering for Causal and Predictive Inference 268
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
10.2 From Principal Components to Autoencoders . . . . . . . . . . . . 270
Variational Autoencoders . . . . . . . . . . . . . . . . . . . . . . . . 274
10.3 From Autoencoders to General Embeddings . . . . . . . . . . . . . 275
10.4 Text Embeddings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Revisiting the Price Elasticity for Toy Cars . . . . . . . . . . . . . . 287
10.5 Image Embeddings . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
10.6 Application: Hedonic Prices . . . . . . . . . . . . . . . . . . . . . . 289
10.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
10.8 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
10.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Topics 298
11 Deeper Dive into DAGs, Good and Bad Controls 299
11.1 Valid Adjustment Sets . . . . . . . . . . . . . . . . . . . . . . . . . . 300
11.2 Other Useful Adjustment Strategies . . . . . . . . . . . . . . . . . . 300
Conditioning on Parents . . . . . . . . . . . . . . . . . . . . . . . . 301
Conditioning on All Common Causes of &#119863; and &#119884; . . . . . . . . . . 302
11.3 Examples of Good and Bad Controls . . . . . . . . . . . . . . . . . 303
Pre-Treatment Variables or Proxies of Pre-Treatment Variables . . . 304
Post-Treatment Variables . . . . . . . . . . . . . . . . . . . . . . . . 309
11.4 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
11.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
11.A Front-Door Criterion via Example . . . . . . . . . . . . . . . . . . . 313
12 Unobserved Confounders, Instrumental Variables, and Proxy Controls 317
12.1 The Difficulty of Causal Inference with an Unobserved Confounder 318
12.2 Impact of Confounders on Causal Effect Identification and Sensitivity
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
12.3 Partially Linear IV Models . . . . . . . . . . . . . . . . . . . . . . . 323
A Wage Equation with Unobserved Ability . . . . . . . . . . . . . . 323
Aggregate Market Demand . . . . . . . . . . . . . . . . . . . . . . . 325
Limits of Average Causal Effect Identification under Partial Linearity326
12.4 Nonlinear IV Models . . . . . . . . . . . . . . . . . . . . . . . . . . 329
The LATE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
The IV Quantile Model★ . . . . . . . . . . . . . . . . . . . . . . . . . 331
12.5 Partially Linear SEMs with Griliches-Chamberlain Proxy Controls . 332
12.6 Nonlinear Models with Proxy Controls★ . . . . . . . . . . . . . . . 334
12.7 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
12.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
12.A Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Latent Confounder Bias Result: Theorem 12.2.1 . . . . . . . . . . . . 338
Partially Linear Outcome IV Model: Theorem 12.3.2 . . . . . . . . . 339
Partially Linear Compliance IV Model: Theorem 12.3.3 . . . . . . . 339
Linear Proxy Model: Theorem 12.5.1. . . . . . . . . . . . . . . . . . 340
13 DML for IV and Proxy Controls Models and Robust DML Inference
under Weak Identification 346
13.1 DML Inference in Partially Linear IV Models . . . . . . . . . . . . . 347
The Effect of Institutions on Economic Growth . . . . . . . . . . . . 349
13.2 DML Inference in the Interactive IV Regression Model (IRM) . . . . 352
DML Inference on LATE . . . . . . . . . . . . . . . . . . . . . . . . 352
The Effect of 401(k) Participation on Net Financial Assets . . . . . . 353
13.3 DML Inference with Weak Instruments . . . . . . . . . . . . . . . . 355
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
DML Inference Robust to Weak-IV in PLMs . . . . . . . . . . . . . . 357
The Effect of Institutions on Economic Growth Revisited . . . . . . 359
13.4 Generic DML Inference under Weak Identification . . . . . . . . . . 360
13.5 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
14 Statistical Inference on Heterogeneous Treatment Effects 366
14.1 CATEs under Conditional Exogeneity . . . . . . . . . . . . . . . . . 367
14.2 Inference on Best Linear Approximations . . . . . . . . . . . . . . . 370
Least Squares Methods for Learning CATEs . . . . . . . . . . . . . 371
Application to 401(k) Example . . . . . . . . . . . . . . . . . . . . . 373
14.3 Non-Parametric Inference for CATEs with Causal Forests . . . . . . 375
Empirical Example: The "Welfare" Experiment . . . . . . . . . . . . 382
14.4 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
15 Estimation and Validation of Heterogeneous Treatment Effects 387
15.1 ML Methods for CATE Estimation . . . . . . . . . . . . . . . . . . . 388
Meta-Learning Strategies for CATE Estimation . . . . . . . . . . . . 388
Qualitative Comparison and Guidelines . . . . . . . . . . . . . . . . 398
Guarding for Covariate Shift . . . . . . . . . . . . . . . . . . . . . . 401
15.2 Scoring for CATE Model Selection and Ensembling . . . . . . . . . 407
Comparing Models with Confidence . . . . . . . . . . . . . . . . . 408
Competing with the Best Model . . . . . . . . . . . . . . . . . . . . 412
15.3 CATE Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . 418
Heterogeneity Test Based on Doubly Robust BLP . . . . . . . . . . 419
Validation Based on Calibration . . . . . . . . . . . . . . . . . . . . 420
Validation Based on Uplift Curves . . . . . . . . . . . . . . . . . . . 424
15.4 Empirical Example: The "Welfare" Experiment . . . . . . . . . . . . 435
15.5 Empirical Example: Digital Advertising A/B Test . . . . . . . . . . 441
15.A Appendix: Lower Bound on Variance in Model Comparison . . . . 445
15.B Appendix: Interpretation of Uplift curves . . . . . . . . . . . . . . . 446
16 Difference-in-Differences 451
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
16.2 The Basic Difference-in-Differences Framework: Parallel Worlds . . 452
The Mariel Boatlift . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
16.3 DML and Conditional Difference-in-Differences . . . . . . . . . . . 457
Comparison to Adding Regression Controls . . . . . . . . . . . . . 459
16.4 Example: Minimum Wage . . . . . . . . . . . . . . . . . . . . . . . 459
16.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
16.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
16.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
16.A Conditional Difference-in-Differences with Repeated Cross-Sections 466
17 Regression Discontinuity Designs 470
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
17.2 The Basic RDD Framework . . . . . . . . . . . . . . . . . . . . . . . 472
Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
17.3 RDD with (Many) Covariates . . . . . . . . . . . . . . . . . . . . . . 474
Motivation for Using Covariates . . . . . . . . . . . . . . . . . . . . 474
Low-Dimensional Covariates . . . . . . . . . . . . . . . . . . . . . . 475
High-Dimensional Covariates . . . . . . . . . . . . . . . . . . . . . 476
Heterogeneous Treatment Effects and Adjustments for Heterogeneity480
17.4 Empirical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
17.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
17.6 Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
17.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483