Causal Inference and Machine Learning In Economics, Social, and Health Sciences.pdf
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因果推断与机器学习结合能够让模型不仅预测结果，还能理解变量间的因果关系，从而支持干预决策和泛化能力提升。核心概念：因果推断关注“为什么会发生”和“如果采取行动会发生什么”，通过因果图（Causal Graph）、潜在结果框架（Potential Outcomes）等方法识别变量间的因果关系 。而机器学习主要依赖数据驱动的模式识别，擅长预测但难以区分相关性与因果性。将两者结合形成因果机器学习（Causal ML），可以在高维复杂系统中提供可解释、可干预的决策支持

1 Introduction 1
1.1 Prediction vs. Estimation               2
1.2 Applications of Machine Learning in Economics and Social Sciences   4
1.3 Machine Learning and Econometrics: Complementary Roles     5
1.4 Core Modeling Frameworks              . 6
1.4.1 Statistical vs. Machine Learning Paradigms       . 6
1.4.2 Parametric and Nonparametric Models         8
1.4.3 Predictive vs. Causal Thinking           9
1.4.4 Model Selection               . 10
1.4.5 The Role of Simulation             . 11
1.5 Concluding Remarks                12
2 From Data to Causality 13
2.1 Qualitative and Quantitative Research Methods        . 16
2.2 Quantitative Research Methods             17
2.3 Data and Visualization               . 19
2.4 Correlation                   20
2.4.1 Correlation and Regression            27
2.5 Effect of X on Y / Regression             . 27
2.5.1 How Can We Estimate the Population Parameters, β0 and β1?  28
2.5.2 From Estimation to Prediction           29
2.6 Causal Effect                   31
3 Learning Systems 34
3.1 Learning Systems                 36
4 Error 40
4.1 Estimation Error                 42
4.2 Efficiency                   . 47
4.3 Mean Square Error                . 49
4.3.1 From One Random Sample to Population Parameters    . 52
4.4 Prediction Error: MSPE               55
4.5 Technical Points and Proofs              . 61
4.5.1 Unbiasedness of a Parameter            61
4.5.2 Unbiasedness of Sample Mean Estimator        62
4.5.3 The Variance of the Sampling Distribution of Sample Means (Sam￾pling Variance)               . 62
4.5.4 Unbiasedness of Sample Variance Estimator       . 63
vii
viii Contents
5 Bias–Variance Trade-off 77
5.1 Bias–Variance Trade-off               . 78
5.1.1 Simulation for Polynomial Regression         80
5.2 Simulation for Population Parameter           . 94
5.3 Biased Estimator as a Predictor             96
6 Overfitting 100
6.1 Out-sample MSPE                 103
6.2 Technical Points about Out-sample and In-sample MSPE      107
7 Parametric Estimation: Basics 109
7.1 The Dichotomy of Statistical Modeling           109
7.1.1 Data versus Algorithmic Approaches         . 109
7.1.2 Parametric versus Nonparametric Models        . 111
7.2 Parametric Estimations               . 112
7.2.1 Linear Probability Model            . 113
7.2.2 Logistic Regression              . 115
7.2.3 Linear vs. Logistic Probability Models         118
8 Nonparametric Estimations: Basics 123
8.1 Density Estimation                . 124
8.1.1 Histogram Density Estimation           124
8.1.2 Naive Estimator (Parzen Windows)         . 125
8.2 Kernel Density Estimation              . 125
8.2.1 Common Kernels               126
8.2.2 Simulation: KDE vs. Histogram           126
8.2.3 Prediction with Kernel Density Estimation       . 128
8.2.4 Kernel Regression              . 129
8.2.5 Simulation: Kernel Regression Example         131
8.2.6 Multivariate and Additive Models          132
8.2.7 Bandwidth Selection in Kernel Density Estimation and Kernel
Regression                 133
8.3 Conclusion Remarks                . 134
9 Hyperparameter Tuning 137
9.1 Training, Validation, and Test Datasets           138
9.2 Data Splitting                  140
9.2.1 How Can We Split the Data Randomly?        . 142
9.3 k-Fold Cross-Validation               . 144
9.3.1 What is k-Fold Cross-Validation?          . 145
9.3.2 Building a Simple k-Fold Cross-Validation Loop      145
9.3.3 Advantages of k-Fold Cross-Validation         146
9.4 Grid Search                  . 147
9.5 Simulation of Grid Search with Cross-Validation        . 148
9.5.1 Repetition for Robust Evaluation           151
9.6 Bootstrapped Grid Search              . 154
9.6.1 Simulation: Bootstrapped Grid Search in R       . 155
10 Classification 160
10.1 Classifying Handwritten Digits             . 160
10.2 Linear Classifiers                 163
10.3 k-Nearest Neighbors                . 167
Contents ix
10.3.1 Example: Finding Nearest Neighbors with k = 2      173
10.3.2 More Realistic Example             175
10.3.3 mnist_27 Dataset               177
10.3.4 Single-run Grid Search for k            179
10.3.5 Multi-run Grid Search (Training the Model) for k      181
10.3.6 Grid search with parallel computing (mclapply)      . 182
10.3.7 knn3 from caret: Single vs Parallel Core Application     184
10.4 Tuning in Classification               . 187
10.4.1 Confusion Matrix               187
10.4.2 Why Accuracy Can Be Misleading          187
10.4.3 Performance Measures Beyond Accuracy        . 188
10.4.4 Kappa Statistic               . 189
10.4.5 Youden’s J Statistic              190
10.4.6 ROC Curve                . 190
10.4.7 ROC Curve and AUC             . 193
10.4.8 Using ROCR and pROC Packages           194
10.4.9 Tuning kNN with AUC             197
10.4.10 Test Score and Threshold            . 198
10.5 Conclusion                   200
11 Model Selection and Sparsity 202
11.1 Model Selection in Econometrics             203
11.2 Model Assessment Criteria              . 203
11.2.1 Adjusted R2 as a Model Selection Criterion       . 204
11.2.2 Mallows’ Cp Statistic              205
11.2.3 Akaike Information Criterion           . 206
11.2.4 Bayesian Information Criterion           206
11.2.5 Cross-Validation and Bootstrap Methods        207
11.3 Subset Variable Selection Methods            . 208
11.3.1 Best Subset Selection             . 208
11.3.2 Forward Selection              . 209
11.3.3 Backward Selection              . 210
11.3.4 Hybrid (Stepwise) Selection            210
11.4 Selecting Functional Form in Econometric Models        . 211
11.4.1 Functional Forms and Transformations         . 211
11.4.2 Models with Structural Changes: Piecewise Linear Models   . 212
11.4.3 Extensions and Alternative Methods         . 213
11.5 Model Selection in Machine Learning           . 214
11.5.1 Comparing Prediction Models           . 214
11.5.2 Balancing Interpretability and Predictive Accuracy     . 217
11.5.3 Practical Guidelines              218
11.6 Sparsity in Model Selection              . 218
11.7 Oracle Properties in Model Selection           . 220
12 Penalized Regression Methods 224
12.1 Ridge Regression                 226
12.1.1 Standardization of Predictors           . 230
12.1.2 Implementation and Simulation of Ridge Regression     . 231
12.2 LASSO Regression                 236
12.3 Coordinate Descent for LASSO Regression          239
12.4 Least Angle Regression for LASSO            . 241
x Contents
12.5 Differences Between Coordinate Descent and LARS       . 242
12.6 Implementation and Simulation of LASSO Regression       244
12.7 The Relationship Between the LASSO and OLS Coefficient Estimates  . 247
12.8 LASSO: Key Takeaways               248
12.9 Adaptive LASSO                 250
12.10 Steps in Adaptive LASSO               251
12.11 Implementation and Simulation of Adaptive LASSO       . 252
12.12 Adaptive LASSO: Practical Notes            . 256
12.13 Elastic Net Regression               . 257
12.13.1 Solution to the Elastic Net Optimization Problem     . 258
12.14 Implementation and Simulation of Elastic Net         259
12.15 Elastic Net: Final Notes               . 262
12.16 Technical: Derivation of Ridge Regression Estimator       . 263
13 Classification and Regression Trees (CART) 267
13.1 Basic Concepts                  270
13.1.1 Gini Index - Impurity Measure           . 271
13.1.2 Finding the Split               272
13.1.3 Can We Find a Better Split?           . 272
13.1.4 Function to Find the Important Variables and Gains     274
13.1.5 Variable Importance: Easy and Heuristic Way       277
13.1.6 Recursive Partitioning: The Tree Model        . 278
13.2 Step-by-Step Tree Construction for Binary Classification      282
13.3 Classification Decision Trees with rpart           288
13.3.1 Pruning the Tree               289
13.4 Regression Trees                 . 292
13.5 Building and Interpreting Regression Trees with rpart: A Step-by-Step Guide295
13.6 Additional Considerations and Extensions for Regression Trees    . 299
13.6.1 Handling Missing Data in Regression Trees       . 300
13.6.2 Weighted Regression Trees            300
13.6.3 Alternative Splitting Criteria           . 300
14 Ensemble Learning and Random Forest 303
14.1 Bagging (Bootstrap Aggregating)            . 303
14.1.1 Application with Multiple Splits          . 308
14.1.2 Tuning?                 . 310
14.1.3 Using Out-of-Bag Error             310
14.1.4 OOB Error Rate               . 311
14.2 Random Forest                 . 312
14.2.1 Random Forest-like Variable Selection         314
14.3 Implementing Random Forest in R            316
14.3.1 Building a Random Forest Model on Titanic Data     . 317
14.3.2 AUC                  . 320
14.3.3 Regression: Hitters              . 325
14.3.4 Importance of Variables             327
14.3.5 Local Importance               . 331
14.3.6 randomForestExplainer             . 335
15 Boosting 339
15.1 Types of Boosting Models              . 339
15.2 Gradient Boosting Machines              340
Contents xi
15.2.1 Gradient Boosting Algorithm Steps          341
15.2.2 Hyperparameter Tuning in GBM          . 344
15.3 GBM in R                   348
15.3.1 Variable Importance in GBM           . 355
15.3.2 External Training              . 357
15.4 AdaBoost                   . 359
15.5 XGBoost                   . 367
15.5.1 Regression Example              368
15.5.2 Classification Example              371
15.5.3 Tuning in XGBoost              375
15.6 The Implementation of Boosting Methods          . 377
16 Counterfactual Framework 380
16.1 Counterfactual Framework              . 382
16.1.1 Assumptions of the Rubin Causal Model        . 384
16.2 Average Treatment Effects              . 385
16.3 Selection Bias and Heterogeneous Treatment Effect Bias      387
16.4 Limitations of RCM                . 389
17 Randomized Controlled Trials 391
17.1 Key Assumptions                 392
17.2 Randomization Inference               392
17.3 Linear Regression in RCTs              . 396
17.4 Regression Adjustment in Randomized Experiments       . 398
17.4.1 Residual Strategy in Randomized Experiments      . 398
17.4.2 Regression Strategy in Randomized Experiments      399
17.4.3 Single Regression with Covariate Adjustment       400
17.4.4 Simulation: Covariate Adjustment in RCTs        401
17.4.5 Missing Data                403
17.5 Fisher’s Randomization Inference            . 404
17.5.1 p-value Calculation and Simulation          405
17.6 Challenges in Randomized Controlled Trials         . 408
18 Selection on Observables 410
18.1 Assumptions and Definitions Behind Selection on Observables     411
18.1.1 Conditional Independence Assumption (Unconfoundedness)   . 411
18.1.2 Common Support Assumption (Overlap Condition)     . 411
18.2 Defining the (Conditional) Average Treatment Effect       412
18.3 Regression-Based Estimation Methods           414
18.3.1 Separate Regressions for Treated and Control Groups    . 415
18.3.2 Single Regression with Covariate Adjustment       416
18.3.3 Inference and Robust Standard Errors         417
19 Double Machine Learning 422
19.1 Double Machine Learning               424
19.1.1 Brief Practical Framework (DML1 and DML2 for LASSO)   425
19.1.2 Inference and Robust Standard Errors         426
19.1.3 Step-by-step DM1-LASSO and Simulation        426
19.1.4 Simulation for DML1             . 428
19.1.5 Step-by-step Procedure for DML2-LASSO        430
19.1.6 Simulation for DML2             . 430
xii Contents
19.1.7 DML2-LASSO with the Plug-In Penalty        . 432
19.1.8 Simulation for DML2 with Plug-In Penalty       . 434
19.1.9 Sparsity in DML-LASSO            . 436
19.2 DML2 -Decision Trees                437
19.3 DML2: Random Forest                441
19.4 Technical Notes: From FWL to DML           . 444
19.4.1 Frisch–Waugh–Lovell Theorem           444
19.4.2 From FWL to Double Machine Learning        . 446
19.4.3 Debiased LASSO               450
20 Matching Methods 453
20.1 Subclassification or Stratification            . 453
20.2 Matching Methods                 456
20.2.1 Factors influence the implementation of matching methods   458
20.2.2 Assessing Balance              . 459
20.2.3 Matching: Benefits and Limitations          464
20.3 Propensity Score Matching              . 466
20.3.1 Estimating the Propensity Score          . 467
20.3.2 Matching Methods in PSM            468
20.3.3 Assessing Balance in PSM            . 470
20.4 Calculation of Treatment Effects             . 471
20.4.1 Regression Adjustment Including Propensity Score      471
20.4.2 Matching and Stratification on Propensity Score      472
20.4.3 Estimation of Standard Errors in PSM         472
20.5 Integrating XGBoost with MatchIt for Propensity Score Matching   . 474
21 Inverse Weighting and Doubly Robust Estimation 482
21.1 Inverse Probability Weighting             . 482
21.2 Doubly Robust Estimators: AIPW            . 488
21.3 Challenges of Selection on Observables           497
21.4 Technical Note: Derivation and Doubly robust of the AIPW Estimator  499
22 Selection on Unobservables and DML-IV 502
22.1 Instrumental Variables               . 503
22.1.1 Core IV Concepts              . 504
22.1.2 IV in the Potential Outcomes Framework and RCTs     506
22.1.3 IV in the Observational Data           . 510
22.1.4 Weak Instrument               513
22.2 Double Machine Learning IV              514
22.2.1 Structural Model and Instrumental Variables Estimation   . 514
22.2.2 Double Machine Learning (DML-IV) Estimation      515
22.2.3 Neyman Orthogonality and Robustness        . 515
22.2.4 Algorithm: DML-IV              516
22.2.5 DML2-IV Simulation using LASSO          518
22.2.6 DML2-IV Simulation using RANDOM FOREST      522
22.3 Closing Remarks: ML for IV              524
22.4 Technical: Connecting IV to potential outcomes to 2sls      . 525
23 Heterogeneous Treatment Effects 531
23.1 Parametric Approaches to Estimating Heterogeneous Treatment Effects  . 531
23.1.1 Interaction Models in Linear Regression         531
Contents xiii
23.1.2 Stratified or Subgroup Analysis           532
23.1.3 Parametric Generalized Linear Models         536
23.1.4 Random Coefficients Models           . 537
23.2 Double Machine Learning for Conditional Average Treatment Effects  . 538
23.3 Fully Nonparametric Methods for HTE Estimation        541
23.3.1 Matching and Weighting Methods for HTE Estimation     541
23.3.2 Kernel-Based Methods for HTE Estimation       . 542
24 Causal Trees and Forests 544
24.1 Honest Causal Tree (CT-H) Method            545
24.1.1 CT-H Algorithm               549
24.1.2 Simulation: Honest Causal Tree           552
24.1.3 “Causal” Random Forests: Ensemble Methods for HTE and Inference555
24.2 Generalized Random Forests              556
24.2.1 GRF Algorithm               560
24.2.2 Simulation with GRF package in R          564
24.3 Application of Causal Forests in Economics, Health, and Social Sciences  576
24.4 Technical: Optimizing Causal Forests and Derivations       577
24.4.1 Equivalence of Step 4 Estimators in the grf Algorithm for the Causal
Forest                  578
25 Meta Learners for Treatment Effects 582
25.1 Meta-learners and CATE               583
25.2 S-Learner (Single Model Approach)            584
25.3 T-Learner (Separate Models for Treatment and Control)      584
25.3.1 Simulation of S-Learner and T-Learner        . 585
25.4 X-Learner (Cross-Fitting)               587
25.4.1 Simulation of X-Learner             588
25.5 R-Learner (Residualized Estimation)            591
25.6 DR-Learner (Doubly Robust Learner)           . 592
25.7 CATE vs. ITE                  594
26 Difference in Differences and DML-DiD 596
26.1 Panel Data, Fixed Effects, and Causal Inference        . 596
26.2 Difference-in-Differences               599
26.2.1 Controlling for Additional Covariates in DiD       602
26.2.2 Two-Way Fixed Effects with Covariates        . 603
26.2.3 Event Study Designs              604
26.2.4 Heterogeneous Treatment Effects in DiD        . 607
26.2.5 Where to Go Next: Tools, Resources, and Recent Advances   608
26.3 Double Machine Learning for DiD Estimation         610
26.3.1 Step-by-Step Implementation           . 612
26.3.2 Double Machine Learning DiD Simulation        614
26.3.3 Extension of DML-DiD to Multiple Time Periods      617
26.4 Time-varying Continuous Treatments           . 619
27 Synthetic DiD and Regression Discontinuity 625
27.1 The Synthetic Control Method             . 625
27.1.1 Generalized Synthetic Control Method         629
27.1.2 Augmented Synthetic Control Method         . 631
27.2 Synthetic Difference-in-Differences            . 633
xiv Contents
27.3 Regression Discontinuity Designs             636
27.3.1 RDD Simulation               640
27.3.2 Credibility and Extensions in RDD Applications      643
28 Time Series Forecasting 647
28.1 ARIMA: A Statistical Model for Time Series Forecasting      647
28.2 Hyndman–Khandakar Algorithm             649
28.3 TS Plots                   . 650
28.4 Box–Cox transformation               652
28.5 Stationarity                  . 654
28.6 Modeling ARIMA                 659
28.7 Grid Search for ARIMA               668
29 Direct Forecasting with Random Forests 672
29.1 Time Series Embedding for Direct Forecasting         672
29.2 VAR for Recursive Forecasting             . 674
29.3 Embedding for Direct Forecast             . 677
29.4 Random Forest with Time Series             684
29.4.1 Univariate                 686
29.4.2 Multivariate                . 688
29.5 Rolling and Expanding Windows             690
30 Neural Networks and Deep Learning 695
30.1 Neural Network: The Idea              . 696
30.2 Neural Network: More inputs              708
30.3 Deep Learning                  710
30.4 Deep Learning with keras package            . 718
30.4.1 Setting up a Keras Model             721
30.4.2 Keras with Python              . 722
30.4.3 Tuning a Keras Model             . 724
30.4.4 Visualizing Model Performance           725
30.4.5 Grid Search with Keras Tuner           727
30.4.6 Grid Search with R              729
30.5 Clasification with keras Package             . 731
30.5.1 Model Outcome and Activation Function        . 731
30.5.2 Probabilistic Model and Thresholding         732
30.5.3 keras Package               . 733
30.6 PyTorch and Keras                . 735
31 Matrix Decomposition and Applications 738
31.1 Eigenvectors and Eigenvalues              739
31.2 Single Value Decomposition              745
31.3 Rank(r) Approximations               748
31.4 Moore–Penrose Inverse               . 753
31.5 Principle Component Analysis             . 757
31.6 Factor Analysis                 . 765
32 Optimization Algorithms: Basics 773
32.1 Brute-Force Optimization               774
32.2 Derivative-based Methods              . 777
32.3 ML Estimation with Logistic Regression          . 782
32.4 Gradient Descent Algorithm              785
Contents xv
32.4.1 One-variable                787
32.4.2 Adjustable lr and SGD             788
32.4.3 Multivariable                792
32.5 Optimization with R                795

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