Introduction |
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xvii | |
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1 | (100) |
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3 | (22) |
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3 | (1) |
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1.2 Estimating the Causal Effect |
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3 | (4) |
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1.2.1 Graphing the Causal Effect |
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3 | (1) |
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1.2.2 A Linear Causal Model |
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4 | (1) |
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1.2.3 Simulation of the Causal Effect |
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4 | (1) |
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1.2.4 Averaging to Estimate the Causal Effect |
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5 | (2) |
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1.2.5 Assumptions of the OLS Model |
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7 | (1) |
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1.3 Matrix Algebra of the OLS Model |
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7 | (6) |
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1.3.1 Standard Algebra of the OLS Model |
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8 | (1) |
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1.3.2 Algebraic OLS Estimator in R |
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9 | (1) |
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9 | (1) |
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1.3.4 Multiplying Matrices in R |
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10 | (1) |
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1.3.5 Matrix Estimator of OLS |
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11 | (1) |
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1.3.6 Matrix Estimator of OLS in R |
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12 | (1) |
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1.4 Least Squares Method for OLS |
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13 | (3) |
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13 | (1) |
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1.4.2 Algebra of Least Squares |
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14 | (1) |
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1.4.3 Estimating Least Squares in R |
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14 | (1) |
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15 | (1) |
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1.5 Measuring Uncertainty |
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16 | (4) |
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16 | (2) |
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1.5.2 Introduction to the Bootstrap |
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18 | (1) |
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18 | (1) |
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19 | (1) |
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20 | (3) |
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1.6.1 A Linear Model of Returns to Schooling |
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20 | (1) |
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20 | (1) |
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1.6.3 Plotting Returns to Schooling |
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21 | (1) |
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1.6.4 Estimating Returns to Schooling |
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22 | (1) |
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1.7 Discussion and Further Reading |
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23 | (2) |
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25 | (26) |
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25 | (1) |
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2.2 Long and Short Regression |
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25 | (6) |
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2.2.1 Using Short Regression |
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25 | (1) |
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2.2.2 Independent Explanatory Variables |
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26 | (1) |
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2.2.3 Dependent Explanatory Variables |
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27 | (1) |
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2.2.4 Simulation with Multiple Explanatory Variables |
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27 | (3) |
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2.2.5 Matrix Algebra of Short Regression |
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30 | (1) |
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2.3 Collinearity and Multicollinearity |
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31 | (2) |
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2.3.1 Matrix Algebra of Multicollinearity |
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32 | (1) |
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2.3.2 Understanding Multicollinearity with R |
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32 | (1) |
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33 | (3) |
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2.4.1 Multiple Regression of Returns to Schooling |
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33 | (1) |
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34 | (1) |
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2.4.3 OLS Estimates of Returns to Schooling |
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34 | (2) |
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36 | (7) |
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36 | (2) |
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2.5.2 Simulation of Dual Path Model |
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38 | (1) |
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2.5.3 Dual Path Estimator Versus Long Regression |
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39 | (3) |
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2.5.4 Matrix Algebra of the Dual Path Estimator |
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42 | (1) |
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2.5.5 Dual Path Estimator in R |
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43 | (1) |
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2.6 Are Bankers Racist or Greedy? |
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43 | (6) |
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44 | (1) |
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2.6.2 Causal Pathways of Discrimination |
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44 | (1) |
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2.6.3 Estimating the Direct Effect |
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45 | (1) |
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2.6.4 Adding in More Variables |
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46 | (1) |
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2.6.5 Bootstrap Dual Path Estimator in R |
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47 | (1) |
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2.6.6 Policy Implications of Dual Path Estimates |
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48 | (1) |
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2.7 Discussion and Further Reading |
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49 | (2) |
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51 | (24) |
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51 | (1) |
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52 | (2) |
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3.2.1 Confounded Model DAG |
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52 | (1) |
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3.2.2 Confounded Linear Model |
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53 | (1) |
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3.2.3 Simulation of Confounded Data |
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54 | (1) |
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54 | (7) |
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3.3.1 Graph Algebra of IV Estimator |
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55 | (1) |
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3.3.2 Properties of IV Estimator |
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56 | (1) |
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3.3.3 IV Estimator with Standard Algebra |
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56 | (1) |
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3.3.4 Simulation of an IV Estimator |
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56 | (1) |
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3.3.5 IV Estimator with Matrix Algebra |
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57 | (1) |
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3.3.6 Two-Stage Least Squares |
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58 | (1) |
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59 | (1) |
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3.3.8 Bootstrap IV Estimator for R |
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59 | (2) |
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61 | (5) |
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3.4.1 Distance to College as an Instrument |
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62 | (1) |
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62 | (1) |
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3.4.3 Simple IV Estimates of Returns to Schooling |
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63 | (1) |
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3.4.4 Matrix Algebra IV Estimates of Returns to Schooling |
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64 | (1) |
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3.4.5 Concerns with Distance to College |
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65 | (1) |
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66 | (3) |
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3.5.1 Test of Instrument Validity |
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67 | (1) |
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3.5.2 Test of Instrument Validity in R |
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68 | (1) |
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3.6 Better LATE than Nothing |
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69 | (4) |
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3.6.1 Heterogeneous Effects |
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69 | (1) |
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3.6.2 Local Average Treatment Effect |
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70 | (2) |
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72 | (1) |
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3.6.4 LATE Estimates of Returns to Schooling |
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72 | (1) |
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3.7 Discussion and Further Reading |
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73 | (2) |
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75 | (26) |
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75 | (1) |
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76 | (3) |
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4.2.1 Model of Potential Outcomes |
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76 | (1) |
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4.2.2 Simulation of Impossible Data |
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76 | (1) |
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4.2.3 Distribution of the Treatment Effect |
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77 | (2) |
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4.3 Average Treatment Effect |
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79 | (3) |
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4.3.1 ATE and Its Derivation |
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79 | (1) |
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4.3.2 ATE and Do Operators |
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80 | (1) |
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4.3.3 ATE and Unconfoundedness |
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81 | (1) |
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4.3.4 ATE and Simulated Data |
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82 | (1) |
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82 | (2) |
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4.4.1 Kolmogorov's Conjecture |
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82 | (1) |
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4.4.2 Kolmogorov Bounds in R |
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83 | (1) |
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4.5 Do "Nudges" Increase Savings? |
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84 | (3) |
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4.5.1 Field Experiment Data |
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85 | (1) |
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4.5.2 Bounds on the Distribution of Balance Changes |
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86 | (1) |
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4.5.3 Intent To Treat Discussion |
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87 | (1) |
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87 | (7) |
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87 | (1) |
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4.6.2 Simulation of Manski Bounds |
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88 | (1) |
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4.6.3 Bounding the Average Treatment Effect |
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88 | (1) |
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4.6.4 Natural Bounds of the Average Treatment Effect |
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89 | (1) |
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4.6.5 Natural Bounds with Simulated Data |
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90 | (1) |
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4.6.6 Are Natural Bounds Useless? |
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90 | (1) |
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4.6.7 Bounds with Exogenous Variation |
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91 | (1) |
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4.6.8 Exogenous Variation in Simulated Data |
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92 | (1) |
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4.6.9 Bounds with Monotonicity |
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92 | (1) |
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4.6.10 Bounds with Monotonicity in Simulated Data |
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93 | (1) |
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4.7 More Guns, Less Crime? |
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94 | (4) |
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94 | (1) |
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4.7.2 ATE of RTC Laws under Unconfoundedness |
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95 | (1) |
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4.7.3 Natural Bounds on ATE of RTC Laws |
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95 | (2) |
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4.7.4 Bounds on ATE of RTC Laws with Exogenous Variation |
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97 | (1) |
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4.7.5 Bounds on ATE of RTC Laws with Monotonicity |
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98 | (1) |
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4.8 Discussion and Further Reading |
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98 | (3) |
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101 | (130) |
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103 | (32) |
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103 | (1) |
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104 | (2) |
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104 | (1) |
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105 | (1) |
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106 | (1) |
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106 | (4) |
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5.3.1 Simple Discrete Choice Model |
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107 | (1) |
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5.3.2 Simulating Discrete Choice |
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108 | (1) |
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5.3.3 Modeling Discrete Choice |
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108 | (2) |
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110 | (7) |
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5.4.1 Binomial Likelihood |
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110 | (2) |
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5.4.2 Binomial Likelihood in R |
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112 | (1) |
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5.4.3 OLS with Maximum Likelihood |
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112 | (2) |
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5.4.4 Maximum Likelihood OLS in R |
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114 | (1) |
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115 | (1) |
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116 | (1) |
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5.4.7 Generalized Linear Model |
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116 | (1) |
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5.5 McFadden's Random Utility Model |
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117 | (4) |
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117 | (1) |
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5.5.2 Probit and Logit Estimators |
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118 | (1) |
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5.5.3 Simulation with Probit and Logit Estimators |
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119 | (2) |
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121 | (6) |
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5.6.1 Multinomial Choice Model |
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121 | (1) |
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122 | (2) |
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5.6.3 Multinomial Probit in R |
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124 | (1) |
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125 | (1) |
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5.6.5 Multinomial Logit in R |
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125 | (1) |
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5.6.6 Simulating Multinomial Choice |
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126 | (1) |
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127 | (5) |
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5.7.1 National Household Travel Survey |
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128 | (1) |
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129 | (2) |
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5.7.3 Estimating Demand for Rail |
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131 | (1) |
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5.7.4 Predicting Demand for Rail |
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131 | (1) |
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5.8 Discussion and Further Reading |
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132 | (3) |
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6 Estimating Selection Models |
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135 | (28) |
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135 | (1) |
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6.2 Modeling Censored Data |
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136 | (5) |
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6.2.1 A Model of Censored Data |
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136 | (1) |
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6.2.2 Simulation of Censored Data |
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136 | (2) |
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138 | (2) |
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140 | (1) |
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6.2.5 Tobit Estimator in R |
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140 | (1) |
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6.3 Censoring Due to Minimum Wages |
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141 | (3) |
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6.3.1 National Longitudinal Survey of Youth 1997 |
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142 | (1) |
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143 | (1) |
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6.4 Modeling Selected Data |
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144 | (6) |
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145 | (1) |
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6.4.2 Simulation of a Selection Model |
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145 | (1) |
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146 | (2) |
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148 | (1) |
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6.4.5 Heckman Estimator in R |
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149 | (1) |
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6.5 Analyzing the Gender Wage Gap |
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150 | (5) |
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150 | (2) |
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152 | (1) |
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6.5.3 Heckman Estimates of Gender Gap |
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152 | (3) |
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6.6 Back to School Returns |
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155 | (7) |
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155 | (2) |
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6.6.2 College vs. No College |
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157 | (1) |
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158 | (1) |
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6.6.4 Heckman Estimates of Returns to Schooling |
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158 | (3) |
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161 | (1) |
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6.7 Discussion and Further Reading |
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162 | (1) |
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7 Demand Estimation with IV |
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163 | (20) |
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163 | (1) |
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164 | (4) |
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7.2.1 Competition is a Game |
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164 | (1) |
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165 | (2) |
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167 | (1) |
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7.3 Estimating Demand in Hotelling's Model |
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168 | (3) |
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7.3.1 Simulation of Hotelling Model |
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168 | (1) |
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7.3.2 Prices are Endogenous |
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168 | (1) |
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169 | (2) |
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171 | (1) |
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7.4 Berry Model of Demand |
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171 | (4) |
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172 | (1) |
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7.4.2 A Problem with Cost Shifters |
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172 | (1) |
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7.4.3 Empirical Model of Demand |
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173 | (1) |
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173 | (1) |
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7.4.5 Demand Shifters to Estimate Supply |
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174 | (1) |
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7.4.6 Demand Estimation from Supply Estimates |
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175 | (1) |
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7.5 Introduction of Apple Cinnamon Cheerios |
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175 | (6) |
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7.5.1 Dominick's Data for Cereal |
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176 | (1) |
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7.5.2 Instrument for Price of Cereal |
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177 | (1) |
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7.5.3 Demand for Apple Cinnamon Cheerios |
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178 | (3) |
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7.5.4 Value of Apple Cinnamon Cheerios |
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181 | (1) |
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7.6 Discussion and Further Reading |
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181 | (2) |
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183 | (24) |
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183 | (1) |
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8.2 Mixed Strategy Nash Equilibrium |
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183 | (8) |
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8.2.1 Coaches' Decision Problem |
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184 | (1) |
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185 | (1) |
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186 | (1) |
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8.2.4 Third and Fourth Down Game |
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187 | (1) |
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8.2.5 Equilibrium Strategies |
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188 | (1) |
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8.2.6 Equilibrium Strategies in R |
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189 | (1) |
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8.2.7 Simulation of Third and Fourth Down Game |
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189 | (2) |
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8.3 Generalized Method of Moments |
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191 | (6) |
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191 | (1) |
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8.3.2 Simulated Moments OLS |
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192 | (2) |
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194 | (1) |
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8.3.4 GMM OLS Estimator in R |
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195 | (1) |
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8.3.5 GMM of Returns to Schooling |
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196 | (1) |
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8.4 Estimating the Third Down Game |
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197 | (2) |
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198 | (1) |
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8.4.2 Third Down GMM Estimator in R |
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198 | (1) |
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8.5 Are NFL Coaches Rational? |
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199 | (6) |
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200 | (1) |
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8.5.2 Estimating Third Down Game in R |
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201 | (2) |
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8.5.3 Predicting the Fourth Down Game |
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203 | (2) |
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8.5.4 Testing Rationality of NFL Coaches |
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205 | (1) |
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8.6 Discussion and Further Reading |
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205 | (2) |
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9 Estimating Auction Models |
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207 | (24) |
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207 | (1) |
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208 | (5) |
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209 | (1) |
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9.2.2 Sealed Bid Simulation |
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210 | (1) |
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9.2.3 Sealed Bid Estimator |
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211 | (1) |
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9.2.4 Sealed Bid Estimator in R |
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212 | (1) |
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213 | (5) |
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214 | (1) |
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9.3.2 Identifying the Value Distribution |
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215 | (1) |
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9.3.3 English Auction Estimator |
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216 | (1) |
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9.3.4 English Auction Estimator in R |
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216 | (2) |
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9.4 Are Loggers Rational? |
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218 | (3) |
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219 | (1) |
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9.4.2 Sealed Bid Auctions |
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220 | (1) |
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221 | (1) |
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9.4.4 Comparing Estimates |
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221 | (1) |
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9.5 Are Loggers Colluding? |
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221 | (6) |
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9.5.1 A Test of Collusion |
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222 | (1) |
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9.5.2 "Large" English Auctions |
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223 | (1) |
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9.5.3 Large English Auction Estimator |
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224 | (1) |
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9.5.4 Large English Auction Estimator in R |
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224 | (1) |
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9.5.5 Evidence of Collusion |
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225 | (1) |
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9.5.6 Large Sealed Bid Auction Estimator |
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226 | (1) |
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9.5.7 Large Sealed Bid Auction Estimator in R |
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227 | (1) |
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9.6 Discussion and Further Reading |
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227 | (4) |
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231 | (70) |
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233 | (18) |
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233 | (1) |
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233 | (3) |
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10.2.1 First Difference Model |
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234 | (1) |
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10.2.2 Simulated Panel Data |
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235 | (1) |
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10.2.3 OLS Estimation of First Differences |
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235 | (1) |
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10.3 Difference in Difference |
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236 | (2) |
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10.3.1 Difference in Difference Estimator |
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236 | (1) |
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10.3.2 Difference in Difference Estimator in R |
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237 | (1) |
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10.4 Minimum Wage Increase in New Jersey |
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238 | (3) |
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10.4.1 Data from Card and Krueger (1994) |
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238 | (1) |
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10.4.2 Difference in Difference Estimates |
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239 | (2) |
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241 | (5) |
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10.5.1 Fixed Effects Estimator |
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241 | (1) |
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10.5.2 Nuisance Parameter |
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242 | (1) |
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10.5.3 Adjusted Fixed Effects Estimator |
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243 | (1) |
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10.5.4 Two Step Fixed Effects Estimator |
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243 | (1) |
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10.5.5 Fixed Effects Estimator in R |
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244 | (2) |
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10.6 Effect of a Federal Minimum Wage Increase |
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246 | (4) |
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247 | (1) |
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10.6.2 Fixed Effects Estimators of the Minimum Wage |
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248 | (1) |
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10.6.3 Are Workers Better Off? |
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249 | (1) |
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10.7 Discussion and Further Reading |
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250 | (1) |
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251 | (26) |
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251 | (1) |
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11.2 Beyond "Parallel Trends" |
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251 | (5) |
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11.2.1 A General Fixed Effects Model |
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252 | (1) |
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11.2.2 A Slightly Less General Model |
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252 | (1) |
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11.2.3 Synthetic Synthetic Control Data |
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252 | (2) |
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11.2.4 Constructing Synthetic Controls with OLS |
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254 | (1) |
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254 | (1) |
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11.2.6 A "Wide" Data Problem |
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255 | (1) |
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256 | (2) |
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11.3.1 Restricting Weights |
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257 | (1) |
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11.3.2 Synthetic Control Estimator in R |
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258 | (1) |
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258 | (3) |
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11.4.1 Turducken Estimation |
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259 | (1) |
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259 | (1) |
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260 | (1) |
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261 | (7) |
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11.5.1 Matrix Factorization |
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262 | (1) |
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11.5.2 Convex Matrix Factorization |
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262 | (2) |
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11.5.3 Synthetic Controls using Factors |
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264 | (1) |
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11.5.4 Estimating the Weights |
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264 | (1) |
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11.5.5 Convex Factor Model Estimator in R |
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265 | (3) |
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11.6 Returning to Minimum Wage Effects |
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268 | (6) |
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268 | (1) |
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11.6.2 Synthetic Control Estimates |
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269 | (1) |
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270 | (1) |
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11.6.4 Factor Model Estimates |
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270 | (4) |
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11.7 Discussion and Further Reading |
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274 | (3) |
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277 | (24) |
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277 | (1) |
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12.2 Two-Type Mixture Models |
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278 | (5) |
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12.2.1 Simulation of Two-Type Mixture |
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278 | (1) |
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12.2.2 Knowing the Component Distributions |
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279 | (1) |
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12.2.3 Observing Multiple Signals |
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280 | (3) |
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12.3 Two Signal Mixture Models |
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283 | (5) |
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12.3.1 Model of Two Signal Data |
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283 | (1) |
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12.3.2 Simulation of Two Signal Data |
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283 | (1) |
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12.3.3 Conditional Independence of Signals |
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284 | (1) |
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12.3.4 Two Signal Estimator |
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284 | (1) |
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12.3.5 Two Signal Estimator Algorithm |
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285 | (1) |
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12.3.6 Mixture Model Estimator in R |
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286 | (2) |
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12.4 Twins Reports and Returns to Schooling |
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288 | (6) |
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12.4.1 Mixture Model of Twin Reports |
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289 | (1) |
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290 | (1) |
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12.4.3 Mixture Model Approach to Measurement Error |
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290 | (2) |
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12.4.4 Estimating Returns to Schooling from Twins |
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292 | (2) |
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12.5 Revisiting Minimum Wage Effects |
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294 | (5) |
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12.5.1 Restaurant Employment |
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294 | (1) |
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12.5.2 Mixture Model Estimation of Restaurant Type |
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295 | (1) |
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12.5.3 Heterogeneous Minimum Wage Effect |
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295 | (4) |
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12.6 Discussion and Further Reading |
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299 | (2) |
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301 | (2) |
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303 | (28) |
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303 | (1) |
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303 | (11) |
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A.2.1 A Model of a Sample |
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304 | (1) |
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A.2.2 Simulation of a Sample |
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304 | (1) |
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A.2.3 Many Imaginary Samples |
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304 | (2) |
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A.2.4 Law of Large Numbers |
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306 | (1) |
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A.2.5 Central Limit Theorem |
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307 | (1) |
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A.2.6 Approximation of the Limiting Distribution |
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308 | (1) |
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A.2.7 Simulation of Approximate Distributions |
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309 | (1) |
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310 | (2) |
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312 | (2) |
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314 | (2) |
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314 | (1) |
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A.3.2 Determining the Posterior |
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314 | (1) |
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A.3.3 Determining the Posterior in R |
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315 | (1) |
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A.4 Empirical Bayesian Estimation |
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316 | (6) |
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A.4.1 A Large Number of Samples |
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316 | (1) |
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A.4.2 Solving for the Prior and Posterior |
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317 | (1) |
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A.4.3 Solving for the Prior in R |
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318 | (2) |
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A.4.4 Estimating the Posterior of the Mean |
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320 | (2) |
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A.5 The Sultan of the Small Sample Size |
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322 | (4) |
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A.5.1 Classical or Bayesian? |
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322 | (1) |
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323 | (1) |
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A.5.3 Estimating the Prior |
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323 | (2) |
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A.5.4 Paciorek's Posterior |
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325 | (1) |
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326 | (3) |
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A.6.1 Decision Making Under Uncertainty |
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327 | (1) |
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327 | (1) |
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A.6.3 What in the World Does Wald Think? |
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328 | (1) |
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A.6.4 Two Types of Uncertainty? |
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329 | (1) |
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A.7 Discussion and Further Reading |
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329 | (2) |
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B Statistical Programming in R |
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|
331 | (24) |
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331 | (1) |
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331 | (7) |
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331 | (2) |
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333 | (2) |
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335 | (2) |
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337 | (1) |
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B.3 Interacting with Objects |
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338 | (6) |
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B.3.1 Transforming Objects |
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338 | (1) |
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B.3.2 Logical Expressions |
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|
339 | (1) |
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B.3.3 Retrieving Information from a Position |
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|
340 | (3) |
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B.3.4 Retrieving the Position from the Information |
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343 | (1) |
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344 | (3) |
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|
345 | (1) |
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|
345 | (1) |
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346 | (1) |
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|
347 | (1) |
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347 | (3) |
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347 | (1) |
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348 | (1) |
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349 | (1) |
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350 | (3) |
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350 | (2) |
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|
352 | (1) |
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B.7 Discussion and Further Reading |
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|
353 | (2) |
Note |
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355 | (2) |
Bibliography |
|
357 | (6) |
Author index |
|
363 | (2) |
Subject index |
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365 | |