A Course in Econometrics

Contents -11......Page 5
Preface -3......Page 13
1.1 Theoretical and Empirical Relations 1......Page 17
1.2 Sample Means and Population Means 5......Page 21
1.4 Estimation 8......Page 24
Exercises 9......Page 25
2.2 Discrete Case 11......Page 27
2.3 Continuous Case 14......Page 30
2.4 Mixed Case 19......Page 35
2.5 Functions of Random Variables 20......Page 36
Exercises 23......Page 39
3.1 Expectations 26......Page 42
3.2 Moments 27......Page 43
3.3 Theorems on Expectations 28......Page 44
3.5 Expectations and Probabilities 30......Page 46
Exercises 32......Page 48
4.1 Joint Distributions 34......Page 50
4.2 Marginal Distributions 37......Page 53
4.3 Conditional Distributions 38......Page 54
Exercises 41......Page 57
5.1 Expectations 44......Page 60
5.2 Conditional Expectations 46......Page 62
5.3 Conditional Expectation Function 49......Page 65
5.4 Prediction 51......Page 67
5.5 Conditional Expectations and Linear Predictors 53......Page 69
Exercises 54......Page 70
6.2 Stochastic Independence 58......Page 74
6.3 Roles of Stochastic Independence 60......Page 76
6.4 Mean-Independence and Uncorrelatedness 61......Page 77
6.5 Types of Independence 64......Page 80
6.6 Strength of a Relation 65......Page 81
Exercises 67......Page 83
7.1 Univariate Normal Distribution 68......Page 84
7.2 Standard Bivariate Normal Distribution 69......Page 85
7.3 Bivariate Normal Distribution 73......Page 89
7.4 Properties of Bivariate Normal Distribution 75......Page 91
7.5 Remarks 77......Page 93
Exercises 78......Page 94
8.1 Random Sample 80......Page 96
8.2 Sample Statistics 82......Page 98
8.3 The Sample Mean 83......Page 99
8.4 Sample Moments 85......Page 101
8.5 Chi-square and Student's t Distributions 87......Page 103
8.6 Sampling from a Normal Population 90......Page 106
Exercises 92......Page 108
9.1 Introduction 94......Page 110
9.2 Sequences of Sample Statistics 97......Page 113
9.3 Asymptotics of the Sample Mean 98......Page 114
9.4 Asymptotics of Sample Moments 100......Page 116
9.5 Asymptotics of Functions of Sample Moments 101......Page 117
9.6 Asymptotics of Some Sample Statistics 103......Page 119
Exercises 104......Page 120
10.1 Introduction 106......Page 122
10.2 Sample Covariance 107......Page 123
10.3 Pair of Sample Means 109......Page 125
10.4 Ratio of Sample Means 110......Page 126
10.5 Sample Slope 111......Page 127
10.6 Variance of Sample Slope 113......Page 129
Exercises 114......Page 130
11.1 Introduction 116......Page 132
11.2 The Analogy Principle 117......Page 133
11.3 Criteria for an Estimator 118......Page 134
11.4 Asymptotic Criteria 121......Page 137
11.5 Confidence Intervals 122......Page 138
Exercises 124......Page 140
12.1 The Score Variable 128......Page 144
12.2 Cramer-Rao Inequality 129......Page 145
12.3 ZES-Rule Estimation 132......Page 148
12.4 Maximum Likelihood Estimation 134......Page 150
Exercises 136......Page 152
13.1 Introduction 138......Page 154
13.2 Estimating a Linear CEF 139......Page 155
13.3 Estimating a Nonlinear CEF 142......Page 158
13.4 Estimating a Binary Response Model 144......Page 160
13.5 Other Sampling Schemes 145......Page 161
Exercises 148......Page 164
14.1 Population Regression Function 150......Page 166
14.2 Algebra for Multiple Regression 152......Page 168
14.3 Ranks of X and Q 155......Page 171
14.4 The Short-Rank Case 156......Page 172
14.5 Second-Order Conditions 157......Page 173
Exercises 158......Page 174
15.1 Matrix Algebra for Random Variables 160......Page 176
15.2 Classical Regression Model 163......Page 179
15.4 Gauss-Markov Theorem 165......Page 181
15.5 Estimation of ct2 and V(b) 166......Page 182
Exercises 168......Page 184
16.1 Interpretation of the Classical Regression Model 170......Page 186
16.2 Estimation of Linear Functions of B 173......Page 189
16.3 Estimation of Conditional Expectation, and Prediction 175......Page 191
16.4 Measuring Goodness of Fit 176......Page 192
Exercises 179......Page 195
17.1 Regression Matrices 182......Page 198
17.2 Short and Long Regression Algebra 183......Page 199
17.3 Residual Regression 185......Page 201
17.4 Applications of Residual Regression 186......Page 202
17.5 Short and Residual Regressions in the Classical Regression Model 189......Page 205
Exercises 192......Page 208
18.2 Multivariate Normality 195......Page 211
18.3 Functions of a Standard Normal Vector 199......Page 215
18.4 Quadratic Forms in Normal Vectors 200......Page 216
Exercises 202......Page 218
19.1 Classical Normal Regression Model 204......Page 220
19.2 Maximum Likelihood Estimation 205......Page 221
19.3 Sampling Distributions 206......Page 222
19.4 Confidence Intervals 207......Page 223
19.5 Confidence Regions 208......Page 224
19.6 Shape of the Joint Confidence Region 210......Page 226
Exercises 213......Page 229
20.2 Test on a Single Parameter 214......Page 230
20.3 Test on a Set of Parameters 216......Page 232
20.4 Power of the Test 217......Page 233
20.5 Noncentral Chi-square Distribution 219......Page 235
Exercises 220......Page 236
21.1 Distribution Theory 223......Page 239
21.2 Confidence Intervals and Regions 225......Page 241
21.3 Hypothesis Tests 227......Page 243
21.4 Zero Null Subvector Hypothesis 228......Page 244
Exercises 231......Page 247
22.2 General Linear Hypothesis 233......Page 249
22.3 One-Sided Alternatives 237......Page 253
22.4 Choice of Significance Level 238......Page 254
22.5 Statistical versus Economic Significance 240......Page 256
22.6 Using Asymptotics 241......Page 257
22.7 Inference without Normality Assumption 242......Page 258
Exercises 243......Page 259
23.1 Introduction 245......Page 261
23.2 Textbook Discussions 246......Page 262
23.3 Micronumerosity 248......Page 264
23.4 When Multicollinearity Is Desirable 250......Page 266
23.5 Remarks 251......Page 267
Exercises 252......Page 268
24.2 Shortening a Regression 254......Page 270
24.3 Mean Squared Error 256......Page 272
24.4 Pretest Estimation 258......Page 274
24.5 Regression Fishing 261......Page 277
Exercises 262......Page 278
25.2 Neoclassical Regression Model 264......Page 280
25.3 Properties of Least Squares Estimation 268......Page 284
25.4 Neoclassical Normal Regression Model 269......Page 285
25.5 Asymptotic Properties of Least Squares Estimation 270......Page 286
Exercises 273......Page 289
26.1 Departures from Random Sampling 274......Page 290
26.2 Stationary Population Model 278......Page 294
26.3 Conditional Expectation Functions 279......Page 295
26.4 Stationary Processes 281......Page 297
26.5 Sampling and Estimation 284......Page 300
26.6 Remarks 287......Page 303
Exercises 288......Page 304
27.2 Least Squares Estimation 292......Page 308
27.3 Generalized Least Squares Estimation 294......Page 310
27.4 Remarks on GLS Estimation 295......Page 311
27.5 Feasible Generalized Least Squares Estimation 297......Page 313
27.6 Extensions of the GCR Model 298......Page 314
Exercises 299......Page 315
28.2 Pure Heteroskedasticity 300......Page 316
28.3 First-Order Autoregressive Process 301......Page 317
28.4 Remarks 304......Page 320
Exercises 306......Page 322
29.1 Nonlinear CEF's 308......Page 324
29.2 Estimation 311......Page 327
29.3 Computation of the Nonlinear Least Squares Estimator 313......Page 329
29.4 Asymptotic Properties 314......Page 330
29.5 Probit Model 317......Page 333
Exercises 319......Page 335
30.1 Introduction 323......Page 339
30.2 Stacking 324......Page 340
30.3 Generalized Least Squares 326......Page 342
30.4 Comparison of GLS and LS Estimators 327......Page 343
30.5 Feasible Generalized Least Squares 329......Page 345
30.6 Restrictions 331......Page 347
30.7 Alternative Estimators 332......Page 348
Exercises 334......Page 350
31.1 Introduction 337......Page 353
31.2 Permanent Income Model 338......Page 354
31.3 Keynesian Model 340......Page 356
31.4 Estimation of the Keynesian Model 342......Page 358
31.5 Structure versus Regression 343......Page 359
Exercises 346......Page 362
32.1 A Supply-Demand Model 349......Page 365
32.2 Specification of the Simultaneous-Equation Model 351......Page 367
32.4 Remarks 354......Page 370
33.1 Introduction 356......Page 372
33.2 Supply-Demand Models 357......Page 373
33.3 Uncorrected Disturbances 361......Page 377
33.4 Other Sources of Identification 362......Page 378
Exercises 363......Page 379
34.1 Introduction 365......Page 381
34.2 Indirect Feasible Generalized Least Squares 366......Page 382
34.3 Two-Stage Least Squares 369......Page 385
34.4 Relation between 2SLS and Indirect-FGLS 372......Page 388
34.5 Three-Stage Least Squares 374......Page 390
Exercises 375......Page 391
Appendix A. Statistical and Data Tables 381......Page 397
Appendix B. Getting Started in GAUSS 391......Page 407
References 397......Page 413
Index 399......Page 415