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CONTENTS
1 Introduction ... 1
1.1 The Nature of the Subjects ... 1
1.2 The Plan of This Book ... 4
Appendix ... 5
Functions and Graphs ... 5
Elasticity ... 7
Problems ... 9
PART...
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목차 전체
CONTENTS
1 Introduction ... 1
1.1 The Nature of the Subjects ... 1
1.2 The Plan of This Book ... 4
Appendix ... 5
Functions and Graphs ... 5
Elasticity ... 7
Problems ... 9
PART Ⅰ Data and Description ... 11
2 Economic Data ... 13
2.1 General Considerations ... 13
2.2 Cross-Section Data ... 16
Errors in Data ... 22
2.3 Time-Series Data ... 23
Change and Growth ... 26
Constructed Variables ... 27
2.4 Plotting a Time-Series Variable ... 29
Appendix ... 33
Logarithms ... 33
Logarithmic Transformations ... 37
Problems ... 40
3 Descriptive Statistics ... 43
3.1 Univariate Statistics ... 43
Measures of Central Tendency ... 43
Measures of Dispersion ... 45
Computation ... 48
3.2 Linear Transformations ... 50
3.3 Bivariate Statistics ... 53
Appendix: Summations ... 57
Problems ... 59
4 Frequency Distributions ... 62
4.1 Discrete Data Variables ... 62
4.2 Continuous Data Variables ... 66
Proportions ... 69
Problems ... 74
PART Ⅱ Specification and Estimation of Regression Models ... 77
5 Simple Regression: Theory ... 79
5.1 Specification of the Model ... 79
5.2 Estimation of the Model ... 82
5.3 Interpretation of the Regression ... 86
5.4 Measures of Fit ... 89
The Standard Error of the Regression, SER ... 90
The Coefficient of Deterinination, R² ... 91
5.5 The Effects of Linear Transformation ... 94
5.6 Regression Through the Origin ... 98
Appendix ... 100
Derivation of the OLS Estimators ... 100
Equivalence of R² and (r)² ... 101
Problems ... 102
6 Simple Regression: Application ... 105
6.1 Interpretation of the Coefficients ... 105
6.2 The Earnings Function and the Consumption Function ... 108
The Earnings Function ... 108
The Consumption Function ... 110
6.3 Alternative Model Specifications ... 111
Ratios of Variables ... 111
Differences of Variables ... 112
Lagged Variables and First Differences ... 113
6.4 The Reciprocal Specification ... 115
6.5 Logarithmic Functional Forms ... 118
The Log-Linear Specification ... 118
The Semilog Specification ... 122
Appendix: The Coefficients in Logarithmic Models ... 126
Problems ... 129
7 Multiple Regression: Theory and Application ... 132
7.1 Two Explanatory Variables ... 132
The Earnings Function ... 136
7.2 The General Case ... 138
Comparing Regressions ... 140
The Consumption Function ... 142
7.3 Dummy Variables ... 143
More Than Two Categories ... 148
7.4 Polynomial Specifications ... 151
7.5 Logarithmic Specifications ... 155
The Demand for Money ... 155
The Earnings Function ... 156
7.6 Specification Questions ... 157
The Causal Nexus ... 157
Consequences of Misspecification ... 159
Multicollinearity ... 161
Problems ... 163
PART Ⅲ Probability Distributions ... 167
8 Probability Theory ... 169
8.1 Outcomes and Probabilities ... 169
8.2 Events ... 171
8.3 Unions and Intersections ... 172
8.4 Conditional Probability and Independence ... 174
8.5 A Pair of Dice ... 177
Problems ... 179
9 Random Variables and Probability Distributions ... 182
9.1 Discrete Random Variables ... 182
Mean and Standard Deviation ... 186
9.2 Random Variables and Samples of Data ... 187
9.3 The Binomial Distribution ... 189
9.4 Continuous Random Variables ... 192
9.5 Transformations ... 199
Appendix ... 201
Joint Probability Distributions ... 201
Linear Combinations ... 204
Problems ... 206
10 The Normal and t Distributions ... 209
10.1 The Normal Distribution ... 209
The Standard Normal ... 209
Other Normal Distributions ... 213
10.2 The t Distribution ... 218
Appendix ... 221
The Chi-Square Distribution ... 221
The F Distribution ... 223
Problems ... 224
PART Ⅳ Inference in Regression ... 227
11 Sampling Theory in Regression ... 229
11.1 The Normal Regression Model ... 229
11.2 An Experiment in Sampling ... 233
11.3 The Sampling Distributions: Theory ... 236
Probability Calculations ... 238
11.4 The Sampling Distributions: Application ... 240
Probability Calculations ... 242
11.5 Interval Estimation ... 243
11.6 A Compendium of Reported Regressions ... 247
Appendix ... 250
Derivation of a Sampling Distribution ... 250
Derivation of the Confidence Interval ... 252
Problems ... 253
12 Hypothesis Testing ... 256
12.1 Specification of Hypotheses ... 256
12.2 The Basic Significance Test ... 257
The Underlying Logic ... 258
Reformulation ... 261
Practical Application ... 262
12.3 The Test for Sign ... 267
12.4 Tests for Specific Coefficient Values ... 272
Hypothesis Testing and Confidence Intervals ... 274
12.5 P-Values ... 276
Problems ... 280
13 Estimation and Regression Problems ... 282
13.1 Confidence Intervals for Prediction ... 282
13.2 Comparing Alternative Estimators ... 285
13.3 Multicollinearity ... 288
13.4 Misspecification ... 290
Specification Strategy ... 294
13.5 Sample Selection ... 294
Appendix: Expectations ... 297
Problems ... 300
PART Ⅴ Topics in Econometrics ... 303
14 F Tests and Dummy Variable Outcomes ... 305
14.1 F Tests in Multiple Regression ... 305
Theory ... 307
Applications ... 309
The Chow Test ... 312
14.2 Models for Dummy Variable Outcomes ... 316
Linear Probability Model ... 317
Probit and Logit Models ... 318
Problems ... 323
15 Heteroscedasticity and Autocorrelation ... 325
15.1 Heteroscedasticity ... 325
The Model and Its Consequences ... 326
Detection ... 328
Estimation ... 331
15.2 Autocorrelation ... 332
The Model ... 333
Consequences of Autocorrelation for OLS ... 337
Testing for Autocorrelation ... 337
Estimation Procedures ... 340
Problems ... 343
16 Regression and Time Series ... 345
16.1 Distributed Lags ... 345
The General Distributed Lag ... 346
The Koyck Model ... 348
Partial Adjustment and Adaptive Expectations ... 351
Estimation Problems ... 352
The Almon Lag Model and Other Lag Specifications ... 353
16.2 Trends and Seasonality ... 357
Trends ... 357
Seasonality ... 359
16.3 Random Walks and Spurious Regressions ... 361
Problems ... 363
17 Simultaneous-Equation Models ... 365
17.1 The Nature of the Models ... 365
The Reduced Form ... 368
Estimation and Simulation ... 371
17.2 Estimation ... 373
Two-Stage Least Squares ... 373
17.3 Identification ... 375
The Order Condition ... 376
Interpretation ... 378
Problems ... 379
PART Ⅵ Topics in Statistics ... 381
18 Inference for the Mean and Variance ... 383
18.1 The Sampling Distribution of X ‾ ... 383
18.2 Inference Regarding μx ... 388
Hypothesis Tests ... 389
Interval Estimates ... 391
18.3 The Sampling Distribution of S²x ... 392
18.4 Inference Regarding σ²x ... 392
Problems ... 394
19 Chi-Square Tests and Analysis of Variance ... 396
19.1 Chi-Square Tests ... 396
Test of Goodness of Fit ... 397
Test of Independence ... 399
19.2 Analysis of Variance and Regression ... 400
ANOVA Table for Regression ... 400
One-Way ANOVA ... 402
Two-Way ANOVA ... 404
Problems ... 405
Statistical Tables ... 407
Answers to Selected Problems ... 421
Bibliography ... 437
Index ... 441
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