List of figures ............................................... xii
List of tables ................................................ xiv
List of charts .............................................. xviii
List of boxes ................................................. xxi
Preface ..................................................... xxiii
A note on the textbook's focus and scope ...................... xxv
A note on the "Where can I find...?" boxes ................... xxvi
1 The role of statistics in economics .......................... 1
1.1 Understanding the economy using empirical evidence ...... 1
1.2 Measuring economic welfare .............................. 2
1.3 Distribution of household income ........................ 2
1.4 Assessing full employment ............................... 4
1.5 Calculating economic growth ............................. 6
1.6 Measuring inflation ..................................... 6
1.7 Theoretical relationships between unemployment and
economic growth ......................................... 9
1.8 The connection between economic theory and statistical
evidence ............................................... 11
Summary ..................................................... 11
Concepts introduced ......................................... 11
Exercises ................................................... 20
2 Visual presentations of economic data ....................... 22
2.1 Economic graphs and charts ............................. 22
2.2 Time-series data and charts ............................ 23
2.3 Cross-section data and charts .......................... 27
2.4 Panel data and charts .................................. 38
2.5 Creating effective charts .............................. 38
2.6 Constructing charts using Excel ........................ 40
Summary ..................................................... 41
Concepts introduced ......................................... 42
Exercises ................................................... 55
PART I Descriptive statistics of an economic variable ......... 57
3 Observations and frequency distributions .................... 59
3.1 The design of observations: an introduction ............ 59
3.2 Attributes and measured variables ...................... 60
3.3 Organizing data: absolute frequency distributions ...... 63
3.4 Organizing data: relative frequency distributions ...... 64
3.5 Visual presentations of frequency distribution:
histograms ............................................. 65
3.6 Classes in a frequency distribution .................... 65
3.7 Constructing a frequency distribution .................. 68
3.8 Frequency polygons ..................................... 72
3.9 Cumulative frequency distributions and ogives .......... 75
Summary ................................................ 80
Concepts introduced ......................................... 80
Exercises ................................................... 85
4 Measures of central tendency ................................ 89
4.1 Desirable properties for descriptive statistics ........ 89
4.2 Three measures of central tendency: mean, median, and
mode ................................................... 90
4.3 Measures of central tendency for frequency
distributions .......................................... 94
4.4 Weighted arithmetic means .............................. 97
4.5 Geometric means ....................................... 100
4.6 Positional measures for ungrouped data ................ 104
4.7 Positional measures for a frequency distribution ...... 106
Summary .................................................... 108
Concepts introduced ........................................ 109
Exercises .................................................. 111
5 Measures of dispersion ..................................... 115
5.1 The concept of dispersion ............................. 115
5.2 Populations and samples ............................... 115
5.3 Range ................................................. 117
5.4 Interquartile range ................................... 117
5.5 Average deviation ..................................... 118
5.6 The concept of the standard deviation ................. 119
5.7 Calculating the standard deviation for ungrouped
data .................................................. 121
5.8 Calculating measures of dispersion for frequency
distributions ......................................... 122
5.9 Locating extreme values ............................... 123
5.10 The shape of frequency distributions .................. 125
5.11 Choosing the appropriate descriptive statistics ....... 126
5.12 Assessing relative dispersion: coefficient of
variation ............................................. 128
5.13 Assessing relative dispersion: index of dispersion .... 132
5.14 Depicting relative dispersion: the Lorenz curve ....... 133
5.15 Assessing relative dispersion: Gini coefficient of
inequality ............................................ 141
Summary .................................................... 144
Concepts introduced ........................................ 146
Exercises .................................................. 152
PART II Temporal descriptive statistics ....................... 155
6 Measuring changes in price and quantity .................... 157
6.1 Important index numbers in empirical economics ........ 157
6.2 Why economists use index numbers ...................... 157
6.3 Constructing a simple price index ..................... 159
6.4 Constructing a weighted price index ................... 161
6.5 Selecting appropriate weights for an index number ..... 163
6.6 Chained price indices ................................. 166
6.7 Price index applications .............................. 169
6.8 Shifting an index's reference period .................. 172
6.9 Quantity indices ...................................... 175
6.10 Composite indices ..................................... 176
Summary .................................................... 179
Concepts introduced ........................................ 179
Exercises .................................................. 189
7 Descriptions of stability: short-run changes ............... 192
7.1 Measuring economic change over time ................... 192
7.2 Calculating percentage growth ......................... 192
7.3 Compound growth ....................................... 196
7.4 Annualized growth rates from sub-annual rates ......... 198
7.5 Annualized growth rates from supra-annual rates ....... 201
7.6 Continuous compound growth ............................ 202
7.7 Continuously compounded annual growth and logarithms .. 205
Summary .................................................... 208
Concepts introduced ........................................ 208
Exercises .................................................. 214
8 Patterns of long-term change ............................... 217
8.1 Economic growth over time ............................. 217
8.2 Constant long-run rates of growth ..................... 217
8.3 Growth by constant amounts ............................ 222
8.4 Change over time by constant rates or by constant
amounts? .............................................. 223
8.5 A complete model for describing change ................ 228
8.6 Seasonal effects ...................................... 228
8.7 Cyclical effects ...................................... 230
8.8 Irregular effects ..................................... 235
Summary .................................................... 235
Concepts introduced ........................................ 237
Exercises .................................................. 240
PART III Statistical inferences about a single variable ....... 243
9 Basic concepts in statistical inference .................... 245
9.1 Populations and samples revisited ..................... 245
9.2 Sampling procedures ................................... 246
9.3 Concepts of probability ............................... 247
9.4 Probability distributions ............................. 248
9.5 Continuous probability distributions: the normal
distribution .......................................... 249
9.6 Continuous probability distributions: standard normal
distribution .......................................... 251
9.7 Identifying a normal distribution ..................... 255
9.8 The concept of the sampling distribution of means ..... 256
9.9 Sampling distribution of means and the Central Limit
Theorem ............................................... 261
9.10 Sampling distribution of the Z-statistic .............. 261
Summary .................................................... 262
Concepts introduced ........................................ 262
Exercises .................................................. 264
10 Statistical estimation ..................................... 266
10.1 Sample surveys as a source of data .................... 266
10.2 Interval estimates of the population mean when the
variance of the population is known ................... 267
10.3 Confidence levels and the precision of an interval
estimate .............................................. 270
10.4 The t-distribution .................................... 272
10.5 Confidence intervals for the population mean when
the variance of the population is not known ........... 274
10.6 Confidence intervals for proportions, percentages,
and rates ............................................. 276
10.7 Confidence intervals for differences between means
and proportions ....................................... 277
Summary .................................................... 279
Concepts introduced ........................................ 280
Exercises .................................................. 285
11 Statistical hypothesis testing of a mean ................... 287
11.1 Testing hypotheses in economics: an analogy to
criminal trials ....................................... 287
11.2 An overview of hypothesis testing in economics:
evaluating truth in advertising ....................... 288
11.3 Economic hypothesis testing: stating the hypotheses ... 291
11.4 Economic hypothesis testing: selecting the level of
significance .......................................... 293
11.5 Economic hypothesis testing: establishing the
decision rule ......................................... 294
11.6 Economic hypothesis testing: constructing the test
statistic and making a decision about the null
hypothesis ............................................ 294
11.7 Testing hypotheses versus estimating confidence
intervals ............................................. 295
11.8 Evaluating a statistical rule in terms of a Type I
error ................................................. 296
11.9 Evaluating a statistical rule in terms of a Type II
error ................................................. 297
11.10 The p-value and hypothesis testing ................... 298
Summary .................................................... 301
Concepts introduced ........................................ 301
Exercises .................................................. 302
PART IV Relationships between two variables ................... 305
12 Correlation analysis ....................................... 307
12.1 Statistical relationships between two variables ....... 307
12.2 Correlation analysis: descriptive statistics .......... 308
12.3 Testing the significance of the correlation
coefficient ........................................... 310
12.4 Testing the sign on the correlation coefficient ....... 314
Summary .................................................... 315
Concepts introduced ........................................ 315
Exercises .................................................. 320
13 Simple linear regression analysis: descriptive measures .... 326
13.1 Introduction to simple linear regression analysis ..... 326
13.2 The algebra of linear relationships for regression
analysis .............................................. 327
13.3 Simple linear regression analysis: education and GDP .. 328
13.4 The algebra of variations in linear regression
relationships ......................................... 330
13.5 The coefficient of determination in regression
analysis .............................................. 333
13.6 Simple linear regression analysis: infant mortality
rates and skilled health personnel at birth ........... 334
Summary .................................................... 337
Concepts introduced ........................................ 337
Exercises .................................................. 338
14 Simple regression analysis: statistical inference .......... 339
14.1 The need for statistical inference in regression
analysis .............................................. 339
14.2 Testing hypotheses about the GDP-education
regression model's slope coefficient .................. 339
14.3 Sampling distributions of the linear regression's
slope and intercept coefficients ...................... 342
14.4 Establishing the null and alternative hypotheses
for the slope coefficient ............................. 344
14.5 Levels of significance and decision rules ............. 347
14.6 The test statistic and p-value for the slope
coefficient ........................................... 348
14.7 An example of a hypothesis about the slope
coefficient: infant mortality rates ................... 348
14.8 What hypothesis testing does and does not prove ....... 350
Summary .................................................... 350
Concepts introduced ........................................ 350
Exercises .................................................. 354
15 Simple regression analysis: variable scales and
functional forms ........................................... 355
15.7 Rescaling variables and interpreting the regression
coefficients .......................................... 355
15.2 Specifying the regression equation: functional forms .. 358
15.3 Semi-log functional forms: the log-lin model .......... 359
15.4 Semi-log functional forms: the lin-log model .......... 361
15.5 Double-log functional form ............................ 362
15.6 Other functional forms ................................ 363
15.7 Selecting the appropriate functional form ............. 364
Summary .................................................... 365
Concepts introduced ........................................ 366
Exercises .................................................. 366
PART V Relationships between multiple variables .............. 369
16 Multiple regression analysis: estimation and
interpretation ............................................. 371
16.1 Simple to multiple regression analysis: an
introduction .......................................... 371
16.2 The multiple-variable linear regression model ......... 371
16.3 Specifying the independent variables and functional
form for the multiple regression model ................ 372
16.4 Specifying a multiple regression model for infant
mortality rates ....................................... 373
16.5 Estimating a multiple regression model for infant
mortality rates ....................................... 375
Summary .................................................... 377
Concepts introduced ........................................ 377
Exercises .................................................. 380
17 Multiple regression analysis: hypothesis tests for
partial regression coefficients and overall goodness of
fit ........................................................ 382
17.1 General procedures for testing the significance of
the partial regression coefficients (b{) .............. 382
17.2 Testing the significance of partial regression
coefficients (bi): MR model ........................... 384
17.3 Evaluating the overall goodness of fit ................ 387
17.4 Interpreting the infant mortality model's overall
goodness of fit ....................................... 388
17.5 Testing joint hypotheses about the regression
model's overall (significance: basic concepts and
procedures ............................................ 389
17.6 Testing joint hypothesis about the IMR multiple
regression model's overall significance ............... 393
17.7 Is each independent variable statistically related
to the dependent variable? ............................ 393
17.8 The "best" statistical multiple regression model ...... 394
17.9 The "better" statistical infant mortality model? ...... 396
17.10 Closing observations about the IMR multiple
regression results ................................... 400
Summary .................................................... 400
Concepts introduced ........................................ 401
Exercises .................................................. 401
18 Multiple regression analysis: dummy variables and
statistical problems ....................................... 404
18.1 Independent dummy variables: basic concepts and
considerations ........................................ 404
18.2 Independent dummy variables: infant mortality rates
and sub-Saharan Africa ................................ 408
18.3 Multicollinearity ..................................... 410
18.4 Model misspecification and omitted variable bias ...... 413
18.5 "Misbehaved" regression residuals:
heteroskedasticity and serial correlation ............. 416
Summary .................................................... 420
Concepts introduced ........................................ 421
Exercises .................................................. 421
Notes ......................................................... 425
Bibliography .................................................. 433
Index ......................................................... 439
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