Rounding of income data: an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel
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| Format: | Buch |
| Sprache: | English |
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Frankfurt am Main [u.a.]
Lang
2007
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| Schriftenreihe: | Schriften zur empirischen Wirtschaftsforschung
9 |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Frankfurt (Main), Univ., Diss., 2006 |
| Beschreibung: | XXIV, 245 S. zahlr. graph. Darst. |
| ISBN: | 082048721X 363155687X |
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| 100 | 1 | |a Hanisch, Jens Ulrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Rounding of income data |b an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |c Jens Ulrich Hanisch |
| 264 | 1 | |a Frankfurt am Main [u.a.] |b Lang |c 2007 | |
| 300 | |a XXIV, 245 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Schriften zur empirischen Wirtschaftsforschung |v 9 | |
| 500 | |a Zugl.: Frankfurt (Main), Univ., Diss., 2006 | ||
| 650 | 7 | |a Datenerhebung - Qualität - Einkommen - Europäische Union |2 swd | |
| 650 | 7 | |a Einkommen - Datenerhebung - Qualität - Europäische Union |2 swd | |
| 650 | 7 | |a Qualität - Datenerhebung - Einkommen - Europäische Union |2 swd | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Income |x Statistics |x Mathematical models | |
| 650 | 4 | |a Smoothing (Statistics) | |
| 651 | 7 | |a Europäische Union - Einkommen - Datenerhebung - Qualität |2 swd | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 830 | 0 | |a Schriften zur empirischen Wirtschaftsforschung |v 9 |w (DE-604)BV012708439 |9 9 | |
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Datensatz im Suchindex
| _version_ | 1804135744036405248 |
|---|---|
| adam_text | Contents
List of Figures xiii
List of Tables xvii
Notation xxi
Abbreviations xxiii
1 Rounded Values 1
1.1 Introduction 1
1.2 The CHINTEX project 3
1.3 Hypotheses 4
1.4 Approach 5
2 Effect of Rounding on Distribut. Figures 7
2.1 The quality of income data 7
2.1.1 A framework for data quality 8
2.1.2 Improving the accuracy of data 9
2.2 Response type as a result of the interview process 12
2.3 Rounding in statistics, a short review 15
2.3.1 Early literature on the effects of rounding 15
2.3.2 Literature on the reasons and types of rounding ... 16
2.3.3 Benford s Law and rounding 17
2.3.4 A psychological model for rounding 18
2.3.5 Hypothetical factors with an effect on rounding ... 20
2.3.6 Literature on methods to use rounded data 21
2.3.7 Applied methods for incomplete data 23
2.4 Types of human rounding in interviews 26
2.5 The rounding indicator 28
2.5.1 Definition 28
2.5.2 An example 29
viii Contents
2.5.3 Denotation of accurate and reported income 31
2.5.4 The rounding error 32
2.6 impact of rounding on an empirical distribution 34
2.6.1 Immediate consequences 34
2.6.2 Impact on cross sectional income distribution .... 36
2.6.3 Excursion: Prom histograms to kernel density esti¬
mation 46
2.6.4 Impact of rounding on measures of change 52
2.7 Impact of rounding on poverty measures 58
2.7.1 Gini coefficient 58
2.7.2 Headcount ratio 60
2.7.3 TIP Curve 62
3 Rounding in Household Panels 71
3.1 Overview 71
3.1.1 The German Socio Economic Panel 72
3.1.2 The European Community Household Panel 75
3.1.3 The Finnish ECHP data for the CHINTEX project . 78
3.2 Frequency of rounding in income variables 82
3.2.1 Comparison of rounding in two German household
surveys 82
3.2.2 Comparison of rounding for the personal data .... 83
3.2.3 Rounding in the Lux ECHP 85
3.2.4 Other national sub samples 86
3.3 Rounding as a sequential process: Digit by digit 86
3.3.1 Empirical results for sequential rounding of house¬
hold income in the Lux ECHP 87
3.3.2 Empirical results for sequential rounding of personal
income in the Lux ECHP 89
3.3.3 Conclusion for Luxembourgian data 90
3.3.4 Frequency of sequential rounding in the GSOEP and
four national sub samples of the ECHP 90
3.4 Comparison of final digit distribution 93
3.5 Rounding of all income variables in the Fin ECHP 95
4 Income brackets 103
4.1 Introduction 103
Contents ix
4.2 Bracket usage in the Lux ECHP 105
4.2.1 Empirical frequency of bracket usage 105
4.2.2 Comparison of value and bracket usage 106
4.2.3 Distribution of values in brackets 107
4.2.4 Distribution of final digits in brackets 110
4.3 Bracket usage in the G ECHP 112
4.3.1 Empirical frequency of bracket usage 112
4.3.2 Switches between response types 113
4.3.3 Comparison of value and bracket usage 115
4.4 Comparison of Bracket Usage G ECHP and GSOEP .... 116
4.4.1 Comparison of G ECHP and GSOEP 116
4.4.2 Distribution of values within income brackets . . . .119
4.5 The design of income brackets 123
4.5.1 The trade off between precision and response .... 123
4.5.2 Variance within simulated bracket limits 124
4.5.3 Empirical results 124
4.5.4 Other approaches to the design of income brackets . 129
4.6 Conclusions and recommendations 129
5 Comparison of Register and Survey Data 131
5.1 Introduction: Register vs. survey data 131
5.2 Distribution of the rounding error 133
5.2.1 A reference value based on annual register data . . .133
5.2.2 Approach A) a direct comparison of register and
survey earnings 134
5.2.3 Approach B) predicting reported earnings from
register earnings using a conversion factor 134
5.2.4 Discussion 138
5.2.5 Approach C): A reference value based on a regres¬
sion equation 139
5.2.6 Differences between reference values and survey values 141
5.3 Diff. in the mobility of reg. and interview incomes 144
5.3.1 Definition of income mobility 144
5.3.2 Empirical distribution of income mobility in the Fin
ECHP 146
5.3.3 Comparison of income mobility based on register
and survey data 149
x Contents
5.3.4 Regression of income mobility dependent on round¬
ing 153
5.3.5 Conclusions 156
6 Models for Response Behavior 159
6.1 Methods 159
6.1.1 A dichotomous dependent variable 159
6.1.2 A binary probit model 160
6.1.3 An ordered probit model 160
6.1.4 A dependent variable with ordered categories .... 161
6.1.5 Ordering of response categories 163
6.1.6 Multidimensionality of response behavior 164
6.1.7 Some results from literature 168
6.1.8 Hypotheses 169
6.2 Empirical results: Panel effect and conditioning 170
6.2.1 Cross sectional comparison of rounding 170
6.2.2 Probit analysis of rounding in early and late waves . 175
6.2.3 Contingency tables for rounding behavior in consec¬
utive waves 176
6.2.4 Probit model for rounding behavior in consecutive
waves 181
6.3 Rounding in the German sub sample of the ECHP 183
6.4 Empirical Results: Ordered Probit Analysis 184
6.4.1 Marginal frequency of rounding 184
6.4.2 Model estimates 187
6.5 Conclusions 189
7 Conclusions 191
Bibliography 195
A Appendix 205
A.I Miscellanea 205
A.1.1 Software used for this work 205
A. 1.2 National Currency Exchange Rates 205
A.1.3 Eurostat definitions 206
A.2 Additional tables and charts 207
Contents xi
A.2.1 Definition of nonresponse on wages 207
A.2.2 Response on gross wage and earnings 209
A.2.3 Rounding of net disposable household income values 211
A.2.4 Rounding of personal gross wage and earning values 213
A.2.5 Rounding in all waves, GSOEP wave 1 18 213
A.2.6 Rounding in all variables Fin ECHP 214
A.2.7 Rounding and bracket usage Lux ECHP 219
A.2.8 Rounding and bracket usage German ECHP .... 220
A.2.9 Rounding and bracket usage Finnish ECHP .... 221
A.2.10 Comparing reference value to survey interview value 223
A. 3 Additional regression models used in the thesis 223
A.3.1 Regression 2: Survey income given reference income
and two covariates 225
A.3.2 Regression 2a: Survey income given the reference
income value 226
A.3.3 Regression 2b: Survey income given the reference
income and several basic characteristics 227
A.3.4 Regression M3: Income mobility depending on round¬
ing and individual attributes 229
A.3.5 Additional regression with an ordered categories de¬
pendent variable 231
A.4 Additional sections 233
A.4.1 Cards in the hat example 233
A.4.2 Rounding digit dy digit, household income 234
A.4.3 Rounding digit by digit, personal wage and earnings 239
A.5 Sample scripts and programs 241
A.5.1 Script used for Simulation 1 and la 241
A.5.2 Program to construct and plot the TIP curve .... 242
List of Figures
2.1 Interview Process and Responses 13
2.2 Frequency of values which are multiples of even numbers k . 30
2.3 Frequency of values accurate by at least b significant digits . 31
2.4 Empirical density of household income (1) 32
2.5 Empirical density of household income (2) 33
2.6 Density of rounded and true values (simulation) 35
2.7 Scatter plot of rounded vs. non rounded values in Simula¬
tion la 39
2.8 Results of Simulation lb 40
2.9 Results of Simulation la: Q Q Plots 42
2.10 Example: Two Histograms for the same values 46
2.11 Example: Two kernel density plots for the same values ... 48
2.12 Kernel density plots for three sets of values 50
2.13 Comparison of different KDE for the same data 51
2.14 Simulation 9: Gini coefficient of yri compared to Gini coef¬
ficient of Xi 60
2.15 Simulation 10: Headcount ratio of yri compared to i, .... 61
2.16 TIP curve for register data (1995) 64
2.17 TIP curves for register data (1995), simulated rounding ... 65
2.18 TIP curves for register data (1999), simulated rounding ... 66
2.19 TIP curves for increasing income data 69
3.1 Structure of the Finnish ECHP data 81
3.2 Ratios h(b i + l)/h(b i) (household income) 88
3.3 Ratios h(b i + l)/h(b i) (wage and earnings) 91
3.4 Histograms of final digits of income values 96
3.5 Histograms of final digits (excluding zero) of income values . 97
3.6 Average precision of income variables in the Fin ECHP ... 99
xiv List of Figures
3.7 Average precision of income variables in the Lux ECHP . . ¦ 101
3.8 Average precision of income variables in the G ECHP .... 102
4.1 Cumulative frequency of values and bracket usage by differ¬
ent income levels 106
4.2 Histograms of values in separate income bracket ranges . . . 109
4.3 Density of household income in brackets Ill
4.4 Response type in consecutive waves 114
4.5 Cumulative Frequency of Values and Bracket Usage 117
4.6 Distribution of values in bracket limits 118
4.7 Quantile Quantile plots of the household income values in
G ECHP and G SOEP 120
4.8 Histograms of income values and bracket limits 121
4.9 Sum of squares within simulated brackets (Lux ECHP 1994) 125
4.10 Sum of squares within simulated brackets (Fin ECHP 1996) 126
4.11 Sums of squares within simulated brackets (G, 1994) . . . .127
4.12 Sum of squares within simulated brackets (random data) . . 128
5.1 Histogram for y/x 136
5.2 Absolute differences between reference and survey value . . .143
5.3 Comparison of ln(l + r) and r 145
5.4 Q Q Plot of tur and tuq 150
5.5 Scatterplot and LOESS regression line oirriQ^ given mR^. . 151
5.6 LOWESS of rriQi given mm for rounded and non rounded
responses 152
6.1 Cooperation in two dimensions 166
6.2 Model for interview response as a sequential process 167
6.3 Accuracy of values in earnings data (I) 171
6.4 Accuracy of values in earnings data (II) 172
6.5 Accuracy of values in earnings data (III) 173
6.6 Precision of wage and earnings data (by income group) . . . 174
6.7 Relative frequency of persons who reported earnings with
the same number of significant digits as in the previous wave 178
6.8 Result for the balanced sample 180
6.9 Phi Coefficient for precision of income reports in adjacent
waves 181
List of Figures xv
A.I Definition of nonresponse on wages 207
A.2 TIP curve for register data (unweighted) 208
A.3 Density of gross wage and earning (empirical) 208
A.4 Lux ECHP final digits (modulo 1000) 219
A.5 G ECHP final digits (modulo 1000) 220
A.6 Fin ECHP final digits (modulo 1000) 221
A.7 Fin ECHP histogram of values in income brackets 222
A.8 Fin ECHP histogram of values in income brackets 223
A.9 Absolute difference between reference and interview value . . 224
A. 10 Residual Scatter Plot for Regression 2a 226
A. 11 Residual Plot for Regression 2b 230
A. 12 Cards in the hat example: Leading digit 234
A. 13 Cards in the hat example: Second digit 235
A.14 Plot of ratios h{Di Di + l) 237
A.15 Plot of ratios corrected by log value of national currency
unit in EUR 238
A. 16 X Y plot of ratios corrected by log value of national currency
in EUR 240
A.17 Sample plot from procedure plot.tip 246
List of Tables
2.1 Simulation 1: Simulated G ECHP household income 37
2.2 Simulation 2: Simulated G ECHP data, personal income . . 41
2.3 Simulation 3: Simulated Fin ECHP data, household income 43
2.4 Simulation 4: Rounding Fin ECHP household register data . 44
2.5 Simulation 5: Rounding Fin ECHP personal register data . . 45
2.6 Simulation 6: Mobility of wage and earning 53
2.7 Simulation 7a: Mobility of wage and earning (register data) 54
2.8 Simulation 7b: Mobility of wage and earnings (registers) . . 55
2.9 Frequency of rounding after certain number of digits 56
2.10 Probability of rounding for Simulation 7c 56
2.11 Simulation 7c: Mobility of wage and earning (register data) . 57
2.12 Simulation 8: Gini coefficient for rounded data 59
3.1 GSOEP sub samples 72
3.2 GSOEP: Interview modes in personal interview 1999 .... 73
3.3 ECHP: Number of interviewed households per country ... 78
3.4 Rounding of Net Disposable Household Income 83
3.5 Rounding of personal gross wage and earnings 84
3.6 Table of Frequencies 85
3.7 Absolute frequency for the number of leading digits b = i . . 87
3.8 Ratios h(B i)/h(B i) (household income) 87
3.9 Table of Frequencies for b = i and b i, individuals 89
3.10 Ratios h(b i + l)/h(b i) (wage and earnings) 90
3.11 Sequential rounding of household income 92
3.12 Frequencies of non response and responses by 1 or more sig¬
nificant digits in the Lux ECHP wage and earnings question 94
3.13 Frequencies in sequential rounding of personal gross wage
and earnings 95
xviii List of Tables
3.14 Frequency of rounded income values in the Fin ECHP. ... 98
4.1 Coding for income brackets in the ECHP 104
4.2 Empirical frequency of response types, Lux ECHP 105
4.3 Frequencies of value and bracket usage in Lux ECHP .... 108
4.4 Empirical frequency of response types 112
4.5 Transition between response types wave 1— 2 115
4.6 Transition between response types wave 2— 3 116
4.7 Middle and mean value of income brackets 122
5.1 Statistics for the ratio c = y/x 135
5.2 Income from self employment according to registers or in¬
terviews 137
5.3 List of individual values (examples) 147
5.4 Marginal distributions m,R and tuq 149
5.5 MODEL MO, mQ ~ mR 153
5.6 MODEL Ml, mQ ~ mR + mR 153
5.7 MODEL M2, Model Ml + rounding effects 155
5.8 Example: Coefficients for j/i = 10000 and y2 = 13000 (Model
M2) 156
6.1 Result for Probit Models for Rounding Behaviour 176
6.2 Coefficients for Rounding Behavior Model 177
6.3 Summary of contingencies B2t given B2U 179
6.4 Summary of probit models 182
6.5 Result of Probit Model for Rounding (G ECHP) 183
6.6 Crosstable sex by rounding 184
6.7 Crosstable interview mode by rounding 185
6.8 Crosstable interview duration (grouped) by rounding .... 185
6.9 Crosstable job type (grouped) by rounding 186
6.10 Parameter estimates for the ordered probit model 188
6.11 Descriptive statistics 189
A.I Response type used in wage and earning question 209
A.2 Rounding: Fin ECHP net disposable household income . . .211
A.3 Rounding: G ECHP net disposable household income ... 211
A.4 Rounding in German SOEP net disposable household in¬
come 212
List of Tables xix
A.5 Rounding in Lux ECHP net disposable household income . . 212
A.6 Rounding in Finland, personal data 213
A.7 Rounding in German ECHP, personal data 213
A.8 Rounding in German SOEP, personal data 214
A.9 Frequency of Rounding in Lux ECHP, personal data 214
A. 10 Precision of values in GSOEP earnings data (all persons) . . 215
A. 11 Precision of values in GSOEP earnings data (balanced) . . .216
A.12 Precision of values in GSOEP earnings data, stratified .... 217
A. 13 Rounding of personal income variables in Fin ECHP inter¬
view data 217
A. 14 MODEL M3, Model M2 + individual attributes 230
A. 15 Crosstabulation of gender vs. number of significant digits
(b) of reported gross wage and earnings 231
A. 16 Parameter estimates for the ordered probit models 232
A. 17 Sequential rounding of net disposable household income . . . 236
A. 18 Sequential rounding of personal gross wage and earnings . . 239
|
| adam_txt |
Contents
List of Figures xiii
List of Tables xvii
Notation xxi
Abbreviations xxiii
1 Rounded Values 1
1.1 Introduction 1
1.2 The CHINTEX project 3
1.3 Hypotheses 4
1.4 Approach 5
2 Effect of Rounding on Distribut. Figures 7
2.1 The quality of income data 7
2.1.1 A framework for data quality 8
2.1.2 Improving the accuracy of data 9
2.2 Response type as a result of the interview process 12
2.3 Rounding in statistics, a short review 15
2.3.1 Early literature on the effects of rounding 15
2.3.2 Literature on the reasons and types of rounding . 16
2.3.3 Benford's Law and rounding 17
2.3.4 A psychological model for rounding 18
2.3.5 Hypothetical factors with an effect on rounding . 20
2.3.6 Literature on methods to use rounded data 21
2.3.7 Applied methods for incomplete data 23
2.4 Types of human rounding in interviews 26
2.5 The rounding indicator 28
2.5.1 Definition 28
2.5.2 An example 29
viii Contents
2.5.3 Denotation of accurate and reported income 31
2.5.4 The rounding error 32
2.6 impact of rounding on an empirical distribution 34
2.6.1 Immediate consequences 34
2.6.2 Impact on cross sectional income distribution . 36
2.6.3 Excursion: Prom histograms to kernel density esti¬
mation 46
2.6.4 Impact of rounding on measures of change 52
2.7 Impact of rounding on poverty measures 58
2.7.1 Gini coefficient 58
2.7.2 Headcount ratio 60
2.7.3 TIP Curve 62
3 Rounding in Household Panels 71
3.1 Overview 71
3.1.1 The German Socio Economic Panel 72
3.1.2 The European Community Household Panel 75
3.1.3 The Finnish ECHP data for the CHINTEX project . 78
3.2 Frequency of rounding in income variables 82
3.2.1 Comparison of rounding in two German household
surveys 82
3.2.2 Comparison of rounding for the personal data . 83
3.2.3 Rounding in the Lux ECHP 85
3.2.4 Other national sub samples 86
3.3 Rounding as a sequential process: Digit by digit 86
3.3.1 Empirical results for sequential rounding of house¬
hold income in the Lux ECHP 87
3.3.2 Empirical results for sequential rounding of personal
income in the Lux ECHP 89
3.3.3 Conclusion for Luxembourgian data 90
3.3.4 Frequency of sequential rounding in the GSOEP and
four national sub samples of the ECHP 90
3.4 Comparison of final digit distribution 93
3.5 Rounding of all income variables in the Fin ECHP 95
4 Income brackets 103
4.1 Introduction 103
Contents ix
4.2 Bracket usage in the Lux ECHP 105
4.2.1 Empirical frequency of bracket usage 105
4.2.2 Comparison of value and bracket usage 106
4.2.3 Distribution of values in brackets 107
4.2.4 Distribution of final digits in brackets 110
4.3 Bracket usage in the G ECHP 112
4.3.1 Empirical frequency of bracket usage 112
4.3.2 Switches between response types 113
4.3.3 Comparison of value and bracket usage 115
4.4 Comparison of Bracket Usage G ECHP and GSOEP . 116
4.4.1 Comparison of G ECHP and GSOEP 116
4.4.2 Distribution of values within income brackets . . . .119
4.5 The design of income brackets 123
4.5.1 The trade off between precision and response . 123
4.5.2 Variance within simulated bracket limits 124
4.5.3 Empirical results 124
4.5.4 Other approaches to the design of income brackets . 129
4.6 Conclusions and recommendations 129
5 Comparison of Register and Survey Data 131
5.1 Introduction: Register vs. survey data 131
5.2 Distribution of the rounding error 133
5.2.1 A reference value based on annual register data . . .133
5.2.2 Approach A) a direct comparison of register and
survey earnings 134
5.2.3 Approach B) predicting reported earnings from
register earnings using a conversion factor 134
5.2.4 Discussion 138
5.2.5 Approach C): A reference value based on a regres¬
sion equation 139
5.2.6 Differences between reference values and survey values 141
5.3 Diff. in the mobility of reg. and interview incomes 144
5.3.1 Definition of income mobility 144
5.3.2 Empirical distribution of income mobility in the Fin
ECHP 146
5.3.3 Comparison of income mobility based on register
and survey data 149
x Contents
5.3.4 Regression of income mobility dependent on round¬
ing 153
5.3.5 Conclusions 156
6 Models for Response Behavior 159
6.1 Methods 159
6.1.1 A dichotomous dependent variable 159
6.1.2 A binary probit model 160
6.1.3 An ordered probit model 160
6.1.4 A dependent variable with ordered categories . 161
6.1.5 Ordering of response categories 163
6.1.6 Multidimensionality of response behavior 164
6.1.7 Some results from literature 168
6.1.8 Hypotheses 169
6.2 Empirical results: Panel effect and conditioning 170
6.2.1 Cross sectional comparison of rounding 170
6.2.2 Probit analysis of rounding in early and late waves . 175
6.2.3 Contingency tables for rounding behavior in consec¬
utive waves 176
6.2.4 Probit model for rounding behavior in consecutive
waves 181
6.3 Rounding in the German sub sample of the ECHP 183
6.4 Empirical Results: Ordered Probit Analysis 184
6.4.1 Marginal frequency of rounding 184
6.4.2 Model estimates 187
6.5 Conclusions 189
7 Conclusions 191
Bibliography 195
A Appendix 205
A.I Miscellanea 205
A.1.1 Software used for this work 205
A. 1.2 National Currency Exchange Rates 205
A.1.3 Eurostat definitions 206
A.2 Additional tables and charts 207
Contents xi
A.2.1 Definition of nonresponse on wages 207
A.2.2 Response on gross wage and earnings 209
A.2.3 Rounding of net disposable household income values 211
A.2.4 Rounding of personal gross wage and earning values 213
A.2.5 Rounding in all waves, GSOEP wave 1 18 213
A.2.6 Rounding in all variables Fin ECHP 214
A.2.7 Rounding and bracket usage Lux ECHP 219
A.2.8 Rounding and bracket usage German ECHP . 220
A.2.9 Rounding and bracket usage Finnish ECHP . 221
A.2.10 Comparing reference value to survey interview value 223
A. 3 Additional regression models used in the thesis 223
A.3.1 Regression 2: Survey income given reference income
and two covariates 225
A.3.2 Regression 2a: Survey income given the reference
income value 226
A.3.3 Regression 2b: Survey income given the reference
income and several basic characteristics 227
A.3.4 Regression M3: Income mobility depending on round¬
ing and individual attributes 229
A.3.5 Additional regression with an ordered categories de¬
pendent variable 231
A.4 Additional sections 233
A.4.1 Cards in the hat example 233
A.4.2 Rounding digit dy digit, household income 234
A.4.3 Rounding digit by digit, personal wage and earnings 239
A.5 Sample scripts and programs 241
A.5.1 Script used for Simulation 1 and la 241
A.5.2 Program to construct and plot the TIP curve . 242
List of Figures
2.1 Interview Process and Responses 13
2.2 Frequency of values which are multiples of even numbers k . 30
2.3 Frequency of values accurate by at least b significant digits . 31
2.4 Empirical density of household income (1) 32
2.5 Empirical density of household income (2) 33
2.6 Density of rounded and true values (simulation) 35
2.7 Scatter plot of rounded vs. non rounded values in Simula¬
tion la 39
2.8 Results of Simulation lb 40
2.9 Results of Simulation la: Q Q Plots 42
2.10 Example: Two Histograms for the same values 46
2.11 Example: Two kernel density plots for the same values . 48
2.12 Kernel density plots for three sets of values 50
2.13 Comparison of different KDE for the same data 51
2.14 Simulation 9: Gini coefficient of yri compared to Gini coef¬
ficient of Xi 60
2.15 Simulation 10: Headcount ratio of yri compared to i, . 61
2.16 TIP curve for register data (1995) 64
2.17 TIP curves for register data (1995), simulated rounding . 65
2.18 TIP curves for register data (1999), simulated rounding . 66
2.19 TIP curves for increasing income data 69
3.1 Structure of the Finnish ECHP data 81
3.2 Ratios h(b i + l)/h(b i) (household income) 88
3.3 Ratios h(b i + l)/h(b i) (wage and earnings) 91
3.4 Histograms of final digits of income values 96
3.5 Histograms of final digits (excluding zero) of income values . 97
3.6 Average precision of income variables in the Fin ECHP . 99
xiv List of Figures
3.7 Average precision of income variables in the Lux ECHP . . ¦ 101
3.8 Average precision of income variables in the G ECHP . 102
4.1 Cumulative frequency of values and bracket usage by differ¬
ent income levels 106
4.2 Histograms of values in separate income bracket ranges . . . 109
4.3 Density of household income in brackets Ill
4.4 Response type in consecutive waves 114
4.5 Cumulative Frequency of Values and Bracket Usage 117
4.6 Distribution of values in bracket limits 118
4.7 Quantile Quantile plots of the household income values in
G ECHP and G SOEP 120
4.8 Histograms of income values and bracket limits 121
4.9 Sum of squares within simulated brackets (Lux ECHP 1994) 125
4.10 Sum of squares within simulated brackets (Fin ECHP 1996) 126
4.11 Sums of squares within simulated brackets (G, 1994) . . . .127
4.12 Sum of squares within simulated brackets (random data) . . 128
5.1 Histogram for y/x 136
5.2 Absolute differences between reference and survey value . . .143
5.3 Comparison of ln(l + r) and r 145
5.4 Q Q Plot of tur and tuq 150
5.5 Scatterplot and LOESS regression line oirriQ^ given mR^. . 151
5.6 LOWESS of rriQi given mm for rounded and non rounded
responses 152
6.1 Cooperation in two dimensions 166
6.2 Model for interview response as a sequential process 167
6.3 Accuracy of values in earnings data (I) 171
6.4 Accuracy of values in earnings data (II) 172
6.5 Accuracy of values in earnings data (III) 173
6.6 Precision of wage and earnings data (by income group) . . . 174
6.7 Relative frequency of persons who reported earnings with
the same number of significant digits as in the previous wave 178
6.8 Result for the balanced sample 180
6.9 Phi Coefficient for precision of income reports in adjacent
waves 181
List of Figures xv
A.I Definition of nonresponse on wages 207
A.2 TIP curve for register data (unweighted) 208
A.3 Density of gross wage and earning (empirical) 208
A.4 Lux ECHP final digits (modulo 1000) 219
A.5 G ECHP final digits (modulo 1000) 220
A.6 Fin ECHP final digits (modulo 1000) 221
A.7 Fin ECHP histogram of values in income brackets 222
A.8 Fin ECHP histogram of values in income brackets 223
A.9 Absolute difference between reference and interview value . . 224
A. 10 Residual Scatter Plot for Regression 2a 226
A. 11 Residual Plot for Regression 2b 230
A. 12 Cards in the hat example: Leading digit 234
A. 13 Cards in the hat example: Second digit 235
A.14 Plot of ratios h{Di \Di + l) 237
A.15 Plot of ratios corrected by log value of national currency
unit in EUR 238
A. 16 X Y plot of ratios corrected by log value of national currency
in EUR 240
A.17 Sample plot from procedure plot.tip 246
List of Tables
2.1 Simulation 1: Simulated G ECHP household income 37
2.2 Simulation 2: Simulated G ECHP data, personal income . . 41
2.3 Simulation 3: Simulated Fin ECHP data, household income 43
2.4 Simulation 4: Rounding Fin ECHP household register data . 44
2.5 Simulation 5: Rounding Fin ECHP personal register data . . 45
2.6 Simulation 6: Mobility of wage and earning 53
2.7 Simulation 7a: Mobility of wage and earning (register data) 54
2.8 Simulation 7b: Mobility of wage and earnings (registers) . . 55
2.9 Frequency of rounding after certain number of digits 56
2.10 Probability of rounding for Simulation 7c 56
2.11 Simulation 7c: Mobility of wage and earning (register data) . 57
2.12 Simulation 8: Gini coefficient for rounded data 59
3.1 GSOEP sub samples 72
3.2 GSOEP: Interview modes in personal interview 1999 . 73
3.3 ECHP: Number of interviewed households per country . 78
3.4 Rounding of Net Disposable Household Income 83
3.5 Rounding of personal gross wage and earnings 84
3.6 Table of Frequencies 85
3.7 Absolute frequency for the number of leading digits b = i . . 87
3.8 Ratios h(B i)/h(B i) (household income) 87
3.9 Table of Frequencies for b = i and b i, individuals 89
3.10 Ratios h(b i + l)/h(b i) (wage and earnings) 90
3.11 Sequential rounding of household income 92
3.12 Frequencies of non response and responses by 1 or more sig¬
nificant digits in the Lux ECHP wage and earnings question 94
3.13 Frequencies in sequential rounding of personal gross wage
and earnings 95
xviii List of Tables
3.14 Frequency of rounded income values in the Fin ECHP. . 98
4.1 Coding for income brackets in the ECHP 104
4.2 Empirical frequency of response types, Lux ECHP 105
4.3 Frequencies of value and bracket usage in Lux ECHP . 108
4.4 Empirical frequency of response types 112
4.5 Transition between response types wave 1— 2 115
4.6 Transition between response types wave 2— 3 116
4.7 Middle and mean value of income brackets 122
5.1 Statistics for the ratio c = y/x 135
5.2 Income from self employment according to registers or in¬
terviews 137
5.3 List of individual values (examples) 147
5.4 Marginal distributions m,R and tuq 149
5.5 MODEL MO, mQ ~ mR 153
5.6 MODEL Ml, mQ ~ mR + mR 153
5.7 MODEL M2, Model Ml + rounding effects 155
5.8 Example: Coefficients for j/i = 10000 and y2 = 13000 (Model
M2) 156
6.1 Result for Probit Models for Rounding Behaviour 176
6.2 Coefficients for Rounding Behavior Model 177
6.3 Summary of contingencies B2t given B2U 179
6.4 Summary of probit models 182
6.5 Result of Probit Model for Rounding (G ECHP) 183
6.6 Crosstable sex by rounding 184
6.7 Crosstable interview mode by rounding 185
6.8 Crosstable interview duration (grouped) by rounding . 185
6.9 Crosstable job type (grouped) by rounding 186
6.10 Parameter estimates for the ordered probit model 188
6.11 Descriptive statistics 189
A.I Response type used in wage and earning question 209
A.2 Rounding: Fin ECHP net disposable household income . . .211
A.3 Rounding: G ECHP net disposable household income . 211
A.4 Rounding in German SOEP net disposable household in¬
come 212
List of Tables xix
A.5 Rounding in Lux ECHP net disposable household income . . 212
A.6 Rounding in Finland, personal data 213
A.7 Rounding in German ECHP, personal data 213
A.8 Rounding in German SOEP, personal data 214
A.9 Frequency of Rounding in Lux ECHP, personal data 214
A. 10 Precision of values in GSOEP earnings data (all persons) . . 215
A. 11 Precision of values in GSOEP earnings data (balanced) . . .216
A.12 Precision of values in GSOEP earnings data, stratified . 217
A. 13 Rounding of personal income variables in Fin ECHP inter¬
view data 217
A. 14 MODEL M3, Model M2 + individual attributes 230
A. 15 Crosstabulation of gender vs. number of significant digits
(b) of reported gross wage and earnings 231
A. 16 Parameter estimates for the ordered probit models 232
A. 17 Sequential rounding of net disposable household income . . . 236
A. 18 Sequential rounding of personal gross wage and earnings . . 239 |
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| genre_facet | Hochschulschrift |
| geographic | Europäische Union - Einkommen - Datenerhebung - Qualität swd |
| geographic_facet | Europäische Union - Einkommen - Datenerhebung - Qualität |
| id | DE-604.BV021819371 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:53:35Z |
| indexdate | 2024-07-09T20:45:22Z |
| institution | BVB |
| isbn | 082048721X 363155687X |
| language | English |
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| physical | XXIV, 245 S. zahlr. graph. Darst. |
| publishDate | 2007 |
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| series | Schriften zur empirischen Wirtschaftsforschung |
| series2 | Schriften zur empirischen Wirtschaftsforschung |
| spelling | Hanisch, Jens Ulrich Verfasser aut Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel Jens Ulrich Hanisch Frankfurt am Main [u.a.] Lang 2007 XXIV, 245 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Schriften zur empirischen Wirtschaftsforschung 9 Zugl.: Frankfurt (Main), Univ., Diss., 2006 Datenerhebung - Qualität - Einkommen - Europäische Union swd Einkommen - Datenerhebung - Qualität - Europäische Union swd Qualität - Datenerhebung - Einkommen - Europäische Union swd Mathematisches Modell Statistik Income Statistics Mathematical models Smoothing (Statistics) Europäische Union - Einkommen - Datenerhebung - Qualität swd (DE-588)4113937-9 Hochschulschrift gnd-content Schriften zur empirischen Wirtschaftsforschung 9 (DE-604)BV012708439 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015031536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hanisch, Jens Ulrich Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel Schriften zur empirischen Wirtschaftsforschung Datenerhebung - Qualität - Einkommen - Europäische Union swd Einkommen - Datenerhebung - Qualität - Europäische Union swd Qualität - Datenerhebung - Einkommen - Europäische Union swd Mathematisches Modell Statistik Income Statistics Mathematical models Smoothing (Statistics) |
| subject_GND | (DE-588)4113937-9 |
| title | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |
| title_auth | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |
| title_exact_search | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |
| title_exact_search_txtP | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |
| title_full | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel Jens Ulrich Hanisch |
| title_fullStr | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel Jens Ulrich Hanisch |
| title_full_unstemmed | Rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel Jens Ulrich Hanisch |
| title_short | Rounding of income data |
| title_sort | rounding of income data an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the european community household panel |
| title_sub | an empirical analysis of the quality of income data with respect to rounded values and income brackets with data from the European Community Household Panel |
| topic | Datenerhebung - Qualität - Einkommen - Europäische Union swd Einkommen - Datenerhebung - Qualität - Europäische Union swd Qualität - Datenerhebung - Einkommen - Europäische Union swd Mathematisches Modell Statistik Income Statistics Mathematical models Smoothing (Statistics) |
| topic_facet | Datenerhebung - Qualität - Einkommen - Europäische Union Einkommen - Datenerhebung - Qualität - Europäische Union Qualität - Datenerhebung - Einkommen - Europäische Union Mathematisches Modell Statistik Income Statistics Mathematical models Smoothing (Statistics) Europäische Union - Einkommen - Datenerhebung - Qualität Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015031536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012708439 |
| work_keys_str_mv | AT hanischjensulrich roundingofincomedataanempiricalanalysisofthequalityofincomedatawithrespecttoroundedvaluesandincomebracketswithdatafromtheeuropeancommunityhouseholdpanel |