Chain indices: a study in price index theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart
Metzler-Poeschel
2001
|
| Series: | Schriftenreihe Spektrum Bundesstatistik
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 291 S. |
| ISBN: | 3824606380 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
List of Figures 7
List of Tables 8
Foreword • 9
Preface 10
0 Introduction 12
0.1 The scope and structure of the book 12
a) The nature and relevance of chain indices 12
b) Aims of the presentation 13
0.2 Introduction to price indices and price statistics 15
a) Definition of index 15
b) Objectives of price indices, concept of deflation 17
c) Two basic methodological principles of price statistics 18
d) The variety of approaches in index theory 20
0.3 Simple and aggregative comparisons 21
a) Simple comparison 21
b) Aggregative comparison 24
1 Towards a clear notion of a chain index 28
1.1 Direct and chain approach, chain and links 28
1.2 Product representation and chainability 32
1.3 Weights in the chain approach 36
2 Elements of (direct) index theory 39
2.1 Index formulas of Laspeyres and Paasche 39
a) Dual interpretation: mean of relatives and ratio of expenditures 39
b) Price and quantity indices, the ill conceived reversal idea .... 42
c) Interpretation of the Laspeyres and Paasche formula in terms of
pure comparison 45
d) Theorem of Ladislaus von Bortkiewicz 49
2.2 The axiomatic approach in index theory 51
a) Usefulness of axioms and axiomatic systems 52
b) A tentative hierarchy of axioms 54
c) Some axioms explained in detail 58
d) Additivity and linearity of index functions 67
e) Some other properties and uniqueness theorems 72
2.3 Deflation and aggregation 79
a) Objectives and types of deflation 79
b) Aggregative properties of index functions and volumes
(overview) 82
Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001 3
Contents c) Aggregative consistency of the index function (Al) and the
equality test 84
d) Structural consistency of volumes (A2) and double deflation ... 89
e) Volumes suitable to serve as substitutes for quantity 92
3 Analysis of properties of chain indices 101
3.1 Traditional interpretations of an index not applicable 101
a) Chain price index as a ratio of expenditures 101
b) Mean value property violated, no mean of relatives
interpretation 104
3.2 Axiomatic reasoning applicable with some limitations only 108
a) Only the link is an index able to satisfy certain axioms 108
b) Changes in the domain of definition, a source of an unknown
error Ill
c) Chain indices may violate identity 113
d) Monotonicity and some other axioms 115
e) Additivity and aggregative consistency reconsidered 117
f) Cyclical movement of prices 121
3.3 Drift functions and growth rates 125
a) Drift function and growth factors of chain indices 125
b) Drift function and the Laspeyres Paasche gap 130
c) The correct and most relevant growth rate of real values
(volumes) 133
d) Comparisons of indices published monthly or quarterly 140
3.4 Intertemporal correlation 141
a) Basic relation between drift and intertemporal covariance .... 141
b) Series of drifts and intertemporal covariances, cyclical price
movement 145
3.5 The effect of changes in prices at different times (nonlinearity in prices) . 149
3.6 Numerical examples, simulations and estimations with real data 154
3.7 Accuracy and cumulation of errors 156
a) Types and sources of errors 157
b) The exaggerated impact of errors in expenditure weights 160
c) Cumulation of errors by multiplication of links 163
4 Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001
Contents
4 Elements of a theory of chain indices 166
4.1 Chaining and chainability (transitivity) 167
a) The theory of comparability of Marco Martini 167
b) Directly incomparable but indirectly comparable? 168
c) Limitations of the analogy with interspatial comparisons 171
d) Temporal aggregation and chainability 175
e) The role of chainability in justifying chain indices 176
f) Additional information and irrelevance of the base 178
g) Restrictions imposed on a time series by transitivity 180
4.2 Chaining and constant adjustment of quantity weights 182
a) Chainability and variable weights 182
b) Chaining and frequency of updating of weights 184
4.3 Chaining and consistency in aggregation 188
4.4 Are the most up to date weights automatically the best weights? .... 191
a) Assumptions needed to equate last observed with most rep¬
resentative 192
b) Representativity over which interval in time? 195
c) Accounting for the development of weights in all intermediate
periods 197
d) Fixed basket as a model 199
5 Deflation with chain indices 201
5.1 The SNA recommends chained Fisher indices 201
5.2 Deflation with direct Fisher indices, a bad solution 202
a) Fisher deflation, additivity and quantity movement 202
b) Fisher s ideal index is far from being ideal 207
5.3 Deflation with chain Fisher indices, an even worse solution 210
5.4 The SNA on how to deal with structural inconsistency 214
6 Arguments in favor of the chain index approach 218
6.1 A parade of arguments for chain indices 218
a) Focus on links rather than on the chain 219
b) Ambiguities concerning the notion of base 221
c) Adjustment of weights, new products and changes in quality . . 224
d) Arguments referring to expected and desired results of index
calculations 226
e) Chain indices recommended for deflation (SNA) 227
6.2 Rebuff of the arguments for chain indices 227
a) General remarks valid for all arguments of chainers 228
b) Special remarks to selected arguments of chainers 234
6.3 Five rules to argue in favor of chain indices 239
Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001 5
Contents 7 Divisia index and its relation to chain index numbers 246
7.1 Procedure to derive Divisia s integral index 246
7.2 Discrete time approximations and chain indices 251
7.3 Uses and limitations of Divisia s approach 253
a) Reich s axiom of simultaneity 254
b) Diewert s skeptical view 256
8 Official statistics and concluding remarks 258
8.1 Aspects of interpretation and official statistics 258
a) Difficulties in compilation, family expenditure surveys (FES),
cost benefit studies 259
b) Acceptance, understandability, room for manipulation 261
c) Applying the chain principle to all kinds of indices and to dou¬
ble deflation 264
8.2 Pure price comparison 268
a) The meaning of pure comparison 268
b) Analytical purpose: elimination of structural change and isola¬
tion of known determinants in an index 274
c) Why constant weights? 278
d) Why linearity in the prices of the current period? 281
References 284
Index 288
6 Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001
List of Figures
0.2.1 Principles of price statistics and price index construction 18
1.1.1 Terminological distinctions referring to chain indices . . . 29
1.3.1 Traditional classification of weighting schemes 36
1.3.2 Alternative principles of defining weights 37
2.2.1 Systems of axioms by Eichhorn Voeller 53
2.2.2 Tentative classification of axioms and their uses 56
2.2.3 Relations among some axiomatic properties 57
2.2.4 Strict and weak monotonicity 63
2.2.5 Linear homogeneity, monotonicity and proportionality 65
2.2.6 Generalisation of Bortkiewicz s theorem 74
2.3.1 Alternative procedures of deflation 82
2.3.2 The usage of the terms additivity in index theory 83
3.7.1 Sources of bias in compilation of chain indices 157
3.7.2 Definition of bias (systematic error) 160
4.1.1 Successive comparisons of partially overlapping circles 167
4.1.2 Objectives and principles of index construction 178
6.1.1 Twelve arguments in favor of chain indices, an overview 218
8.2.1 Comparability and chain indices (part 1. Dimensions of comparability) . 274
8.2.2 Comparability and chain indices (part 2: Inconsistencies, comparability
with respect to the number of commodities) 276
Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001 7
List of Tables
0.3.1 Axioms satisfied by price and quantity relatives . . . 23
2.1.1 Dual interpretation of price indices 40
2.1.2 Quantity indices of the Laspeyres and Paasche type . . 43
2.1.3 The interpretation of the Laspeyres and Paasche price index and quan¬
tity index formula 49
2.2.1 Some examples for indices satisfying the value dependence test 78
3.1.1 Quantities underlying the expenditure in the numerator of some indices 103
3.2.1 Some indices expressed as ratios of expenditures 120
3.3.1 Price indices and drifts in terms of growth factors 127
3.4.1 Relationships between indices, growth factors and covariances 144
3.5.1 Relation between changes of individual prices and the price index .... 151
4.1.1 Time reversibility in case of chain indices 174
4.2.1 Chaining and frequency (x) of updating weights 185
4.4.1 Price index using mid point weights 196
5.3.1 Comparison of different deflation methods 213
6.2.1 Summary table of the twelve arguments for chain indices 232
8.2.1 Independence of two notions of pure price comparisons . 273
8 Federal Statistical Office, Spectrum of Federal Statistics, Vol. 16/2001
|
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| author | Lippe, Peter von der 1942-2016 |
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| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV013653349 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:39Z |
| institution | BVB |
| isbn | 3824606380 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009328871 |
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| physical | 291 S. |
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| series | Schriftenreihe Spektrum Bundesstatistik |
| series2 | Schriftenreihe Spektrum Bundesstatistik |
| spelling | Lippe, Peter von der 1942-2016 Verfasser (DE-588)121138615 aut Chain indices a study in price index theory Peter von der Lippe Stuttgart Metzler-Poeschel 2001 291 S. txt rdacontent n rdamedia nc rdacarrier Schriftenreihe Spektrum Bundesstatistik 16 Price indexes Kettenindex Statistik (DE-588)4501156-4 gnd rswk-swf Preisindex der Lebenshaltung (DE-588)4125507-0 gnd rswk-swf Umstellung (DE-588)4135121-6 gnd rswk-swf Preisindex (DE-588)4128399-5 gnd rswk-swf Berechnung (DE-588)4120997-7 gnd rswk-swf Festbasisindex (DE-588)4501157-6 gnd rswk-swf Laspeyres-Index (DE-588)4501158-8 gnd rswk-swf Deutschland (DE-588)4011882-4 gnd rswk-swf Deutschland (DE-588)4011882-4 g Preisindex der Lebenshaltung (DE-588)4125507-0 s Berechnung (DE-588)4120997-7 s DE-604 Laspeyres-Index (DE-588)4501158-8 s Festbasisindex (DE-588)4501157-6 s Umstellung (DE-588)4135121-6 s Kettenindex Statistik (DE-588)4501156-4 s Preisindex (DE-588)4128399-5 s Schriftenreihe Spektrum Bundesstatistik 16 (DE-604)BV008877029 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328871&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lippe, Peter von der 1942-2016 Chain indices a study in price index theory Schriftenreihe Spektrum Bundesstatistik Price indexes Kettenindex Statistik (DE-588)4501156-4 gnd Preisindex der Lebenshaltung (DE-588)4125507-0 gnd Umstellung (DE-588)4135121-6 gnd Preisindex (DE-588)4128399-5 gnd Berechnung (DE-588)4120997-7 gnd Festbasisindex (DE-588)4501157-6 gnd Laspeyres-Index (DE-588)4501158-8 gnd |
| subject_GND | (DE-588)4501156-4 (DE-588)4125507-0 (DE-588)4135121-6 (DE-588)4128399-5 (DE-588)4120997-7 (DE-588)4501157-6 (DE-588)4501158-8 (DE-588)4011882-4 |
| title | Chain indices a study in price index theory |
| title_auth | Chain indices a study in price index theory |
| title_exact_search | Chain indices a study in price index theory |
| title_full | Chain indices a study in price index theory Peter von der Lippe |
| title_fullStr | Chain indices a study in price index theory Peter von der Lippe |
| title_full_unstemmed | Chain indices a study in price index theory Peter von der Lippe |
| title_short | Chain indices |
| title_sort | chain indices a study in price index theory |
| title_sub | a study in price index theory |
| topic | Price indexes Kettenindex Statistik (DE-588)4501156-4 gnd Preisindex der Lebenshaltung (DE-588)4125507-0 gnd Umstellung (DE-588)4135121-6 gnd Preisindex (DE-588)4128399-5 gnd Berechnung (DE-588)4120997-7 gnd Festbasisindex (DE-588)4501157-6 gnd Laspeyres-Index (DE-588)4501158-8 gnd |
| topic_facet | Price indexes Kettenindex Statistik Preisindex der Lebenshaltung Umstellung Preisindex Berechnung Festbasisindex Laspeyres-Index Deutschland |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328871&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008877029 |
| work_keys_str_mv | AT lippepetervonder chainindicesastudyinpriceindextheory |