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Intertemporal versus interspatial comparison

2017-11-13T01:25:25Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref name="drechsler">{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings, e.g. an approach where structurally similar countries are compared to each other)<ref name="drechsler" />{{rp|32}}
|-
| The thing against which other things are compared || Base year || [[wikipedia:Numéraire|Numéraire]] country
|-
| Symmetry in treatment of the base || Time-reversal test || Country reversal test (bilateral) or base-country invariance (multilateral)<ref name="icrgp1982" />{{rp|71–72}}
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:28:48Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|-
| The thing against which other things are compared || Base year || [[wikipedia:Numéraire|Numéraire]] country
|-
| Symmetry in treatment of the base || Time-reversal test || Country reversal test (bilateral) or base-country invariance (multilateral)<ref name="icrgp1982" />{{rp|71–72}}
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:28:16Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|-
| The thing against which other things are compared || Base year || [[wikipedia:Numéraire|Numéraire]] country
|-
| || Time-reversal test || Country reversal test (bilateral) or base-country invariance (multilateral)<ref name="icrgp1982" />{{rp|71–72}}
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:27:14Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|-
| The thing against which other things are compared || Base year || [[wikipedia:Numéraire|Numéraire]] country
|-
| || Time-reversal test || Country reversal test/base-country invariance
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:24:33Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|-
| The thing against which other things are compared || Base year || [[wikipedia:Numéraire|Numéraire]] country
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Comparison of PPP formulas

2017-11-12T18:13:47Z

Issa Rice: /* See also */

This page is a '''comparison of PPP formulas'''. A [[PPP formula]] is used to calculate price matrices.<ref>{{cite web |url=https://en.wikipedia.org/wiki/Purchasing_power_parity#Measurement_issues |title=Purchasing power parity § Measurement issues |accessdate=October 27, 2017 |publisher=English Wikipedia}}</ref>

==General comparison==

<ref>{{cite web |url=https://www.princeton.edu/~deaton/downloads/PPP_Exchange_rates_may04_relabeled_mar11.pdf |title=Purchasing power parity exchange rates from household survey data: India and Indonesia |date=May 2004 |first1=Angus |last1=Deaton |first2=Jed |last2=Friedman |first3=Vivi |last3=Alatas |accessdate=October 27, 2017 |quote=Originally developed by the International Price Comparison Project for the Penn World Table (PWT), there are now a number of different variants, most notably by the OECD, Eurostat and the World Bank. Although the formulas differ, all of these PPP estimates are based on prices and quantities for each country |publisher=[[wikipedia:Princeton University|Princeton University]]}}</ref>

{| class="sortable wikitable"
|-
! Index name !! Type !! First publication year !! Used in !! Notes
|-
| Laspeyres || Bilateral ||
|-
| Paasche || Bilateral ||
|-
| GEKS-Fisher || ||
|-
| Geary–Khamis || Multilateral || 1958, 1972<ref name="diewert-index-numbers" />{{rp|33}} || ICP 1975 (Kravis, Kenessey, Heston, and Summers)
|-
| Superlative method || || || || I think this is a ''class'' of methods defined by [[Walter Erwin Diewert]]; they are all the ones that satisfy a list of properties, see [https://en.wikipedia.org/wiki/List_of_price_index_formulas#Superlative_indices]
|-
| Gerardi<ref name="un-gk" /> || || || EUROSTAT<ref name="un-gk">{{cite web |url=https://unstats.un.org/unsd/methods/icp/ipc7_htm.htm |title=United Nations Statistics Division |accessdate=November 3, 2017}}</ref>
|-
| Binary-Fisher<ref name="un-gk" /> || ||
|-
| Gini–Eltetö–Köves–Szulc (GEKS, sometimes just EKS)<ref name="un-gk" /><ref name="diewert-index-numbers" />{{rp|33}} || Multilateral || || OECD–Eurostat (a variant with representativity, sometimes called GEKS*)<ref>{{cite web |url=https://www.oecd.org/std/prices-ppp/13-3012041ec015.pdf |title=Eurostat-OECD Methodological Manual on Purchasing Power Parities - Calculation and aggregation of PPPs |publisher=OECD/Eurostat |year=2012 |accessdate=November 10, 2017}}</ref>{{rp|235}}
|-
| [[Walsh price index|Walsh]]<ref name="un-gk" /> || ||
|-
| Van Yzeren<ref name="un-gk" /> || Multilateral || || European Coal and Steel Community (1960)<ref name="icrgp1982" /> ||
|-
| Exchange rate<ref name="un-gk" /> || ||
|-
| Young<ref name="diewert-index-numbers">{{cite web |url=https://www.business.unsw.edu.au/research-site/centreforappliedeconomicresearch-site/Documents/E.%20Diewert%20-%20Index%20Numbers.pdf |title=Index Numbers (working paper) |date=December 16, 2006 |journal=Journal of Economic Literature Classification Numbers |author=W. Erwin Diewert |publisher=Centre for Applied Economic Research (The University of New South Wales) |accessdate=November 4, 2017}}</ref> || ||
|-
| Sidgwick–Bowley<ref name="diewert-index-numbers" /> || Bilateral || || || Arithmetic mean of Laspeyres and Paasche
|-
| Fisher ideal<ref name="diewert-index-numbers" /> (same as "Fisher"?) || Bilateral || || NIPA 1999 in part of the contribution to percent change calculation<ref>{{cite web |url=https://www.bea.gov/scb/pdf/national/nipa/1999/1099niw.pdf |title=A Preview of the 1999 Comprehensive Revision of the National Income and Product Accounts: Statistical Changes, October 1999 SCB - 1099niw.pdf |first1=Brent R. |last1=Moulton |first2=Eugene P. |last2=Seskin |date=October 1999 |publisher=Survey of Current Business |accessdate=November 5, 2017}}</ref>
|-
| Marshall–Edgeworth<ref name="diewert-index-numbers" />{{rp|7}} || ||
|-
| Carli<ref name="diewert-index-numbers" />{{rp|7}} || Bilateral || 1764
|-
| Jevons<ref name="diewert-index-numbers" />{{rp|8}} || Bilateral || 1865 ||
|-
| Törnqvist<ref name="diewert-index-numbers" />{{rp|9}} || Bilateral || 1936 ||
|-
| Konüs–Byushgens<ref name="diewert-index-numbers" />{{rp|28}} || || 1926 ||
|-
| Star method<ref name="diewert-index-numbers" />{{rp|33}} || Multilateral ||
|-
| Democratic weights method<ref name="diewert-index-numbers" />{{rp|33}} || Multilateral ||
|-
| Plutocratic weights method<ref name="diewert-index-numbers" />{{rp|33}} || Multilateral ||
|-
| Own share method<ref name="diewert-index-numbers" />{{rp|33}} || Multilateral ||
|-
| Average basket method<ref name="diewert-index-numbers" />{{rp|33}} || Multilateral ||
|-
| Country Product Dummy<ref name="diewert-index-numbers" />{{rp|34}} || Multilateral || 1973 || ICP<ref name="icrgp1982" />{{rp|86}} ||
|-
| Unit-country weighting method<ref name="icrgp1982" />{{rp|78}} || Multilateral || || Common Market (1975) || Developed by Dino Gerardi. Potentially the same as the Gerardi index.
|-
| Iklé method<ref name="balk-2001" />{{rp|16}} || Multilateral || 1972
|-
| Iklé–Dikhanov–Balk (IDB)<ref name="diewert-2011-methods">{{cite web |url=http://siteresources.worldbank.org/ICPINT/Resources/270056-1255977254560/6483625-1291755426408/05_ICPBOOK_AggregationAboveBH_Final.pdf |title=Measuring the Size of the World Economy - Chapter 5: Methods of Aggregation above the Basic Heading Level within Regions |author=W. Erwin Diewert |year=2011 |archiveurl=https://web.archive.org/web/20171109004616/http://siteresources.worldbank.org/ICPINT/Resources/270056-1255977254560/6483625-1291755426408/05_ICPBOOK_AggregationAboveBH_Final.pdf |archivedate=November 9, 2017 |dead-url=no |accessdate=November 9, 2017}}</ref>{{rp|3}} || 1972<ref name="diewert-2011-methods" />{{rp|9}} || Multilateral || Africa region of ICP 2005<ref name="diewert-2011-methods" />{{rp|3}} ||
|-
| Neary's GAIA system<ref name="diewert-2011-methods" />{{rp|19}} || Multilateral || 2004 || || This method "allows for nonhomothetic preferences on the part of final demanders" but "uses a single set of relative prices to value consumption or the gross domestic product (GDP) in all countries, no matter how different are the actual relative prices in each country".<ref name="diewert-2011-methods" />{{rp|19}}
|-
| Minimum spanning tree (MST)<ref name="diewert-2011-methods" /> ||
|}

==Properties of bilateral indices==

{| class="sortable wikitable"
|-
! Formula name !! Superlative? !! Additive?<ref name="un-gk" /> !! Transitive/circular?
|-
| Laspeyres || No ||
|-
| Paasche || No ||
|}

==Properties of multilateral indices==

Comparison style is one of:

* uses selective binary comparisons
* uses binary comparisons
* makes no use of any binary comparisons

{| class="sortable wikitable"
|-
! Formula name !! Comparison style !! Reduces to in the case of two countries !! Base country invariant? !! Transitive? !! Matrix consistency? !! Factor-reversal test? !! Additive?
|-
| Van Yzeren || Uses binary comparisons (Fisher) || Fisher || Yes
|-
| EKS || Uses binary comparisons (Fisher) || Fisher || Yes
|-
| Walsh || || || Yes
|-
| Geary–Khamis || || || Yes || || || || Yes (strongly)<ref name="balk-2001">{{cite web |url=https://www.oecd.org/std/prices-ppp/2424931.pdf |first=Bert M. |last=Balk |date=June 15, 2001 |title=Aggregation Methods in International Comparisons: What Have We Learned? |archiveurl=https://web.archive.org/web/20171108203336/https://www.oecd.org/std/prices-ppp/2424931.pdf |archivedate=November 8, 2017 |dead-url=no |accessdate=November 8, 2017}}</ref>{{rp|13}}
|-
| Iklé–Dikhanov–Balk || || || || || || || Yes<ref name="diewert-2011-methods" />{{rp|3}}
|}

==Notes/scratch work==

{{quotation|Four multilateral methods are considered in detail: (1) Walsh, (2) EKS, (3) Van Yzeren, and (4) Geary-Khamis. Each method goes beyond the binary procedures of Chapter 4 by drawing upon price and quantity data of all countries simultaneously in aggregating up from the category level. They all are base country invariant, and have the transitivity property, and can be adapted to a form that gives additive consistency. The EKS method meets the factor-reversal test. The Geary-Khamis method also satisfies the test at the GDP level. Only in a purely definitional sense (that is, by deriving either the PPPs or the quantity index indirectly) can the Walsh and Van Yzeren methods and the Geary-Khamis subaggretates be said also to meet the test.<ref>{{cite web |url=http://documents.worldbank.org/curated/en/199981467988893189/pdf/multi-page.pdf |title=World Bank Document - multi-page.pdf |accessdate=November 3, 2017}}</ref>}}

What methods do the following use?

* OECD
* Eurostat
* World Bank
* IDB

chained/chain-linked vs fixed-base versions for each of the above? [https://www.oecd.org/std/prices-ppp/2424597.pdf]{{rp|6}} [https://www.um.edu.mt/__data/assets/pdf_file/0010/149266/food_imports_update.pdf]{{rp|7}}

I think there's also bilateral vs multilateral versions of the above?

What parameters do each ''p'' (price) or ''q'' (quantity) variables take? I have seen time period (usually ''t'' or ''n''), commodity/basic heading (''c'' or ''i''), country (''j'').

A lower bound on the number of price indices: "But Walsh (1901) and Fisher (1922) presented hundreds of functional forms for bilateral price indexes".<ref name="diewert-index-numbers" /> My current understanding is that only a handful are commonly used in practice, perhaps because the others fail to satisfy nice properties.

The multilateral indices can be divided into those that use binary comparisons (i.e. make use of some binary index) and ones that don't. Examples of the former are EKS and Van Yzeren. Examples of the latter are Walsh indices (apparently there are multiple).<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|76, 77}} This is probably why Walsh is listed as both a binary and a multilateral index: there is some binary formulation, and you can probably generalize it for multilateral comparison, but that multilateral index does not use the binary comparisons from the binary version. (My guess at what's going on.)

For multilateral indices, there is the question of what bilateral index it reduces to when the number of countries goes down to two.

A bilateral/binary index works just as well for locations as time periods. You just need as inputs two price vectors and two quantity vectors (where the coordinates are the different goods). The two price vectors can be two periods or two countries.

Balk lists the following multilateral methods: GEKS, Van IJzeren, Gerardi, WFBS (weighted Fisher blended system), WDOS (Diewert's Own Share system), YKS (Kurabayashi and Sakuma), Q-YKS, GK, EWGK (equally weighted GK method), KS-S (Kurabayashi and Sakuma), SRK (Sakuma, Rao, and Kurabayashi), Sergueev, Gerardi, Iklé, Rao.<ref name="balk-2001" />

One taxonomy of multilateral indices is given by Hill.<ref>{{cite web |url=http://www.roiw.org/1997/49.pdf |author=Robert J. Hill |title=A Taxonomy of Multilateral Methods for Making International Comparisons of Prices and Quantities |journal=Review of Income and Wealth |date=March 1997 |accessdate=November 8, 2017}}</ref>

==See also==

* [[Intertemporal versus interspatial comparison]]

==External links==

* {{W|Price index}} (Wikipedia)
* {{W|List of price index formulas}} (Wikipedia)

==References==

{{Reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:13:05Z

Issa Rice:

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, aspects of intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Aspect !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:12:10Z

Issa Rice:

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]]. In particular, properties seen in intertemporal comparisons have counterparts in interspatial comparisons, so the table catalogs these.

==Comparison table==

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:10:05Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]].

==Comparison table==

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler |date=March 1973 |accessdate=November 12, 2017}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:09:17Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]].

==Comparison table==

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared<ref>{{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler}}</ref>{{rp|19}} || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:07:53Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]].

==Comparison table==

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year (or other granularity of time periods) || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:07:20Z

Issa Rice: /* Comparison table */

The following table examines '''intertemporal versus interspatial comparison''' in PPP calculation/[[index number theory]].

==Comparison table==

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared || Up-to-dateness || Characteristicity
|-
| Tendency of Paasche quantity indices to be lower than Laspeyres indices<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|75}} || [[Gerschenkron effect]] || Own-weight effect
|-
| Ordering || Natural ordering by year || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Intertemporal versus interspatial comparison

2017-11-12T18:06:29Z

Issa Rice: /* Comparison table */

Intertemporal versus interspatial comparison

2017-11-12T18:03:19Z

Issa Rice:

Intertemporal versus interspatial comparison

2017-11-12T18:00:23Z

Issa Rice: Created page with "'''Intertemporal versus interspatial comparison''' {| class="sortable wikitable" |- ! Property !! Intertemporal !! Interspatial |- | How well the weights match the thing bein..."

'''Intertemporal versus interspatial comparison'''

{| class="sortable wikitable"
|-
! Property !! Intertemporal !! Interspatial
|-
| How well the weights match the thing being compared || Up-to-dateness || Characteristicity
|-
| || || [[Gerschenkron effect]]
|-
| Ordering || Natural ordering by year || No natural ordering (but some have devised orderings)
|}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Characteristicity versus universality trade-off

2017-11-12T03:47:50Z

Issa Rice: /* History */

In the context of PPP calculation, the '''characteristicity versus universality trade-off''' refers to the trade-off between maintaining the characteristicity of binary comparisons and the universality of multilateral comparisons. Here:

* ''Characteristicity'' means an index more faithfully represents the constituent countries, i.e. the index is more ''characteristic'' of those countries. Binary comparisons have more characteristicity because the index is only ''about'' the two countries in question, whereas a multilateral index incorporates information from other countries that aren't directly being compared.
* ''Universality'' means all countries are compared according to a "common standard".

==History==

The term "country characteristicity" was introduced by Drechsler in 1975 or 1973 ({{cite web |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1475-4991.1973.tb00871.x/full |title=Weighting of index numbers in multilateral international comparisons |journal=Review of income and wealth |first=László |last=Drechsler}}).<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|73}}

The trade-off is covered in the United Nations International Comparison Project Phase III, published in 1982.<ref name="icrgp1982" />{{rp|101}}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Characteristicity versus universality trade-off

2017-11-12T03:46:15Z

Issa Rice: /* History */

In the context of PPP calculation, the '''characteristicity versus universality trade-off''' refers to the trade-off between maintaining the characteristicity of binary comparisons and the universality of multilateral comparisons. Here:

* ''Characteristicity'' means an index more faithfully represents the constituent countries, i.e. the index is more ''characteristic'' of those countries. Binary comparisons have more characteristicity because the index is only ''about'' the two countries in question, whereas a multilateral index incorporates information from other countries that aren't directly being compared.
* ''Universality'' means all countries are compared according to a "common standard".

==History==

The term "country characteristicity" was introduced by Drechsler in 1975 ("Weighting of index numbers in multilateral international comparisons", ''Review of income and wealth'').<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|73}}

The trade-off is covered in the United Nations International Comparison Project Phase III, published in 1982.<ref name="icrgp1982" />{{rp|101}}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Characteristicity versus universality trade-off

2017-11-12T03:14:03Z

Issa Rice:

In the context of PPP calculation, the '''characteristicity versus universality trade-off''' refers to the trade-off between maintaining the characteristicity of binary comparisons and the universality of multilateral comparisons. Here:

* ''Characteristicity'' means an index more faithfully represents the constituent countries, i.e. the index is more ''characteristic'' of those countries. Binary comparisons have more characteristicity because the index is only ''about'' the two countries in question, whereas a multilateral index incorporates information from other countries that aren't directly being compared.
* ''Universality'' means all countries are compared according to a "common standard".

==History==

The term "country characteristicity" was introduced by Drechsler in 1975.<ref name="icrgp1982">{{cite web |url=http://documents.worldbank.org/curated/en/974171468766774952/pdf/multi-page.pdf |title=World Product and Income: International Comparisons of Real Gross Product (United Nations International Comparison Project Phase III) |year=1982 |first1=Irving B. |last1=Kravis |first2=Alan |last2=Heston |first3=Robert |last3=Summers |publisher=Johns Hopkins University Press |accessdate=November 5, 2017}}</ref>{{rp|73}}

The trade-off is covered in the United Nations International Comparison Project Phase III, published in 1982.<ref name="icrgp1982" />{{rp|101}}

==See also==

* [[Comparison of PPP formulas]]

==External links==

==References==

{{reflist|30em}}

Characteristicity versus universality trade-off

2017-11-12T03:03:25Z

Issa Rice: /* See also */

Characteristicity versus universality trade-off

2017-11-12T03:02:24Z

Issa Rice: /* History */

Issa Rice: /* As a function */

The '''Geary–Khamis dollar''' (also known as the '''international dollar''') is a hypothetical currency.

==History==

==As a function==

Currency conversions involving PPP can be conceptualized as a 6-place function taking as parameters:

{| class="sortable wikitable"
|-
! Parameter !! Unit !! Set of possible values !! Example !! Notes
|-
| Target currency || Whatever unit the currency is in (e.g. [[wikipedia:Yuan (currency)|yuan]] if the currency is [[wikipedia:Renminbi|renminbi]]) || {''x'' : ''x'' is a currency} = {US dollar, renminbi, ...} || US dollar ||
|-
| Year associated with the currency || Time || '''Z''' \ {0} || 2005 ||
|-
| Location with respect to the PPP calculation || Unitless || 𝒫({''x'' : ''x'' is a point on Earth}), i.e. some subset of points on Earth || United States || (this is almost always the location where the target currency is used; this can also be some artificial combination of multiple regions, e.g. OECD dollars are US dollars valued at average OECD price levels)<ref>{{cite web |url=http://ec.europa.eu/eurostat/documents/728703/728974/FAQ-PPP.pdf/5a92e63b-1c73-4d15-8acd-f3e5e734cbf2 |title=FAQ about Purchasing Power Parities |date=April 12, 2012 |accessdate=November 11, 2017 |archiveurl=https://web.archive.org/web/20171111022010/http://ec.europa.eu/eurostat/documents/728703/728974/FAQ-PPP.pdf/5a92e63b-1c73-4d15-8acd-f3e5e734cbf2 |archivedate=November 11, 2017 |dead-url=no}}</ref>
|-
| Year associated with the location || Time || '''Z''' \ {0} || 2005 || (this is almost always the same as the year associated with the currency)
|-
| Some [[Market basket|basket of goods]] || Unitless || 𝒫(Goods), where Goods is the set of goods and 𝒫 denotes the [[wikipedia:Power set|power set]] || {[[wikipedia:Big Mac Index|McDonalds Big Mac]]} || Is a market basket really just a set? Do we need to specify weights (e.g. via sales volume) on the goods (in which case the basket is more like a set of tuples (''g'', ''w''))?
|-
| [[Comparison of PPP formulas|Price index]]/aggregation method/PPP formula || Unitless || {''x'' : ''x'' is a PPP formula} || Gini–Eltetö–Köves–Szulc (GEKS) method || (could this be taken outside the unit? the different formulas can be seen to be "competing" to find the "best" PPP, so that the concept of PPP itself is independent, and this could be more of an algorithmic/empirical question. i.e. the unit might conceptually make sense without specifying a formula. A PPP value should tell a story like "[Value] is how much [target currency] from [currency year] buys in [location] during [location year]", and this story might make sense without the basket of goods and price index being specified [i.e. fixing those is still a practical question, but is not required to tell the story]. Maybe the story ''doesn't'' make sense unless you add "... where by 'buy' we mean 'buy things in this basket of goods' and by 'how much' we mean 'how much according to this conversion formula'.")
|}

Only after fixing all the parameters can the unit make sense next to a number.

Of these, the Geary–Khamis dollar [[wikipedia:Currying|partially fixes]] the parameters: it sets the target currency to the US dollar and the location to the United States. The other parameters are decided by the author of the publication. Therefore formally the Geary–Khamis dollar can be seen as a "unit schema" or "unit-producing function" that takes a year as input and outputs an actual unit.

On the source side:

* Source currency
* Year associated with the currency

==Difference with the US dollar for a particular year==

e.g. 2000 GK dollar vs 2000 US dollar

Is there a difference?

==Devec database==

Multiple metrics in the devec database use the Geary–Khamis dollar (at various years) for units. At the MySQL prompt:

<pre>select metric,units from data
where region = 'Japan' and units REGEXP 'international dollar'
group by metric,units;
</pre>

The <code>where region = 'Japan'</code> is just to restrict the search space, since <code>region</code> is an indexed column in the table.

==See also==

==External links==

* {{W|Geary–Khamis dollar}} (Wikipedia)

==References==

{{Reflist|30em}}

Geary–Khamis dollar

2017-11-11T03:20:02Z

Issa Rice: /* As a function */

The '''Geary–Khamis dollar''' (also known as the '''international dollar''') is a hypothetical currency.

==History==

==As a function==

Currency conversions involving PPP can be conceptualized as a 6-place function taking as parameters:

{| class="sortable wikitable"
|-
! Parameter !! Unit !! Set of possible values !! Example !! Notes
|-
| Target currency || Whatever unit the currency is in (e.g. [[wikipedia:Yuan (currency)|yuan]] if the currency is [[wikipedia:Renminbi|renminbi]]) || {''x'' : ''x'' is a currency} = {US dollar, renminbi, ...} || US dollar ||
|-
| Year associated with the currency || Time || '''Z''' \ {0} || 2005 ||
|-
| Location with respect to the PPP calculation || Unitless || || United States || (this is almost always the location where the target currency is used; this can also be some artificial combination of multiple regions, e.g. OECD dollars are US dollars valued at average OECD price levels)<ref>{{cite web |url=http://ec.europa.eu/eurostat/documents/728703/728974/FAQ-PPP.pdf/5a92e63b-1c73-4d15-8acd-f3e5e734cbf2 |title=FAQ about Purchasing Power Parities |date=April 12, 2012 |accessdate=November 11, 2017 |archiveurl=https://web.archive.org/web/20171111022010/http://ec.europa.eu/eurostat/documents/728703/728974/FAQ-PPP.pdf/5a92e63b-1c73-4d15-8acd-f3e5e734cbf2 |archivedate=November 11, 2017 |dead-url=no}}</ref>
|-
| Year associated with the location || Time || '''Z''' \ {0} || 2005 || (this is almost always the same as the year associated with the currency)
|-
| Some [[Market basket|basket of goods]] || Unitless || 𝒫(Goods), where Goods is the set of goods and 𝒫 denotes the [[wikipedia:Power set|power set]] || {[[wikipedia:Big Mac Index|McDonalds Big Mac]]} || Is a market basket really just a set? Do we need to specify weights (e.g. via sales volume) on the goods (in which case the basket is more like a set of tuples (''g'', ''w''))?
|-
| [[Comparison of PPP formulas|Price index]]/aggregation method/PPP formula || Unitless || {''x'' : ''x'' is a PPP formula} || Gini–Eltetö–Köves–Szulc (GEKS) method || (could this be taken outside the unit? the different formulas can be seen to be "competing" to find the "best" PPP, so that the concept of PPP itself is independent, and this could be more of an algorithmic/empirical question. i.e. the unit might conceptually make sense without specifying a formula. A PPP value should tell a story like "[Value] is how much [target currency] from [currency year] buys in [location] during [location year]", and this story might make sense without the basket of goods and price index being specified [i.e. fixing those is still a practical question, but is not required to tell the story]. Maybe the story ''doesn't'' make sense unless you add "... where by 'buy' we mean 'buy things in this basket of goods' and by 'how much' we mean 'how much according to this conversion formula'.")
|}

Only after fixing all the parameters can the unit make sense next to a number.

Of these, the Geary–Khamis dollar [[wikipedia:Currying|partially fixes]] the parameters: it sets the target currency to the US dollar and the location to the United States. The other parameters are decided by the author of the publication. Therefore formally the Geary–Khamis dollar can be seen as a "unit schema" or "unit-producing function" that takes a year as input and outputs an actual unit.

On the source side:

* Source currency
* Year associated with the currency

==Difference with the US dollar for a particular year==

e.g. 2000 GK dollar vs 2000 US dollar

Is there a difference?

==Devec database==

Multiple metrics in the devec database use the Geary–Khamis dollar (at various years) for units. At the MySQL prompt:

<pre>select metric,units from data
where region = 'Japan' and units REGEXP 'international dollar'
group by metric,units;
</pre>

The <code>where region = 'Japan'</code> is just to restrict the search space, since <code>region</code> is an indexed column in the table.

==See also==

==External links==

* {{W|Geary–Khamis dollar}} (Wikipedia)

==References==

{{Reflist|30em}}