## Appendix 1. Examples by Data Structure

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---

### I. INTRODUCTION
- Purpose:
  - Data and metadata exchange between statistical organizations requires a common language for describing structure and content of statistical data and metadata.
  - The Statistical Data and Metadata Exchange (SDMX) consortium develops technical exchange standards and content oriented guidelines to recommend harmonized cross-domain concepts and terminology to increase the efficiency of data and metadata exchange.
  - One of the major current challenges of this harmonization effort is a recommended code list for the unit of measure.
- Observations on "unit of measure":
  - Diverse meta-information is packed into the broad concept “unit of measure”, including:
    - comparison periods of growth rates,
    - numerator / denominator of ratios,
    - index types,
    - scaling factors, and
    - aggregation functions.
  - The current SDMX content-oriented guidelines (COG) (SDMX Initiative, 2009) treat only some of these components separately.
- Aim:
  - Analyse diversity of “unit of measure” in practice, identify decomposition and interdependencies of respective meta-information, and identify possible value domains for identified components.

### II. CURRENT PRACTICE
- Method:
  - Use examples from dissemination databases of various international organizations and IMF internal databases to illustrate current practice of modeling unit of measure and related concepts.
- Databases used as examples (numbered list preserved exactly):
  1. Principal Global Indicators (PGI) Website of the Inter-Agency Group on Economic and Financial Data (IAG)
  2. World Economic Outlook (WEO) of the International Monetary Fund (IMF)
  3. OECD.Stat Data Warehouse of the Organization for Economic Cooperation and Development (OECD), three datasets
  4. Statistics Website of the Bank for International Settlements (BIS)
  5. Statistical Data Warehouse of the European Central Bank (ECB)
  6. Eurostat's Selected Principal European Economic Indicators (PEEI)
  7. Eurostat's EUROIND Database
  8. World Development Indicators (WDI) Online Database (World Bank)
  9. Millennium Development Goals Indicators Database (UNStats)
- Representation of unit of measure across surveyed databases:
  - Of the 14 datasets surveyed:
    - Four do not separate the economic indicator from the unit of measure or provide the unit information as reference metadata.
    - Four split concepts such as unit multiplier or adjustment method from the unit.
    - Six separate unit of measure from economic indicator.
- Heterogeneity observed:
  - Unit descriptors for the same conceptual unit vary (examples: “Percent Change over Previous 5 Period”, “Growth previous period”, “Percentage Change”; or “%”, “Percent”, “Percentage Rate”).
  - Some databases embed frequency in the unit (example: “% (Q/Q-1)” meaning “Percent Change over Previous Period” for quarters).
  - Some databases use generic unit types (e.g., “Percent”, “Level, ratio, or USD Millions”, “Index”), while others pack detailed metadata into the unit (examples: “Per head, at current prices and current PPPs, in US dollars”; “In percentage of Net National Income”).
  - Base specification practices vary: “Index” appears without specification, with base period, with base period and adjustment method, and sometimes with a “base method” (e.g. moving average).
- Examples of decomposition practices (tables referenced):
  - Table 3: mixed dimensions combining measured indicator, type of unit, unit of measure, adjustment method, and frequency; some items fail to provide unit information completely (examples: “Personal computers”; “Youth unemployment rate, aged 15-24, men”).
  - Table 4: lists 20 examples with unit presented as a separate dimension, illustrating heterogeneous unit descriptors and inclusion of frequency in unit values.
  - Table 5: examples with separate unit and unit multiplier; unit multiplier appears under different names (magnitude, power code, power of ten, (unit) multiplier, scale) and values specified as multiples of 10 (e.g. 0.1), exponents (e.g. -1), or text (tenth); some databases leave multiplier missing instead of 0 (for 10^0), 1, or “units”.
  - Tables 6, 7, and 8: examples separating further concepts from indicator and unit, viz. type of measure and types of adjustment.

### ASSESSMENT OF EXISTING STANDARDS AND ADOPTION
- Observations:
  - Existing standards/guidelines are only partially met in practice and incompletely cover or specify required concepts.
  - Two physical-unit standards (SI and UCUM) do not cover all social/economic units, but their structure (i) base units, (ii) derived units, (iii) dimensionless units is generalizable and worth adopting.
- Compliance with SDMX COG among the 14 databases:
  - None of the 14 investigated databases entirely follow SDMX COG recommendations for separating unit and measurement information from the economic indicator and decomposing into unit, unit multiplier, base period, and adjustment.
  - Distribution among the 14:
    - Four: do not split economic indicator and unit of measure or only use reference metadata.
    - Six: separate unit from indicator but heterogeneous regarding base period, adjustment, and unit multiplier placement.
    - Remaining four: split one or more additional concepts from indicator and unit but differ on which concepts are separate (one database has separate unit multiplier; two use a “type of measure” containing adjustment or aggregation methodology; one splits two types of adjustment but lacks unit multiplier and base period separately).
- Practical reasons for mixed vs. separated modeling:
  - Mixed dimensions can prevent invalid value combinations (helpful in data collection) and be more comprehensible for executive users.
  - Finer modeling granularity (splitting components) benefits analytic users and is preferable for inter-organizational data and metadata exchange.

### SDMX CONTENT-ORIENTED GUIDELINES (COG) SPECIFICS
- SDMX sponsorship: BIS, ECB, EUROSTAT, IMF, OECD, UN, World Bank.
- COG cross-domain concepts related to unit of measure: unit of measure (item 65), adjustment (3), base period (5), unit multiplier (64).
  - Representation: unit of measure, adjustment, and base period divided into code and free text; no code lists provided except unit multiplier which has a code list.
  - Unit of measure defined by three components: (i) type (currency example), (ii) unit code, (iii) unit of measure detail. “Type” not further explained in COG.
  - Unit defined as “a quantity or increment by which something is counted or described”; examples include kg, Euro, counts, index numbers.
  - Unit multiplier: specifies exponent to basis 10 by which observation values were divided (e.g., multiplier 3 indicates thousands); code list lacks negative multipliers.
  - Unit of measure detail: free text for additional information; no linkage to adjustment or base period.
  - Base period: relevant for interpreting index data, real terms, change measures; may require base value specification; COG includes base period but not a separate base value concept; time stamp required for base period.
  - Adjustment: defined separately (changes in definitions, exchange rates, prices, seasons, other factors); split into code (type) and free text; no comprehensive code list, only examples (trading day, seasonal, trend-cycle).

### SI AND UCUM RELEVANCE
- SI (International System of Units):
  - Foundation: seven base quantities and base units (meter, kilogram, second, ampere, Kelvin, mole, candela).
  - 22 SI derived units; includes supplemental units for civil time.
  - Prefixes for scaling from yotta- (10^24) to yocto- (10^-24).
- UCUM (Unified Code for Units of Measure):
  - Intended to include all units used in international science, engineering, business; based on ISO/ANSI but resolves name conflicts and has broader coverage.
  - Distinguishes seven base units (partly differing from SI), derived units, units from other standards, customary/imperial units, and defines “dimensionless” units used for counts or ratios often provided in percent.

### PROPOSAL: DECOMPOSITION AND GENERIC UNIT TYPES
- Rationale:
  - SDMX COG not sufficiently specific/restrictive for decomposition of unit of measure and guidance on value domains (code lists).
- Generic unit types proposed (classification reflecting measurement vs. calculation):
  - Base types:
    - Count: unit specifies what is counted (examples: persons, personal computers, mobile internet subscriptions, jobs); requires unit multiplier and time series adjustment method.
    - Currency: unit specifies currency or currency group (examples: Euro, SDR, domestic currency); requires unit multiplier, time series adjustment, method of price adjustment (constant prices, current prices, chain-linked), method of exchange rate adjustment (e.g. constant); “constant” and index-based adjustments require base period specification.
    - Base SI/UCUM quantities subset (e.g. length, mass, time) for physical measures.
  - Derived unit types:
    - Defined by derivation method applied to base or derived unit types (difference, sum, ratio, product).
    - Categories: ratio, product, difference, sum; SI/UCUM derived quantities (area, volume, velocity) are subtypes.
    - Derived indicators can reference underlying indicators/units to calculate unit type, unit, and multiplier (e.g., USD/hour, Euro/USD, national currency/person).
    - Ratios of same units yield a dimensionless “fraction” (USD/USD = 1, person/person = 1).
    - Derived unit subtypes suggested (examples): area, volume (product); absolute change over reference period (difference); currency exchange rate, relative change over reference period, index, velocity (ratio).
    - Base period: absolute (date part, e.g., year or quarter) or relative (previous period, same period previous year, last day previous month); base value may need specification.
- Implementation notes:
  - Recursive approach: derive units and multipliers from underlying units; enables flexibility without enumerating all combinations.
  - Recommendation to pre-specify broad families of derived units and attach familiar descriptors for ease of use and comparability.
  - Restrictions on units, multipliers, or related concepts may be necessary for specific subtypes.

### UNIT TYPE RATIO: CASE DISTINCTIONS AND IMPLICATIONS
- Ratio as unit type may vary depending on comparisons of unit type, unit, and unit multiplier of numerator and denominator.
- Key outcomes:
  - If numerator and denominator share type, unit, and multiplier: result = fraction, multiplier = 1 (examples: Rate/Share of total; Military spending as % of GDP; Ratio of subgroups).
  - If units or multipliers differ, result unit labeled UN/UD and multipliers calculated as MN/MD, unless rescaled (e.g., to percent).
  - Percent often behaves like a unit multiplier rather than a unit; for fractions the unit multiplier is especially important and the underlying base unit should be provided.
  - Special cases:
    - “Interest rate in % per annum”: underlying numerator unit type ratio (fraction) and denominator time; typical descriptor “Percent per annum”.
    - Difference of ratios expressed in percentage points: if both ratios provided as fraction with multiplier 0.01 (=%), the difference is measured in “percentage points” — may be assigned a joint descriptor combining unit type (=difference), unit (=fraction), multiplier (=0.01).
    - Ratio of subgroups used for parity indices may have a “base value” indicating balanced situation (usually 1 or 100) that should be provided.

### RECOMMENDED DECOMPOSITION OF UNIT OF MEASURE AND RELATED CONCEPTS
- Decompose unit of measure into components:
  - Unit type
  - Unit (dependent on unit type)
  - Unit multiplier (distinct concept; include negative multipliers in code list)
  - Base period (time stamp and predefined relative values)
  - Base value (default value 100; mandatory for Unit Type=Index or Balance Indicator)
  - Types of adjustment split into at least three components:
    - Price Adjustment (e.g., Constant, Current, Reference Chained, Chain-Linked) — Mandatory for Unit Type=Currency, Derived and Base Unit=Currency (recursion)
    - Econometric/Time Series Adjustment (e.g., Seasonal, Working Day, Trading Day, Trend Cycle, Amplitude, Ratio to Trend MCD Smoothed)
    - Exchange Rate Adjustment (e.g., Constant, Current) — Mandatory for Unit Type=Currency, Derived and Base Unit=Currency (recursion)
  - Base Unit (underlying unit for derived units; mandatory for Unit Type=Difference; Unit=Fraction)
  - Base Indicator (components of a derived Indicator with role specified, e.g., numerator) — Mandatory for Unit Type=Ratio (with a few exceptions)
- Rules and constraints:
  - Unit depends on Unit Type.
  - Unit Multiplier with restrictions based on Unit Type and Unit (e.g., Units with Unit Type=Index usually have Multiplier=1).
  - Base Period value domain includes time stamps extended by predefined values (e.g., previous period, corresponding period of previous year, previous three months, December of previous year, years since time stamp, moving average of years since time stamp).
  - For indices and chain-linked series, include base period, base value, and adjustment methods; aggregation and methodological metadata (e.g., Laspeyres, weighting) may be required.
  - Provide value domains (code lists) for decomposed components to improve interoperability and machine-readability while allowing free-text detail where necessary.

### UNIT FAMILIES, STANDARD UNITS, AND CONVERSION FACTORS
- Unit families: metric, US, and British systems.
- Within a family, designate one unit as standard unit, and define conversion factors to that standard unit.
- Conversion factors between standard units of different unit families of one unit type are specified where applicable.
- For currencies, time-dependency of exchange rates increases complexity.

### TABLE 2: UNIT TYPES, UNITS, AND CONSTRAINTS (SELECTED ENTRIES)
- Base
  - Count
    - Person -
    - Mobile Phone -
    - ... ...
  - Currency
    - List according to ISO 4217 (2010) Requires Price Adjustment
    - Different currency groups Requires Price Adjustment
    - National Currency Requires Price Adjustment
  - Length
    - List according to SI/UCUM -
  - Other relevant SI/UCUM base quantities
    - Lists according to SI/UCUM -
- Derived
  - Difference
    - = Base Unit Constraints on admissible Units may apply
  - Absolute Change over Reference Period
    - = Base Unit Requires Price Adjustment if Type of Base Unit = Currency
  - Balance Indicator Diff.
    - = Base Unit requires Base Value
  - Product
    - = Product of Base Units Constraints on admissible Units may apply
  - Area
    - List according to SI/UCUM -
  - Volume
    - List according to SI/UCUM -
  - Ratio
    - = Ratio of Base Units if Ratio=1 then Unit=Fraction Constraints on admissible Units may apply
  - Velocity
    - List according to SI/UCUM -
  - Numerator=Denominator
    - Fraction Base Unit and Type of Base Unit the same for denominator and numerator
  - Balance Indicator Ratio
    - Fraction Base Unit=Fraction, requires Base Value
  - Index
    - Fraction Requires Base Period, Base Value Unit Multiplier = 1
  - Currency Exchange Rate
    - = Ratio of Base Units Type of Base Units = Currency, C_N ≠ C_D
  - Interest Rate
    - = Fraction / Year -
  - Relative Change over Reference Period
    - = Fraction (=Difference/Type of Base Unit of Difference) Type of Base Units must match
  - Sum
    - = Base Unit Constraints on admissible Units may apply

### CONCLUSION: FINDINGS AND RECOMMENDATIONS
- Findings:
  - The SDMX COG provide a reasonable basis for harmonization and standardization of the unit of measure cross-domain concept.
  - Two challenges identified: (i) a lack of compliance in practice and (ii) room for improvement in definition of concepts (including code lists) and decomposition of concepts.
  - Degree of compliance with the SDMX COG varies between the 14 examined databases, but none provides the four concepts recommended in the SDMX COG (unit, unit multiplier, base period, and adjustment) separately.
  - Disagreement exists even between databases that display a particular concept separately.
- Recommendations / Conclusions:
  - Provide more precise definitions of concepts and include code lists in the SDMX COG to achieve harmonized representation.
  - Decompose “unit of measure” into basic building blocks and derive an extendable set of generic unit types and subtypes, assigned units, and cross-domain concepts related to unit of measure.
  - Extend work to define representation of derived indicators, unit types, units, and unit families as well as required constraints.
  - Develop a unit (type) calculus to better account for and make use of calculability characteristic of units.

### APPENDIX: EXAMPLES BY STRUCTURE AND UNIT TYPE (SELECTED EXCERPTS)
- Examples for Indicator including Unit of Measure (Table 3):
  - Share Prices, Monthly, Index (base 2005 = 100)
  - Industrial Production Index, Monthly, (base 2005 = 100), seasonally adjusted
  - Currency exchange rates, Monthly, National units per US-Dollar
  - Personal computers
  - Youth unemployment rate, aged 15-24, men
  - Adolescent fertility rate (births per 1,000 women ages 15-19)
  - Electric power consumption (kWh per capita)
  - Long-term interest rates, Monthly, Per cent per annum
  - Primary completion rate, total (% of relevant age group)
  - Ratio of youth unemployment rate to adult unemployment rate, men
  - Military expenditure (% of GDP)
  - GDP growth (annual %)
- Examples for separate Indicator and Unit (Table 4, excerpts):
  - Population — Number of Persons, Millions
  - GDP Nominal — National Currency, Seas. Adjusted, Millions
  - Oil Price — US Dollars per Barrel
  - Economic Sentiment Indicator — Index
  - GDP Volume — Index, 2005=100, Seasonally Adjusted
  - GDP Volume Percent Change over Previous Period
- Examples for separate Indicator, Unit, and Unit Multiplier (Table 5, excerpts):
  - Gross domestic product per capita, constant prices — National currency Units
  - Current account balance — U.S. dollars Billions
  - Employment — Persons Millions
- Examples for Indicator, Unit, and Adjustments (Table 7, excerpts):
  - Taxes less subsidies on production and imports — Millions of euro (from 1.1.1999) / ECU (up to 31.12.1998) — Not seasonally adjusted data — Chain-linked volumes, reference year 2000 (at 2000 exchange rates)
  - GDP at market prices — Millions of euro / ECU — Seasonally adjusted & adjusted by working days — Current prices
- Examples by Unit Type (Appendix 2, excerpts):
  - Count Type Units (Table 9): Internet users; Employment, seasonally adjusted — Persons Millions
  - Currency Type Units (Table 10): Reserve Assets, Monthly, SDR millions; Current account balance U.S. dollars Billions; Taxes less subsidies on production and imports — Millions of euro (from 1.1.1999) / ECU (up to 31.12.1998)
  - Index Type Units (Table 11): Industrial Production Index, Monthly, (base 2005 = 100), s.a.; Net barter terms of trade (2000 = 100); GDP Volume Index, 2005=100; Inflation, average consumer prices Index, 2000=100
  - Units of Derived Unit Type (Table 12): examples include Difference (Billions of US dollars), Ratio (Unemployment rate % of total labor force), Index (Index Units with base periods), Relative Change over Reference Period (GDP Volume Percent Change over Previous Period)

*Source: _wp11152 - Appendix 1. Examples by Data Structure; _wp11152 - 10. IMF Internal Databases, three datasets; _wp11152 - 1. Unit Type as discussed above (IMF PDF).*

### Appendix 1. Examples by Data Structure ............................................................................... 1

### _wp11152 - Appendix 1. Examples by Data Structure

### I. INTRODUCTION
- Purpose:
  - Data and metadata exchange between statistical organizations requires a common language for describing structure and content of statistical data and metadata.
  - The Statistical Data and Metadata Exchange (SDMX) consortium develops technical exchange standards and content oriented guidelines to recommend harmonized cross-domain concepts and terminology to increase the efficiency of data and metadata exchange.
  - One of the major current challenges of this harmonization effort is a recommended code list for the unit of measure.
- Observations on "unit of measure":
  - Diverse meta-information is packed into the broad concept “unit of measure”, including:
    - comparison periods of growth rates,
    - numerator / denominator of ratios,
    - index types,
    - scaling factors, and
    - aggregation functions.
  - The current SDMX content-oriented guidelines (COG) (SDMX Initiative, 2009) treat only some of these components separately.
- Aim of the paper:
  - Thoroughly analyse the diversity of “unit of measure” in practice, including potential decomposition and interdependencies of the respective meta-information beyond the current SDMX recommendations.
  - Identify possible value domains for the identified components.
- Structure of the paper:
  - Section 2 investigates international organizations' current practice of representing unit of measure.
  - Section 3 introduces existing standards and guidelines for unit of measure, in particular the relevant parts of the SDMX COG (Annex 1 & 2).
  - Section 4 discusses different modeling requirements for different stages in the life cycle of statistical products, develops an approach to modeling unit of measure and related concepts for data and metadata exchange that extends the suggestions of the current SDMX COG, and proposes usage of available standards where appropriate.
  - Section 5 provides a short wrap-up and an outlook on potential future developments.
- Note:
  - As the SDMX COG are continuously evolving, the paper’s approach can be regarded as a suggestion for further development of the guidelines.

### II. CURRENT PRACTICE
- Method:
  - Illustrate current practice of modeling the concept of unit of measure and related concepts using examples from dissemination databases of various international organizations and IMF internal databases.
  - Use these examples as a basis for recommendations on further developments of the SDMX Content Oriented Guidelines and on representation of unit of measure in different stages of the life cycle of statistical data products.
- Databases used as examples (numbered list preserved exactly):
  1. Principal Global Indicators (PGI) Website of the Inter-Agency Group on Economic and Financial Data (IAG)
  2. World Economic Outlook (WEO) of the International Monetary Fund (IMF)
  3. OECD.Stat Data Warehouse of the Organization for Economic Cooperation and Development (OECD), three datasets
  4. Statistics Website of the Bank for International Settlements (BIS)
  5. Statistical Data Warehouse of the European Central Bank (ECB)
  6. Eurostat's Selected Principal European Economic Indicators (PEEI)
  7. Eurostat's EUROIND Database
  8. World Development Indicators (WDI) Online Database (World Bank)
  9. Millennium Development Goals Indicators Database (UNStats)

### Tables and Appendices referenced
- Appendices:
  - Appendix 1. Examples by Data Structure (page indicator present)
  - Appendix 2. Examples by Unit Type
- Tables listed (table numbers and titles preserved):
  - Table 1. Unit Type Ration: Case Distinction
  - Table 2. Unit Types, Units, and Constraints
  - Table 3. Examples for Indicator including Unit of Measure
  - Table 4. Examples for separate Indicator and Unit
  - Table 5. Examples for separate Indicator, Unit, and Unit Multiplier
  - Table 6. Examples for separate Indicator, Unit, and Type of Measure
  - Table 7. Examples for Indicator, Unit, and Adjustments
  - Table 8. Examples for separate Indicator, Type of Measure, and Unit (as free text)
  - Table 9. Examples for Count Type Units
  - Table 10. Examples for Currency Type Units
  - Table 11. Examples for Index Type Units
  - Table 12. Examples for Units of Derived Unit Type

*Source: _wp11152 - Appendix 1. Examples by Data Structure; _wp11152 - Appendix 1. Examples by Data Structure ............................................................................... 1 (PDF chapter/section).*

### 10. IMF Internal Databases, three datasets

### 10. IMF Internal Databases, three datasets

### Representation of unit of measure across surveyed databases
- Of the 14 datasets surveyed:
  - Four do not separate the economic indicator from the unit of measure or provide the unit information as reference metadata.
  - Four split concepts such as unit multiplier or adjustment method from the unit.
  - Six separate unit of measure from economic indicator.
- Heterogeneity observed:
  - Unit descriptors for the same conceptual unit vary (examples: “Percent Change over Previous 5 Period”, “Growth previous period”, “Percentage Change”; or “%”, “Percent”, “Percentage Rate”).
  - Some databases embed frequency in the unit (example: “% (Q/Q-1)” meaning “Percent Change over Previous Period” for quarters).
  - Some databases use very generic unit types (e.g., “Percent”, “Level, ratio, or USD Millions”, “Index”), while others pack detailed metadata into the unit (examples: “Per head, at current prices and current PPPs, in US dollars”; “In percentage of Net National Income”).
  - Base specification practices vary: “Index” appears without specification, with base period, with base period and adjustment method, and sometimes with a “base method” (e.g. moving average).

### Examples of decomposition practices (Tables referenced)
- Table 3: mixed dimensions combining measured indicator, type of unit, unit of measure, adjustment method, and frequency; some items fail to provide unit information completely (examples: “Personal computers”; “Youth unemployment rate, aged 15-24, men”).
- Table 4: lists 20 examples with unit presented as a separate dimension, illustrating heterogeneous unit descriptors and inclusion of frequency in unit values.
- Table 5: examples with separate unit and unit multiplier; unit multiplier appears under different names (magnitude, power code, power of ten, (unit) multiplier, scale) and values specified as multiples of 10 (e.g. 0.1), exponents (e.g. -1), or text (tenth); some databases leave multiplier missing instead of 0 (for 10^0), 1, or “units”.
- Tables 6, 7, and 8: examples separating further concepts from indicator and unit, viz. type of measure and types of adjustment.
  - Table 6: mixed unit and multiplier but separate type of measure distinguishing “change” and “level”; adjustment information included in type of measure.
  - Table 7: unit and multiplier combined; seasonal and price adjustment presented separately (both combinations observable).
  - Table 8: unit of measure represented in a free text field containing referential metadata items (type of unit (index), base value, base period, underlying currency, index unit); type of measure presented separately.

### Assessment of existing standards and adoption
- Observations:
  - Existing standards/guidelines are only partially met in practice and incompletely cover or specify required concepts.
  - Two physical-unit standards (SI and UCUM) do not cover all social/economic units, but their structure (i) base units, (ii) derived units, (iii) dimensionless units is generalizable and worth adopting.
- Compliance with SDMX COG among the 14 databases:
  - None of the 14 investigated databases entirely follow SDMX COG recommendations for separating unit and measurement information from the economic indicator and decomposing into unit, unit multiplier, base period, and adjustment.
  - Distribution among the 14:
    - Four: do not split economic indicator and unit of measure or only use reference metadata.
    - Six: separate unit from indicator but heterogeneous regarding base period, adjustment, and unit multiplier placement.
    - Remaining four: split one or more additional concepts from indicator and unit but differ on which concepts are separate (one database has separate unit multiplier; two use a “type of measure” containing adjustment or aggregation methodology; one splits two types of adjustment but lacks unit multiplier and base period separately).
- Practical reasons for mixed vs. separated modeling:
  - Mixed dimensions can prevent invalid value combinations (helpful in data collection) and be more comprehensible for executive users.
  - Finer modeling granularity (splitting components) benefits analytic users and is preferable for inter-organizational data and metadata exchange.

### SDMX Content-Oriented Guidelines (COG) specifics
- SDMX sponsorship: BIS, ECB, EUROSTAT, IMF, OECD, UN, World Bank.
- SDMX COG cross-domain concepts related to unit of measure: unit of measure (item 65), adjustment (3), base period (5), unit multiplier (64).
  - Representation: unit of measure, adjustment, and base period divided into code and free text; no code lists provided except unit multiplier which has a code list.
  - Unit of measure defined by three components: (i) type (currency example), (ii) unit code, (iii) unit of measure detail. “Type” not further explained in COG.
  - Unit defined as “a quantity or increment by which something is counted or described”; examples include kg, Euro, counts, index numbers.
  - Unit multiplier: specifies exponent to basis 10 by which observation values were divided (e.g., multiplier 3 indicates thousands); code list lacks negative multipliers.
  - Unit of measure detail: free text for additional information; no linkage to adjustment or base period.
  - Base period: relevant for interpreting index data, real terms, change measures; may require base value specification; COG includes base period but not a separate base value concept; time stamp required for base period.
  - Adjustment: defined separately (changes in definitions, exchange rates, prices, seasons, other factors); split into code (type) and free text; no comprehensive code list, only examples (trading day, seasonal, trend-cycle).

### SI and UCUM relevance
- SI (International System of Units):
  - Foundation: seven base quantities and base units (meter, kilogram, second, ampere, Kelvin, mole, candela).
  - 22 SI derived units; includes supplemental units for civil time.
  - Prefixes for scaling from yotta- (10^24) to yocto- (10^-24).
- UCUM (Unified Code for Units of Measure):
  - Intended to include all units used in international science, engineering, business; based on ISO/ANSI but resolves name conflicts and has broader coverage.
  - Distinguishes seven base units (partly differing from SI), derived units, units from other standards, customary/imperial units, and defines “dimensionless” units used for counts or ratios often provided in percent.

### Proposal: decomposition and generic unit types
- Rationale: SDMX COG not sufficiently specific/restrictive for decomposition of unit of measure and guidance on value domains (code lists).
- Generic unit types proposed (classification reflecting measurement vs. calculation):
  - Base types:
    - Count: unit specifies what is counted (examples: persons, personal computers, mobile internet subscriptions, jobs); requires unit multiplier and time series adjustment method.
    - Currency: unit specifies currency or currency group (examples: Euro, SDR, domestic currency); requires unit multiplier, time series adjustment, method of price adjustment (constant prices, current prices, chain-linked), method of exchange rate adjustment (e.g. constant); “constant” and index-based adjustments require base period specification.
    - Base SI/UCUM quantities subset (e.g. length, mass, time) for physical measures.
  - Derived unit types:
    - Defined by derivation method applied to base or derived unit types (difference, sum, ratio, product).
    - Categories: ratio, product, difference, sum; SI/UCUM derived quantities (area, volume, velocity) are subtypes.
    - Derived indicators can reference underlying indicators/units to calculate unit type, unit, and multiplier (e.g., USD/hour, Euro/USD, national currency/person).
    - Ratios of same units yield a dimensionless “fraction” (USD/USD = 1, person/person = 1).
    - Derived unit subtypes suggested (examples): area, volume (product); absolute change over reference period (difference); currency exchange rate, relative change over reference period, index, velocity (ratio).
    - Base period: absolute (date part, e.g., year or quarter) or relative (previous period, same period previous year, last day previous month); base value may need specification.
- Implementation notes:
  - Recursive approach: derive units and multipliers from underlying units; enables flexibility without enumerating all combinations.
  - Recommendation to pre-specify broad families of derived units and attach familiar descriptors for ease of use and comparability.
  - Restrictions on units, multipliers, or related concepts may be necessary for specific subtypes.

### Unit Type ratio: detailed case distinctions and implications
- Ratio as unit type may vary depending on comparisons of unit type, unit, and unit multiplier of numerator and denominator.
- Key outcomes:
  - If numerator and denominator share type, unit, and multiplier: result = fraction, multiplier = 1 (examples: Rate/Share of total; Military spending as % of GDP; Ratio of subgroups).
  - If units or multipliers differ, result unit labeled UN/UD and multipliers calculated as MN/MD, unless rescaled (e.g., to percent).
  - Percent often behaves like a unit multiplier rather than a unit; for fractions the unit multiplier is especially important and the underlying base unit should be provided.
  - Special cases:
    - “Interest rate in % per annum”: underlying numerator unit type ratio (fraction) and denominator time; typical descriptor “Percent per annum”.
    - Difference of ratios expressed in percentage points: if both ratios provided as fraction with multiplier 0.01 (=%), the difference is measured in “percentage points” — may be assigned a joint descriptor combining unit type (=difference), unit (=fraction), multiplier (=0.01).
    - Ratio of subgroups used for parity indices may have a “base value” indicating balanced situation (usually 1 or 100) that should be provided.
- Table 1 (Unit Type Ratio: Case Distinction) summarizes eight distinct cases by comparison of numerator and denominator type, unit, multiplier and shows example subtypes and examples (referenced in source).

### Recommended decomposition of unit of measure and related concepts
- Observations and recommendations derived from examples:
  - Decompose unit of measure into components such as unit type, unit, unit multiplier, base period, base value, types of adjustment (seasonal, price, exchange rate), and type of measure (e.g., change vs level).
  - Treat unit multiplier as a distinct concept with a well-specified code list (including negative multipliers where relevant).
  - Represent base period (time stamp) and base value explicitly rather than implicitly assuming base value = 100.
  - Represent adjustment types (time series adjustment, price adjustment, exchange rate adjustment) separately with both code and free-text detail.
  - For indices and chain-linked series, include base period, base value, and adjustment methods; aggregation method (e.g. end of period, moving average) and methodological metadata (e.g. Laspeyres, weighting) may be required.
  - Provide value domains (code lists) for decomposed components to improve interoperability and machine-readability while allowing free-text detail where necessary.

*Source: _wp11152 - 10. IMF Internal Databases, three datasets*

### 1.      Unit Type as discussed above

### _wp11152 - 1.      Unit Type as discussed above

### Unit components and mandatory rules
- 1. Unit Type as discussed above
- 2. Unit depending on Unit Type (see table below)
- 3. Unit Multiplier with some restrictions based on Unit Type and Unit, for example Units with Unit Type=Index usually have Multiplier=1
- 4. Base Period with value domain including time stamps (in different granularity) extended by predefined values such as previous period, corresponding period of previous year, previous three months, December of previous year, years since time stamp, moving average of years since time stamp (moving average and similar methods that define how the value is calculated in the base period could even be put into a separate concept (or sub-concept).
  - Mandatory for: Unit Type=Index, Absolute or Relative Change over Base Period; Price Adjustment=Constant Prices, Reference Chained, Chain-Linked
- 5. Base Value with default value 100
  - Mandatory for: Unit Type=Index or Balance Indicator
- 6. Adjustment split into (at least) three components:
  - a. Price Adjustment such as Constant, Current, Reference Chained, Chain-Linked
    - Mandatory for: Unit Type=Currency, Derived and Base Unit=Currency (recursion)
  - b. Econometric/Time Series Adjustment such as Seasonal, Working Day, Trading Day, Trend Cycle, Amplitude, Ratio to Trend MCD Smoothed
  - c. Exchange Rate Adjustment such as Constant, Current
    - Mandatory for: Unit Type=Currency, Derived and Base Unit=Currency (recursion)
- 7. Base Unit refers to the underlying Unit of the components of derived Units, especially of a Difference (minuend and subtrahend) or of a Fraction (numerator and denominator)
  - Mandatory for: Unit Type=Difference; Unit=Fraction
- 8. Base Indicator refers to the components of a derived Indicator that may be the reason for the usage of a derived Unit; role of the Indicator must be specified (e.g. numerator)
  - Mandatory for: Unit Type=Ratio (with a few exceptions, such as SI/UCUM Unit Types)

### Table 2: Unit Types, Units, and constraints (selected entries and constraints)
- Base
  - Count
    - Person -
    - Mobile Phone -
    - ... ...
  - Currency
    - List according to ISO 4217 (2010) Requires Price Adjustment
    - Different currency groups Requires Price Adjustment
    - National Currency Requires Price Adjustment
  - Length
    - List according to SI/UCUM -
  - Other relevant SI/UCUM base quantities
    - Lists according to SI/UCUM -
- Derived
  - Difference
    - = Base Unit Constraints on admissible Units may apply
  - Absolute Change over Reference Period
    - = Base Unit Requires Price Adjustment if Type of Base Unit = Currency
  - Balance Indicator Diff.
    - = Base Unit requires Base Value
  - Product
    - = Product of Base Units Constraints on admissible Units may apply
  - Area
    - List according to SI/UCUM -
  - Volume
    - List according to SI/UCUM -
  - Ratio
    - = Ratio of Base Units if Ratio=1 then Unit=Fraction Constraints on admissible Units may apply
  - Velocity
    - List according to SI/UCUM -
  - Numerator=Denominator
    - Fraction Base Unit and Type of Base Unit the same for denominator and numerator
  - Balance Indicator Ratio
    - Fraction Base Unit=Fraction, requires Base Value
  - Index
    - Fraction Requires Base Period, Base Value Unit Multiplier = 1
  - Currency Exchange Rate
    - = Ratio of Base Units Type of Base Units = Currency, C_N ≠ C_D
  - Interest Rate
    - = Fraction / Year -
  - Relative Change over Reference Period
    - = Fraction (=Difference/Type of Base Unit of Difference) Type of Base Units must match
  - Sum
    - = Base Unit Constraints on admissible Units may apply

### Unit families, standard units, and conversion factors
- Unit families: metric, US, and British systems (examples given).
- Within a family, one unit is designated as standard unit, and conversion factors relate each member to that standard unit.
- Conversion factors between standard units of different unit families of one unit type are specified.
- For currencies, time-dependency of exchange rates increases complexity.
- The paper notes these concepts are important but are not discussed in more detail due to focus and space constraints.

### Conclusion: findings and recommended extensions
- Findings:
  - The SDMX COG provide a reasonable basis for harmonization and standardization of the unit of measure cross-domain concept.
  - Two challenges identified: (i) a lack of compliance in practice and (ii) room for improvement in definition of concepts (including code lists) and decomposition of concepts.
  - Degree of compliance with the SDMX COG varies between the 14 examined databases, but none provides the four concepts recommended in the SDMX COG (unit, unit multiplier, base period, and adjustment) separately.
  - Disagreement exists even between databases that display a particular concept separately.
- Recommendations / Conclusions drawn by the paper:
  - A more precise definition of the concepts and the inclusion of code lists in the SDMX COG are necessary to achieve harmonized representation.
  - Motivated by empirical findings, the paper decomposes the concept “unit of measure” into basic building blocks and derives an extendable set of generic unit types and subtypes, assigned units, and a set of cross-domain concepts related to unit of measure.
  - The conceptual disaggregation provides a sound basis for an extension and further development of the SDMX COG with respect to cross-domain concepts and code lists in the context of unit of measure.
  - Ongoing and future work requires extension to define in greater detail the representation of derived indicators, unit types, units, and unit families as well as the required constraints.
  - One overall objective is development of a unit (type) calculus to better account for and make use of the calculability characteristic of units based on ideas developed by Froeschl (1997).

### Appendix: examples by structure and unit type (selected examples)
- Examples for Indicator including Unit of Measure (Table 3):
  - Share Prices, Monthly, Index (base 2005 = 100)
  - Industrial Production Index, Monthly, (base 2005 = 100), seasonally adjusted
  - Currency exchange rates, Monthly, National units per US-Dollar
  - Personal computers
  - Youth unemployment rate, aged 15-24, men
  - Adolescent fertility rate (births per 1,000 women ages 15-19)
  - Electric power consumption (kWh per capita)
  - Long-term interest rates, Monthly, Per cent per annum
  - Primary completion rate, total (% of relevant age group)
  - Ratio of youth unemployment rate to adult unemployment rate, men
  - Military expenditure (% of GDP)
  - GDP growth (annual %)
- Examples for separate Indicator and Unit (Table 4, excerpts):
  - Population — Number of Persons, Millions
  - GDP Nominal — National Currency, Seas. Adjusted, Millions
  - Oil Price — US Dollars per Barrel
  - Economic Sentiment Indicator — Index
  - GDP Volume — Index, 2005=100, Seasonally Adjusted
  - GDP Volume Percent Change over Previous Period
- Examples for separate Indicator, Unit, and Unit Multiplier (Table 5, excerpts):
  - Gross domestic product per capita, constant prices — National currency Units
  - Current account balance — U.S. dollars Billions
  - Employment — Persons Millions
- Examples for Indicator, Unit, and Adjustments (Table 7, excerpts):
  - Taxes less subsidies on production and imports — Millions of euro (from 1.1.1999) / ECU (up to 31.12.1998) — Not seasonally adjusted data — Chain-linked volumes, reference year 2000 (at 2000 exchange rates)
  - GDP at market prices — Millions of euro / ECU — Seasonally adjusted & adjusted by working days — Current prices
- Examples by Unit Type (Appendix 2, excerpts):
  - Count Type Units (Table 9): Internet users; Employment, seasonally adjusted — Persons Millions
  - Currency Type Units (Table 10): Reserve Assets, Monthly, SDR millions; Current account balance U.S. dollars Billions; Taxes less subsidies on production and imports — Millions of euro (from 1.1.1999) / ECU (up to 31.12.1998)
  - Index Type Units (Table 11): Industrial Production Index, Monthly, (base 2005 = 100), s.a.; Net barter terms of trade (2000 = 100); GDP Volume Index, 2005=100; Inflation, average consumer prices Index, 2000=100
  - Units of Derived Unit Type (Table 12): examples include Difference (Billions of US dollars), Ratio (Unemployment rate % of total labor force), Index (Index Units with base periods), Relative Change over Reference Period (GDP Volume Percent Change over Previous Period)

*Source: _wp11152 - 1.      Unit Type as discussed above (IMF PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11152.pdf_