## _wp16133

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---

### Overview
- Purpose: Investigates whether chain-linked volume measures of GDP yield superior results than a fixed-base year method in three Sub-Saharan African (SSA) countries.
- Novelty: First such study for SSA countries using detailed source data and compilation worksheets provided by three SSA countries (anonymized).
- Coordination: IMF’s statistics advisors in African Regional Technical Assistance Centers coordinated data collection.

### Theoretical background and approaches
- Two alternative methods per the System of National Accounts:
  - Fixed-base year method: Volume changes aggregated using the price structures and weights of the base year (Laspeyres fixed-base).
  - Annual chain linking: Update base year annually and link year-on-year changes; when expressed as an index with reference year t=100, called a chained volume index with reference year “t.”
- 2008 SNA ideal practice:
  - Work at a very detailed level, preferably using the supply and use tables (SUT) framework.
  - Deflate each component by a strictly appropriate price index.
  - Example: diversified advanced economy would use about 50 different price indices to produce a volume measure.
- 2008 SNA cautions and recommendation:
  - Chaining can be worse when individual prices and quantities fluctuate and earlier relative changes are reversed later (2008 SNA para 15.43).
  - “On balance, situations favorable to the use of chain Laspeyres over time seem more likely than those that are unfavorable... it is generally recommended that annual indices be chained” (2008 SNA para 15.44).
- Practical considerations:
  - Chain-linked indices are computationally difficult, demand additional resources and tailored software.
  - Chain-linked growth estimates are non-additive and require explanation to users.

### Empirical focus, simulations, and data requirements
- Scope:
  - Comparison between fixed-base and chain-linked approaches using recent fixed bases, compatible with a revised base at five-year intervals.
  - Simulations included complete recalculation using most detailed components.
- Data quality and granularity required:
  - Volume estimates of GDP by production should be obtained from volume estimates of economic activities with at least 2-digit ISIC.
  - High quality price indices at detailed levels of expenditures and/or outputs are necessary; without them no overall measure of economic growth will be of high quality.
- Emphasis: Level of classification and deflation technique materially affect measured growth irrespective of chaining.

### Experience of advanced countries (summary)
- Empirical patterns:
  - Chain linking tends to produce superior results when economies have structural changes and systematic relative price/quantity trends (e.g., technology).
  - Examples of differences for last year of study periods (Table 1, Chain Linking minus Fixed Base):
    - Australia: Difference 0.2 (1996/97) — Fixed Base Year 1989/90; Study Period 1989/90-1996/97
    - Netherlands: Difference -0.5 (1993) — Fixed Base Year 1986; Study Period 1986-93
    - United Kingdom: Difference -0.5 (1999) — Fixed Base Year 1994; Study Period 1994-99
    - United States: Difference -1.0 (1995) — Fixed Base Year 1987; Study Period 1987-95
- Implementation detail levels in advanced countries:
  - Canada: expenditure GDP based on 435 series (130 household final expenditure, 24 government final consumption, 69 exports, 68 imports).
  - Netherlands SUT: 250 industries, 850 commodities, 10 final demand categories; value at current prices, value in prices of previous year, volume index and deflator available for every SUT cell.
  - EU requirement: implement volume measures at least as detailed as P60 level (approximate two-digit industry level) for output and intermediate and final use.
  - UK study: chain linking at four-digit ISIC with ~300 input series produced lower growth estimates (lower by 0.5 percentage points) for 1999 compared with a two-digit implementation.

### GDP volume measures in Sub‑Saharan African (SSA) countries
- Adoption and structure:
  - About a third of SSA countries apply an annual chain-linked approach starting in the early 2000s.
  - Most Francophone countries and some others implemented chain linking as part of national accounts harmonization.
  - Out of eight oil-exporting SSA countries, Cameroon and Gabon use chain linking.
- Commodity dependence:
  - For about one-third of SSA countries, more than 40 percent of GDP comes from agriculture and mining; for more than two-thirds, more than one quarter of GDP is contributed by agriculture and mining.
- Shares of agriculture and mining in GDP for selected SSA countries (2013) — share (percent):
  - Equatorial Guinea 89
  - Congo 68
  - Liberia 67
  - Sierra Leone 65
  - Angola 65
  - Central African Republic 53
  - Niger 47
  - Guinea-Bissau 47
  - Gabon 46
  - Ethiopia 46
  - Togo 45
  - Mali 42
  - Chad 42
  - Burkina Faso 40
  - Nigeria 36
  - Ghana 27
  - Mauritius 3
  - Seychelles 2
- Price index coverage and vintage (As of April 2016):
  - Most SSA countries compile CPI monthly; only eight compile PPI.
  - Only five countries update CPI weights in five years or less.
  - CPI and PPI weights vintage and coverage vary widely; many CPI weights vintage listed as “Older than 5” or “3–5”; coverage types include “Capital city”, “Main cities”, “Nation-wide”, “Urban areas”.
  - Use of outdated or incomplete CPI/PPI data can bias GDP volume measures irrespective of fixed-base or chain-linked approach.

### IV. Data analysis of chain linking in three SSA countries (Country A, B, C)
- Study design:
  - Country A: mainly commodity producer; primary sector about half of GDP for most years; sample period 2006–13 (eight years).
  - Country B: relatively higher proportion of services; compiled at very detailed level using double indicator method in SUT framework; sample period 2005–10 (six years).
  - Country C: services-dominant; manufacturing a major contributor compiled by extrapolation at two-digit level; sample period 2007–13 (seven years).
  - Two countries apply chain linking; third uses fixed-base.
  - Analysis uses production GDP and components; expenditure GDP not analyzed due to weak expenditure data in SSA.
- Country A findings:
  - Primary sector accounts for about half of GDP; agricultural volatility due to climatic shocks.
  - Chain-linked approach shows significantly higher volume growth than fixed-base for agriculture; difference most pronounced (about 1 percentage point) for year farthest from fixed base year.
  - For manufacturing and total services, fixed-base reduces growth by 0.5 and 0.1 percentage points respectively for the year 2013.
  - Overall GDP: chain linking reduces growth in 2012 and 2013 by about 0.7 and 0.2 percentage points respectively, mostly driven by surge in primary production.
  - Differences in GDP growth rates are more volatile for Country A; same volume index for 2013 from both approaches when taking 2007=100.
  - Cumulative growth for 2006–13 almost the same from both approaches.
  - Compilation practices:
    - Agriculture: detailed product-level estimation using single deflation.
    - Manufacturing: compiled at two-digit ISIC through extrapolation (single indicator).
    - About 75 percent of services volume measures based on single indicator methods (extrapolation or deflation) at higher ISIC levels.
    - CPI coverage only for capital city and uses outdated weights.
  - Implication: single indicator methods produce same growth rates from fixed-base and chain-linked approaches at application level, reducing aggregate differences; improper deflators and higher classification levels can introduce bias in both approaches.
- Country B findings:
  - High proportion of services.
  - Differences in annual GDP growth rates are very small for all years; for year farthest from fixed base there is no difference.
  - Chain linking reduced growth for total services in last year, but other activities offset this effect.
  - Cumulative growth for 2005–10: chain linking produces only slightly smaller cumulative growth.
  - Compilation practices:
    - Very detailed level using double indicator method in SUT framework (double deflation where possible; single extrapolation where detailed current-price intermediate consumption not known).
    - For formal sector and government, intermediate consumption known at current prices and double deflation used; informal sector and some NPISH use single extrapolation.
  - Interpretation: nil difference for the farthest year and insignificant cumulative difference suggest differences reflect underlying economic reality rather than methodological artifact.
- Country C findings:
  - Services-dominant; differences in GDP growth rates small and mostly positive; highest difference 0.2 percentage points in 2010 and 2012; farthest year difference 0.1.
  - Except transportation and storage, activities showed positive or no difference for 2013.
  - Higher cumulative growth from chain linking for 2006–13.
  - Manufacturing compiled by extrapolation at two-digit level: no differences at two-digit level but significant differences at aggregate level, suggesting volatility in sub-sectors.
  - Services: single indicator methods at higher classification levels yield almost no differences for many services; lower growth for transportation and storage from chain linking offset by other services.
  - Overall: differences for services may reflect statistical method more than economic structure.
- Aggregate results across three countries:
  - Insignificant difference in growth rates for the farthest year.
  - Volatile differences in growth rates across years.
  - Negligible or zero differences in cumulative growth for the study periods.
  - Results contrast with advanced economies where chain linking often produced substantial differences.
  - Deflation techniques and classification levels appear to affect growth rates and the observed impact of chain linking; further assessment needed.

### V. Simulation analysis of deflation techniques and classification detail
- 2008 SNA reiterated recommendation: obtain GDP volume estimates at very detailed level preferably using the SUT framework and deflate each component by a strictly appropriate price index.
- Two simulations using project data:
  1. Replace double deflation with single deflation (Country B data).
  2. Use overly-aggregated classification levels instead of detailed classification levels (Country C data).
- Impact of deflation technique (Country B simulation):
  - Recomputing volume measures using single deflation instead of double deflation yielded significant differences in growth rates.
  - Observed pattern (Figure 4 referenced):
    - Single deflation reduces growth rate for three years, increases it for two years.
    - Magnitude: differences are large (around 0.5 percent in four of five years and by 1.5 percent for one year).
  - Interaction with chain linking:
    - Difference between chain-linked and fixed-base approaches did not change significantly when comparing single versus double deflation (red bars vs yellow bars in referenced Figure 4).
    - Empirical implication: chain linking has limited ability to correct bias introduced by using single instead of double deflation.
- Impact of overly aggregated classifications (Country C simulation):
  - Method: compare manufacturing value added compiled at detailed sub-activity (DCL) versus higher classification level (HCL).
  - Key results:
    - For 2013: difference is 2.8 percentage points using fixed-base approach and 1.9 percentage points using chain-linked approach.
    - For 2010: use of higher classification level reduces manufacturing growth rates by 2.8 percentage points from chain-linked and 2 percentage points for fixed-base approach.
  - Interaction with chain linking:
    - Fixed-base approach provides higher growth rates in two years (2012 and 2013).
    - Chain linking provides higher growth rates in two years (2010 and 2011).
    - Overall: no consistent pattern across years; chain linking does not correct aggregation-induced distortions.
- Overall implications from simulations:
  - Use of improper deflation techniques and overly-aggregated classifications can lead to significant distortions in growth rates and provide wrong conclusions regarding which approach (fixed-base or chain-linked) is appropriate.
  - Improvements in deflation methods and implementation at detailed classification levels are likely to yield more reliable volume measures irrespective of chaining.

### Interaction between deflation technique, classification detail, and chain linking
- Empirical finding: Failure of single deflation to account for changes in relative prices of inputs and output is a material practical issue; replacing single deflation with double deflation is a high priority.
- Chain linking interaction:
  - Chain linking has limited influence in correcting bias introduced by improper deflation techniques and overly-aggregated classifications.
  - Where single indicator/extrapolation methods predominate at the application level, fixed-base and chain-linked approaches often produce similar results.

### Policy recommendations and priority actions
- Priority sequencing for SSA countries with limited resources:
  - Implement a good system of double deflation at a very detailed classification level (at least two-digit level of ISIC) before prioritizing chain linking.
  - Improve price and volume indices, and develop new indices such as the PPI that are more appropriate for output GDP activities.
  - Ensure suitable price and volume indices are available for all activities (at least at two-digit level of ISIC) and that resources exist for their regular update before assessing chain linking suitability.
- Guidance for national accounts compilers and managers:
  - Implementation of chain linking should be driven by the economic structure of a particular country and the availability and timeliness of required underlying detailed data.
  - Countries not applying chain-linked volume measures should not be judged as lagging in implementing an important recommendation of the 2008 SNA.
  - Further research and assessments are suggested for developing countries in other regions to assess generalizability of these results.

### Conclusions
- Main conclusion: Chain linking provides no substantial gains vis-à-vis the fixed-base approach in terms of providing accurate growth rates for the three SSA countries examined.
- Effective improvements:
  - Fixed-base approach at a detailed level (at least two-digit ISIC) using appropriate deflation techniques and regular base year revisions yield more significant improvements in volume measures of GDP for SSA countries.
- Emphasis: Quality of price and volume indices and the classification level of implementation should be given priority in countries with limited resources as they lead to major improvements in growth estimates irrespective of aggregation approach.

*Source: _wp16133 (IMF staff analysis and appendix data contained in the original PDF).*

### References .............................................................................................................

### _wp16133 - References

### Overview
- Purpose: Investigates whether chain-linked volume measures of GDP yield superior results than a fixed-base year method in three Sub-Saharan African (SSA) countries.
- Novelty: First such study for SSA countries using detailed source data and compilation worksheets provided by three SSA countries (anonymized).
- Coordination: IMF’s statistics advisors in African Regional Technical Assistance Centers coordinated data collection.

### Theoretical background and approaches
- Two alternative methods for separating volume and price changes per the System of National Accounts:
  - Fixed-base year method: Volume changes in subsequent periods are aggregated using the price structures and weights of the base year.
  - Annual chain linking (introduced in the 1993 edition of the SNA): Requires updating the base year annually and linking year-on-year changes; when expressed as an index with reference year t=100, the index is called a chained volume index with reference year “t.”
- Ideal practice per 2008 SNA:
  - Work at a very detailed level, preferably using the supply and use tables (SUT) framework.
  - Deflate each component by a strictly appropriate price index.
  - Example complexity: A typically diversified advanced economy would use 50 different price indices to produce a volume measure.
- Volume changes definition: Changes in quantity and quality of products over time.

### Empirical focus, simulations, and data
- Scope of empirical work:
  - Comparison between fixed-base and chain-linked approaches carried out with recent fixed bases, compatible with a revised base at five-year intervals.
  - Simulations involved a complete recalculation of the data using the most detailed components.
  - Simulations assessed the impact of deflation techniques and level of classification on volume growth from fixed-base and chain-linked approaches.
- Required data quality and granularity:
  - Volume estimates of GDP by production should be obtained from volume estimates of economic activities with at least 2-digit level of International Standard Industrial Classification (ISIC).
  - High quality price indices at detailed levels of expenditures and/or outputs are necessary; without them no overall measure of economic growth will be of high quality.

### Findings on suitability of chain linking versus fixed-base
- General consensus from advanced economies:
  - Chain linking produces superior results when economies have significant structural changes and movements of relative prices with a relatively consistent trend (e.g., new technologies play an important role).
- Limitations of chain linking (as recognized by the SNA):
  - If prices and quantities of underlying products fluctuate and relative price and quantity changes of earlier periods are reversed in later periods, chain linking can produce inferior estimates of growth compared to the fixed-base approach.
- Implication:
  - It is essential to assess whether the economic structure of a particular country over time is favorable for implementation of chain-linked volume measures.

### Study design and structure
- Country sample: Three SSA countries provided detailed compilation worksheets (countries anonymized; only results published).
- Sections in the paper (as structured in the source):
  - Section II: Theoretical background of chain-linked and fixed-base approaches and experiences of some advanced countries.
  - Section III: Prevailing practices of volume measures of SSA countries.
- Empirical outputs referenced (figures and tables listed in the source):
  - Figures include country-specific comparisons of differences in growth rates of GDP and components and comparisons of single vs double deflation.
  - Tables include differences in growth rates of selected advanced countries; shares of agriculture and mining in GDP for selected SSA countries (2013); and CPI and PPI weights vintage and coverage for Sub-Saharan African countries.
  - Appendix 1: GDP base / reference year, and weights vintage and coverage of CPI and PPI for SSA countries.

*Source: _wp16133 - References*

### Section IV provides a detailed comparison of growth using the fixed-base and chain-linked

### _wp16133 - Section IV provides a detailed comparison of growth using the fixed-base and chain-linked

### II. Experience of advanced countries
- Fixed-base (Laspeyres) approach: weights derived from a specific year (fixed-base year). Laspeyres fixed-base index allocates higher weights to products whose relative prices have decreased and volumes increased faster (example: electronic devices). Over time produces higher growth rates with upward bias as weights become outdated.
- Chain-linked approach: uses more up-to-date weights and eliminates the bias in growth rates for items with systematic relative price and quantity trends.
- 2008 SNA cautions: “if individual prices and quantities fluctuate so that the relative price and quantity changes occurring in earlier periods are reversed in later periods, chaining will produce worse results than a simple index” (2008 SNA para 15.43).
- 2008 SNA recommendation: “On balance, situations favorable to the use of chain Laspeyres over time seem more likely than those that are unfavorable... it is generally recommended that annual indices be chained” (2008 SNA para 15.44). Recommendation mainly tested using advanced-country data.
- Implementation considerations:
  - Chain-linked indices are computationally difficult and demand additional resources and tailored software (2008 SNA note).
  - Chain-linked growth estimates are non-additive; this non-additivity must be explained to users and requires resources.
- Historical adoption:
  - Netherlands: early 1980s.
  - Other advanced economies (Australia, Canada, Japan, New Zealand, United States): late 1990s or early 2000s.
  - Most European Union member states: around 2005 (driven by European Union Commission decision of November 1998 clarifying annex to Council Regulation (EC) No. 2223/96).
- Detail levels in advanced countries:
  - Canada: expenditure GDP based on 435 series (130 household final expenditure, 24 government final consumption, 69 exports, 68 imports).
  - Netherlands SUT: 250 industries, 850 commodities, 10 final demand categories. Value at current prices, value in prices of previous year, volume index and deflator available for every SUT cell.
  - EU requirement: volume measures implemented at least as detailed as P60 level (approximate two-digit industry level) for output and intermediate and final use.
  - UK: implemented chain linking at four-digit ISIC; study period 1995–99 showed four-digit implementation produced the lowest growth estimates (lower by 0.5 percentage points) for 1999 (farthest from fixed base). More than 300 input series at broadly four-digit level vs less than 60 series at broadly two-digit level.
- Empirical study findings for advanced countries:
  - United States: chain-linked GDP volume growth estimates consistently lower than fixed-base around mid-1990s; difference for 1995 (farthest from fixed base year 1987) around 1 percentage point; driven by computer equipment price changes (Steindel, 1995).
  - France: chain-linked GDP growth generally lower than fixed-base over 1980–1997, difference generally small, less than 0.2 percentage points; chain linking yields better results for all industries except agriculture where high fluctuation in quantities and prices makes chaining less desirable (Berthier, 2002).
  - Netherlands: chain linking provided significantly higher growth for agriculture for years farthest from fixed base (0.7 and 0.9 percentage points).
- Table 1: Differences in Growth Rates (Chain Linking minus Fixed Base) for last year of study period:
  - Australia: Fixed Base Year 1989/90; Study Period 1989/90-1996/97; Difference 0.2 (1996/97)
  - Netherlands: Fixed Base Year 1986; Study Period 1986-93; Difference -0.5 (1993)
  - United Kingdom: Fixed Base Year 1994; Study Period 1994-99; Difference -0.5 (1999)
  - United States: Fixed Base Year 1987; Study Period 1987-95; Difference -1.0 (1995)
- Exception: Australia (Australian Bureau of Statistics, 1998) showed chain-linked GDP growth higher than fixed-base for 1989–90 to 1996–97; cumulative growth for the period following fixed-base approach 0.4 percentage points lower than chain indices. Australian output has relatively larger commodity share; relevance for many SSA commodity producers.

### III. GDP volume measures in Sub‑Saharan African (SSA) countries
- Adoption:
  - About a third of SSA countries apply an annual chain-linked approach starting in the early 2000s.
  - Most Francophone countries and some others implemented chain-linked measures as part of national accounts harmonization.
  - Out of eight oil-exporting SSA countries, Cameroon and Gabon use chain linking.
- Structure and implications:
  - SSA countries are typically commodity producers (agriculture and mining), characteristics that tend to make chain linking less suitable.
  - For about one-third of SSA countries, more than 40 percent of GDP comes from agriculture and mining; for more than two-thirds, more than one quarter of GDP is contributed by agriculture and mining.
- Table 2: Share of agriculture and mining in GDP for selected SSA countries (2013) — share (percent):
  - Equatorial Guinea 89
  - Congo 68
  - Liberia 67
  - Sierra Leone 65
  - Angola 65
  - Central African Republic 53
  - Niger 47
  - Guinea-Bissau 47
  - Gabon 46
  - Ethiopia 46
  - Togo 45
  - Mali 42
  - Chad 42
  - Burkina Faso 40
  - Nigeria 36
  - Ghana 27
  - Mauritius 3
  - Seychelles 2
- Price and index data availability concerns:
  - Most SSA countries compile CPI monthly; only eight compile PPI.
  - In absence of PPI, reliance on CPI as deflator for non-consumer goods/services is a major weakness.
  - CPI quality issues: only five countries update CPI weights in five years or less.
- Table 3: CPI and PPI weights vintage and coverage (As of April 2016) — selected entries:
  - Benin: CPI weights vintage Older than 5; Coverage Main cities; PPI X (not compiled)
  - Burkina Faso: CPI Older than 5; Coverage Capital city
  - Cameroon: CPI Weights vintage 3–5; Coverage Nation-wide
  - Malawi: CPI Weights vintage 3–5; Coverage Nation-wide
  - Mauritius: CPI Weights vintage 3–5; Coverage Nation-wide; PPI Weights vintage Older than 5
  - Togo: CPI Weights vintage Older than 5; Coverage Capital city; PPI X
- Annex I (not reproduced here) provides base/reference year and weights vintage and CPI/PPI coverage for all SSA countries.
- Use of outdated or incomplete CPI/PPI data can bias GDP volume measures irrespective of fixed-base or chain-linked approach.

### IV. Data analysis of chain linking in three SSA countries (Country A, B, C)
- Study design:
  - Three SSA countries selected with different structures and income levels:
    - Country A: mainly commodity producer (primary sector about half of GDP for most years), highly volatile GDP growth driven by agricultural production volatility.
    - Country B: relatively higher proportion of services; compilation at very detailed level using double indicator method in SUT framework.
    - Country C: relatively services-dominant; manufacturing a major GDP contributor compiled by extrapolation at two-digit level.
  - Two countries apply chain linking; third uses fixed-base.
  - Time coverage and sample sizes:
    - Country A: eight years (2006–13)
    - Country B: six years (2005–10)
    - Country C: seven years (2007–13)
  - Analysis uses production GDP and components; expenditure GDP not analyzed due to weak expenditure data in SSA.
- Country A key findings:
  - Primary sector accounts for about half of GDP; agricultural volatility due to climatic shocks.
  - Chain-linked approach shows significantly higher volume growth than fixed-base for agriculture; difference most pronounced (about 1 percentage point) for year farthest from fixed base year.
  - For manufacturing and total services, fixed-base reduces growth by 0.5 and 0.1 percentage points respectively for the year 2013.
  - Overall GDP: chain linking reduces growth in 2012 and 2013 by about 0.7 and 0.2 percentage points respectively, mostly driven by surge in primary production.
  - Differences in GDP growth rates are more volatile for Country A; same volume index for 2013 from both approaches when taking 2007=100.
  - Cumulative growth for 2006–13 almost the same from both approaches.
  - Compilation practices:
    - Agriculture: detailed product-level estimation using single deflation.
    - Manufacturing: compiled at two-digit ISIC through extrapolation (single indicator).
    - About 75 percent of services volume measures based on single indicator methods (extrapolation or deflation) at higher ISIC levels.
    - CPI coverage only for capital city and uses outdated weights.
  - Implication: single indicator methods produce same growth rates from fixed-base and chain-linked approaches at application level, reducing aggregate differences; improper deflators and higher classification levels can introduce bias in both approaches.
- Country B key findings:
  - High proportion of services.
  - Differences in annual GDP growth rates are very small for all years; for year farthest from fixed base there is no difference.
  - Chain linking reduced growth for total services in last year, but other activities offset this effect.
  - Cumulative growth for 2005–10: chain linking produces only slightly smaller cumulative growth.
  - Compilation practices:
    - Very detailed level using double indicator method in SUT framework (double deflation where possible; single extrapolation where detailed current-price intermediate consumption not known).
    - For formal sector and government, intermediate consumption known at current prices and double deflation used; informal sector and some NPISH use single extrapolation.
  - Interpretation: nil difference for the farthest year and insignificant cumulative difference suggest differences reflect underlying economic reality rather than methodological artifact.
- Country C key findings:
  - Services-dominant; differences in GDP growth rates small and mostly positive; highest difference 0.2 percentage points in 2010 and 2012; farthest year difference 0.1.
  - Except transportation and storage, activities showed positive or no difference for 2013.
  - Higher cumulative growth from chain linking for 2006–13.
  - Manufacturing compiled by extrapolation at two-digit level: no differences at two-digit level but significant differences at aggregate level, suggesting volatility in sub-sectors.
  - Services: single indicator methods at higher classification levels yield almost no differences for many services; lower growth for transportation and storage from chain linking offset by other services.
  - Overall: differences for services may reflect statistical method more than economic structure.
- Aggregate results across three countries:
  - Insignificant difference in growth rates for the farthest year.
  - Volatile differences in growth rates across years.
  - Negligible or zero differences in cumulative growth for the study periods.
  - Results contrast with advanced economies where chain linking often produced substantial differences.
  - Deflation techniques and classification levels appear to affect growth rates and the observed impact of chain linking; further assessment needed.

### V. Simulation analysis of deflation techniques and classification detail
- 2008 SNA recommendation reiterated: obtain GDP volume estimates at very detailed level preferably using the SUT framework, deflating each component by a strictly appropriate price index (implies detailed classification and appropriate deflators improve accuracy irrespective of fixed-base or chain-linked approach).
- Two simulations conducted using the detailed project data:
  1. Replace double deflation with single deflation (Country B data).
  2. Use overly-aggregated classification levels instead of detailed classification levels (Country C data).
- Key conclusions from simulations:
  - Use of improper deflation techniques and overly-aggregated classifications can lead to significant distortions in growth rates and provide wrong conclusions regarding which approach (fixed-base or chain-linked) is appropriate for obtaining GDP volume measures.
  - Chain linking has limited influence in correcting the bias introduced by improper deflation techniques and overly-aggregated classifications.
- Impact of deflation technique (Country B simulation):
  - In existing system, large portion of Country B’s volume measures compiled through double deflation.
  - Recomputing volume measures using single deflation instead of double deflation yielded significant differences in growth rates.
  - Figure 4 (referenced): ‘yellow bars’ represent differences in GDP growth rates for Country B from single versus double deflation using fixed-base approach:
    - Positive yellow bars: growth rate from single deflation is higher.
    - Negative yellow bars: growth rate from single deflation is lower.
    - Observed: use of single deflation reduces growth rate for three years, increases it for two years.
    - Magnitude: differences are large (around 0.5 percent in four of five years and by 1.5 percent for one year).
- Overall implication:
  - The choice of deflation technique (single vs double) and level of aggregation of classification materially affects measured growth rates.
  - Improvements in deflation methods and implementation at detailed classification levels are likely to yield more reliable volume measures irrespective of whether fixed-base or chain-linked indices are used.

*Source: IMF staff analysis as provided in the content unit.*

### introduction to these techniques, please see the Eurostat’s Handbook on Price and Volume Measures in

### _wp16133 - introduction to these techniques, please see the Eurostat’s Handbook on Price and Volume Measures in National Accounts.

### Interaction Between Deflation Technique and Chain Linking
- Empirical finding: The difference in GDP growth rates between single deflation and double deflation is substantial for Country B, with single deflation producing a much higher growth rate for 2009.
- Chain linking interaction: The difference in growth rates between chain-linked and fixed-base approaches did not change significantly when comparing single versus double deflation. In Figure 4, ‘red bars’ present differences in GDP growth rates obtained from single and double deflation using the chain linking.
- Implication: Failure of single deflation to account for changes in relative prices of inputs and output is a material practical issue, suggesting replacement of single deflation is a relatively high priority for compilers.

### Impact of Overly Aggregated Classifications (Country C)
- Method: Volume estimates of manufacturing value added were compiled at sub-activity levels (divisions in the ISIC) and aggregated; sub-activity level value added extrapolated using the index of industrial production (IIP) sub-components. A simulation compared volume measures using a higher classification level (HCL) versus a detailed classification level (DCL).
- Key results (fixed-base and chain-linked comparisons):
  - For 2013: difference is 2.8 percentage points using fixed-base approach (yellow bar) and 1.9 percentage points using chain-linked approach (red bar).
  - For 2010: use of higher classification level reduces manufacturing growth rates by 2.8 percentage points from chain-linked and 2 percentage points for fixed-base approach.
- Empirical note: Extrapolation and single deflation of GVA create no differences in growth rates from the fixed base and chain-linked approaches. Difference in growth rates comes only at the level of aggregation.

### Interaction Between Classification Levels and Chain Linking
- Observation from Country C simulation:
  - Fixed-base approach provides higher growth rates in two years (2012 and 2013).
  - Chain linking provides higher growth rates in two years (2010 and 2011).
  - Overall: no consistent pattern across years.
- Implication: Overly aggregated classification has a significant impact on growth rates; chain linking does not appear to correct aggregation-induced distortions.

### Policy Recommendations and Priority Actions
- Priority sequencing for SSA countries with limited resources:
  - Implement a good system of double deflation at a very detailed classification level (at least two-digit level of ISIC) before prioritizing chain linking.
  - Improve price and volume indices, and develop new indices such as the PPI that are more appropriate for output GDP activities.
  - Ensure suitable price and volume indices are available for all activities (at least at two-digit level of ISIC) and that resources exist for their regular update before assessing chain linking suitability.
- Guidance for national accounts compilers and managers:
  - Implementation of chain linking should be driven by the economic structure of a particular country and the availability and timeliness of required underlying detailed data.
  - Countries not applying chain-linked volume measures should not be judged as lagging in implementing an important recommendation of the 2008 SNA.
  - Further research and assessments are suggested for developing countries in other regions to assess generalizability of these results.

### Conclusions
- Main conclusion: Chain linking provides no substantial gains vis-à-vis the fixed-base approach in terms of providing accurate growth rates for the three SSA countries examined.
- Effective improvements: Fixed-base approach at a detailed level (at least two-digit ISIC) using appropriate deflation techniques, and regular base year revisions, yield more significant improvements in volume measures of GDP for SSA countries.
- Emphasis: Quality of price and volume indices and the classification level of implementation should be given priority in countries with limited resources as they lead to major improvements in growth estimates irrespective of aggregation approach.

### Appendix highlights: GDP base/reference years and CPI/PPI coverage for SSA countries (As of April 2016)
- The appendix lists the base/reference year, weights vintage (years), and coverage for CPI and PPI for SSA countries as of April 2016.
- Notable patterns:
  - Many countries use Fixed Base (FB) or Chain Linking (CL) with base/reference years ranging widely (examples include FB 2002 for Angola; CL 2007 for Benin; FB 2011 for Ethiopia; FB 1984 for Madagascar; FB 2010 for South Africa).
  - Weights vintage commonly cited as “Older than 5” or “3–5”.
  - Coverage types include “Capital city”, “Main cities”, “Nation-wide”, and “Urban areas”.
  - The appendix marks PPI non-compilation with “X” for certain countries.
  - Footnote: * Base year applies to countries using fixed base approach and reference year for countries using chain linking. ** Liberia has no official GDP data.

*Source: Staff calculations and appendix data contained in the original PDF.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16133.pdf_