Formulas and Definitions of Different Growth Rates Commonly Used by Statistical Offices (NSOs)

 

1. Average annual growth rate (AAGR)       
2. Compound annual growth rate (CAGR)  
3. Period-on-previous-period (POP) change (or growth rate)            
4. Year-on-year (YoY) change (or growth rate)        
5. Annualised level/value data       
6. Annualised growth rate (Annualised rate of change)       
7. Linear approximation of the annualised growth rate       
8. Annualised semi-annual growth rate       
9. References  

Average annual growth rate (AAGR)

Definition

Average annual growth rate (AAGR) shows the average annual growth for n years. OR Average annual growth rate (AAGR) shows the average change between the current year and n years ago;  assuming linear growth, geometric growth or exponential growth.

Formula

GR 1st year  : annual growth rate for 1st year GR nth year : annual growth rate for nth year n :  number of years   P:  level/ value y:  current year y-1:  preceding year   OR   Assuming linear growth,   P:  level/ value y:  current year y-n:  n years ago n :  number of years   For details on geometric growth or exponential growth, refer to OECD Data and Metadata Reporting and Presentation Handbook 2007.

Alternate Names

Average rate of return or growth

Examples in Write-up

The population of Lane County grew 12 percent between 1980 and 1990 or at a rate of 1.2 percent annually.

 

 

Compound annual growth rate (CAGR)

Definition

Compound annual growth rate (CAGR) shows the growth rate required  for a level/value at the beginning period to reach its new level at the ending period.

Formula

P:  level/ value y:  beginning period y+n:  ending period n:  number of years   Note: n is usually years. Other frequencies should be converted to years.

Alternate Names

Average annual (compound) growth rates

Examples in Write-up

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Period-on-previous-period (POP) change (or growth rate)

Definition

Period-on-previous-period (POP) change (or growth rate) shows the growth between the current period and the preceding period.   POP is usually quarter-on-previous- quarter (QoQ) or month-on-previous- month (MoM).

Formula

OR   (for POP change)   P:  level/ value fth:  current period fth -1:  preceding period

Alternate Names

Period-to-period* growth rates/changes; Period-over-period* growth rates/changes; 1-period* rate of change; Rate of change on the previous period*;   *Can be substituted with month or quarter   For GDP, Japan's NSO terms “Changes from the previous term” for quarterly SA data:

Examples in Write-up

GDP is estimated to have fell by 2.2% in Quarter 2 2020.   The Australian economy contracted by 0.3% in seasonally adjusted chain volume terms in the March quarter 2020.

 

 

Year-on-year (YoY) change (or growth rate)

Definition

Year-on-year (YoY) change (or growth rate) shows the growth between the current period and the corresponding period of the previous year.    Year-on-year change (or growth rate) can be used for monthly, quarterly or annual data.

Formula

OR (for yoy change)   P:  level/ value t:  current period t-12:  preceding 12 months     Example for quarterly data: Q11:  value for 1st Qtr in 2018 Q1:  value for 1st Qtr in 2017   Example for annual data: A11:  value for 2018 A1:  value for 2017

Alternate Names

Year-over-year growth rates; Year-to-year growth rate; Rate of change from the previous year; 12-month rate of change; Through-the-year change; Annual growth rates/change   For GDP, Australia’s NSO (ABS) terms "y-o-y change" solely for annual data: Year -on-year Growth %   For GDP, Australia’s NSO (ABS) terms "through-the-year change" for quarterly data: Through-the-year Growth %   For GDP, Japan's NSO terms “Changes from the previous year” solely for annual data:   For GDP, Japan's NSO terms “Changes from the previous term” for quarterly NSA data:

Examples in Write-up

GDP contracted by 2.2% in Quarter 2  from a year earlier.   GDP contracted by 2.2% over the same period last year.   Based on advance estimates, the economy contracted by 13 per cent on a year-on-year basis in the second quarter of 2020, …   Australia’s NSO (ABS) Through the year GDP was up 1.4%.

 

 

Annualised level/value data

Definition

For a single period: Annualised level/value data shows the level that would be registered if the level for the current period was maintained for a full year.   For multiple periods: Annualised level/value data shows the level that would be registered if the level for the periods were maintained for a full year.

Formula

For a single period: P:  level / value fth:  current period f:  frequency /number of data points in a year   Example for quarterly data: For multiple periods: P:  level / value f:  frequency /number of data points in a year

Alternate Names

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Examples in Write-up

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Annualised growth rate (Annualised rate of change)

Definition

For period-on-previous period (POP): Annualised growth rate (Annualised rate of change) shows the growth that would be registered if the period-on-previous period (POP) rate of change were maintained for a full year.   POP is usually QoQ or MoM.   Annualised growth rates are often used for seasonally adjusted (SA) data. Users often compute the SA data QoQ or MoM change. Annualising the QoQ or MoM change will allow for comparison on the same magnitude as an annual growth or yoy growth rate.   SA data annualised rate of change is known as seasonally adjusted annualised rate (SAAR).   “Annualised growth rate” is sometimes used to describe the quarterly or monthly growth rate multiplied by 4 or 12. However, this is more appropriately referred to as “Linear approximation of the annualised growth rate” – refer below.   For year-to-date: Annualised growth rate (Annualised rate of change) shows the growth that would be registered if the rate of change between the current period and last period of the previous year was maintained for a full year.

Formula

For period-on-previous period (POP): OR   P:  level/ value fth:  current period fth -1:  preceding period f:  frequency /number of data points in a year   Example for quarterly data:   For year-to-date: OR   P:  level/ value fth:  current period lastfth:  last period of the previous year f:  frequency /number of data points in a year   Example for quarterly data:   Q4:  value for 4th Qtr 2019 Q2:  value for 2nd Qtr 2020

Alternate Names

1-month rate of change, annualized;  etc

Examples in Write-up

Real GDP decreased at an annual rate of xx% in the first Qtr of 2020   On a quarter-on-quarter seasonally-adjusted annualised basis, the economy shrank by 41.2 per cent in the second quarter.

 

 

Linear approximation of the annualised growth rate

Definition

Linear approximation of the annualised growth rate is a quick calculation of the annualised growth rate that show the rate of change that would be measured for a quarter, month or other frequency  if maintained for a full year.

Formula

P:  level / value fth:  current period fth -1:  preceding period f:  frequency /number of data points in a year   Example for quarterly data:

Alternate Names

Sometimes mis-named as Annualised growth rate; 1-month rate of change, annualized

Examples in Write-up

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Annualised semi-annual growth rate

Definition

Annualised semi-annual growth rates show the growth that would be registered if the rate of change measured with reference to a 6-month period were maintained for a full year.

Formula

OR P:  level/ value t:  current period t-6:  preceding 6 months   Example for quarterly data:   Q1:  value for 1st Qtr Q3:  value for 3rd Qtr   Example for monthly data:   M1:  value for Dec M6:  value for Jun

Alternate Names

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Examples in Write-up

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References

OECD Data and Metadata Reporting and Presentation Handbook 2007, "Chapter 4. Guidelines for the reporting of different types of data" https://www.oecd.org/sdd/37671574.pdf   https://pages.uoregon.edu/rgp/PPPM613/class8a.htm https://study.com/academy/lesson/population-growth-rate-definition-formula-examples.html http://ocw.jhsph.edu/courses/DemographicMethods/PDFs/Session11Exercise.pdf https://www.investopedia.com/terms/a/aagr.asp https://www.investopedia.com/terms/c/cagr.asp https://www.investopedia.com/terms/a/annualize.asp https://www.dallasfed.org/research/basics/annualizing.aspx https://thesmartmethod.com/a-formula-or-easy-way-to-annualize-data-based-on-month/ https://bizfluent.com/how-8684386-annualize-quarterly-numbers.html https://www.quora.com/Using-an-annual-growth-rate-how-can-I-convert-monthly-revenue-growth-to-quarterly-revenue-growth