Growth rates

Types and calculation

Jul 29, 2015

Growth rate

• Growth rate: Change in value of a given variable per unit of time.

Types of Growth Rates

• Arithmetic/linear /Simple growth rate

• Compound /semi-log/least-squares

• Exponential growth rate

• Geometric growth rate

Simple/Arithmetic growth rate

• Simple change in variable over a period divided by period

• This method assumes that the variable increases by a fixed amount of units in each period

Compound/least-squares growth rate

Xn= Xo (1 + r)n

logarithmic transformation of the compound growth equation

Where “n” is time, and

Growth rate r = [exp(β) – 1]

Compound/least-squares growth rate

• It is used when there is a long time series• Most widely used• It takes into consideration of all values in the

period of consideration. • But, it does not necessarily match the actual

growth rate between any two points in the period.

Exponential growth rate• Takes continuous compounding and the variable

grows at a constant rate at every infinitesimal of time.

• Takes into account only the first and last observation of the time series, and not the intermediate values.

Exponential growth rate

• It will not comparable to the annual growth rate measured by arithmetic or geometric rates

• Exponential growth is mainly used for indicators related to population/demographic indicators

Geometric growth rate

• The geometric growth rate represents compound growth over discrete periods.

• Takes into account only the first and last observation of the time series, and not the intermediate values.

Geometric growth rate

• It is also referred to as the geometric average method, as it can be expressed as the geometric average of annual growth rates.

• For 1-period interval geometric and arithmetic growth rates are equal, as the arithmetic and geometric formulae become equal.

• Geometric growth rate is widely used for indicators on economic phenomena, such as GDP or trade by agencies like WB, FAO, IMF etc

Exercises

• Extract data from EPWRFITS on any GDP or Industrial production

• Calculate all the growth rates