Growth accounting
Growth accounting is a procedure used in economics to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy.
[1] Growth accounting decomposes the growth rate of an economy's total output into that which is due to increases in the contributing amount of the factors used—usually the increase in the amount of capital and labor—and that which cannot be accounted for by observable changes in factor utilization.
The unexplained part of growth in GDP is then taken to represent increases in productivity (getting more output with the same amounts of inputs) or a measure of broadly defined technological progress.
The technique has been applied to virtually every economy in the world and a common finding is that observed levels of economic growth cannot be explained simply by changes in the stock of capital in the economy or population and labor force growth rates.
Hence, technological progress plays a key role in the economic growth of nations, or the lack of it.
As an abstract example consider an economy whose total output (GDP) grows at 3% per year.
Over the same period its capital stock grows at 6% per year and its labor force by 1%.
The contribution of the growth rate of capital to output is equal to that growth rate weighted by the share of capital in total output and the contribution of labor is given by the growth rate of labor weighted by labor's share in income.
This means that the portion of growth in output which is due to changes in factors is .06×(1⁄3)+.01×(2⁄3)=.027 or 2.7%.
This remainder is the increase in the productivity of factors that happened over the period, or the measure of technological progress during this time.
Growth accounting can also be expressed in the form of the arithmetical model, which is used here because it is more descriptive and understandable.
In this case the accounting result is 0.015 which implies a productivity growth by 1.5%.
In this case productivity is defined as follows: input consumption per one unit of output volume.
As demonstrated above we cannot draw correct conclusions based on average productivity numbers.
This is due to the fact that productivity is accounted as an independent variable separated from the entity it belongs to, i.e. real income formation.
We have to know separately income effects of productivity change and production volume change or their combined income effect in order to understand which one result is better and how much better.
This kind of scientific mistake of wrong analysis level has been recognized and described long ago.
If we focus the review on small components of the whole, in this case the elements oxygen and hydrogen, we come to the conclusion that hydrogen is an explosive gas and oxygen is a catalyst in combustion.
This incorrect conclusion arises from the fact that the components have been separated from the entity.
[9]: 10 The total output of an economy is modeled as being produced by various factors of production, with capital and labor being the primary ones in modern economies (although land and natural resources can also be included).
where Y is total output, K is the stock of capital in the economy, L is the labor force (or population) and A is a "catch all" factor for technology, role of institutions and other relevant forces which measures how productively capital and labor are used in production.
Wages paid to labor are denoted by w and the rate of profit or the real interest rate is denoted by r. Note that the assumption of perfect competition enables us to take prices as given.
For simplicity we assume unit price (i.e. P =1), and thus quantities also represent values in all equations.
denotes the partial derivative with respect to factor i, or for the case of capital and labor, the marginal products.
or denoting a growth rate (percentage change over time) of a factor as
are all observable and can be measured using standard national income accounting methods (with capital stock being measured using investment rates via the perpetual inventory method).
however is not directly observable as it captures technological growth and improvement in productivity that are unrelated to changes in use of factors.
This term is usually referred to as Solow residual or Total factor productivity growth.
Slightly rearranging the previous equation we can measure this as that portion of increase in total output which is not due to the (weighted) growth of factor inputs:
Another way to express the same idea is in per capita (or per worker) terms in which we subtract off the growth rate of labor force from both sides:
