Solow Growth Accounting
Growth Accounting
The Solow growth model presents a theoretical framework for understanding the sources of economic growth, and the consequences for long-run growth of changes in the economic environment and in economic policy. But suppose that we wish to examine economic growth in a freer framework, without necessarily being bound to adopt in advance the conclusions of our economic theories. In order to conduct such a less theory-bound analysis, economists have built up an alternative framework called growth accounting to obtain a different perspective on the sources of economic growth. We start with a production function that tells us what output Yt will be at some particular time t as a function of the economy’s stock of capital Kt, its labor force Lt, and the economy’s total factor productivity At. The Cobb-Douglas form of the production function is: Yt = At × ( Kt ) (Lt ) α 1− α
If output changes, it can only be because the economy’s capital stock, its labor force, or its level of total factor productivity changes.
Changes in Capital
Consider, first, the effect on output of a change in the capital stock from its current value Kt to a value Kt + ∆K—an increase in the capital stock by a proportional amount ∆K/Kt. In this production function Kt is raised to a power, α, so we can apply our rule-of-thumb for the proportional growth rate of a quantity raised to a power to discover
2
that the proportional increase in output from this change in the capital stock is: ∆Y ∆K =α Yt Kt Thus if the diminishing-returns-to-scale parameter α were equal to 0.5, and if the proportional change in the capital stock were 3%, then the proportional change in output would be: ∆Y = 0.5 × 3% = 1.5% Yt
Changes in Labor
Now consider, second, the effect on output of a change in the labor force from its current value Lt to a value Lt + ∆L—an increase in the capital stock by a proportional amount ∆L/Lt. In this production function Lt is raised to a power, 1-α, so we can
The Solow growth model presents a theoretical framework for understanding the sources of economic growth, and the consequences for long-run growth of changes in the economic environment and in economic policy. But suppose that we wish to examine economic growth in a freer framework, without necessarily being bound to adopt in advance the conclusions of our economic theories. In order to conduct such a less theory-bound analysis, economists have built up an alternative framework called growth accounting to obtain a different perspective on the sources of economic growth. We start with a production function that tells us what output Yt will be at some particular time t as a function of the economy’s stock of capital Kt, its labor force Lt, and the economy’s total factor productivity At. The Cobb-Douglas form of the production function is: Yt = At × ( Kt ) (Lt ) α 1− α
If output changes, it can only be because the economy’s capital stock, its labor force, or its level of total factor productivity changes.
Changes in Capital
Consider, first, the effect on output of a change in the capital stock from its current value Kt to a value Kt + ∆K—an increase in the capital stock by a proportional amount ∆K/Kt. In this production function Kt is raised to a power, α, so we can apply our rule-of-thumb for the proportional growth rate of a quantity raised to a power to discover
2
that the proportional increase in output from this change in the capital stock is: ∆Y ∆K =α Yt Kt Thus if the diminishing-returns-to-scale parameter α were equal to 0.5, and if the proportional change in the capital stock were 3%, then the proportional change in output would be: ∆Y = 0.5 × 3% = 1.5% Yt
Changes in Labor
Now consider, second, the effect on output of a change in the labor force from its current value Lt to a value Lt + ∆L—an increase in the capital stock by a proportional amount ∆L/Lt. In this production function Lt is raised to a power, 1-α, so we can