Economic growth and economic development 118

Introduction to Modern Economic Growth
markets, also gives us a framework for accounting for the sources of economic growth.
In particular, Solow (1957) developed what has become one of the most common
tools in macroeconomics, the growth accounting framework.
For our purposes, it is sufficient to expose the simplest version of this framework.
Consider a continuous-time economy and differentiate the production function (2.1)
with respect to time. Dropping time dependence and denoting the partial derivatives
of F with respect to its arguments by FA , FK and FL , this yields
(3.1)

Y˙
FA A A˙ FK K K˙
FL L L˙
=
+
+
.
Y
Y A
Y K
Y L

Now denote the growth rates of output, capital stock and labor by g ≡ Y˙ /Y ,
˙
˙
and gL ≡ L/L,
and also define
gK ≡ K/K
x≡

FA A A˙

Y A

as the contribution of technology to growth. Next, recall from the previous chapter
that with competitive factor markets, we have w = FL and R = FK (equations (2.5)
and (2.6)) and define the factor shares as αK ≡ RK/Y and αL ≡ wL/Y . Putting

all these together, (3.1) can be written as
(3.2)

x = g − αK gK − αL gL .

This is the fundamental growth accounting equation. At some level it is no more than
an identity. However, it also allows us to estimate the contribution of technological
progress to economic growth using data on factor shares, output growth, labor force
growth and capital stock growth. This contribution from technological progress
is typically referred to as Total Factor Productivity (TFP) or sometimes as Multi
Factor Productivity.
In particular, denoting an estimate by “ˆ”, we have the estimate of TFP growth
at time t as:
(3.3)

xˆ (t) = g (t) − αK (t) gK (t) − αL (t) gL (t) .

we only put the “ˆ” on x, but one may want to take into account that all of the terms
on the right hand side are also “estimates” obtained with a range of assumptions
from national accounts and other data sources.
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