# 11.11 Accounting for the Sources of Economic Growth

Economists not only need a theoretical framework for understanding the

causes of growth; they also require a simple method of calculating the relative

importance of capital, labour and technology in the growth experience of

actual economies. The established framework, following Solow’s (1957) seminal

contribution, is called ‘growth accounting’ (see Abel and Bernanke, 2001.

Some economists remain highly sceptical about the whole methodology and

theoretical basis of growth accounting, for example Nelson, 1973). As far as

the proximate causes of growth are concerned we can see by referring back to

equation (11.28) that increases in total GDP (Y) come from the combined

weighted impact of capital accumulation, labour supply growth and technological

progress. Economists can measure changes in the amount of capital

and labour that occur in an economy over time, but changes in technology

(total factor productivity = TFP) are not directly observable. However, it is

possible to measure changes in TFP as a ‘residual’ after taking into account

the contributions to growth made by changes in the capital and labour inputs.

Solow’s (1957) technique was to define technological change as changes in

aggregate output minus the sum of the weighted contributions of the labour

and capital inputs. In short, the Solow residual measures that part of a change

in aggregate output which cannot be explained by changes in the measurable

quantities of capital and labour inputs. The derivation of the Solow residual

can be shown as follows. The aggregate production function in equation

(11.28) shows that output (Y) is dependent on the inputs of capital (K), labour

(L) and the currently available technology (A), which acts as an index of total

factor productivity. Output will change if A, K or L change. In equation

(11.28) the exponent on the capital shock α measures the elasticity of output

with respect to capital and the exponent on the labour input (1 – α) measures

the elasticity of output with respect to labour. The weights α and 1 – α are

estimated from national income statistics and reflect the income shares of

capital and labour respectively. Since these weights sum to unity, this indicates

that (11.28) is a constant returns to scale production function. Hence an

equal percentage increase in both factor inputs (K and L) will increase Y by

the same percentage. Since the growth rate of the product of the inputs will

be the growth rate of A plus the growth rate of Kα plus the growth rate of L1–α,

equation (11.28) can be rewritten as (11.31), which is the basic growth

accounting equation used in numerous empirical studies of the sources of

economic growth (see Maddison, 1972, 1987; Denison, 1985; Young, 1995,

Crafts, 2000; Jorgenson, 2001).

ΔY/Y = ΔA/A + αΔK/K + (1− α)ΔL/L (11.31)

Equation (11.31) is simply the Cobb–Douglas production function written in

a form representing rates of change. It shows that the growth of aggregate

output (ΔY/Y) depends on the contribution of changes in total factor productivity

(ΔA/A), changes in the weighted contribution of capital, αΔK/K, and

changes in the weighted contribution of labour (1 – α)ΔL/L. By rearranging

equation (11.28) we can represent the productivity index (TFP) which we

need to measure as equation (11.32):

TFP = A = Y / KαL1−α (11.32)

As already noted, because there is no direct way of measuring TFP it has to

be estimated as a residual. By writing down equation (11.32) in terms of rates

of change we can obtain an equation from which the growth of TFP (technological

change) can be estimated as a residual. This is shown in equation

(11.33):

ΔA/A = ΔY/Y −[αΔK/K + (1− α)ΔL/L] (11.33)

Data relating to output and the capital and labour inputs are available. Estimates

of α and hence 1 – α can be acquired from historical national income

data. For example, in Solow’s original paper covering the US economy for

the period 1909–49 he estimated that the rate of growth of total output (ΔY/Y)

had averaged 2.9 per cent per year, of which 0.32 percentage points could be

attributed to capital (αΔK/K), 1.09 percentage points could be attributed to

labour (1 – αΔL/L), leaving a ‘Solow residual’ (ΔA/A) of 1.49 percentage

points. In other words, almost half of the growth experienced in the USA

during this period was due to unexplained technological progress! In Denison’s

(1985) later work he found that for the period 1929–82, ΔY/Y = 2.92 per cent,

of which 1.02 percentage points were be attributed to ΔA/A. More recent

controversial research by Alwyn Young (1992, 1994, 1995) on the sources of

growth in the East Asian Tiger economies has suggested estimates of rates of

growth of TFP for Taiwan of 2.6 per cent, for South Korea of 1.7 per cent, for

Hong Kong of 1.7 per cent and for Singapore a meagre 0.2 per cent! So

although these economies have experienced unprecedented growth rates of

GDP since the early 1960s, Young’s research suggests that these economies

are examples of miracles of accumulation. Once we account for the growth of

labour and physical and human capital there is little left to explain, especially

in the case of Singapore (see Krugman, 1994b; Hsieh, 1999; Bhagwati,

2000). Going further back in history, Nick Crafts (1994, 1995) has provided

estimates of the sources of growth for the British economy during the period

1760–1913. Crafts’s estimates suggest that ‘by twentieth century standards

both the output growth rates and the TFP rates are quite modest’ (Crafts,

1995).

The most obvious feature of the post-1973 growth accounting data is the

well-known puzzle of the ‘productivity slowdown’. This slowdown has been

attributed to many possible causes, including the adverse impact on investment

and existing capital stocks of the 1970s oil price shocks, a slowdown in

the rate of innovation, adverse demographic trends, an increasingly regulatory

environment and problems associated with measurement such as

accounting for quality changes (Fischer et al., 1988).

In a recent survey of the growth accounting literature Bosworth and Collins

(2003) reaffirm their belief that growth accounting techniques can yield

useful and consistent results. In the debate over the relative importance of

capital accumulation v. TFP in accounting for growth Bosworth and Collins

conclude that ‘both are important’ and that ‘some of the earlier research

understates the role of capital accumulation because of inadequate measurement

of the capital input’.

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