The Harrod–Domar Model
Following the publication of Keynes’s General Theory in 1936, some economists
sought to dynamize Keynes’s static short-run theory in order to investigate
the long-run dynamics of capitalist market economies. Roy Harrod (1939,
1948) and Evsey Domar (1946, 1947) independently developed theories that
relate an economy’s rate of growth to its capital stock. While Keynes emphasized
the impact of investment on aggregate demand, Harrod and Domar
emphasized how investment spending also increased an economy’s productive
capacity (a supply-side effect). While Harrod’s theory is more ambitious than
Domar’s, building on Keynesian short-run macroeconomics in order to identify
the necessary conditions for equilibrium in a dynamic setting, hereafter we will
refer only to the ‘Harrod–Domar model’, ignoring the subtle differences between
the respective contributions of these two outstanding economists.
A major strength of the Harrod–Domar model is its simplicity. The model
assumes an exogenous rate of labour force growth (n), a given technology
exhibiting fixed factor proportions (constant capital–labour ratio, K/L) and a
fixed capital–output ratio (K/Y). Assuming a two-sector economy (households
and firms), we can write the simple national income equation as (11.5):
Yt = Ct + St (11.5)
where Yt = GDP, Ct = consumption and St = saving.
Equilibrium in this simple economy requires (11.6):
It = St (11.6)
Substituting (11.6) into (11.5) yields (11.7):
Yt = Ct + It (11.7)
Within the Harrod–Domar framework the growth of real GDP is assumed to
be proportional to the share of investment spending (I) in GDP and for an
economy to grow, net additions to the capital stock are required. The evolution
of the capital stock over time is given in equation (11.8):
Kt+1 = (1− δ)Kt + It (11.8)
where δ is the rate of depreciation of the capital stock. The relationship
between the size of the total capital stock (K) and total GDP (Y) is known as
the capital–output ratio (K/Y = v) and is assumed fixed. Given that we have
defined v = K/Y, it also follows that v = ΔK/ΔY (where ΔK/ΔY is the incremental
capital–output ratio, or ICOR). If we assume that total new investment
is determined by total savings, then the essence of the Harrod–Domar model
can be set out as follows. Assume that total saving is some proportion (s) of
GDP (Y), as shown in equation (11.9):
This simply states that the growth rate (G) of GDP is jointly determined by
the savings ratio (s) divided by the capital–output ratio (v). The higher the
savings ratio and the lower the capital–output ratio and depreciation rate, the
faster will an economy grow. In the discussion that follows we will ignore the
depreciation rate and consider the Harrod–Domar model as being represented
by the equation (11.14):
The Harrod–Domar model, as Bhagwati recalls, became tremendously
influential in the development economics literature during the third quarter of
the twentieth century, and was a key component within the framework of
economic planning. ‘The implications of this popular model were dramatic
and reassuring. It suggested that the central developmental problem was
simply to increase resources devoted to investment’ (Bhagwati, 1984). For
example, if a developing country desired to achieve a growth rate of per
capita income of 2 per cent per annum (that is, living standards double every
35 years), and population is estimated to be growing at 2 per cent, then
economic planners would need to set a target rate of GDP growth (G*) equal
to 4 per cent. If v = 4, this implies that G* can only be achieved with a desired
savings ratio (s*) of 0.16, or 16 per cent of GDP. If s* > s, there is a ‘savings
gap’, and planners needed to devise policies for plugging this gap.
Since the rate of growth in the Harrod–Domar model is positively related
to the savings ratio, development economists during the 1950s concentrated
their research effort on understanding how to raise private savings ratios in
order to enable less developed economies to ‘take off’ into ‘self-sustained
growth’ (Lewis, 1954, 1955; Rostow, 1960; Easterly, 1999). Reflecting the
contemporary development ideas of the 1950s, government fiscal policy was
also seen to have a prominent role to play since budgetary surpluses could (in
theory) substitute for private domestic savings. If domestic sources of finance
were inadequate to achieve the desired growth target, then foreign aid could
fill the ‘savings gap’ (Riddell, 1987). Aid requirements (Ar) would simply be
calculated as s* – s = Ar (Chenery and Strout, 1966). However, a major
weakness of the Harrod–Domar approach is the assumption of a fixed capital–
output ratio. Since the inverse of v (1/v) is the productivity of investment
(φ), we can rewrite equation (11.14) as follows:
G = sφ (11.15)
Unfortunately, as Bhagwati (1993) observes, the productivity of investment is
not a given, but reflects the efficiency of the policy framework and the
incentive structures within which investment decisions are taken. The weak
growth performance of India before the 1980s reflects, ‘not a disappointing
savings performance, but rather a disappointing productivity performance’
(Bhagwati, 1993). Hence the growth–investment relationship turned out to be
‘loose and unstable’ due to the multiple factors that influence growth (Easterly,
2001a). Furthermore, economists soon became aware of a second major
flaw in the ‘aid requirements’ or ‘financing gap’ model. The model assumed
that aid inflows would go into investment one to one. But it soon became
apparent that inflows of foreign aid, with the objective of closing the savings
gap, did not necessarily boost total savings. Aid does not go into investment
one to one. Indeed, in many cases inflows of aid led to a reduction of
domestic savings together with a decline in the productivity of investment
(Griffin, 1970; White, 1992). The research of Boone (1996) confirms that
inflows of foreign aid have not raised growth rates in most recipient developing
countries. A further problem is that in many developing countries the
‘soft budget constraints’ operating within the public sector created a climate
for what Bhagwati calls ‘goofing off’. It is therefore hardly surprising that
public sector enterprises frequently failed to generate profits intended to add
to government saving. In short, ‘capital fundamentalism’ and the ‘aid-financed
investment fetish’, which dominated development thinking for much
of the period after 1950, led economists up the wrong path in their ‘elusive
quest for growth’ (King and Levine, 1994; Easterly, 2001a, 2003; Easterly et
al., 2003; Snowdon, 2003a). Indeed, William Easterly (1999), a former World
Bank economist, argues that the Harrod–Domar model is far from dead and
still continues to exercise considerable influence on economists working
within the major international financial institutions even if it died long ago in
the academic literature. Easterly shows that economists working at the World
Bank, International Monetary Fund, Inter-American Bank, European Bank
for Reconstruction and Development, and the International Labour Organization
still frequently employ the Harrod–Domar–Chenery–Strout methodology
to calculate the investment and aid requirements needed in order for specific
countries to achieve their growth targets. However, as Easterly convincingly
demonstrates, the evidence that aid flows into investment on a one-for-one
basis, and that there is a fixed linear relationship between growth and investment
in the short run, is ‘soundly rejected’.
A further weakness of the Harrod–Domar framework is the assumption of
zero substitutability between capital and labour (that is, a fixed factor proportions
production function). This is a ‘crucial’ but inappropriate assumption
for a model concerned with long-run growth. This assumption of the Harrod–
Domar model also leads to the renowned instability property that ‘even for
the long run an economic system is at best balanced on a knife-edge equilibrium
growth’ (Solow, 1956). In Harrod’s model the possibility of achieving
steady growth with full employment was remote. Only in very special circumstances
will an economy remain in equilibrium with full employment of
both labour and capital. As Solow (1988) noted in his Nobel Memorial
lecture, to achieve steady growth in a Harrod–Domar world would be ‘a
miraculous stroke of luck’. The problem arises from the assumption of a
production function with an inflexible technology. In the Harrod–Domar
model the capital–output ratio (K/Y) and the capital–labour ratio (K/L) are
assumed constant. In a growth setting this means that K and Y must always
grow at the same rate to maintain equilibrium. However, because the model
also assumes a constant capital–labour ratio (K/L), K and L must also grow at
the same rate. Therefore, if we assume that the labour force (L) grows at the
same rate as the rate of growth of population (n), then we can conclude that
the only way that equilibrium can be maintained in the model is for n = G =
s/v. It would only be by pure coincidence that n = G. If n > G, the result will
be continually rising unemployment. If G > n, the capital stock will become
increasingly idle and the growth rate of output will slow down to G = n.
Thus, whenever K and L do not grow at the same rate, the economy falls off
its equilibrium ‘knife-edge’ growth path. However, the evidence is overwhelming
that this property does not fit well with the actual experience of
growth (for a more detailed discussion of the Harrod–Domar model see Hahn
and Matthews, 1964; H. Jones, 1975).
Following the publication of Keynes’s General Theory in 1936, some economists
sought to dynamize Keynes’s static short-run theory in order to investigate
the long-run dynamics of capitalist market economies. Roy Harrod (1939,
1948) and Evsey Domar (1946, 1947) independently developed theories that
relate an economy’s rate of growth to its capital stock. While Keynes emphasized
the impact of investment on aggregate demand, Harrod and Domar
emphasized how investment spending also increased an economy’s productive
capacity (a supply-side effect). While Harrod’s theory is more ambitious than
Domar’s, building on Keynesian short-run macroeconomics in order to identify
the necessary conditions for equilibrium in a dynamic setting, hereafter we will
refer only to the ‘Harrod–Domar model’, ignoring the subtle differences between
the respective contributions of these two outstanding economists.
A major strength of the Harrod–Domar model is its simplicity. The model
assumes an exogenous rate of labour force growth (n), a given technology
exhibiting fixed factor proportions (constant capital–labour ratio, K/L) and a
fixed capital–output ratio (K/Y). Assuming a two-sector economy (households
and firms), we can write the simple national income equation as (11.5):
Yt = Ct + St (11.5)
where Yt = GDP, Ct = consumption and St = saving.
Equilibrium in this simple economy requires (11.6):
It = St (11.6)
Substituting (11.6) into (11.5) yields (11.7):
Yt = Ct + It (11.7)
Within the Harrod–Domar framework the growth of real GDP is assumed to
be proportional to the share of investment spending (I) in GDP and for an
economy to grow, net additions to the capital stock are required. The evolution
of the capital stock over time is given in equation (11.8):
Kt+1 = (1− δ)Kt + It (11.8)
where δ is the rate of depreciation of the capital stock. The relationship
between the size of the total capital stock (K) and total GDP (Y) is known as
the capital–output ratio (K/Y = v) and is assumed fixed. Given that we have
defined v = K/Y, it also follows that v = ΔK/ΔY (where ΔK/ΔY is the incremental
capital–output ratio, or ICOR). If we assume that total new investment
is determined by total savings, then the essence of the Harrod–Domar model
can be set out as follows. Assume that total saving is some proportion (s) of
GDP (Y), as shown in equation (11.9):
This simply states that the growth rate (G) of GDP is jointly determined by
the savings ratio (s) divided by the capital–output ratio (v). The higher the
savings ratio and the lower the capital–output ratio and depreciation rate, the
faster will an economy grow. In the discussion that follows we will ignore the
depreciation rate and consider the Harrod–Domar model as being represented
by the equation (11.14):
The Harrod–Domar model, as Bhagwati recalls, became tremendously
influential in the development economics literature during the third quarter of
the twentieth century, and was a key component within the framework of
economic planning. ‘The implications of this popular model were dramatic
and reassuring. It suggested that the central developmental problem was
simply to increase resources devoted to investment’ (Bhagwati, 1984). For
example, if a developing country desired to achieve a growth rate of per
capita income of 2 per cent per annum (that is, living standards double every
35 years), and population is estimated to be growing at 2 per cent, then
economic planners would need to set a target rate of GDP growth (G*) equal
to 4 per cent. If v = 4, this implies that G* can only be achieved with a desired
savings ratio (s*) of 0.16, or 16 per cent of GDP. If s* > s, there is a ‘savings
gap’, and planners needed to devise policies for plugging this gap.
Since the rate of growth in the Harrod–Domar model is positively related
to the savings ratio, development economists during the 1950s concentrated
their research effort on understanding how to raise private savings ratios in
order to enable less developed economies to ‘take off’ into ‘self-sustained
growth’ (Lewis, 1954, 1955; Rostow, 1960; Easterly, 1999). Reflecting the
contemporary development ideas of the 1950s, government fiscal policy was
also seen to have a prominent role to play since budgetary surpluses could (in
theory) substitute for private domestic savings. If domestic sources of finance
were inadequate to achieve the desired growth target, then foreign aid could
fill the ‘savings gap’ (Riddell, 1987). Aid requirements (Ar) would simply be
calculated as s* – s = Ar (Chenery and Strout, 1966). However, a major
weakness of the Harrod–Domar approach is the assumption of a fixed capital–
output ratio. Since the inverse of v (1/v) is the productivity of investment
(φ), we can rewrite equation (11.14) as follows:
G = sφ (11.15)
Unfortunately, as Bhagwati (1993) observes, the productivity of investment is
not a given, but reflects the efficiency of the policy framework and the
incentive structures within which investment decisions are taken. The weak
growth performance of India before the 1980s reflects, ‘not a disappointing
savings performance, but rather a disappointing productivity performance’
(Bhagwati, 1993). Hence the growth–investment relationship turned out to be
‘loose and unstable’ due to the multiple factors that influence growth (Easterly,
2001a). Furthermore, economists soon became aware of a second major
flaw in the ‘aid requirements’ or ‘financing gap’ model. The model assumed
that aid inflows would go into investment one to one. But it soon became
apparent that inflows of foreign aid, with the objective of closing the savings
gap, did not necessarily boost total savings. Aid does not go into investment
one to one. Indeed, in many cases inflows of aid led to a reduction of
domestic savings together with a decline in the productivity of investment
(Griffin, 1970; White, 1992). The research of Boone (1996) confirms that
inflows of foreign aid have not raised growth rates in most recipient developing
countries. A further problem is that in many developing countries the
‘soft budget constraints’ operating within the public sector created a climate
for what Bhagwati calls ‘goofing off’. It is therefore hardly surprising that
public sector enterprises frequently failed to generate profits intended to add
to government saving. In short, ‘capital fundamentalism’ and the ‘aid-financed
investment fetish’, which dominated development thinking for much
of the period after 1950, led economists up the wrong path in their ‘elusive
quest for growth’ (King and Levine, 1994; Easterly, 2001a, 2003; Easterly et
al., 2003; Snowdon, 2003a). Indeed, William Easterly (1999), a former World
Bank economist, argues that the Harrod–Domar model is far from dead and
still continues to exercise considerable influence on economists working
within the major international financial institutions even if it died long ago in
the academic literature. Easterly shows that economists working at the World
Bank, International Monetary Fund, Inter-American Bank, European Bank
for Reconstruction and Development, and the International Labour Organization
still frequently employ the Harrod–Domar–Chenery–Strout methodology
to calculate the investment and aid requirements needed in order for specific
countries to achieve their growth targets. However, as Easterly convincingly
demonstrates, the evidence that aid flows into investment on a one-for-one
basis, and that there is a fixed linear relationship between growth and investment
in the short run, is ‘soundly rejected’.
A further weakness of the Harrod–Domar framework is the assumption of
zero substitutability between capital and labour (that is, a fixed factor proportions
production function). This is a ‘crucial’ but inappropriate assumption
for a model concerned with long-run growth. This assumption of the Harrod–
Domar model also leads to the renowned instability property that ‘even for
the long run an economic system is at best balanced on a knife-edge equilibrium
growth’ (Solow, 1956). In Harrod’s model the possibility of achieving
steady growth with full employment was remote. Only in very special circumstances
will an economy remain in equilibrium with full employment of
both labour and capital. As Solow (1988) noted in his Nobel Memorial
lecture, to achieve steady growth in a Harrod–Domar world would be ‘a
miraculous stroke of luck’. The problem arises from the assumption of a
production function with an inflexible technology. In the Harrod–Domar
model the capital–output ratio (K/Y) and the capital–labour ratio (K/L) are
assumed constant. In a growth setting this means that K and Y must always
grow at the same rate to maintain equilibrium. However, because the model
also assumes a constant capital–labour ratio (K/L), K and L must also grow at
the same rate. Therefore, if we assume that the labour force (L) grows at the
same rate as the rate of growth of population (n), then we can conclude that
the only way that equilibrium can be maintained in the model is for n = G =
s/v. It would only be by pure coincidence that n = G. If n > G, the result will
be continually rising unemployment. If G > n, the capital stock will become
increasingly idle and the growth rate of output will slow down to G = n.
Thus, whenever K and L do not grow at the same rate, the economy falls off
its equilibrium ‘knife-edge’ growth path. However, the evidence is overwhelming
that this property does not fit well with the actual experience of
growth (for a more detailed discussion of the Harrod–Domar model see Hahn
and Matthews, 1964; H. Jones, 1975).
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