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# 11.9 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):

St = sYt (11.9)

Since K = vY and It = St, it follows that we can rewrite equation (11.8) as

equation (11.10):

vYt+1 = (1− δ)vYt + sYt (11.10)

Dividing through by v, simplifying, and subtracting Yt from both sides of

equation (11.10) yields equation (11.11):

Yt+1 − Yt = [s/v − δ]Yt (11.11)

Dividing through by Y t gives us equation (11.12):

[Yt+1 − Yt ]/Yt = (s/v) − δ (11.12)

Here [Yt + 1 – Yt]/Yt is the growth rate of GDP. Letting G = [Yt + 1 – Yt]/Yt, we

can write the Harrod–Domar growth equation as (11.13):

G = s/v − δ (11.13)

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):

G = s/v (11.14)

Thus it is evident from (11.14) that the Harrod–Domar model ‘sanctioned the

overriding importance of capital accumulation in the quest for enhanced

growth’ (Shaw, 1992).

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).