2003).

The fundamental or deep sources of growth relate to those variables that

have an important in¬‚uence on a country™s ability and capacity to accumulate

factors of production and invest in the production of knowledge. For exam-

ple, Temple (1999) considers the following ˜wider™ in¬‚uences on growth:

population growth, the in¬‚uence of the ¬nancial sector, the general macr-

oeconomic environment, trade regimes, the size of government, income

distribution and the political and social environment. To this list Gallup et al.

The renaissance of economic growth research 597

(1998) would add the neglected in¬‚uence of geography. Moving from the

proximate to the fundamental causes of growth also shifts the focus of atten-

tion to the institutional framework of an economy, to its ˜social capability™

(Abramovitz, 1986), ˜social infrastructure™ (Hall and Jones, 1997, 1999) or

˜ancillary variables™ (Baumol et al., 1994). There is now widespread accept-

ance of the idea that ˜good™ governance and institutions and incentive structures

are an important precondition for successful growth and development (World

Bank, 1997, 2002).

In his historical survey of economic growth analysis, Rostow (1990) put

forward a central proposition that ˜from the eighteenth century to the present,

growth theories have been based on one formulation or another of a universal

equation or production function™. As formulated by Adelman (1958), this can

be expressed as equation (11.4):

Yt = f ( Kt , Nt , Lt , At , St ) (11.4)

where Kt, Nt and Lt represent the services ¬‚owing from the capital stock,

natural resources (geography) and labour resources respectively, At denotes

an economy™s stock of applied knowledge, and St represents what Adelman

calls the ˜sociocultural milieu™, and Abramovitz (1986) more recently has

called ˜social capability™, within which the economy functions. More sophis-

ticated models distinguish between human and physical capital. Indeed, many

authors regard human capital as the key ingredient of economic growth

(Lucas, 1988; Galor and Moav, 2003). Heckman (2003), for example, argues

that China™s below average spending on investment in education compared to

physical capital accumulation is ˜a serious distortion™ of policy that is likely

to retard progress in China. Goldin (2001) has also attributed much of the US

economic success in the twentieth century to the accumulation of human

capital.

According to Rostow (1990), ˜something like the basic equation is embed-

ded equally in Hume™s economic essays, Adam Smith™s The Wealth of Nations,

the latest neoclassical growth model, and virtually every formulation in be-

tween™. This universal equation encompasses both proximate and fundamental

causes of economic growth and Abramovitz drew attention to the importance

of these factors 50 years ago (see Nelson, 1997). Clearly, St contains the

in¬‚uence of non-economic as well as economic variables which can in¬‚uence

the growth potential and performance of an economy including the institu-

tions, incentives, rules and regulations that determine the allocation of

entrepreneurial talent (Baumol, 1990). Hence in recent years economists™

research into the ˜deeper™ determinants of growth has led some to stress the

importance of institutions and incentive structures (North, 1990; Olson, 2000),

trade and openness (Krueger, 1997; Dollar and Kraay, 2003) and the much-

598 Modern macroeconomics

neglected impact of geography (Bloom and Sachs, 1998). It is important to

note that Adam Smith had highlighted all three of these ˜deeper™ determinants

of growth over 200 years ago!

In sections 11.17“11.20 we will examine the ˜deeper™ determinants of

economic growth in more detail, but ¬rst, in sections 11.8“11.10, we survey

the three main waves of growth theory that have been in¬‚uential in the

second half of the twentieth century to date. All three approaches emphasize

the proximate determinants of growth, namely:

1. the neo-Keynesian Harrod“Domar model;

2. the Solow“Swan neoclassical model; and

3. the Romer“Lucas-inspired endogenous growth models.

In each case the ideas developed represent interesting examples of multiple

discovery. The ¬rst wave of interest focused on the neo-Keynesian work of

Roy Harrod (1939, 1948) and Evsey Domar (1946, 1947). In the mid-1950s

the development of the neoclassical growth model by Robert Solow (1956)

and Trevor Swan (1956) stimulated a second, more lasting and substantial,

wave of interest, which, after a period of relative neglect between 1970 and

1986, has been reignited (Mankiw et al., 1992; Mankiw, 1995; Klenow and

Rodriguez-Clare, 1997a, 1997b). The third and most recent wave, initiated by

the research of Paul Romer (1986) and Robert Lucas (1988), led to the

development of endogenous growth theory, which emerged in response to

perceived theoretical and empirical de¬ciencies associated with the neoclas-

sical model (P. Romer, 1994a; Crafts, 1996; Blaug, 2002).

11.9 The Harrod“Domar Model

Following the publication of Keynes™s General Theory in 1936, some econo-

mists 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 empha-

sized 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 be-

tween 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

The renaissance of economic growth research 599

exhibiting ¬xed factor proportions (constant capital“labour ratio, K/L) and a

¬xed capital“output ratio (K/Y). Assuming a two-sector economy (house-

holds and ¬rms), 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 evolu-

tion 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 ¬xed. Given that we have

de¬ned v = K/Y, it also follows that v = ∆K/∆Y (where ∆K/∆Y is the incre-

mental 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)

600 Modern macroeconomics

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):