Unit 9 Uneven development on a global scale

9.8 How poor countries get stuck at low growth and how they can grow rapidly

The simple grain-only economy of Section 9.5 helps us to understand what can set off a process of sustained growth of per capita output in an economy, which can take it from low- to middle- or high-income levels. We highlighted there that a windfall harvest provides resources for investment that do not require a fall in consumption. We can generalize the insight that saving enough to expand the level of capital per worker (whether imposed by governments or chosen by households) is more likely to be sustainable when it does not entail reduced current consumption. Reasons relate both to individual psychology and political processes.

Another mechanism through which higher investment can arise without a simultaneous fall in average consumption is through changes in institutions that result in a shift in the distribution of income away from landlords and other elites who save and invest in assets (such as palatial houses and monuments), to capitalists who have to invest in order to survive the competition with other capitalists. The rate of growth in European economies in the late eighteenth and early nineteenth century is thought to have increased in part due to institutional changes of this kind, resulting in a shift in what wealthy people did with the resources at their command. Prior to 1700, the largest buildings in many European towns were churches; after 1800, the largest buildings were factories.

The growth dynamics model

growth dynamics model

A growth dynamics model is an economic model of the process by which a variable changes (grows) over time, in which the growth rate in one period depends in a systematic way on the growth rate in previous periods.

exogenous growth

Growth in aggregate output (GDP) which occurs as a result of independent, unintentional effects such as ‘learning by doing’. This contrasts with endogenous growth, which occurs as a result of intentional actions by economic agents.

endogenous growth

Growth in aggregate output (GDP) which occurs as a result of intentional actions by economic agents, such as investment to raise the capital stock, or R&D to develop a better production process. This contrasts with exogenous growth, which occurs as a result of unintentional effects such as ‘learning by doing’.

In this section, we build on the grain economy model in Section 9.5, but we drop the simplifying assumption that output increases at a constant rate with capital (grain planted), to allow for more general technologies. As before, there is a single good (grain) that is produced, consumed, and invested in by a fixed population of farmers. We will develop a model that distinguishes between two sources of growth—exogenous growth and endogenous growth. And we will explain why we call it the growth dynamics model.

Exogenous growth happens irrespective of the investment decisions made by the farmers. Suppose, for example, that independently of the level of investment, output can be increased by learning and adopting better ways to produce, which we call learning by doing and from others. Perhaps farmers find out from experience (or from observing neighbouring farms) that planting a bit earlier in the spring yields a larger harvest. Exogenous growth is often labelled as ‘technological change’, but it should be thought of much more broadly because it will reflect not only advances in technology but also the institutional framework of the economy. Whether or not new ways of doing things are readily shared and spread across the economy depends on the nature of intellectual property rights and practices, the level and nature of schooling, and the organization of the production process.

Endogenous growth arises through the decisions of farms to invest some of their grain as capital, to raise future output.

To understand how exogenous and endogenous growth combine, we can use the growth accounting equation, which relates the rate of growth of output to the growth rates of the inputs to production and technological progress (explained in Section 9.4). Output growth, \(g^Y\), is the sum of technological progress, \(g^z\), and a weighted average of the growth rates of the inputs. Here we interpret \(g^z\) more widely as exogenous growth, to include learning by doing. In the grain model, the inputs are capital and labour, but the number of farmers does not change (\(g^N = 0\)), and so we can write:

\[g^Y = g^z + \beta g^K\]

where \(g^K\) is the endogenous growth rate of the capital stock. The parameter, \(\beta\), captures the effect on output of net capital investment.

To model net investment, we pick up the idea introduced in Section 9.5 that higher growth in this period (from a bumper harvest, for example) provides the resources for increasing the capital stock without decreasing consumption. This means that investment contributes to growth but, in addition, growth contributes to investment.

Specifically, we assume that net investment is proportional to last year’s output growth rate. So if \(g_t\) is the growth rate from year \(t-1\) to year \(t\), the growth in the capital stock from year \(t-1\) to year \(t\) is given by:

\[g^K_t = \alpha g^Y_{t-1} \text{where } \alpha > 0\]

In this equation, \(𝛼\) (the Greek letter, alpha) is the fraction of last year’s growth that is invested. To understand this investment rule, suppose for example that \(𝛼 = 0.75\). If output had increased by 4% last year, from 100 to 104 units, and last year’s capital stock was 40 units, the investment rule tells you to increase the capital stock by 3%, from 40 to 41.2 units. You would use 1.2 units of the extra output for net investment (in addition to what is required to allow for depreciation), and the other 2.8 units for extra consumption.

Substituting the investment rule into the equation for the growth of output, we can show that this year’s growth rate, \(g^Y_t\), depends on the exogenous growth rate, \(g_z\), and last year’s growth rate:

\[g^Y = g^z + \alpha\beta g^Y_{t-1}\]

More precisely, this relationship captures what we expect the growth rate to be in year \(t\), given the investment resulting from the previous year’s growth. Unexpected weather conditions could result in a higher or low harvest than predicted.

growth dynamics curve

The growth dynamics curve is a graph of the relationship between the growth rate in period \(t\) (on the horizontal axis) and the growth rate in period \(t+1\) (on the vertical axis). A point where the graph crosses the 45-degree line represents an equilibrium growth rate: once the economy reaches this rate of growth, it will remain there unless there is an unexpected shock.

price dynamics curve

The price dynamics curve is a graph of the relationship between the price of a good in period \(t\) (on the horizontal axis) and the price in period \(t + 1\) (on the vertical axis). A point where the graph crosses the 45-degree line represents a market equilibrium: at this price demand = supply so the price stays constant from one period to the next. At other prices excess demand or excess supply leads to a change in price.

We will assume that \(𝛼\), \(𝛽\), and \(g_z\) are all positive constants. Figure 9.17a shows this relationship between growth rates in two successive years graphically. We call this relationship the growth dynamics curve, although in this model it is a straight line with a slope of \(𝛼𝛽\). Considering point A first, if growth in period 0 is close to zero, the expected growth rate in period 1 is only just above the exogenous growth rate, \(g_z\). Point B illustrates how high growth in period 0 leads to high growth in period 1 as well, because it stimulates investment.

The growth dynamics curve in Figure 9.17a is drawn for the case, \(𝛼𝛽 < 1\), which means that it crosses the 45-degree line. Work through the steps to understand why there is a stable equilibrium growth rate at the crossing point.

Figure 9.17a illustrates a stable growth equilibrium. Although the economy may temporarily experience periods of higher or lower growth, it will always tend to return to a steady growth rate equal to \(g^*\).

Raising the equilibrium growth rate

If the equilibrium rate, \(g^*\), is low, this economy is stuck in a low-growth trap. An occasional good harvest or other source of an increase in income does not last, and growth returns to the equilibrium rate.

To shift from a low-growth trap with low GDP per capita to one in which the economy grows rapidly year after year, to reach a substantially higher level of GDP per capita—as observed in the hockey stick charts—the equilibrium rate of growth must be higher, at least for a time. And this in turn requires changing how the economy works, as represented in the model by \(𝛼\), \(𝛽\), and \(g_z\). Therefore, a policy that aims to sustainably raise incomes in a country would aim to raise one or more of these variables.

In the aggregate economy the fraction, \(𝛼\), of growth that is invested could be increased by:

• wealthy private individuals choosing to consume less (for example on luxuries) and instead invest some of their increased income to construct privately owned capital goods—for example, building factories and not palatial mansions, as happened in the eighteenth century; and in the twenty-first century, building data centres and not mega-yachts or resorts on private islands
• the financial system successfully facilitating the investment of an increase in saving in the economy (as discussed in Unit 6)
• a government devoting more tax revenues to building infrastructure (for example, roads and education)
• forms of redistribution that incentivize the accumulation of productive capital goods.

Factors that increase \(𝛽\), the benefit to growth of additional investment, include the quality of institutions, infrastructure, and schooling. Figure 9.17b shows how a rise in \(𝛼\) or \(𝛽\) (or both) would change the slope of the growth dynamics curve, and hence raise the equilibrium growth rate.

The second step in Figure 9.17b shows that higher exogenous growth also raises the equilibrium growth rate. This could come about, for example, if a better educated or more cooperative population were willing to share knowledge, increasing the rate of learning by doing.

Disequilibrium growth

If the policymaker succeeded in raising \(α\) or \(β\) sufficiently such that \(αβ > 1\), the growth process would take a completely different form, as illustrated in Figure 9.17c. There is no equilibrium rate of growth because the slope of the growth dynamics curve is greater than the slope of the 45-degree line. The growth dynamics curve lies in the region where growth is increasing. So a high growth rate in one period leads to an even higher one in the next period.

If growth in period 0 is \(g′\), in the next period it will be higher (\(g″\)), and in the following period higher still. Growth increases (output accelerates) from period to period.

Although in the real world, growth cannot go on increasing indefinitely, the model can be extended to be more realistic by combining a phase of disequilibrium growth with equilibrium growth to produce an S-shaped growth dynamics curve (like the models in Unit 8). The S-shaped model incorporates a negative feedback process around two equilibria, one at low and one at high growth. Between them is an unstable equilibrium (the tipping point), where the growth dynamics curve (GDC) has a slope greater than one. Explosive growth is dampened in the S-shaped model. The model is explained in the extension.