Principles of Macroeconomics: Section 15 Main

Unit 15 - Applications of the Solow Model

Now that we have considered the basic elements of economic growth theory, let us extend our model to help explain several real-world situations. We will take a look at the following circumstances:

Why are some less-developed countries (LDCs) growing rapidly (the Asian Tigers, for example) and others contracting over time?
We will discuss the convergence hypothesis, which theorizes that rapidly developing LDCs will eventually catch-up in living standards to the level enjoyed in the United States, Japan, and many of the nations of Western Europe.
An analysis can be made of the role of technology in promoting improved economic growth rates and other public policy issues.
We will consider how changes in population and savings rates impact the rate of economic growth and potential improvements in living standards.
Recognize that for economies with low or negative economic growth, special attention must be paid to economic and social circumstances to encourage improved economic expansion.
Look at the positive contribution of education in LDCs, especially when the education of females is promoted.

High Savings Rates Promote Economic Growth

Let us consider the case of the fast-growing LDCs. The category includes many of the Pacific Rim countries as well as other countries scattered globally. The catalyst for high economic growth rates is high levels of total (usually domestic) savings. Total savings equals:

Total Savings = Private Savings + Public Savings + Net Foreign Savings

The above equation indicates that a nation's total savings is composed of domestic private savings by individuals and businesses, total public savings by governments, and the net inflow of foreign savings.(1)

(1) A government that runs budget deficits has negative public savings that reduce the total. Net foreign savings is the difference between savings by domestic citizens and firms, which is saved abroad, and the inflow of foreign savings into the domestic economy.

In the previous section, we developed the theory of economic growth. The expected expansion of an economy's productive capacity, and thus the long-run potential growth rate, equals the sum of labor force growth, the rate of change in technology, and the rate of net investment. (2)

(2) To achieve this potential growth, it is assumed that depreciated capital is replaced. With positive net investment, there are net additions to the capital stock, increasing the capital-labor ratio, worker productivity, and output per worker.

For a developed economy like the United States, the steady-state growth model indicates that total savings is sufficient to replace depreciated capital, equip new workers with the same capital as all other workers to maintain a constant capital-labor ratio, and update the capital stock to new technology. In this case, total savings are equivalent to the depreciation rate (delta), plus n (population growth rate), plus a (rate of improvement in technology). Steady-state growth, or the long-run expansion of productive capacity, equals n + a for a developed economy.

In the United States, the growth of productive capacity roughly equals 2% to 2.5% a year. In contrast, many of the Asian Tigers enjoy average annual increases in growth of double, triple, or even greater amounts than seen in the United States. The differential in potential output growth can be explained using the Solow model. LDCs, almost by definition, have lower standards of living, smaller economies, less capital, and a lower capital-labor ratio than the developed nations. As a result, LDCs need to devote less of their total savings to the replacement of depreciated capital, leaving a possible surplus for the purchase of additional capital.

The key is savings. The majority of rapidly growing LDCs share a common trait of high rates of private savings and little or no public deficits. As the growth model indicates, when there is positive net investment, the rate of net investment (the change in k) adds to the annual rate of growth. In this case, annual growth equals n + a + the rate of change in the capital stock. As a result, the capital-labor ratio rises and so do worker productivity and output per worker.

The Solow model predicts that LDCs with high internal savings rates will grow at a faster pace than developed countries. The relatively higher economic growth rates enjoyed by these countries will help to narrow the gap in output per worker and living standards between them and the developed nations. But the rapid pace of growth must eventually slow down to the steady-state growth rate. The reason is that for a given savings rate, positive net investment increases the capital stock over time. As the capital stock accumulates, so does the total level of depreciation of capital (for a fixed rate of depreciation, delta). As total depreciation increases, so does the proportion of savings required to offset depreciation, leaving less surplus savings for net investment.

The convergence hypothesis predicts that rapidly growing LDCs will enjoy faster economic growth rates than the developed countries for a time. Eventually, as the capital stock and output per worker rises in these LDCs, economic growth will slowly fall down to the steady-state level found in today's developed countries. By then, these LDCs will have converged in the amount of capital available per worker and output per worker. The once fast-growing LDCs will have reached a standard of living comparable to those attained in the developed countries (3),(4).

(3) It is important to note that this says nothing about the distribution of income and issues of fairness.
(4) For an alternative view of the emergence and direction of the newly industrialized countries in Asia, read a summary of Paul Krugman's article published in Foreign Affairs.

The present conclusion is that relatively underdeveloped countries can catch up to the developed countries, and their chances are maximized when there are high levels of domestic savings and the government promotes:

free-market policies, open and competitive markets,

foreign trade liberalisation,

investment in education (human capital) and infrastructure (physical capital),

the maintenance of property rights,

a smaller public or government sector, and low taxes.

When Savings Is Scarce

Savings and economic growth have a positive correlation. It is easier to save when your income is increasing, in contrast to when it is declining. In contrast to the rapid growth enjoyed in many Asian NICs are the stagnant or deteriorating economic circumstances found in other LDCs. The basic problem is that poor countries have a hard time generating much domestic savings, since living standards are so low. If subsistence level incomes are combined with rapid rates of population growth, the outcome is often a continuous economic stagnation, or even contraction over time.

We earlier considered the economic impact of an increase in the savings rate. The resulting positive capital accumulation allows for an increase in economic growth rate above the steady state. We can reverse the outcome when savings are below the steady state. Returning to a the steady-state growth rate, we now look at the impact of an increase in population growth rates.

Higher population growth rates allow for higher growth rates in the labor force, n. An increase in n creates the potential for higher steady-state growth, but only if total savings also increase. To accomplish this higher potential growth as n increases imposes the same restrictions as the original steady-state. Each new worker must be equipped with the same endowment of capital as all previous workers. The maintenance of a fixed capital-labor ratio allows for constant output per worker and steady-state growth equal to n plus the rate of technological advancement.

In reality, high population growth rates are more often a handicap to growth than a contributing factor. Not surprisingly, many LDCs are promoting lower fertility rates as a way to encourage long-run economic growth. In 1994, the United Nations held a conference on population growth that emphasized this theme. This was followed by the 1995 UN conference on education. It is widely recognized that the most effective solution to reducing fertility rates and the rate of global population increase is educating girls and women in developing countries. Lower values of n allow for all members of society to benefit with potentially higher standards of living.

Click on a part of the graph for further information.

To show the benefit to economic growth of lower population growth rates, we begin by assuming a steady-state equilibrium at k₁*. From this point in Figure 15-1, the population growth rate and the labor force growth rate, n, is reduced. As the graph shows, the line showing the constant rates of change in n plus delta (depreciation of capital) rotates downward reflecting the lower value of n.
For example, if n₁ had equalled 2%, the line rotates downward if n₂ now equals 1% annually (3). Assuming that the savings rate, s, remains constant, the economy benefits from a growth spurt as total savings allows for positive net investment. Eventually, a new steady-state is reached at k₂*. At the new steady state, output per worker and potential living standards are higher than at the original steady state, k₁*.

(3) It is obvious that when considering changes in population growth rates, the long run is truly the long run given the significant period of time between birth and full-time entry into the labor force. Social policies that effectively reduce the birth rate may not translate into higher living standards for a generation or two after they are implemented.

Promoting Growth in a Low Savings Environment

As we can see from using the framework of the Solow growth model, savings is the catalyst for economic growth. It is easy to understand the problem faced by many poor developing countries: it is difficult to generate meaningful levels of savings when average incomes are at a subsistence level. Some possible solutions to a lack of significant domestic private savings include:

Countries with abundant exportable natural resources and commodities should use the revenues wisely. Investment in human and physical capital is a necessity. For further discussion of this issue, link to a discussion of the World Bank's new measure for GDP accounting that considers the depletion of natural resources and their potential conversion into capital.

Many countries lack a resource base that can significantly raise per capita incomes and savings. The next possibility is to attract savings from abroad in the form of direct investment or purchases of domestically issued debt and equity. As we have seen with the Mexican currency crisis, using highly liquid debt and equity markets can create more problems than solutions, when this money flees at the first sign of any trouble. There are several requirements to emphasize for a domestic economy to attract significant amounts of foreign direct investment and savings:

Low government budget deficits. High public sector deficits will discourage and potentially offset the contribution of foreign investment and savings. When government budget deficits become a significant percentage of GDP, the expectations and risk of future inflation increases. Rates of return on saving and inflation are often inversely correlated.

Sound political and social systems and an organized network of financial intermediaries. Savers must be assured that their money goes into areas of high return.

Governments need to ensure that resources are not wasted or squandered. For various reasons, many developing countries fail to use labor, capital and natural resources efficiently. Dramatic improvements in economic growth may be achieved not by attracting new resources, but by using existing factors of production more efficiently.

Finally, we should note that abundant natural resources are no guarentee of successful development for a LDC. In fact, history has shown that the greatest strides are made by countries which do not depend on a huge resource base, but rather on the knowledge and skills of their people. For further discussion of this issue link here.