Growth Factors and Production Function

Economists measure the economic output of a country by gross domestic product (GDP). A country’s standard of living, however, is best measured by GDP per capita. Of particular concern to investors is not just the level of economic output but the growth rate of output.

Historically, there have been large variations in both GDP growth rates and per capita GDP across countries. Research has identified several factors that influence both the growth of GDP and the level of GDP.

Preconditions for Growth

1. Savings and investment are positively correlated with economic development. For countries to grow, private and public sector investment must provide a sufficient level of capital per worker. If a country has insufficient domestic savings, it must attract foreign investment in order to grow.

2. Financial markets and intermediaries augment economic growth by efficiently allocating resources in several ways. First, financial markets determine which potential users of capital offer the best returns on a risk adjusted basis. Second, financial instruments are created by intermediaries that provide investors with liquidity and opportunities for risk reduction.

Finally, by pooling small amounts of savings from investors, intermediaries can finance projects on larger scales than would otherwise be possible.

Some caution is in order, however. Financial sector intermediation may lead to declining credit standards and/or increases in leverage, increasing risk but not economic growth.

3. The political stability, rule of law, and property rights environment of a country also influence economic growth. Countries that have not developed a system of property rights for both physical and intellectual property will have difficulty attracting capital. Similarly, economic uncertainty caused by wars, corruption, and other disruptions poses unacceptable risk to many investors, reducing potential economic growth.

4. Investment in human capital, the investment in skills and well being of workers, is thought to be complementary to growth in physical capital. Consequently, countries that invest in education and health care systems tend to have higher growth rates. Developed countries benefit the most from post secondary education spending, which has been shown to foster innovation.

Less developed countries benefit the most from spending on primary and secondary education, which enables the workforce to apply the technology developed elsewhere.

5. Tax and regulatory systems need to be favorable for economies to develop. All else equal, the lower the tax and regulatory burdens, the higher the rate of economic growth. Lower levels of regulation foster entrepreneurial activity (startups), which have been shown to be positively related to the overall level of productivity.

6. Free trade and unrestricted capital flows are also positively related to economic growth. Free trade promotes growth by providing competition for domestic firms, thus increasing overall efficiency and reducing costs. Additionally, free trade opens up new markets for domestic producers.

Unrestricted capital flows mitigate the problem of insufficient domestic savings as foreign capital can increase a country’s capital, allowing for greater growth. Foreign capital can be invested directly in assets such as property, physical plant, and equipment (foreign direct investment), or invested indirectly in financial assets such as stocks and bonds.

Equity prices are positively related to earnings growth. Economy wide, aggregate corporate earnings can grow if GDP grows or if the share of corporate earnings in GDP grows. However, the share of corporate profits in the GDP cannot increase indefinitely, because labor will be unwilling to work for a lower and lower proportion of the GDP.

Therefore, the potential GDP of a country, the upper limit of real growth for an economy, is the long run limit of earnings growth, and is an important factor in predicting returns on aggregate equity markets.

The Grinold Kroner (2002) model provides the appropriate framework to understand this:

We can further decompose the capital gains yield into EPS growth and growth in the P/E ratio:

EPS growth can be decomposed into real EPS growth, inflation, and change in the number of shares outstanding via stock buybacks (i.e., the dilution effect).

The full model then is:

Dividend yield tends to be stable over time. The repricing term (change in P/E) does fluctuate with the business cycle: when GDP growth is high, market multiples rise as perception of risk declines. The repricing term, however, cannot continue to grow.

Therefore, in the long run, the key factor driving equity returns is $\Delta {\mathrm{EPS}}_R$ which is itself subject to an upper limit of potential GDP growth.

The dilution effect (ΔS) sometimes plays a role in determining equity returns, but its impact differs by country depending on its level of development and the sophistication of its financial markets. Recognize that on an aggregate basis, the dilution effect is comprised of net stock buybacks (nbb) as well as issuance by privately held small and medium entrepreneurial companies (it would actually be more appropriate to call nbb “net issuance,” where net issuance = new issuance minus buybacks). We call the role of these small and medium entrepreneurial companies the relative dynamism (rd) of the economy.

Relative dynamism captures the difference between the overall economic growth of the country and the earnings growth of listed companies.

As indicated earlier, all else equal, higher GDP growth will be associated with higher equity returns. However, equity returns are significantly affected by dilution (due to share buybacks, mergers, privatizations of public companies, etc.). Economic growth can also be attributed to privately held companies.

Potential GDP also has implications for real interest rates. Positive growth in potential GDP indicates that future income will rise relative to current income. When consumers expect their incomes to rise, they increase current consumption and save less for future consumption (i.e., they are less likely to worry about funding their future consumption).

To encourage consumers to delay consumption (i.e., to encourage savings), investments would have to offer a higher real rate of return. Therefore, higher potential GDP growth implies higher real interest rates and higher real asset returns in general.

In the short term, the relationship between actual GDP and potential GDP may provide insight to both equity and fixed income investors as to the state of the economy. For example, since actual GDP in excess of potential GDP results in rising prices, the gap between the two can be used as a forecast of inflationary pressures, useful to all investors but of particular concern to fixed income investors. Furthermore, central banks are likely to adopt monetary policies consistent with the gap between potential output and actual output.

When actual GDP growth rate is higher (lower) than potential GDP growth rate, concerns about inflation increase (decrease) and the central bank is more likely to follow a restrictive (expansionary) monetary policy.

In addition to predicting monetary policy, the relationship between actual and potential GDP can also be useful in analyzing fiscal policies. It is more likely for a government to run a fiscal deficit when actual GDP growth rate is lower than its potential growth rate.

Finally, because of the credit risk assumed by fixed income investors, growth in GDP may be used to gauge credit risk of both corporate and government debt. A higher potential GDP growth rate reduces expected credit risk and generally increases the credit quality of all debt issues.

Factor Inputs and Economic Growth

Economies are complex systems of many economic inputs. To simplify analysis, we examine a 2 factor (labor and capital) aggregate production function in which output (Y) is a function of labor (L) and capital (K), given a level of technology (T).

To examine the effect of capital investment on economic growth and labor productivity, consider a Cobb Douglas production function, which takes the form:

The Cobb Douglas function essentially states that output (GDP) is a function of labor and capital inputs and their productivity. It exhibits constant returns to scale; increasing both inputs by a fixed percentage leads to the same percentage increase in output.

Dividing both sides by L in the Cobb Douglas production function, we can obtain the output per worker (labor productivity).

Labor productivity is similar to GDP per capita, a standard of living measure. The previous equation has important implications about the effect of capital investment on the standard of living. Assuming the number of workers and α remain constant, increases in output can be gained by increasing capital per worker (capital deepening) or by improving technology (increasing TFP).

However, since α is less than one, additional capital has a diminishing effect on productivity: the lower the value of α, the lower the benefit of capital deepening.

Developed markets typically have a high capital to labor ratio and a lower α compared to developing markets, and therefore developed markets stand to gain less in increased productivity from capital deepening.

In steady state (i.e., equilibrium), the marginal product of capital (MPK = αY/K) and marginal cost of capital (i.e., the rental price of capital, r) are equal; hence:

or

The productivity curves in Figure 6.1 show the effect of increasing capital per worker on output per worker. Capital deepening is a movement along the productivity curve. The curvature of the relationship derives from the diminishing marginal productivity of capital.

Economies will increase investment in capital as long as MPK > r. At the level of K/L for which MPK = r, capital deepening stops and labor productivity becomes stagnant.

However, as technological progress occurs, both capital and labor can produce a higher level of output. An investment in capital leading to technological progress enhances the productivity of existing labor and capital. Technological progress, therefore, can lead to continued increases in output despite diminishing marginal productivity of capital.

Technological progress shifts the productivity curve upward and will lead to increased productivity at all levels of capital per worker.

Figure 6.1: Productivity Curves

As stated earlier, for developed countries, the capital per worker ratio is relatively high (e.g., level $C_1$ in Figure 6.1), so those countries gain little from capital deepening and must rely on technological progress for growth in productivity. In contrast, developing nations often have low capital per worker ratios (e.g., $C_0$ in Figure 6.1), so capital deepening can lead to at least a short term increase in productivity.