Question

Worksheet: Using the Growth Equation

The growth of a nation can be decomposed into the various components that caused it using a simple formula:

g_Y = g_A + αg_K  +(1-α)g_L

where g = growth rate of a variable, measured in %∆;   Y = GDP; A = technology;   α = the share of GDP distributed to owners of capital, K, and   1 – α = share of GDP distributed to laborers, L.

The growth equation allows us to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy. The residual which is also called the Solow residual (after Robert Solow, the Nobel Laureate who developed the theory) is the portion of an economy's output growth that cannot be attributed to the accumulation of capital and labor, the factors of production. It is a measure of productivity growth that is usually referred to as total factor productivity (TFP).

Read the information above and answer the following questions.

1. Growth accounting is seen a useful way to estimate the contribution of inputs to growth. Which of the  following input is generally hard to measure directly and consequently can be reasonably estimated with the growth accounting equation is:

a. Land

b. Labor

c. Capital

d. Entrepreneurship

e. Technology

2. If a country’s labor and capital grow at the same rate, is this likely to have the same impact on the growth rate of output?

a. No. Growth in capital always has a bigger impact than growth in labor.

b. No. Growth in labor always has a bigger impact than growth in capital.

c. Yes. If labor and capital are growing at the same rate, the impact on the growth rate of output is the same.

d. It depends on whether the capital share of output is larger than the labor share of output

3. If a country experiences growth in "total factor productivity" (i.e., the "Solow residual"), then

a. all growth in real GDP can be explained by new innovations

b. there is some growth in real GDP that cannot be accounted for by growth in capital or the labor force

c. all growth in real GDP can be explained by growth in the capital stock.

d. all growth in real GDP can be explained by growth in the labor force

4. Suppose labor's share of output is 70% and capital's share of output is 30%. The country finds that its output grew at a rate of 3.4% during the past year, its labor force grew by 2%, and its capital grew by 3%. In this case, labor contributed ____ percent to the growth of output, capital contributed___ percent to the growth of output, and the implied rate of growth in technology was ___ percent.

Answer 1

1. Which of the following input is generally hard to measure directly...?

Correct answer: e. Technology

The term technology enters the Solow equation as a residual, since it can't be directly measured.

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2. If a country’s labor and capital grow at the same rate, is this likely to have the same impact on the growth rate of output?

Correct answer: d. It depends on whether the capital share of output is larger than the labor share of output

The impact of a variable on output depends on the growth rate and the share, both. Even if growth rates are the same, the shares of both have to be estimated.

For example, if a country has capital intensive techniques and has a large share of capital, the main contributor to GDP will be capital.

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3. If a country experiences growth in "total factor productivity" (i.e., the "Solow residual"), then

Correct answer: b. there is some growth in real GDP that cannot be accounted for by growth in capital or the labor force

If the Solow residual rises, there is some part of the real GDP growth which is not being explained by capital or labor. It can't be claimed that all of the growth is unexplained, as capital and labor are the basic essential inputs required. TFP acts as a catalyst in the process.

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4. Given that:

g_Y = g_A + αg_K  +(1-α)g_L

α = 0.3, and   1 – α = 0.7

g_Y = 3.4%

g_K = 3%

g_L = 2%

Thus, contribution of labor = (0.02) X (0.7) = 0.014 = 1.4%

Contribution of capital = (0.03) x (0.3) = 0.009 = 0.9%

Growth rate of technology = 3.4 - 1.4 - 0.9 = 1.1%

Correct answer: Out of the total output growth of 3.4%, contribution of labor was 1.4%, contribution of capital was 0.9% and technology grew by 1.1%