CFA Level II Exam · Economic Growth

Measuring Economic Growth and Growth Accounting Explained

Updated 7 October 2026 · Fact-checked

Economic growth is the percentage change in real GDP, or real GDP per capita for living standards. Growth accounting splits output growth into contributions from capital, labor and total factor productivity (TFP). TFP growth is the Solow residual: output growth minus α × capital growth minus (1 − α) × labor growth.

Understand Measuring Economic Growth and Growth Accounting

Growth is measured with real GDP, which removes price changes so only the quantity of output is tracked. Nominal GDP can rise just from inflation, so it is a poor measure of growth. The growth rate of real GDP shows how fast the economy's total output expands. It matters for the size of the economy and for market size.

To judge living standards, use real GDP per capita, which is real GDP divided by population. If real GDP grows 3% and population grows 1%, per capita growth is about 2%. An economy can grow in total yet leave each person no better off if population grows as fast.

Growth accounting asks where growth came from. It starts from a Cobb-Douglas production function: Y = A × K^α × L^(1 − α). Y is output, K is capital, L is labor, and A is total factor productivity (TFP). The exponent α is capital's share of income. Labor's share is 1 − α. Taking growth rates gives the growth accounting equation.

TFP is the part of growth that more capital and more labor cannot explain. It captures technology, better management, institutions and efficiency. Because it is calculated as what is left over, it is called the Solow residual. You cannot observe it directly. You compute it from the other three numbers.

A useful variant is per worker. Dividing by labor gives growth in labor productivity: ΔY/Y − ΔL/L = ΔA/A + α × (ΔK/K − ΔL/L). So productivity growth comes from TFP plus capital deepening, meaning more capital per worker. In a vignette, check whether the question asks about total output, per capita output or output per worker.

Key formulas to remember

Real GDP growth rate: g = (Real GDP this year ÷ Real GDP last year) − 1; Use real, not nominal, GDP. Nominal GDP growth is approximately real growth plus inflation.
Real GDP per capita growth: Per capita growth ≈ real GDP growth − population growth; The subtraction is an approximation. For exact work, divide real GDP by population in each year and compare.
Cobb-Douglas production function: Y = A × K^α × L^(1 − α); Assumes constant returns to scale. α is capital's share of income.
Growth accounting equation: ΔY/Y = ΔA/A + α × ΔK/K + (1 − α) × ΔL/L; Growth rates are in percent. Output growth equals TFP growth plus weighted input growth.
Solow residual (TFP growth): ΔA/A = ΔY/Y − α × ΔK/K − (1 − α) × ΔL/L; Rearranged form. It is the unexplained growth after capital and labor.
Labor productivity growth: Δ(Y/L)/(Y/L) = ΔA/A + α × [ΔK/K − ΔL/L]; Output per worker growth equals TFP growth plus α times growth in capital per worker. This form relies on the Cobb-Douglas constant-returns assumption, meaning the exponents α and 1 − α sum to 1.

How to solve Measuring Economic Growth and Growth Accounting questions

Use this order for any measurement or growth accounting question in an item set.

1Read the question stem to see what is asked: total output growth, per capita growth, output per worker, a factor contribution, or TFP growth.
2Find the data in the vignette or exhibit. List output growth, capital growth, labor growth, population growth and capital share α. Check each is a real growth rate and for the same period.
3Identify α. If the vignette gives labor's share (the exponent on L), compute α = 1 − labor share.
4Choose the equation. For TFP, use the Solow residual. For output growth, use the growth accounting equation. For per worker, use the labor productivity form.
5Calculate each contribution separately: α × capital growth, then (1 − α) × labor growth. Writing them out stops weighting errors.
6Add or subtract as the equation requires, and keep the units in percent.
7Sanity check: contributions should sum with TFP to total growth. Then compare with the answer options and pick the one that matches.

Quickest way: Contribution table shortcut

When to use it: Use it when you are given growth rates for output, capital and labor and must find TFP growth or a factor's contribution in under two minutes.

Write three lines: capital contribution = α × g(K); labor contribution = (1 − α) × g(L); TFP = g(Y) − both.
Compute the two weighted terms mentally using round weights such as 0.3 and 0.7.
Subtract them from output growth to get TFP, or add them to TFP to get output growth.
For per capita questions, subtract population growth from real GDP growth first and treat the result as approximate.
Eliminate options that use the wrong weight, for example one that multiplies labor growth by α.

Common mistakes in Measuring Economic Growth and Growth Accounting

Applying α to labor and 1 − α to capital.
Students forget which input the exponent belongs to and match the order of the terms in the equation by habit.
Fix: Remember that α is always capital's share. The exponent on K is α and the exponent on L is 1 − α. Check the vignette for which share is given.
Treating TFP growth as an observed input.
It looks like a third factor beside capital and labor, so students expect it to be reported.
Fix: TFP is the residual. Compute it as output growth minus the weighted growth of capital and labor unless the question gives it.
Using nominal GDP growth.
Exhibits sometimes show nominal and real figures side by side and a student picks the first.
Fix: Growth measurement and growth accounting use real output. Check the label and deflate if only nominal GDP and inflation are given.
Confusing growth in total GDP with per capita growth.
Both are called growth, and the question may mention living standards in passing.
Fix: If the stem says per capita or per person, subtract population growth. If it says per worker, subtract labor force growth.
Adding the factor contributions without weights.
Students sum capital growth, labor growth and TFP directly.
Fix: Multiply each input growth rate by its share before adding. Output growth is smaller than the raw sum when shares are below one.
Reading a contribution as a growth rate of the input.
Wording such as capital contributed 1.2 points sounds like capital grew 1.2%.
Fix: A contribution is α × g(K). To get capital growth, divide the contribution by α.

Worked examples

Example 1

An analyst studies Country X over one year. Real GDP grew 4.0%, the capital stock grew 5.0% and the labor force grew 1.0%. Capital's share of income is 0.35. Population grew 0.8%. (1) What was the contribution of capital to growth? (2) What was TFP growth? (3) What was approximate real GDP per capita growth?

Show the solution

Capital contribution = α × g(K) = 0.35 × 5.0% = 1.75%.
Labor contribution = (1 − 0.35) × 1.0% = 0.65 × 1.0% = 0.65%.
TFP growth = 4.0% − 1.75% − 0.65% = 1.60%.
Per capita growth ≈ 4.0% − 0.8% = 3.2%.

Answer: (1) 1.75%. (2) 1.60%. (3) About 3.2%.

Example 2

Country Y's TFP grew 1.5% a year. Capital grew 3.0% a year and labor grew 2.0% a year. Labor's share of income is 0.60. (1) What is α? (2) What is output growth? (3) What is growth in output per worker?

Show the solution

α = 1 − labor share = 1 − 0.60 = 0.40.
Output growth = TFP + α × g(K) + (1 − α) × g(L) = 1.5% + 0.40 × 3.0% + 0.60 × 2.0%.
Compute: 1.5% + 1.2% + 1.2% = 3.9%.
Output per worker growth = output growth − labor growth = 3.9% − 2.0% = 1.9%.
Check with the per worker form: 1.5% + 0.40 × (3.0% − 2.0%) = 1.5% + 0.4% = 1.9%.

Answer: (1) α = 0.40. (2) Output growth is 3.9%. (3) Output per worker grew 1.9%.

Exam tips

Look for the share given in the vignette. If it is labor's share, convert to α before you calculate.
When the stem says per capita, per worker or total, circle that word before you touch the numbers.
Use the per worker form to check your answer: TFP plus α times capital deepening should match.
Expect conceptual follow-ups: higher TFP growth reflects technology or efficiency, and growth driven only by capital accumulation faces diminishing returns, so sustained growth requires TFP growth (technology).
There is no penalty for wrong answers, so never leave an item blank.

Measuring Economic Growth and Growth Accounting: frequently asked questions

What is the growth accounting equation?

It is ΔY/Y = ΔA/A + α × ΔK/K + (1 − α) × ΔL/L. Output growth equals TFP growth plus capital growth weighted by capital's share plus labor growth weighted by labor's share.

How do I calculate total factor productivity growth?

Subtract the weighted growth of capital and labor from real output growth. TFP growth = ΔY/Y − α × ΔK/K − (1 − α) × ΔL/L. The answer is the Solow residual.

Why use real GDP per capita instead of real GDP?

Real GDP per capita shows output per person, which is a better indicator of living standards. Total real GDP can rise while per person output stagnates if population grows quickly.

What does TFP capture?

TFP captures everything that raises output beyond more capital and labor. This includes technology, efficiency, organization and institutions. Since it is a residual, it also absorbs measurement error.