Growth Accounting: Overview and Calculations

What Is Growth Accounting?

Growth accounting is a quantitative tool used to break down how specific factors contribute to economic growth. Growth accounting focuses on three primary factors: the labor market, capital, and technology.

Understanding Growth Accounting

The concept of growth accounting was introduced by Robert M. Solow in 1957. Solow was an American economist and a Professor Emeritus at the Massachusetts Institute of Technology. His concept has also been referred to as the Solow residual. Solow provided economists with a tool for quantitatively breaking down gross domestic product (GDP), the primary economic growth statistic. With the growth accounting model, Solow brought technological advancement onto the stage as a GDP contributor.

The growth accounting equation is a weighted average of the growth rates of the factors involved. Solow’s economic growth accounting model looks at three factors: labor market growth, capital investment, and technology. Capital investment is often the key component obtained from statistical data releases. Solow also introduced technological progress as a third factor to explain the residual gap.

The Growth Accounting Equation

To calculate the growth accounting equation, economists must obtain the following key data points:

• GDP: annual growth and annual GDP. Annual GDP is reported by the Bureau of Economic Analysis (BEA) in the U.S.
• Labor: annual growth and annual contribution
• Capital: annual growth and annual contribution

The growth accounting equation is as follows:

$\begin{aligned}\textit{GDP Growth}&=\textit{Capital Growth}\\&\quad\times(\textit{Weight of Capital Contribution})\\&\quad+\textit{Labor Growth}\\&\quad\times(\textit{Weight of Labor Contribution})\\&\quad+\textit{Technological Progress}\end{aligned}$GDP Growth​=Capital Growth×(Weight of Capital Contribution)+Labor Growth×(Weight of Labor Contribution)+Technological Progress​

Labor growth accounts for the remainder of inputs after capital or vice versa depending on the data used. Technological progress is the residual growth. Without technological progress, the equation wouldn’t balance. With technological progress, the equation shows how technology is influencing production.

Growth Accounting Example

While the growth accounting equation can seem somewhat simple, identifying the data factors and calculating it can be tedious. The Conference Board (CB) can help as it provides an annual breakdown of economic growth accounting by region.

Below is a look at the growth accounting factors along with one-year data results for a pretend nation, Investopedialand.

• GDP: Investopedialand's annual GDP was $20.5 trillion while the GDP growth rate was 2.90%.
• Capital: Adding capital to the economy should, among other things, increase productivity. Capital investment is of key importance to the growth accounting equation. Capital investment was $3.65 trillion for a capital contribution of 17.82%. Capital investment grew from $3.25 trillion at a growth rate of 13%.
• Labor: Labor looks at the number of people employed to identify a growth rate. Typically, more workers will generate more economic goods and services. In Investopedialand, the labor market for full-time workers grew from 125.97 million to 128.57 million or 2.06%. Its weight is identified by subtracting the capital weight, considering that capital and labor are the only two factors. Thus, labor would have had a weight of 82.18%.
• Technology: In the growth accounting equation, technology is a third residual factor. Cutting-edge technology can bring many benefits, including facilitating greater output with the same stock of capital goods.

Using the above example, Solow’s growth accounting model can be calculated as:

$\begin{aligned}2.9\%=13\%(17.82\%)+2.06\%\times(82.18\%)+\text{Technological Progress}\end{aligned}$2.9%=13%(17.82%)+2.06%×(82.18%)+Technological Progress​

The technology factor turns out to be -1.11% in 2018.

The CB uses a two-year average with some slightly different data pulls. 

Real-World Growth Accounting In Practice

Growth accounting is generally used by economists as one way to break down the percentage of a country’s economic growth coming from key factors. Solow’s economic growth accounting model looks at three key factors which provide a simplified view.

The Bureau of Labor Statistics uses growth accounting to analyze movements in broader sectors. In 2022, growth accounting analysis revealed that the private business sector's output growth was influenced by the contributions of labor input, capital input, and total factor productivity (TFP) growth. Despite positive contributions from labor input and capital input, a substantial decline in TFP resulted in minimal overall output growth for the private business sector.

Note that this type of growth accounting analysis can be narrowed down and is perhaps more useful when looking at specific industries. For example, that same growth accounting exercise from the BLS noted that TFP contributions for private business output growth were negative for finance, insurance, and real estate from 1990 to 2007 but had since turned positive. Strangely enough, the opposite trend (positive from 1990 to 2007, negative since) is present in the manufacturing sector. Therefore, growth accounting can drill into more niche applications to drive more thoughtful economic policy.

Growth Accounting and Analytical Tools

In the realm of growth accounting, understanding the intricate relationships between different economic factors may demand analytical tools. Here are several that can be used to better explain the complexities of why something is growing.

• Regression Analysis: Regression analysis is used to model the relationship between a dependent variable (such as economic output) and one or more independent variables (such as capital stock, labor input, and total factor productivity). Economists employ regression analysis to estimate the impact of different factors on economic growth by discerning the relative importance of each factor. Regression analysis can also be used to spot places where policy intervention may be needed.
• Quantitative Tools: Growth accountants may also use various quantitative tools to conduct empirical studies. These tools include time-series analysis, panel data analysis, and econometric models. Examining data over time allows economists to identify trends, patterns, and cyclical movements. This can give some insight about the evolution of economic variables and how factors may have changed over time.
• Causality and Counterfactual Analysis: Establishing causal relationships is crucial in growth accounting. Econometric methods can help researchers identify the direction of causality between different economic variables. Counterfactual analysis can be used to estimate what would have happened if a specific policy didn't exist or some external shock was to have theoretically happened.

Limitations and Criticisms of Growth Accounting

Growth accounting is not without its challenges and criticisms. Let's explore the common hurdles faced by growth accountants and their analytical approach.

• Endogeneity Concerns: Endogeneity happens when the relationship between variables is bidirectional. This can lead to potential biases in estimating the causal impact of factors on economic growth. Researchers can employ advanced econometric techniques, such as instrumental variables, to address endogeneity and enhance the reliability of their findings.
• Data Limitations: Growth accounting heavily relies on data quality and availability. Incomplete or inaccurate data can prevent accurate assessments.
• Ignores Non-Market Activities: Growth accounting tends to focus on market-based activities. This potentially neglects the contributions of non-market activities, informal sectors, or unaccounted factors. Critics may push for a more comprehensive, broader approach that loops in more activity.
• Technology and Measurement Challenges: Measuring technological progress poses inherent challenges. It can be tough to judge and measure advancement due to rapid change and evolving innovation.
• Dynamic Nature of Labor and Capital: Labor and capital are not static over time either. Their quality and characteristics evolve and may be tough to evaluate, as principles that may have guided labor and capital may no longer be relevant. Researchers could consider incorporating more dynamic models to capture more variability.
  

The Bottom Line

Growth accounting is an analytical framework in economics that quantifies the contributions of different factors, such as capital, labor, and total factor productivity, to the overall economic growth of a country or region. By dissecting and attributing the sources of growth, it provides insights into the drivers behind changes in economic output over time.