# One-Third Rule

## What is the third rule?

The third rule estimates the variation in labor productivity as a function of the variations in capital devoted to labor. The rule is used to determine the impact that changes in technology or capital have on production.

Labor productivity is an economic term that describes the cost of a worker’s hourly production based on the amount of gross domestic product (GDP) spent to produce that hour of work. In particular, the rule states that for a 1% increase in capital expenditure on labor, an increase in productivity of 0.33% will occur. The third rule also assumes that all other variables remain static. Thus, no change in technology or in human capital occurs. Human capital is the knowledge and experience of a worker.

Labor productivity can be difficult to quantify precisely. If it is simple enough to link the number of goods produced by factory work in one hour of work, for example, it is more difficult to put a value on the service. How much is an hour waitress worth? What about an accounting hour? What about a nurse? Statisticians can estimate the monetary value of work in these occupations, but without tangible goods to assess, an exact assessment is impossible.

## Calculation with the rule of the third

Using the third rule, an economy or a business can estimate the amount of technology or labor that contributes to overall productivity. For example, suppose your business experiences a 6% increase in capital for one hour of work during a given period. In other words, it costs you more to get your employees to work. At the same time, the company’s physical capital stock also increased by 6%.

You can use the equation% increase in productivity = 1/3 (% increase in physical capital / hours of work) +% increase in technology to infer that 4% in increase in productivity is due to advances in technology.

### Key points to remember

• The third rule is an empirical rule which estimates the change in labor productivity as a function of changes in capital per hour of work.
• The more a worker can produce goods and services in one hour of work, the higher the standard of living in this economy.
• It can be difficult to get more human capital, especially in countries where the labor force participation rate or the percentage of the workforce is lower.

## The basics of the third rule

An increase in a country’s labor productivity will in turn lead to growth in real GDP per person. Since productivity indicates the number of goods an average worker can produce in one hour of work, it can give clues to a country’s standard of living.

For example, during the industrial revolution in Europe and the United States, rapid industrial technological advances allowed workers to make big gains in hourly productivity. This increase in production has raised the standard of living in Europe and the United States. In general, this happens because when workers can produce more goods and services, their wages also increase.

## Example from the real world

For example, according to “Trading Economics.com”, only 37% of the population of Japan participates in the labor force, while in the United States the participation rate is around 63%.

When a country lacks human capital, it must either focus on increasing human capital through immigration and offer incentives to raise birth rates, or it must focus on increasing capital investment or the development of new technological advances.