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# Okun's Law

If I were to ask you to go back and pull from the core of your memory the beginning of the economic cycle, would you be able to remember what it is? If you said investment, you'd be correct. Every economic cycle begins with investment. When individuals invest in a firm, it stimulates the entire sector. Investing leads to a rise in output levels, which necessitates a larger workforce, resulting in a boost in the rate of employment. As a result, lowering the rate of unemployment boosts the GDP of a nation. This rationale underpins Okun's law. To learn more about what Okun's law is, the formula(s), examples, and more keep reading on!

## Okun's Law Explanation

Arthur Okun was an economist in the mid-20th century, and he found what seemed to be a link between joblessness and the GDP of a nation. Okun's law is merely an analysis of the link between unemployment and rates of economic growth. It is designed to inform the people how much of a nation's gross domestic product (GDP) might well be compromised when the rate of unemployment is over its natural rate. More precisely, the law specifies that the GDP of a nation must increase by 1% above potential GDP in order to obtain a 1/2% drop in the rate of unemployment.

Economists can also utilize this law to estimate how much GDP would be lost when unemployment rates go up!

Okun's law is the link between GDP and unemployment, where if GDP increases by 1% above potential GDP, the unemployment rate drops by 1/2%.

Okun's Law has a straightforward rationale. Because the output is determined by the quantity of labor utilized in the manufacturing process, a negative link exists between unemployment and production. Total employment is equal to the labor force minus the number of unemployed, implying an inverse connection between production and joblessness. As a result, Okun's Law may be quantified as a negative link between changes in productivity and changes in unemployment.

A fun fact: the Okun coefficient (slope of the line comparing the output gap to the unemployment rate) can never be zero!

If it's zero, it indicates that divergence from potential GDP would cause no change in the unemployment rate. In reality, however, there is always a change in the unemployment rate when there is a change in the GDP gap.

### Okun's Law: The Difference Version

Okun's initial connection recorded how quarterly fluctuations in the rate of unemployment shifted with quarterly development in real production. It turned into:

$$\hbox{Change in Unemployment Rate} = b \times \hbox{Real Output Growth}$$

This is known as the difference version of Okun's law. It captures the connection between production growth and variations in unemployment—that is, how output growth fluctuates concurrently with variations in the rate of unemployment. The parameter b is also known as Okun's coefficient. It would be expected to be negative, implying that output growth is related to a dropping rate of unemployment while sluggish or negative production is linked to a rising rate of unemployment.

### Okun's Law: The Gap Version

Although Okun's initial connection was based on easily attainable macroeconomic data, his second connection linked the degree of unemployment to the difference between possible and real output. Okun aimed to determine how much the economy would produce under full employment in terms of potential production. He viewed full employment as a level of unemployment low enough for the economy to produce as much as possible without causing excessive inflationary pressure.

He argued that a significant rate of unemployment would often be linked to inactive resources. If that were the truth, one might anticipate that the real rate of output would be lower than its potential. The opposite scenario would be linked with an extremely low unemployment rate. As a result, Okun's gap version adopted the following form:

$$\hbox{Unemployment Rate} = c + d \times \hbox{Output Gap Percentage}$$

The variable c represents the rate of unemployment linked to full employment (the natural rate of unemployment). To comply with the aforementioned notion, the coefficient d must be negative. Both potential production and full employment have the disadvantage of not being readily observable statistics. This results in a great deal of interpretation.

For example, at the point in time that Okun was publishing, he believed that full employment happened when joblessness was at 4%. He was able to develop a trend for potential output based on this supposition. However, modifying the supposition of what rate of unemployment constitutes full employment results in a different estimate of potential production.

## Okun's Law Formula

The following formula shows Okun's Law:

$$u = c + d \times \frac{(y - y^p)} {y^p}$$

$$\hbox{Where:}$$$$y = \hbox{GDP}$$$$y^p = \hbox{Potential GDP}$$$$c = \hbox{Natural Rate of Unemployment}$$

$$d = \hbox{Okun's Coefficient}$$$$u = \hbox{Unemployment Rate}$$$$y - y^p = \hbox{Output Gap}$$$$\frac{(y - y^p)} {y^p} = \hbox{Output Gap Percentage}$$

Essentially, Okun's Law predicts the unemployment rate to be the natural rate of unemployment plus Okun's coefficient (which is negative) multiplied by the output gap. This shows the negative relationship between the unemployment rate and the output gap.

Traditionally, the Okun coefficient would always be set at -0.5, but that's not always the case in today's world. More often than not, the Okun coefficient changes depending on the economic situation of the nation.

## Okun's Law Example

To gain a better understanding of how this works, let's go through an example of Okun's Law.

Imagine you're given the following data and asked to calculate Okun's coefficient.

 Category Percent GDP Growth (actual) 4% GDP Growth (potential) 2% Current Unemployment Rate 1% Natural Unemployment Rate 2%
Table 1. GDP and Unemployment RateStep 1: Calculate the output gap. The output gap is calculated by subtracting the potential GDP growth from the actual GDP growth.

$$\hbox{Output Gap = Actual GDP Growth - Potential GDP Growth}$$

$$\hbox{Output Gap} = 4\% - 2\% = 2\%$$

Step 2: Use Okun's formula and input the correct numbers.

Okun's Law formula is:

$$u = c + d \times \frac{(y - y^p)} {y^p}$$

$$\hbox{Where:}$$$$y = \hbox{GDP}$$$$y^p = \hbox{Potential GDP}$$$$c = \hbox{Natural Rate of Unemployment}$$

$$d = \hbox{Okun's Coefficient}$$$$u = \hbox{Unemployment Rate}$$$$y - y^p = \hbox{Output Gap}$$$$\frac{(y - y^p)} {y^p} = \hbox{Output Gap Percentage}$$

By rearranging the formula and putting in the right numbers, we have:

$$d = \frac{(u - c)} {\frac{(y - y^p)} {y^p}}$$

$$d = \frac{(1\% - 2\%)} {(4\% - 2\%)} = \frac{-1\%} {2\%} = -0.5$$

Thus, Okun's coefficient is -0.5.

## Okun's Law Diagram

The diagram below (Figure 1) shows the general illustration of Okun's law using fictitious data. How so? Well because it demonstrates that changes in unemployment are accurately followed and predicted by the rate of GDP growth!

Figure 1. Okun's Law, StudySmarter

As shown in Figure 1, as the rate of unemployment increases, the rate of real GDP growth slows down. As the main parts of the graph follow a steady drop instead of a sharp decline, the general consensus would be that the Okun's Law parameter would be fairly stable.

## Limitations of Okun's Law

Although economists support Okun's Law, it has its limitations and it isn't universally accepted as being completely accurate. Aside from unemployment, several other variables influence a country's GDP. Economists believe there's an inverse link between unemployment rates and GDP, although the amount to which they are influenced differs. Much research on the link between unemployment and output takes into account a broader range of factors like the size of the labor market, the number of hours worked by employed people, employee productivity statistics, and so on. Since there are many factors that can contribute to changes in the rate of employment, productivity, and output, this makes precise projections solely based on Okun's law challenging.

## Okun's Law - Key takeaways

• Okun's law is the link between GDP and unemployment, where if GDP increases by 1% above potential GDP, the unemployment rate drops by 1/2%.
• Okun's Law is seen as a negative link between changes in production and changes in employment.
• Okun's coefficient can never be zero.
• Actual GDP - Potential GDP = Output Gap
• Although economists support Okuns' law, it isn't universally accepted as being completely accurate.

It explains the link between unemployment and rates of economic growth.

The formula for Okun's Law is:

u = c + d*((y - yp )/ yp)

Where:

y = GDP

yp = potential GDP

c = natural rate of unemployment

d = Okun coefficient

u = unemployment rate

y - yp = output gap

(y - yp) / yp = output gap percentage

Rearranging the equation we can solve for the output gap percentage:

((y - yp )/ yp) = (u - c) / d

Okun's law is a negative link between changes in production and changes in unemployment.

You derive Okun's Law using the following formula:

u = c + d*((y - yp )/ yp)

Where:

y = GDP

yp = potential GDP

c = natural rate of unemployment

d = Okun coefficient

u = unemployment rate

y - yp = output gap

(y - yp) / yp = output gap percentage

Okun's Law is a rule of thumb used to observe the correlation between production and levels of unemployment.

## Final Okun's Law Quiz

Question

What's Okun's Law?

It's an analysis of the link between unemployment and rates of economic growth.

Show question

Question

What's the quantitative relationship between GDP and unemployment?

The GDP of a nation must increase by 1% in order to obtain a 1/2% drop in the rate of unemployment.

Show question

Question

Economists can also utilize Okun's Law to estimate how much GDP would be lost when unemployment rates go up.

True

Show question

Question

Can the Okun coefficient ever be zero?

No. If it's zero, it indicates that an output gap has no effect on the unemployment rate, but in reality an output gap always has an effect on the unemployment rate

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Question

Is Okun's Law seen as positive or negative?

Negative

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Question

The difference version of Okun's Law captures what?

The connection between production growth and variations in unemployment

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Question

Okun aimed to determine how much the economy would produce under full employment in terms of potential production.

True

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Question

Okun viewed full employment as a level of unemployment low enough to produce to the greatest extent without causing excessive _______ _______.

inflationary pressure

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Question

Okun argued that a significant rate of unemployment would often be linked to inactive resources.

True

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Question

Traditionally, Okun's coefficient would always be set at what?

-0.5

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Question

How does one calculate the output gap?

By subtracting potential GDP from actual GDP

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Question

Although economists support Okuns' law, it isn't universally accepted as being completely accurate.

True

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Question

What makes accurate projections based on Okun's Law complicated?

The many factors that can contribute to changes in the rate of employment or productivity.

Show question

Question

What is Okun's Law used for?

It's used to observe the correlation between productivity and levels of unemployment.

Show question

Question

Is Okun's Law always right?

While it's accurate more often than not, there have been moments where it has been completely inaccurate, and so it best serves as a "rule of thumb".

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