Okun's Law Calculator

Created by Tibor Pal, PhD candidate
Reviewed by Dominik Czernia, PhD and Jack Bowater
Based on research by
Krugman, P.; Wells R. Economics, Fifth Edition (2017)
Last updated: Oct 13, 2022

The Okun's law calculator helps you to study the relationship between the output gap and unemployment, framed by Okun's law.

Continue reading where we explain the fundamental causalities behind the relationships in Okun's law formula and what Okun's law actually is. You can also learn how can GDP gap be calculated using Okun's law.

If you are not familiar with the concept of GDP, you may check our GDP calculator before delving into Okun's law.

What is Okun's law?

Okun's law implies a stable negative relationship between the change in the unemployment rate from its long-run level (or its natural rate) and the deviation of output growth from its trend (or potential output growth).

This statistical relationship was first observed in the 1960's by economist Arthur Okun which we now call Okun's law.

For example, when output is below its long-run trend by 2 percent (or in other words, the output gap is 2 percent), the unemployment rate tends to be above its natural level by one percentage point.

But what is behind this relationship? To explain this, we need to get some insight into the forces of the labor market and its structure.

When the real GDP rises, workers who have been employed but have not been working full time may be fully utilized, resulting in higher GDP growth without a change in employment. We call the phenomenon labor hoarding. Moreover, some part of the rise in employment may not reduce the unemployment rate since part of the new labor force may come from the economically inactive population due to favorable economic conditions.

The combination of labor hoarding and changes in the labor force means that changes in the GDP growth don't lead to one-to-one changes in the employment rate. The Okun coefficient, which is part of our online Okun's law calculator, reflects this disparity.

Therefore, a large negative GDP gap implies that the unemployment rate is considerably above its natural or long-run level, resulting in a cyclical unemployment.

What is the Okun's law formula in macroeconomics?

As we familiarize ourselves with the Okun's law definition, we can translate it into a mathematical form, namely the Okun's law formula in macroeconomics.

Based on the relations we introduced above, an upward shift in the aggregate demand (for example, people start to consume more or investment grows) causes GDP output to rise above its potential or long-run growth rate.

The Okun's law cartoon showing an employer asking a potential employee to spend money first..

As a result, when firms utilize all their labor capacities, they start to hire workers, and employment starts to increase. The below equations, which we used in the Okun's law calculator, represent this causality:

EtEt=α(YtYt)E_t - E^*_t = \alpha(Y_t - Y^*_t)
Y~t=YtYt\tilde{Y}_t=Y_t - Y^*_t

where:

  • EtE_t - Actual employment at time tt;
  • EtE^*_t - Long-run, or trend level, of employment;
  • Y~t\tilde{Y}_t - GDP gap (or Okun gap);
  • YtY_t - Actual GDP;
  • YtY^*_t - Trend growth rate; and
  • α\alpha - A coefficient, above zero (α>0)(\alpha > 0), that represent additional utilization of firms (labor hoarding).

Higher employment, in turn, reduces the unemployment rate leading to the following equation:

UtUt=δ(EtEt)U_t - U^*_t = \delta (E_t - E^*_t)

where:

  • UU - Actual unemployment rate;
  • UU^* - Natural rate of unemployment; and
  • δ\delta - A coefficient, below zero (δ<0)(\delta < 0), representing changes in the labor force.

If we substitute in the two above equations, we can derive the final form of Okun’s law formula:

UtUt=β(YtYt)U_t - U^*_t = \beta (Y_t - Y^*_t)
β=α×δ\beta = \alpha \times \delta

where:

  • β\beta - The Okun coefficient, representing fractions on the labor market (labor hoarding and changes in the labor force). In other words, the Okun coefficient represents the degree of responsiveness of the unemployment rate to output variation.

We use the above equations in our Okun's law calculator to show how to calculate GDP gap using Okun's law.

How do I calculate GDP gap using Okun's law definition?

After rearranging the basic Okun's law formula and using an appropriate Okun coefficient, we can estimate the GDP gap associated with the deviation of the unemployment rate from its long-run trend:

Y~t=UtUtβ\tilde{Y}_t = \frac{U_t - U^*_t}{\beta}

FAQ

What is the Okun coefficient in the US?

Empirical analysis conducted by Ball, Leigh, and Loungani (2012) suggests an Okun's coefficient of -0.45 for the United States. Okun's coefficient varies significantly between different countries, however.

For example, it is -0.85 for Spain and -0.15 for Japan. The considerable variation of the Okun coefficient across countries implies different degrees of responsiveness of the unemployment rate to output variation.

How do I calculate Okun's law coefficient?

After rearranging the basic Okun's law formula, you can estimate the Okun's law coefficient (β) by measuring the degree of responsiveness of the unemployment rate (U - U*) to the deviation of output from its potential level (Y - Y*):

β = (U - U*) / (Y - Y*).

Can the Okun coefficient be zero?

In practice, no. An Okun coefficient of zero would mean that there is no fraction on the labor market; that is, a deviation from the GDP growth rate and the trend growth rate of output induces a change in unemployment at a rate of one to one.

The Okun coefficient typically takes a value between -0.15 and -0.85.

How do I compute output gap by Okun's law?

To calculate the output gap using Okun's law:

  1. Find the unemployment rate.
  2. Estimate the natural rate of unemployment.
  3. Determine the Okun coefficient. For the USA, it is -0.45.
  4. When you have all the above parameters, subtract the unemployment rate from the natural rate of unemployment and divide the result by the Okun coefficient. You will receive the estimated output gap.
Tibor Pal, PhD candidate
Labor market
Unemployment rate (U)
%
Natural rate of unemployment (U*)
%
Okun coefficient (β)
Output
Actual GDP growth rate (Y)
%
Trend growth rate of GDP (Y*)
%
Output gap (Okun gap, Ỹ)
%
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