Okun's Law Calculator
Enter your economy's unemployment rate, the natural rate of unemployment, and choose a country preset or supply a custom Okun coefficient. The calculator instantly solves for the output gap (GDP gap) and shows you the full working. Switch to reverse mode to find the implied unemployment gap from a known GDP gap. Results update as you type.
Formula
Worked example
US example: actual unemployment 5.5%, natural rate 4.0%, beta = -0.45. Unemployment gap = 5.5 - 4.0 = 1.5 pp. Output gap = 1.5 / (-0.45) = -3.33%, meaning the US economy is running about 3.3% below its potential GDP.
What is Okun's Law?
Okun's Law is an empirically observed negative relationship between the unemployment rate and the output gap (the deviation of actual GDP from potential GDP). Named after economist Arthur Melvin Okun, who first documented it in 1962, the relationship holds that when unemployment rises above its natural rate, real GDP falls below its potential level by a predictable multiple. The ratio between these two gaps is the Okun coefficient (beta), which is negative by construction because the two deviations move in opposite directions: higher unemployment corresponds to lower output relative to potential.
The formula and its two mechanisms
The standard gap version of Okun's Law states: U - U* = beta x (Y - Y*). Here U is the actual unemployment rate, U* is the natural rate (NAIRU), Y is actual GDP and Y* is potential GDP. The coefficient beta captures two labour-market mechanisms. First, labour hoarding: during downturns, firms keep workers on even when production falls, so employment drops less than output. Second, labour-force participation changes: in good times, more people enter the workforce seeking jobs, adding to measured unemployment; the reverse happens in bad times. Together these two effects determine how strongly the unemployment gap responds to a given output gap. The coefficient beta is therefore the product of the labour-hoarding coefficient (alpha) and the labour-force-change coefficient (delta).
Why the Okun coefficient varies by country
The Okun coefficient is not universal. It ranges from about -0.15 in Japan to -0.85 in Spain, reflecting fundamental differences in labour-market institutions. Japan has a tradition of lifetime employment and strong labour hoarding: firms absorb output shocks mainly through cuts to hours and bonuses rather than layoffs, so unemployment barely moves even in a deep recession. Spain, by contrast, historically relied heavily on fixed-term contracts that can be terminated quickly, making unemployment highly sensitive to economic swings. Germany sits closer to Japan because of its Kurzarbeit (short-time working) scheme. The United States sits around -0.45 in most modern estimates, a widely used benchmark. Choosing the right coefficient for your analysis is therefore important: using the US value for a European economy with rigid labour markets can significantly understate the unemployment impact of a recession.
Limitations and caveats
Okun's Law is an empirical regularity, not a structural economic law, and it has exhibited instability over time. The relationship appeared to break down in the US during the 2009-2013 period, when unemployment fell more slowly than the output gap would predict, a phenomenon sometimes called 'jobless recovery'. Possible explanations include labour-force participation drops (discouraged workers leaving the count), shifts in the natural rate itself, and sector-specific disruptions. The Cleveland Fed's research (Daly and Hobijn, 2010) documented this breakdown in detail. Similarly, short-run deviations occur around financial crises, supply shocks, and periods of rapid productivity change. The calculator should be used as an approximate guide to macroeconomic conditions, not as a precise forecast tool. Always cross-check against official estimates from bodies such as the IMF, OECD, or your country's central bank.
Okun's coefficient by country
| Country | Okun coefficient (beta) | Interpretation |
|---|---|---|
| Japan | -0.15 | Very weak (heavy labour hoarding) |
| Germany | -0.26 | Weak (flexible hours contracts) |
| France | -0.32 | Moderate-weak |
| United Kingdom | -0.38 | Moderate |
| Australia | -0.40 | Moderate |
| United States | -0.45 | Moderate (OECD reference) |
| Canada | -0.48 | Moderate-strong |
| Spain | -0.85 | Strong (rigid labour market) |
Empirical estimates from Ball, Leigh & Loungani (2012) and OECD research. A larger absolute value means unemployment is more sensitive to changes in GDP.
Frequently asked questions
What is the Okun coefficient for the United States?
The most widely cited modern estimate for the US is -0.45, based on Ball, Leigh, and Loungani (2012). Older estimates by Okun himself suggested a ratio closer to -0.5. The sign is always negative: a 1 percentage-point rise in the unemployment gap corresponds to roughly a 2.2% fall in GDP relative to potential (1/0.45).
Why is the Okun coefficient negative?
Because unemployment and output move in opposite directions relative to their equilibrium levels. When the economy grows faster than its potential rate, firms hire more workers and unemployment falls below its natural rate (a negative unemployment gap), while output rises above potential (a positive output gap). The coefficient is negative by construction to capture this inverse relationship.
What is the natural rate of unemployment (NAIRU)?
The natural rate of unemployment, also called the NAIRU (Non-Accelerating Inflation Rate of Unemployment), is the level of unemployment consistent with stable inflation when the economy is at its potential output. It includes frictional unemployment (people between jobs) and structural unemployment (skills mismatches), but not cyclical unemployment. For the US, the Congressional Budget Office estimates NAIRU at roughly 4 to 4.5% in recent years.
What does a negative output gap mean?
A negative output gap (Y - Y* < 0) means actual GDP is below potential GDP. The economy has spare capacity: unemployed workers, idle factories, and underused resources. This is the typical condition during or after a recession. A negative gap usually means inflation is subdued and there is room for expansionary policy (lower interest rates or fiscal stimulus) without immediately overheating the economy.
Can I use this calculator for any country?
Yes. Select the country preset that matches your economy, or choose 'Custom coefficient' and enter your own value. The presets are based on empirical estimates from Ball, Leigh & Loungani (2012) and OECD research. If your country is not listed, the academic literature for your region is the best source for a local coefficient estimate. Remember that the coefficient can shift over time as labour-market institutions change.
What is the difference between the gap and the difference version of Okun's Law?
The gap version (used here) compares levels: actual unemployment versus its natural rate, and actual GDP versus potential GDP. The difference version (original Okun formulation) relates changes: how much does unemployment change when GDP growth deviates from trend growth? Both versions capture the same underlying relationship but with different inputs. The gap version is more commonly used in modern macroeconomic analysis because potential GDP and the NAIRU are now routinely estimated by central banks and international organisations.