Macroeconomics & Business Cycle Forecasting
Okun’s Law Output Gap & Unemployment Change Formula
Calculate the Okun’s Law percentage GDP output gap -beta * (u - u*), lost dollar GDP, and growth-rate unemployment change Delta_u = -(1/beta) * (g_Y - g_Y*).
Translate cyclical unemployment points into lost real GDP and speed-limit growth
Arthur Okun (1962) documented one of macroeconomics’ most reliable empirical regularities: each +1.0 percentage-point rise in cyclical unemployment (u - u*) above the natural rate u* is associated with roughly a -2.0% shortfall of actual real GDP Y below potential GDP Y*: (Y - Y*) / Y* = -beta_Okun * (u - u*)! Why is beta_Okun (~2.0) greater than 1? Because recessions simultaneously depress hours per worker, labor-force participation (discouraged workers), and on-the-job productivity (labor hoarding). In growth-rate ("difference") form, reducing unemployment requires real GDP growth g_Y to exceed potential growth g_Y*: Delta_u = -(1 / beta_Okun) * (g_Y - g_Y*).
Verify on potential GDP Y* = 25,000 (B2), NAIRU u* = 0.045 (B3, 4.5%), actual unemployment u = 0.065 (B4, 6.5% -> +2.0 pp cyclical slack), Okun coefficient beta_Okun = 2.0 (B5), potential growth g_Y* = 0.020 (B6, 2.0%/yr), and next-year forecast GDP growth g_Y = 0.035 (B7, 3.5%/yr): output gap is -2.0 * 0.02 = -0.0400 (-4.00%), implied real GDP is 25,000 * 0.96 = 24,000.00 (1,000B output loss!), and 3.5% GDP growth trims unemployment by -(1 / 2.0) * (0.035 - 0.020) = -0.0075 (-75 bps to 5.75%)!
| Okun’s Law Metric (Y*=25k, u*=4.5%, u=6.5%, beta=2.0) | Formula | Verified Output |
|---|---|---|
| Cyclical Unemployment Gap | u - u* | +0.0200 (+2.00 pp) |
| Percentage GDP Output Gap | -beta_Okun * (u - u*) | -0.0400 (-4.00%) |
| Implied Actual Real GDP (Y) | Y* * (1 - beta_Okun * (u - u*)) | 24,000.00 |
| Forecast Unemployment Change | -(1 / beta_Okun) * (g_Y - g_Y*) | -0.0075 (-0.75 pp at g_Y=3.5%) |
Okun’s Law Percentage Output Gap -beta_Okun * (u - u*) Formula
Validate Y* > 0, unemployment rates in (0, 1), and Okun multiplier beta_Okun > 0.
=LET(y_pot, B2, u_nat, B3, u_act, B4, bt_ok, B5, IF(OR(y_pot <= 0, u_nat <= 0, u_nat >= 1, u_act <= 0, u_act >= 1, bt_ok <= 0), "Invalid Okun Input", ROUND(-bt_ok * (u_act - u_nat), 4)))Difference-Version Forecast Unemployment Rate Change Delta_u Formula
When actual GDP grows exactly at potential speed g_Y = g_Y*, unemployment stays flat (Delta_u = 0) because productivity plus labor-force growth absorbs all new output.
=LET(bt_ok, B5, gy_pt, B6, gy_ac, B7, IF(bt_ok <= 0, "Invalid Okun Input", ROUND(-(1 / bt_ok) * (gy_ac - gy_pt), 4)))Try the example
Use the original values or change them to test your understanding.