Monetary Policy & Macroeconomics
Disinflation Sacrifice Ratio & Okun Misery Index Formula
Calculate Laurence Ball’s (1994) Disinflation Sacrifice Ratio SR = Cum_Output_Loss / (pi_peak - pi_trough), Unemployment Point-Years per 1-pp disinflation, and Arthur Okun’s Misery Index.
Quantify the real GDP and jobless cost of breaking entrenched inflation!
When a central bank tightens monetary policy to bring trend inflation down from Peak_Trend_Inflation pi_0 to Trough_Trend_Inflation pi_T (Disinflation Magnitude Delta_pi = pi_0 - pi_T > 0 percentage points), sticky wages and adaptive expectations open a multi-year output gap! Laurence Ball (1994) defined the Disinflation Sacrifice Ratio as SR = Cumulative_Percent_Output_Loss / (pi_0 - pi_T) — measuring percentage-point-years of lost real GDP per 1 percentage point of permanent disinflation! Dividing SR by Okun’s Law Coefficient beta_okun converts GDP loss into Point-Years of Excess Cyclical Unemployment per 1-pp disinflation!
Verify on Peak_Inflation pi_0 = 9.0 (9.0%, B2), Post_Disinflation_Trough pi_T = 3.0 (3.0%, B3 -> Delta_pi = 6.0 pp), Cumulative_GDP_Gap_Loss = 10.5 pp-years (B4), Okun_Law_Coefficient beta_okun = 2.0 (B5), and Current_Unemployment_Rate u_T = 6.8% (B6): Ball Sacrifice Ratio is 10.5 / (9.0 - 3.0) = 1.7500% of annual GDP per 1-pp inflation drop; Excess Unemployment Cost is 1.7500 / 2.0 = 0.8750 point-years of unemployment per 1-pp disinflation; and Post-Disinflation Okun Misery Index (u_T + pi_T) drops to 6.8 + 3.0 = 9.80 (down from peak misery when pi_0 = 9.0%)! Under a high-credibility rapid disinflation where Cumulative_GDP_Gap_Loss shrinks to 4.5 pp-years, SR falls to 0.7500 ("Credible Low-Cost Disinflation")!
| Disinflation Cost Metric (pi_0=9%, pi_T=3%, Loss=10.5, beta=2.0, u=6.8%) | Formula | Verified Output |
|---|---|---|
| Disinflation Magnitude (Delta_pi, pp) | pi_0 - pi_T | 6.00 pp |
| Ball (1994) GDP Sacrifice Ratio (SR) | Cum_GDP_Loss / (pi_0 - pi_T) | 1.7500 (%-yr GDP / pp) |
| Unemployment Point-Years per pp | SR / beta_okun | 0.8750 (pt-yr u / pp) |
| Current Okun Misery Index (MI) | u_T + pi_T | 9.80 |
Laurence Ball (1994) Disinflation Sacrifice Ratio Formula
Ensure pi_0 > pi_T (an actual disinflation episode of at least > 0 pp); if inflation rose or held flat, the disinflation denominator is undefined!
=LET(pi_pk, B2, pi_tr, B3, ls_ym, B4, IF(OR(pi_pk <= pi_tr, B5 <= 0, B6 < 0), "Invalid Disinflation Episode", ROUND(ls_ym / (pi_pk - pi_tr), 4)))Unemployment Sacrifice Ratio & Okun Misery Index Formula
Validate beta_okun > 0 and u_T >= 0.
=IF(ISTEXT(E2), E2, ROUND(E2 / B5, 4))Try the example
Use the original values or change them to test your understanding.