The sacrifice ratio (SR) explains why the Fed is hell bent to take interest rates higher. SR is not widely followed by financial market media. That's a shame because the rise in the SR is critical to understanding how Greenspan and Bernanke make Fed policy.

We will try to explain this very technical concept. We will offer a simplified SR definition first and then discuss what it means for interest rates.

What is the SR?

SR attempts to measure the tradeoff that occurs between employment and inflation when the Fed fights inflation by raising interest rates. Let's think of it as a single number. You get the SR by dividing A by B. A is the amount of additional unemployment the Fed creates when it slows the economy by raising interest rates. B is the amount by which inflation drops as a result of that slowing.

The lower the SR, the less painful the result of a tightening in Fed policy. The higher the SR, the more painful Fed policy becomes because a high SR means more jobs are "sacrificed" in the fight against inflation.

Example A: Suppose the Fed wanted to reduce inflation by 1% and do it in one year. The Fed would raise interest rates and slow the economy. Output would fall and unemployment would rise. Suppose in this case the increase in the unemployment rate was 1% and it occurred within the one year. The SR would also be 1. An SR of 1 means the economy is operating such that one unit of lower inflation may be achieved at the cost of 1 unit of unemployment and accomplished in one year.

(Please note: this is a terribly simplified example as readers will see at the end of this commentary. The actual estimation process is much more complex.)

Example B: Suppose the economy has changed over time and wages and salaries are harder to alter, prices are sticky, trade relations have barriers or protectionism, currency fluctuation has added risk premia, deficits and debt structures are high, inflation expectations are rising. Suppose these and other things have brought the economy to a point where the SR is now 4. In our simple example, that means a 1% drop in the inflation rate is achieved with a cost of a 4 point rise in the unemployment rate within a year.

(Please note: readers can see that time is now an important factor in Fed policymaking. Adding 4 points to the unemployment rate within a single year means enormously higher interest rates and a whale of a recession. Stretching things out for several years means a prolonged period of pain administered with reduced intensity. This is a Hobson's choice for the Fed; hence, the time dimension is critical to the Fed's policymaking decisions.)

Clearly a low and falling SR is more desirable for Fed policymaking than a high and rising SR. This is where and why the rubber hits the road in 2005.

What is the SR now? What was the SR in the Volcker and early Greenspan period?

Here are the September 29 words of Fed Governor Don Kohn. Remember: Kohn was the Secretary and an economist to the Board of Governors of the Greenspan Fed before he became a Governor himself.

"......the sacrifice ratio rose from around 2 or 3 in the mid-1980s to around 4 currently. Imbalances between demand and potential supply would thus now be slow to show through convincingly to inflation, but when they do, they may be costly to correct."

Here is Chairman designate and then Fed Governor Bernanke's SR reference in a 2003 speech. Bernanke said: "Now make the assumption that the sacrifice ratio is 4.0, a high value by historical standards but one in the range of many current estimates."

What does a rising SR mean for interest rates?

It means the Fed is likely to persist hiking rates higher and longer than the market expects. We have looked at the changes in Fed Funds futures pricing. It is clear that these futures are short term oriented and do not capture this element of Fed policymaking.

The Fed believes the SR at 4 is higher than in the past (1980s when it was 2 or 3) and that it is rising. They fear that inflation in the future will be much more painful to fight because the SR is this high. That is why the Fed is acting preemptively. It wants to keep inflation low. It does not want to fight a future higher inflation when the SR is this high.

The Fed is forward looking in its work. The Fed's staff generates the estimates of the SR from very complex equations. In simple terms, the staff's forecasts and their econometric work are warning the Fed that the SR is at a level where risk is compellingly great.

Therefore the Fed would rather take rates higher now and deter inflation rather than fight the actual inflation later. The Fed's research work also suggests that a gradual policy application has the effect of lowering the SR over time. This is why the Fed has been "measured" in its rate hiking.

Fed policy is currently driven by more than just rising energy prices. The Fed's raising of interest rates also ignores the current low core inflation. There is a precise reason. These rate increases are a response to the Fed's examination of the tradeoff between inflation and output in this globalized world. Kohn's and Bernanke's comments gives us the clues.

Conclusion: if the SR is now estimated at 4, we should not expect the Fed to ease back in policymaking in the near term. That means rates are headed higher and for longer than many expect.

For serious readers we recommend a visit to the Federal Reserve Board website: www.federalreserve.gov . Use the advanced search and put the term "sacrifice ratio" in quotes. You will find a few references. We suggest reading Gov. Kohn's September 29 speech and also Gov. Bernanke's speech of July 23, 2003. We also recommend the research paper by J. Benson Durham entitled "Sacrifice Ratios and Monetary Policy Credibility."

One can also read Bernanke's detailed explanation of the SR in his textbook "Macroeconomics" jointly published with Andrew Abel.

We must add acknowledgments to two non-Fed individuals who were helpful to this writer in examining the SR. Thank you to Stephen Jen, a very smart and perceptive economist based in Morgan Stanley's London office. And a special thank you to my good friend and colleague, Bill "Dunk" Dunkelberg, Chief Economist at the National Federation of Independent Business.

Dunk provided this more technical description of the SR. He teaches graduate economics at Temple University using Bernanke's textbook.

"The sacrifice ratio is more precisely defined as the POINT YEARS OF UNEMPLOYMENT / DECREASE IN INFLATION. A point year of excess unemployment is the difference between the natural or full employment unemployment rate and the actual unemployment rate of one point for one year. If full employment is 5%, an unemployment rate of 8% for four years in a row corresponds to 4 x (8-5) = 12 point years of excess unemployment.

Assume the Fed wants to reduce inflation from 14% to 4% (= 10 points for the denominator). Based on the Phillips curve tradeoff where Pt - Pt-1 = a x (U-Unat) where a=1, if the Fed wants to do this in 2 years, what is required is unemployment rate 5 points above full or natural rate. Accomplishing the same reduction over 5 years requires 5 years of unemployment 2 points above the full employment rate. To do it in 10 years requires 10 years of unemployment 1 point above the natural rate.

The unemployment implication is then translated into output implications using Okuns Law: Ut-Ut-1 = .4 (growth rate - full emp growth rate). 10 = .4 (growth - 3%). solving for growth we get 10%/.4 + 3 = -22% decline in GDP to do this in one year. Largest decline was crash time at around 15%!!!!

Obviously this is complex and depends on how quickly unemployment affects inflation (via wages and price cuts due to inventory, etc). High numbers for Germany, low for less regulated structures. Now you see the importance of the time dimension for policy. Bernanke's estimates simply look at the actual reduction in inflation and the actual loss in GDP relative to potential actually experienced. Implicit in this is the choice of time period to accomplish the reduction. Bernanke's text uses output, not unemployment rates.