Bringing inflation down: credibility and the sacrifice ratio

Disinflation is a fall in the rate of inflation: prices still rise, more slowly. It is different from deflation, a fall in the price level. With expectations equal to last year’s inflation (θ = 1), the Phillips curve of Lesson 7 says inflation falls by β points for each point that unemployment is held above the natural rate for a year. So bringing inflation down by x points takes x/β point-years of unemployment above the natural rate. Okun’s law (Lesson 6) turns point-years of unemployment into lost output: each point of unemployment above the natural rate costs about β_O per cent of output, where β_O is Okun’s coefficient (2 in the exam problems of Lesson 6).

The ratio is large when β is small: when wages and prices respond only slowly to slack, a lot of unemployment is needed to move inflation. That is the answer to the opening question. A sluggish response of wages and prices to monetary contraction raises the output cost of disinflation (B). The ratio is an estimate, as the Okun coefficient it uses is (Lesson 6), so it is not a constant of nature.

Inflation starts above a 2% target. The central bank brings it down along a straight line over K years, holding unemployment above 5% by just enough to stay on the line. Start with “Cold turkey, not believed” (K = 1, c = 0) and then “Gradual, not believed” (K = 5): the total is the same. The unemployment peak is not. Then raise c, the weight on the announced target in expected inflation, and watch the bill fall.

Rational expectations is the limit case: people know the policy and its consequences, so the announced path is built into wages from the start. On that view, accurate expectations and rational expectations lower the cost of disinflation, which is why options A and D do not raise the cost (UGC NET 2025). A gradual policy response, with expectations that do not move, costs the same as a fast one, so it does not raise the cost either (C). The IS–LM module’s lesson on expectations takes up rational expectations and policy.

• Credibility is an input here. In practice whether an announced target is believed may depend on the central bank’s record and on how firmly it acts, so the lab’s comparison of different K at the same c should not be read as a statement about which speed is believed.
• β is not fixed. It reflects how wages and prices are set. A different regime can change it, so a sacrifice ratio estimated in one period may not apply in another.
• Hysteresis. If a long slump raises the natural rate (Lesson 8), the bill is bigger than the arithmetic says, because unemployment stays high after the policy ends.
• Supply side help. A favourable supply shock lowers inflation with no slump. Lesson 9 had the other sign.

How hard should the central bank tighten when inflation is above target and the economy is below potential? A policy rule answers with a formula. The best known sets the policy rate from inflation and the output gap, so that the real rate rises when inflation rises:

Inflation targeting is the other idea worth one paragraph. A central bank that targets inflation announces a numerical target and is judged against it. Announcing is a way of trying to build the credibility the lab’s c stands for; whether it works depends on whether the bank is believed. India’s own framework, with its target and its dates, is outside this module.

A recent paper asked which statements are correct when inflation has been trending down towards the central bank’s target. The question gives no model, so the key has to be read as: which two things explain the fall? Tighter monetary policy acts on the demand side, and supply chains adapting to uncertainty act on the supply side (option A as printed says “adopting”, which presumably means adapting). Easing monetary policy would push inflation up, and so would a rise in aggregate demand greater than the rise in aggregate supply, so neither explains a fall. The official key is A and C only (UGC NET 2025). Treat it as a statement of causes, and notice that a central bank might well ease after inflation reaches target, which is a different question.