Naar de inhoud
Steven’s StudyHub

Lecture 2A: How the model works: transmission and shocks

Start here if this is new to you

Now the three equations are used. "Transmission" is the chain of events from a change in the policy rate to a change in inflation. Follow the chain in order every time: the central bank raises the nominal rate; prices are sticky, so expected inflation does not jump and the real rate rises; a higher real rate makes saving attractive, so spending and output fall (IS curve); output below natural means lower marginal cost, so firms raise prices less and inflation falls (Phillips curve). Each arrow is one of the equations from the previous chapter.

The second theme is that not all shocks are alike. A demand shock (households suddenly spend more or less) moves inflation and the output gap in the same direction, so the central bank can fix both at once by moving the rate. A cost-push shock (oil, energy, markups) moves them in opposite directions, so the central bank must choose between fighting inflation and protecting output. Keeping those two cases apart answers most exam questions about this lecture.

The transmission mechanism

nominal rate it → (sticky prices) → real rate it − Etπt+1 → (IS curve) → output gap xt → (Phillips curve) → inflation πt

  • Because prices are sticky, a change in it changes the real rate.
  • The real rate moves demand (IS); demand moves marginal cost and inflation (NKPC).
  • Both equations are forward-looking, so expected future policy matters as much as today's rate, and expectations feed back into today.
  • With ψ = 0 (flexible prices): xt = 0 always, and monetary policy only affects inflation.

Example: a monetary tightening, step by step

The central bank unexpectedly raises it by 1 percentage point.

  1. Real rate: prices are sticky, so expected inflation does not rise one-for-one. The real rate it − Etπt+1 rises.
  2. Households (IS curve): saving becomes more attractive; consumption falls. Output falls below natural: xt < 0.
  3. Labor market: firms need fewer hours; the real wage falls, and so does marginal cost.
  4. Firms (Phillips curve): with lower costs, firms raise prices by less. Inflation falls.
  5. Expectations: if the tightening is expected to last, expected future gaps are negative too, and inflation falls further today.
The cost of disinflation

Inflation falls only because output falls below its natural level. How much output must be given up depends on κ: the flatter the Phillips curve, the higher the cost. Example: with κ = 0.1, lowering inflation by 0.5 points through today's gap alone needs xt = −5%; with κ = 0.5 only −1%.

Two kinds of shocks

Shocks to rnt (demand, productivity)Cost-push shocks ut
Move the natural rate.For example markup or energy cost shocks.
If the central bank sets the real rate equal to rnt, then xt = 0 and πt = 0.Stabilising inflation requires a negative output gap.
No trade-off.A genuine trade-off.
The divine coincidence

Without cost-push shocks, stabilising inflation also closes the output gap (Blanchard & Galí, 2007). Cost-push shocks break it, and that is where optimal policy, and the mandate, start to matter.

In plain words

A productivity boom is easy: let the rate follow the natural rate and both inflation and the gap stay at zero. An energy price shock is hard: to keep inflation down, the central bank has to accept a weaker economy for a while, or accept higher inflation to protect jobs.

Summary

  • Households give the Euler equation, which becomes the IS curve: demand depends on the expected path of real rates.
  • Monopolistic competition gives price-setting firms with a markup; costly price adjustment makes pricing forward-looking, which gives the Phillips curve.
  • Marginal cost is proportional to the output gap; the natural rate rnt is the real rate that keeps output at its natural level.
  • Sticky prices give the central bank control of the real rate.

Next, Lecture 2B: what should the central bank do? Long-run optimal inflation, short-run stabilisation, and why the answer looks like a Taylor rule. Readings: Galí (2015), ch. 3; Clarida, Galí and Gertler (1999), section 2; Rotemberg (1982).

The exercises from the slides, with answers

  1. Derive Yjt = (Pjt/Pt)−εYt. Take the retail FOC PtYt1/εYjt−1/ε = Pjt, raise both sides to the power −ε: Yjt = (Pjt/Pt)−εYt.
  2. With ψ = 0, Pjt/Pt = ε/(ε − 1) mct. As ε → ∞ the markup ε/(ε − 1) → 1: price equals marginal cost (perfect competition).
  3. Verify the linear Phillips curve. Use πt(1 + πt) ≈ πt, replace Qt,t+1Yt+1/Yt by β, and (1 − ε) + ε mct = (ε − 1)m̂ct; divide by ψ.
  4. Prices become stickier (ψ up): κ falls, so a given output gap moves inflation less (flatter Phillips curve), and disinflation costs more output.
  5. σ rises: the IS slope 1/σ falls, so output reacts less to the real rate (weaker interest rate channel); κ rises, because marginal cost rises faster with output. Through demand, monetary policy becomes less effective at moving output.
  6. Expected productivity growth rises: rnt rises. If the central bank keeps it unchanged, the real rate is now below the natural rate: policy is effectively loose, so xt rises and, through the NKPC, πt rises.

Andere hoofdstukken van International Monetary Relations and Policy

Test jezelf met oefenvragen