§8 The IS-LM-PC Model

The IS-LM-PC Model

• The name of the model explains what it is: An integration of the IS-LM model with the Phillips curve.

• Its logic is quintessential IS-LM in the very short run, but supply constraints (embodied in the Phillips curve) gradually prevail over time.

• The IS-LM model

  $$Y = C(Y-T) + I(Y, \underbrace{\bar{i} - \pi^e}_{\bar{r}} + x) + G$$

• We will simplify things a little by assuming the central banks sets the real interest rate $r$ (otherwise we get too many curves moving during dynamics).

• The Phillips curve:

  $$\pi = \pi^e - \alpha (u - u^n)$$

• We can write output and potential output as:

  $$Y = L(1 - u)$$

  $$Y^n = L(1 - u^n)$$

• And the output gap as:

  $$Y - Y^n = -L(u - u^n)$$

• Which allows us to write the PC in terms of the output gap rather than unemployment:

  $$\pi - \pi^e = \frac{\alpha}{L}(Y - Y^n)$$

From the Short to the Medium Run

• Clearly, in the short run we have an interest rate that is too low $r < r^n$, where the latter (natural, neutral, Wicksellian interest rate) is defined implicitly from

  $$Y^n = C(Y^n - T) + I(Y, r^n + x) + G$$

• In the medium run, real variables are independent of monetary policy.

• Monetary policy determines the rate of inflation and the nominal interest rate.

• The fact that monetary policy does not affect real variable in the medium run is referred to as the neutrality of money.

• The adjustment in the figure looks easy… not so in practice…

  • It is difficult for the central bank to know where potential output is exactly and thus how far output is from potential.
  • It takes time for he economy to respond.

— Apr 16, 2025

§8 The IS-LM-PC Model by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.