The NKM with a Supply Shock: Matrix Representation

Macroeconomics (M8674), May 2026

Vivaldo Mendes, ISCTE

vivaldo.mendes@iscte-iul.pt

The New Keynesian Model with a supply shock

The linearized baseline version of the NKM with supply shocks can be written with 7 equations:

Variables and parameters

• Endogenous variables: are, respectively, the output-gap, inflation, nominal interest rate, the consumption-gap, supply shock, labor supply, and technology.
• Exogenous variables: , which represent, respectively, the natural level of the real interest rate, the target inflation rate, and a random disturbance.
• Parameters:
• Forward-looking variables:
• Backward-looking variables:
• Static variables:

4 equations vs 4 unknowns

• The model can be fully simulated only with 4 equations and 4 unknowns:
  
  

• The first two are non-forward looking variables, and the last two are forward looking variables.
• To separate the two blocks of equations, the order we write them matters:
  • First write down the non-forward looking block
  • Then write down the forward looking block

Matrix representation

• The 4 equations can be written as:

• Passing the equations into matrices gives:

The model is ready for the computer