Hysteresis & Nonlinearity

Consider the following depiction of the Phillips curve as an error correction mechanism.

w = + U + pe + U-1 + pe-1 - w-1

where w, p and U respectively denote wages, prices and the unemployment rate (all measured in logs).
The operators , superscript e and subscript -1 respectively denote change, expectation, and lag.

In long run equilibrium

w = ( + pe)/ + (/)U
w = ( + pe)/ + (/)U
w = ( + pe)/ + (/)U
w = ( + pe)/ + (/)U

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