# Barro-Gordon

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Governments choose expansionary policies in order to induce increased economic activity and reduce unemployment, but once this is recognized anticipated inflation will have no significant impact on equilibrium economic activity. Time-consistency can explain why politicians who realize this still succumb to the short-run temptation to inflate in a vain attempt to induce such an effect.

The monetary authority chooses a sequence of inflation rates to minimize the discounted expected social loss (assumed to be quadratic in inflation and unemployment). The social loss function is assumed quadratic in inflation and unemployment.

Optimal unemployment rate is assumed to be below the natural rate of unemployment so there is a “pre-existing distortion” in the natural rate because of some governmental intervention so that the natural rate is above what the monetary authority considers optimal. This distortion exists because of taxes and transfers from fiscal policy moving first.

Result:

As long as the government finds it optimal to try to lower the unemployment rate the optimal rate of inflation is one higher than the public’s expected rate of inflation. In other words, as long as there is a pre-existing labor market distortion by government which makes the natural rate of unemployment higher than that desired by the monetary policymakers, there is a positive inflation bias. Thus setting inflation equal to optimal inflation cannot be a an equilibrium because infinitesimal increases in inflation can increase welfare.

• Equilibrium inflation exceeds socially optimum inflation by:
• -Ú / θ so positive inflation bias, as long as Ú is negative.(Ú = socially optimal inflation rate)