Question

In simple terms, how does one write out the Phillips curve equation? What figures/information is required?

Answer 1

The Phillips curve is an attempt to describe the macroeconomic tradeoff between unemployment and inflation. In the late 1950s, economists such as A.W. Phillips started noticing that, historically, stretches of low unemployment were correlated with periods of high inflation, and vice versa. This finding suggested that there was a stable inverse relationship between the unemployment rate and the level of inflation, as shown in the example above.

SIMPLE PHILLIPS CURVE

Inflation = -h *( Unemployment - UN )

π = -h * ( U - UN )

This simple Phillips curve is generally written with inflation as a function of the unemployment rate and the hypothetical unemployment rate that would exist if inflation were equal to zero. Typically, the inflation rate is represented by pi and the unemployment rate is represented by u. The h in the equation is a positive constant that guarantees that the Phillips curve slopes downwards, and the un is the "natural" rate of unemployment that would result if inflation were equal to zero. (This is not to be confused with the NAIRU, which is the unemployment rate that results with non-accelerating, or constant, inflation.)

Inflation and unemployment can be written either as numbers or as percents, so it's important to determine from context which is appropriate. For example, an unemployment rate of 5 percent could either be written as 5% or 0.05.

MODIFIED PHILLIPS CURVE

π = πt-1 -h * ( U - UNairu )

Since people tend to form expectations based on past behavior, the expectations-augmented Phillips curve suggests that a (short-run) decrease in unemployment can be achieved via accelerating inflation. This is shown by the equation above, where inflation in time period t-1 replaces expected inflation. When inflation is equal to last period's inflation, unemployment is equal to uNAIRU, where NAIRU stands for "Non-Accelerating Inflation Rate of Unemployment." In order to reduce unemployment below the NAIRU, inflation must be higher in the present than it was in the past.

Accelerating inflation is a risky proposition, however, for two reasons. First, accelerating inflation imposes various costs on the economy that potentially outweigh the benefits of lower unemployment. Second, if a central bank exhibits a pattern of accelerating inflation, it's entirely likely that people will start expecting the accelerating inflation, which would negate the effect of the changes in inflation on unemployment.