第五讲 奥肯定律与菲利普斯曲线

ut − ut −1 = − 0.4( g yt − 3%)
Changes in the Unemployment Rate Versus Output Growth in the United States, 1970-2000 1970-
ut − ut −1 = − 0.4( g yt − 3%)
§2. The Phillips Curve: From Curve: Unemployment to Inflation
In 1958, A.W.Phillips drew a diagram π plotting the rate of inflation against the PC rate of unemployment in the United Kingdom for each year from 1861 to 1957. He found a clear evidence of a negative relation between inflation and unemployment: When unemployment was low, inflation was high, and when unemployment was high, inflation was low, often even negative. 0 u Two years later, Paul Samuelson and Robert Solow replicated Phillips’ exercise for the United States, there • Samuelson and Solow appeared to be a negative relation baptized this relation the between inflation and unemployment in Phillips Curve. the United States also.
Y P = P (1 + µ ) F 1 − , z L
e
This relation can be rewritten to establish a relation between inflation, expected inflation, and the inflation, inflation, unemployment rate. rate. First, the function F, assumes the form:
The actual relation between output growth and the change in the unemployment rate is known as Okun’s law.
Using thirty years of data, the line that best fits the data is given by:
F( u,z ) = 1- αu + z
Then, replace this function in the one above:
P = P ( 1 + µ )( 1- αu+z )
e
1 ... p t = p t e (1 + µ )(1 − α u t + z ) e pt pt 2 ... = (1 + µ )(1 − α u t + z ) pt − 1 pt − 1 pt pt − pt − 1 + pt − 1 pt − pt − 1 3 ... = = 1+ = 1 + πt pt − 1 pt − 1 pt − 1 4 ...( 1 + π t ) = (1 + π t e )(1 + µ )(1 − α u t + z ) devide both sides by (1 + π t )(1 + µ ) (1 + π t ) 5 ... = 1 − α ut + z e (1 + π t )(1 + µ )
ut - ut- 1 = - β( g yt - g y )
Output growth above normal leads to a decrease in the unemployment rate. This is Okun’s law:
g yt > g y ⇒ ut < ut −1 g yt < g y ⇒ ut > ut −1
1. “Fixed production units” (e.g. the accounting
department of a firm)+ Labor hoarding 2. Increase in the labor force
Using letters rather than numbers:
Mutations
The negative relation between unemployment and inflation held throughout the 1960s, but it vanished after that, for two reasons:
An increase in the price of oil, but more importantly, A change in the way wage setters formed expectations due to a change in the behavior of the rate of inflation.
Mutations
Inflation versus Unemployment in the United States, 19701970-2000
Mutations
U.S. Inflation, 1900-2000 1900-
The Formation of Expectations
Suppose expectations of inflation are formed according to
ut − ut − 1 = − ∆y
Change it slightly, we can obtain what we need----a relation between output growth and the change of unemployment.
ut − ut − 1 = −β ( gyt − gy)
The Phillps curve rapidly became central to macroeconomic thinking and policy. It appeared to imply that countries could choose between different combinations of unemployment and inflation. They could achieve low unemployment if they were willing to tolerate higher inflation. Or they could achieve price stability if they were willing to tolerate higher unemployment. Much of the discussion about macroeconomic policy became a discussion about which point to choose on the Phillips curve. In the 1970s, however, the relation broke down. There was both high inflation and high unemployment in both the United States and most OECD countries. A relation reappeared, but it was now a relation between the unemployment rate and the change in the inflation rate.
• The inflation rate became consistently positive, and • Inflation became more persistent.
MutationsInfltion versus Unemployment in the United States, 19481948-1969
e
Rearranging gives:
πt = πt + (µ + z ) − α ut
e
2-2
The Phillips Curve
If we set
πt = 0 then: πt = (µ + z) − α ut
e
This is the original Phillips curve The wage-price spiral: wagespiral: Given Pet =Pt-1: Low unemployment at time t ⇒ Wt ↑ Wt ↑⇒ Pt ↑ ⇒ Pet+1↑ ⇒ Wt+1↑⇒ Pt+1↑ ⇒ Pet+1↑ ⇒ Wt+2↑⇒ Pt+2↑ , and so on…
According to the equation above,
If g yt > 3% , then ut − ut −1 = − 0.4( + ) < 0 If g yt < 3% , then ut − ut −1 = − 0.4( − ) > 0 −1 If g yt = 3% , then ut − ut −1 = − 0.4(0) = 0 To maintain the unemployment rate constant, output growth must be 3% per year. This growth rate of year. output is called the normal growth rate.