## Saturday, December 5, 2015

### Two curves

As I said in my last post, most discussions of the "Phillips curve" consider the relationship between unemployment and prices, but Phillip's idea (which is a straightforward application of supply and demand reasoning) implies a relationship between unemployment and real wages.  Of course, the two are related, because the change in real wages is the difference between the change in money wages and change in the price level.  I calculated the equilibrium values of the annual rate of change in both for different levels of unemployment (see note 1 at the end for details):

unemp             Inflation             Wages       Difference
3.5%                     4.1%               5.6%              1.5%
4.0%                     3.6%               5.0%              1.4%
4.5%                     3.2%               4.4%              1.2%
5.0%                     2.9%               4.0%              1.1%
5.5%                     2.7%               3.7%              1.0%
6.0%                     2.5%               3.4%              0.9%
6.5%                     2.3%               3.1%              0.8%
7.0%                     2.1%               2.9%              0.8%
7.5%                     2.0%               2.8%              0,8%

There's a good deal of uncertainty about the exact numbers, but the general pattern is that growth in real wages is substantially higher when unemployment is lower (the median unemployment rate in the US since the late 1940s is about 5.6%, and about 85% of the values fall in the range shown above).  So the "cost" of low inflation is not just higher unemployment, but slower growth in real wages.

Note:  the price and wage data are monthly.  The change in prices in a given month can be predicted pretty well by regressing it on the change in prices in each of the last 12 months and the change in money wages in each of the last four months.  The change in wages can be predicted by change in prices in each of the last twelve months and the current inverse of the rate of unemployment.  Unemployment doesn't directly affect prices, but it affects them indirectly through wages.  I used the coefficients from those two regressions with a given rate of unemployment to get the figures above.