Ylan Mui at The Washington Post’s Wonkblog had a piece Thursday titled “This is why the Fed should start worrying about inflation again.” The main bit of evidence is a graph attributed to Kevin Logan showing a negative relationship between the unemployment rate and increasing rates of inflation. But this graph actually says far less than Mui says.
Indeed there is a relationship between unemployment and inflation. The Federal Reserve is tasked with balancing inflation and unemployment, and when the Fed fears inflation, it raises interest rates with the intent of slowing the economy and creating unemployment. To some extent, then, the relationship is the Fed’s doing.
Let us put that aside, however, and take the observed relationship at face value. First, it is far from obvious that 6.5 percent unemployment represents a threshold below which inflation is as likely to rise as fall– particularly given the small sample size. In Figure 1, I was unable to reproduce exactly Logan’s figure, but according to data available at the Fed, four of the five years with the highest unemployment rates under 6.5 percent are associated with decreasing inflation.
Figure 1: Unemployment and Changes in Inflation
Source: FRED, series JCXFE and UNRATE and author’s calculations
Rather than cherry picking, we may regress changes in inflation against the unemployment rate. As it turns out, the relationship is statistically weak. The expected change in inflation switches between positive and negative somewhere between 2.5 and 7 percent. Likewise, this suggests that the 50/50 point lies closer to 5 percent than 6.5.
Table 1: Regression results
(1) 
(2) 
(3) 

β_{0} 
constant 
0.52 (0.37) 
0.52 (0.43) 
0.52 (0.39) 
β_{1} 
unemployment rate 
0.11 (0.06)# 
0.11 (0.07) 
0.11 (0.06)# 
variance/covariance estimator 
OLS 
jackknife 
bootstrap 

 β_{0}/ β_{1} 
2.67.1 
2.96.8 
3.06.7 
# significant at 10percent level
Source: FRED, series JCXFE and UNRATE and author’s calculations
In Figure 2, we see the probability that inflation will be higher in 2014 than it was in 2013– assuming various yearround average unemployment rates for 2014. At 6.5 percent unemployment, the probability is closer to one in three than one in two.
Figure 2: Probability of Increased Inflation in 2014
Note: The widest (lightest) confidence band covers 95 percent of outcomes and the most narrow (darkest) band covers 50 percent.
Source: FRED, series JCXFE and UNRATE and author’s calculations
More importantly, increasing inflation is the wrong consideration. The Fed has tolerated inflation below 2.0 percent ever since 2007, and in 2013 core inflation ran only 1.2 percent. If the Fed must target some rate of inflation, it should target a higher rate of inflation. Yet, even if the relationship is meaningful then there is less than a 5 percent chance that 2014 inflation will run even as high as 2.0 percent.
Figure 3: Probability of At Least 2% Inflation in 2014
Note: The widest (lightest) confidence band covers 95 percent of outcomes and the most narrow (darkest) band covers 50 percent.
Source: FRED, series JCXFE and UNRATE and author’s calculations
To the extent that the relationship is both meaningful and a result of Fed activity, then, this suggests that meeting a 2% inflation target would require the Fed to be less hawkish than would be normal for the rate of unemployment. It may yet be some time before the Fed raises interest rates.