So if the Fed raises interest rates, how much and how soon will that help inflation? For another project, I went back to Valerie Ramey's classic review. Here is her replication and update of two classic estimates:

The left side tells us what the federal funds rate typically does after the Fed raises it. The right shows the effect of the rate rise on the

*level*of the CPI. Inflation is the slope of the curve. The horizontal axis is quarters. The top panel uses a vector autoregression. The bottom panel uses the Romer and Romer reading of the Fed minutes to isolate a monetary policy shock.

Top pane (VAR): Multiplying by 10, a 2 percentage point rise in the funds rate (blue dash) might lower cumulative inflation by one percentage point in three years (12 quarters), before it runs out of steam. The black line is the most hopeful, but it is essentially the 1980 experience. Still, multiplying by 5, a 2 percentage point rise in the funds rate only lowers inflation half a percent in those first three years (12 quarters), though after 10 years (40 quarters) you get a full percentage point reduction in the price level.

Bottom panel (Narrative): In the black and red lines that include the 1980 shock, a 3% rise in interest rate produces no noticeable decline in inflation for the first three years. 10 years later, the price level is a decent 4 percent lower, but that is 0.4% per year reduction in inflation. The blue lines that exclude 1980 show a plausible longer-lasting shock, but 1% higher interest rate only produces 1% lower price level in 10 years, m 0.1% per year.

The problem is the ephemeral Phillips curve, which I emphasized in my WSJ oped. In the VARs, the Fed is pretty good at inducing a recession. Here are the Romer-Romer shocks' effects on output and unemployment:

It's just that inducing recessions is not particularly effective at lowering inflation.*any*effect on inflation, or even a positive one:

No theory today, just the facts. This is the empirical basis for the idea that the Fed can swiftly stop inflation by raising interest rates. The underlying machinery does the best that 50 years on the topic has been able to do to separate causation from correlation, and to isolate the Fed's actions from other influences on inflation. Perfect, no, but this is what we have.

*Update:*A few Twitter commenters say that we really don't get much out of "normal times" and we have to look to big "regime shifts." 1980 is an example, and the results with and without 1980 are telling. But that is perhaps the point. If so, then it will take a "regime shift" to tame inflation not the usual "tools."

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