The New York Times suggests that rising insurance costs help to explain stubbornly high inflation:

“Insurance of various different kinds — housing insurance, but also automobile insurance, and things like that — that’s been a significant source of inflation over the last few years,” Jerome H. Powell, the Federal Reserve chair, said during congressional testimony last week. “And it’s to do with a million different factors.”

Vehicle insurance is the one adding notably to overall inflation, said Omair Sharif, founder of the research firm Inflation Insights. Part of the increase in car insurance comes from the fact that parts and replacement vehicles have become a lot more expensive over recent years, and that is slowly feeding through to insurance premiums, he said.

These comments confuse relative and absolute prices.  More expensive auto parts might cause the relative price of auto insurance to rise, but they do not cause a rise in the overall cost of living.  

There are cases where “supply shocks” cause both an increase in the relative price of one good, and also an increase in the overall Consumer Price Index.  That occurs when the adverse supply shock reduces real output—say a sharp cutback in global oil production.  For any given rise in nominal spending, lower real output leads to a higher price level.

But that is not what is happening in the US.  Recent economic growth has been quite robust.  Inflation remains above the Fed’s 2% target because nominal GDP growth is running at 5.8% over the past year, way too high.  

In any economy, some prices will rise faster than others.  Instead of singling out the prices of various goods and services, the Fed needs to look in the mirror.  We have high inflation because monetary policy has pushed NGDP growth up to a rate that is not consistent with “price stability” (even if defined as 2% inflation.)  The Fed is the institution that created the high inflation of the 2020s, not supply chain problems.  The excess inflation since 2019 is very similar in magnitude to the excess NGDP growth.