The latest CPI number was released this morning by the Labor Department, and it showed average prices increasing at an annual rate of 3.4 percent for April with core inflation of 3.0 percent. This is still above the Fed’s target of 2 percent.

Financial markets took this news in stride and markets rallied, because it was below what financial forecasters had expected and suggested a slight downward trend. The rate of job growth has diminished somewhat in recent months, also suggesting a softening economy. So presumably the Fed won’t raise rates and eventually will have to lower them, even if it takes longer than the Fed signaled earlier this year.

But both the Fed and the typical story in the financial press miss what’s beneath the headline inflation rate. This isn’t that hard to find. It’s right in the charts that the Bureau of Labor Statistic releases along with the aggregate inflation number. But taking a deeper look requires breaking ranks with the assumption that what matters is the overall rate.

Take housing. It accounts for fully one-third of the CPI. Rents were up at an annual rate of 4.8 percent in April. This has nothing to do with an overheated economy and everything to do with America’s failure to have an affordable-housing policy. The Fed’s tight money aggravates that shortage by raising credit costs to builders and developers.

The supposed increase in owner-occupied housing costs is even more misleading. The CPI uses the imputed rental value to owners and shows that number increasing at an annual rate of 4.8 percent in April. But this indicator is months if not years out of date, since most homeowners do not sell their homes in most years. The real question is what homebuyers pay. This chart from the St. Louis Fed shows the CPI without housing; the result is more than one-third lower.

According to Zillow, which uses real-time data, the average housing price is projected to increase by just 1.9 percent in the next 12 months. Housing prices are also heavily regional. High prices in hot markets skew the data. In depressed areas, housing prices are flat or declining. The Fed’s tight money policy only further depresses regional economies that are already hurting.

Why doesn’t the BLS use real-time sales data for the homeownership component of its price index? Long ago, technical economists decided that the imputed rental value was a better indicator. It may be for some purposes, but not for calculating changes in the current rate of inflation.

And there’s more. Several other areas of sharp price hikes in recent months reflect structural factors that are not affected by monetary policy at all.

According to the BLS, the cost of motor vehicle insurance increased 22.8 percent over the past year. That reflects factors ranging from increased road rage to more complex cars that are more expensive to repair. In the CPI, auto repair costs also rose by 7.6 percent over the past year. These sectoral price hikes have nothing to do with whether the economy as a whole is overheated. Likewise homeowner insurance, which got more expensive because insurers took big hits from floods and hurricanes and compensated by hiking rates generally.

Hospital costs rose by 7.2 percent over a year ago, and drug costs by 6.0 percent. And price-gouging in rental housing has been driven by the growing number of absentee private equity owners. All this reflects increasing concentration and market power in these sectors, not the overall strength of the economy.

Strip out housing, where the index is misleading, and these other factors where price hikes are structural and opportunistic, and the real inflation rate is well below the nominal 3 percent. And there’s one other key trend which suggests that we may never get back to 2 percent inflation. That is global climate change.

Climate change will increase costs in ways large and small, which have nothing to do with interest rates. Insurance costs will keep rising. Electricity costs are likely to rise, as we invest in a more reliable grid, and until we complete the transition to renewables. Building costs will increase as both homes and offices need to spend additional money on needed resiliance.

In short, the Fed needs a more realistic target and the BLS needs better indicators, especially when it comes to housing costs. Economists and commentators need to start looking at the structural factors behind many price hikes.