We’ve been warning that inflation would run out of control as multi-trillion-dollar federal stimulus crashed against broken US supply chains.

So-called “core” inflation (without food and energy) has increased at an annual rate of nearly 11% during the past three months, something the US hasn’t seen since 1981.

The overall inflation rate briefly touched the 10% mark in 2005 and 2008 due to spikes in the oil price.

Bad as the headline numbers are, the actual situation is much worse.

The US Bureau of Labor Statistics shows low inflation in the cost of shelter, despite a 23% year-on-year jump in the median sale price of existing homes (according to the National Association of Realtors) and a 14% increase in the estimated price of US homes (according to the Case-Shiller Index).

Housing makes up about a third of the overall consumer price index. The US government uses an arcane measure, “owner-equivalent rent,” to estimate the price of housing assuming that homeowners rented their houses to themselves.

Home price increases work their way into that measure over time, which suggests that the housing bubble will keep upward pressure on CPI for the next couple of years.

The chart below shows components in terms of year-on-year change (rather than annualized monthly change, which is off the charts).

The biggest contributor to the June headline number was used vehicles, up 45% year-on-year. That pushed up the inflation gauge for durable goods by 15%. But inflation for new cars was reported at just 5.3% year-on-year, which is a vast underestimate: Dealers don’t change the sticker price in the parking lot, but rather eliminate discounts on car options.

I don’t think that inflation will continue at the 10% level, but we are likely to see 5% to 6% inflation for the next several years, enough to erode real earnings and squeeze family budgets. How long the Federal Reserve will pretend that inflation is “transitory” is anyone’s guess.