Notably, the CPI for durable goods, most of which are imported or manufactured with imported content, decreased by a seasonally adjusted 0.1% month-to-month (-1.3% annualized), indicating that President Donald Trump's tariffs have not yet been fully passed through to the final consumer.

May's CPI inflation data was uneventful. Check out if underlying trends could signal a shift toward higher inflation or not.

Consumer prices showed little sign of tariff-related increases for the third month in a row, defying expectations of a significant rise in inflation tied to ongoing U.S. trade wars.

Pressure on the Fed to trim interest rates is growing. In other words, the perception that the inflation problem is solved is raising the specter of more inflation.

Take a look at how various financial markets are trading after the release of May's consumer-price index: stock futures, Treasury yields, the dollar, oil and gold.

The rate of inflation fell in the spring to the lowest level in more than four years even as high U.S. tariffs threatened to increase prices again. Is the bill from trade wars about to come do?

Michelle Girard, NatWest head of U.S. coverage and CEO of NatWest Markets Securities, joins 'Squawk Box' to preview May's CPI data, state of the economy, and more.

CPI inflation slows with a 0.1% rise in May, boosting stocks and treasuries. Click here to learn how tariffs and future CPI trends could affect markets.