Rising rents and higher food costs could have given a slight boost to consumer inflation in July.
The consumer price index, released at 8:30 a.m. is expected by economists to show a 0.1 percent increase, but 0.2 percent for core, or CPI when excluding food and energy.
"This is not a flare. It's barely a flame," said Diane Swonk, chief U.S. economist at Mesirow Financial.
Deutsche Bank economists say they expect CPI at 0.2 percent, a year-on-year rate of change of 2 percent. The Deutsche Bank economists also see inflation picking up, and they expect CPI to cross above the 2 percent annualized rate for a sustained period. CPI was at 2 percent in early 2013 and then again in May of this year.
Markets have been on inflation watch, particularly for wage inflation, because a hotter pace may affect Fed policy. The Federal Reserve watches inflation but its preferred metric is the personal consumption expenditures, or PCE, running at about 1.5 percent.
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It's a big week for the Fed, with its Jackson Hole symposium at the end of the week, and minutes from the last Fed meeting to be released Wednesday.
Markets are expecting a fairly dovish message from the Fed, and that was part of the talk Monday as stocks surged and bond yields rose. The Dow Monday jumped 175 points to 16,838. Stocks rallied on a calming of geopolitical tensions. The was up 16 points at 1,158, and the Nasdaq reached a new 14-year high of 4,508. The 10-year Treasury edged up to 2.39 percent from a low of 2.34 earlier in the session.
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"Energy prices have been tame, but if we look at the food inflation pipeline, it's definitely looking like food prices and food inflation is accelerating," said Carl Riccadonna, an economist at Deutsche Bank. "Food inflation year-on-year is running at 2.4 percent."
Shelter costs, over the past 12 months, contributed 1.2 percent to the 1.9 percent increase on core CPI.
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Riccadonna said other services categories are also picking up, such as medical care, transportation and education. But there has been a significant pickup in shelter, which has been rising at a 2.8 percent rate. The supply of rental units is a factor and they have been affected by a lack of new construction. Riccadonna notes that the rental vacancy rate last quarter was 7.5 percent, the lowest level since 1995.
"You have rents driving the index, and that's been the story for the last year, if not more. The chorus is increasing that we're in a world with inflation running ahead of 2 percent. That certainly has implications for the Fed," Riccadonna said.
He added that other categories are picking up and core CPI, without shelter was up 1.3 percent in June, compared with 0.9 percent in the first quarter.
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Rental construction should show up in housing starts data Tuesday, also reported at 8:30 a.m. EST. Construction of 950,000 units is expected, up from 893,000 last month.
There are also earnings expected Tuesday, including Home Depot, TJX, Dick's Sporting Goods, Medtronic, Elizabeth Arden and La-Z-Boy.
—By CNBC's Patti Domm