People shop in a clothing store on Broadway on Feb. 7, 2013 in New York City. In another indicator of a slowly strengthening economy, chain stores including Macy's Inc., Target Corp and Gap Inc. reported January sales that exceeded analysts' estimates. (Spencer Platt/Getty Images)

Some of the nation’s largest retailers posted solid gains in January even though shoppers were hitting the malls with smaller paychecks.

The results reported Thursday offer the first glimpse into how the expiration of the payroll tax cut is affecting household budgets. A worker making $50,000 a year faces a decrease of $1,000 in take-home pay over the course of the year, and economists predicted spending would fall off. But many companies found that shoppers were more resilient than expected.

According to the International Council of Shopping Centers, retail sales rose 4.5 percent in January compared with a year ago. The data cover sales at stores open at least a year for 22 national chain stores.

“Simply put, January was an outstanding month,” Macy’s chief executive Terry J. Lundgren said.

Sales at Macy’s rose 12 percent in January, and it was not the only retailer to post double-digit growth. Nordstrom was up 11 percent, and Kohl’s jumped 13 percent.

January sales take a big jump.

Although individual companies performed well last month, economists cautioned that this may not translate into broader gains in consumer spending. Key players such as Wal-Mart, the world’s largest retailer, do not report monthly sales results and were not included in Thursday’s tally. Government data scheduled to be released next week should provide a more comprehensive look at consumers’ financial health.

“When you take away a certain amount of money, people don’t rush off and go to the mall,” said Chris Christopher, director of global and U.S. consumer markets for IHS Global Insight.

Michael Niemira, who is ICSC’s chief economist and compiles the monthly results for the industry, said several factors may have offset the tax increase in January. He noted that several states implemented minimum-wage increases that took effect in January, helping to ease the effect of the payroll-tax increase. He estimated that the wage increase affected about 1 million workers. He also expects the full effect of the payroll tax to show up later in the year.

“I wouldn’t expect it to hit that hard that quickly,” Niemira said. “The payroll tax is one of these things that accumulates.”

Target chief executive Gregg Steinhafel noted that even though the chain’s 3 percent sales growth was in line with expectations, consumers still seemed restrained.

“Our guests continue to shop with discipline in the face of a slow economic recovery and new pressures, including recent payroll tax increases,” he said in a statement.

Research released this month by the Federal Reserve of New York found that consumers planned to reduce their spending by 71 percent of the size of the tax increase. They expected to cover the rest of it by saving less and taking on more debt.

But actions don’t always line up with intentions. When the payroll tax cut took effect, households spent only 36 percent of the extra money — half the amount they are now pledging to cut back.

“How workers plan to respond to a hypothetical situation may be different from what they actually do when confronted with that situation,” the report said.

Niemira predicted that consumer spending would begin to pick up in the second half of the year. But that may not be enough to push back against fiscal headwinds.

“The broader economy will ultimately then hold back consumer spending,” he said.