WASHINGTON — Consumer borrowing increased for a fourth straight month in January, led by a gain in installment loans such as those for automobiles and education, the Federal Reserve reported Monday.

The $5.01 billion rise in credit followed a revised $4.09 billion gain in December that was less than the previous estimate, the Fed said in Washington. Economists projected a $3.5 billion increase in the measure of credit card debt and installment loans, according to the median forecast in a Bloomberg News survey.

The pickup in installment credit signals Americans may be growing more confident about their financial situations to purchase big-ticket goods such as automobiles. The expansion may get a bigger lift from consumer spending, which accounts for about 70 percent of the economy, as the unemployment rate keeps falling.

“When consumers start to take on more debt, it is a sign that confidence over job security is growing,” said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi UFJ in New York. “There are tentative signs that the deleveraging of consumer balance sheets is now complete.”

Estimates in the Bloomberg survey of 35 economists ranged from a $2 billion decrease to a $7.5 billion gain after an initially reported $6.1 billion increase in December.

Revolving debt, which includes credit cards, decreased $4.25 billion in January, according to the Fed’s statistics. Installment debt, including loans for cars and mobile homes, rose $9.26 billion for the month. The report doesn’t track debt secured by real estate, such as home equity lines of credit.

January’s advance in installment debt reflected, in part, an unadjusted $24.9 billion increase in federal government lending for education, according to the statistics.

Borrowing, which rose to $2.41 trillion in January, is showing signs of recovery since reaching an almost four-year low of $2.39 trillion in September.

The economy, which grew in 2010 by the most in five years, is creating more jobs. Payrolls increased 192,000 in February, the most since last May, and the unemployment rate fell to 8.9 percent, Labor Department figures showed last week.

General Motors and Toyota increased incentives for U.S. customers in January, contributing to the biggest sales gains in the auto industry. GM increased spending on marketing promotions by $498, or 16 percent, to an estimated $3,663 per sold vehicle, according to researcher Autodata Corp.

“Growing consumer confidence combined with pent-up demand will continue to have a positive influence on industry sales going forward,” Donald R. Johnson, vice president for North American sales at Detroit-based General Motors, said in a teleconference March 1. “We continue to believe that we’re going to see this slow but steady growth throughout the year.”

Americans also filed into dealer showrooms in February to take advantage of incentives. Auto sales rose to an annual rate of 13.38 million, the highest level since August 2009 when the government’s cash-for-clunkers program boosted purchases, according to industry data.

Borrowing may have picked up last month. Sales at stores open at least a year at the more than 30 chains tracked by Retail Metrics climbed 4.3 percent in February from a year earlier, an 18th straight monthly gain, surpassing analysts’ estimates for a 3.8 percent increase.

Household balance sheets are improving. Charge-offs on credit cards declined to 7.45 percent in January, according to the Moody’s Credit Card Index. It was the fifth consecutive monthly decline, Moody’s said Feb. 23. Credit-card rules that took effect last year curbed interest rate increases and late fees, according to the new U.S. Consumer Financial Protection Bureau.

Lenders are also benefiting. Banks reported net income of $21.7 billion in the fourth quarter of last year, boosting earnings for the full year to $87.5 billion — the highest since 2007, the Federal Deposit Insurance Corp. said Feb. 23.