Overall U.S. wage pressures remain “modest,” but employers are preparing for further pay bumps as minimum-wage increases take effect, according to the Federal Reserve’s latest survey of regional economic conditions.

Most of the Fed’s 12 districts reported stronger wage growth for qualified or higher-skilled workers in industries such as construction, information technology and trucking. Several districts noted rising pressure on employers to raise wages to compete for workers due to minimum-wage policies boosting pay.

The anecdotal survey by the Fed’s regional banks covers the period from mid-May through June. Its picture of “optimistic” businesses and a generally tightening labor market in most of the U.S. could support Fed officials calling for an interest-rate increase sooner rather than later.

Federal Reserve Chairwoman Janet Yellen said Wednesday that the central bank was on a path to raise short-term U.S. interest rates this year as the domestic economy improves, despite a backdrop of global threats.

The central bank has kept short-term interest rates near zero since the end of 2008 in order to spur economic activity during the financial crisis and subsequent recession. The uneven recovery, which has seen job growth pick up but wages and inflation remain relatively flat, has led to debate about whether and when to raise interest rates.

“Too many people are not searching for a job but would likely do so if the labor market was stronger,” she told lawmakers Wednesday.

Demand for specialized workers was a consistent theme across districts. Business contacts told the Cleveland Fed that the construction industry “remains challenged by a labor shortage,” and carpenters and drywallers are “the most difficult to find,” a problem they are trying to remedy with apprenticeship and co-op programs.

The Boston Fed said openings for high-technology positions, M.B.A.s and expert analysts “are reportedly hard to fill.” The New York Fed reported “increased demand for human resource professionals to recruit new employees—particularly in the finance and legal sectors.”

Recent legislative and private-sector initiatives to boost the minimum wage are starting to ripple through the business landscape. The Dallas Fed reported “some primary metals manufacturers increased starting salaries in part due to skilled labor shortages and to keep up with pay raises at Walmart,” although that wage boost did not extend to food-service or petrochemical workers in the district.

In Cleveland, one chain noted its employees “are more enthusiastic and turnover is lower as a result of an increase in the hourly wage rate.” Another contact observed that “retail employees will readily change jobs for an additional 10 cents per hour.”

The yearlong drop in energy prices has had mixed effects. Drilling for oil and natural gas fell in the Cleveland, Minneapolis, Kansas City and Dallas districts. But several districts “noted that low energy prices were a contributing factor to improved consumer spending at some retail locations and restaurants.” The Cleveland Fed reported that convenience stores selling gasoline “continue to report stronger sales of nonfuel items due, in part, to the ongoing, relatively low price of gas.”

The Minneapolis and Dallas regions reported soft growth along their borders due to continued strength of the U.S. dollar. But a strong dollar, combined with “restrained costs across a number of commodities” boosted margins for Atlanta-area firms relying heavily on commodities or imported goods.