“I won on groceries,” the president-elect said in an interview Sunday on “Meet the Press.” In his nomination-acceptance speech at the Republican National Convention in July, Trump said he would “end the devastating inflation crisis immediately.”

Despite his pledge to lower inflation, if Trump follows through on some of his tariff and immigration plans , economists worry he might do just the opposite .

The pace of inflation had significantly cooled before the election. But anger hasn’t subsided, and costs are far higher than they were before the pandemic. On Wednesday, new inflation numbers suggested that progress on driving down rising costs had stalled. Prices for groceries, for example, were up 1.6% from a year earlier in November. But they were up 27% from February 2020.

Overall consumer prices were up 2.7% in November from a year earlier, a far cry from the 9.1% notched in 2022 but still a tad higher than the month before. New data Thursday showed that a month-over-month change in producer prices was more than economists had expected .

Any rise, even a small one, comes on top of already-high prices vexing Americans. What can Trump do?

The problem presidents face with inflation is that there is only so much they really can do to cool it off. Bringing overall prices down would be even harder— and unwelcome . Falling prices, or deflation, would make it harder for borrowers to repay their loans, stifling the economy.

Many of the measures that economists might prescribe to reduce inflation, such as increasing innovation, reducing regulatory burdens or boosting the U.S. workforce’s skills, would take years, if not decades, to bear fruit.

The effectiveness of past presidential efforts to control inflation has been mixed. Inflation cooled in response to Richard Nixon ’s price controls and then burst higher when those controls were removed. Gerald Ford ’s “Whip Inflation Now” campaign was widely derided. Jimmy Carter persuaded the Fed in March 1980 to introduce stringent controls on the use of credit, tanking spending and leading to large job losses. The controls were removed that July.

There are also plenty of things outside the president’s direct control that can raise prices. Think supply-chain disruptions, natural disasters, far-off wars or Fed policy mistakes.

Consider Trump’s promise to reduce energy costs through faster permitting and weaker environmental regulations—to “drill, baby, drill.” Trump’s oil and natural-gas supporters love his antiregulatory bent, but they don’t actually seem as eager to drill more. A fossil-fuel glut during Trump’s first term caused debt strains for many drillers, leading them to focus more on returning capital to shareholders than investing in new production.

Even if U.S. oil production, which has been at a record high, doesn’t move up meaningfully, energy costs might still be poised to fall as a result of factors outside the U.S. The International Energy Agency last month lowered its oil-demand-growth projections for 2025, citing “below-par underlying global economic conditions, as well as clean energy technology deployment.” Oil production, meanwhile, looks poised to rise, “so what you have is too much oil chasing too few consumers,” said the energy economist Phil Verleger .

So, with all that in mind, what should Americans expect for inflation in 2025? Will it continue its bumpy path downward, stall out or turn higher?

There are signs that favor lower inflation in the year ahead. One is that there has been a degree of “catch-up inflation” in the recent data , such as car insurers that get regulatory approval to raise rates to offset higher costs. But those effects should fade.

Also, U.S. productivity growth looks to have picked up, which probably has something to do with the reordering of work that the pandemic set off. Improved productivity can help lower inflation, since a more efficient workforce can produce goods and services at a lower cost.

The general view among economists on inflation is that, absent any big changes to government policy, “We’re just on some kind of glide path back to something in the ballpark of where we were before,” said Emi Nakamura , an economist at the University of California, Berkeley.

Trump has threatened high duties against Chinese goods in particular and 25% tariffs against Mexico and Canada . If he follows through, that could push up prices on an array of products , including Canadian lumber and oil and Mexican fruits and vegetables. Prices for autos, in particular, could go higher, since car companies rely on a complex manufacturing network that spans the U.S., Canada and Mexico.

There could be at least partial offsets. If tariffs bite into consumers’ buying power, for example, their demand for other products might drop, weighing on prices for those items. Retaliatory tariffs would lower the demand for U.S. goods abroad, boosting domestic supplies. The dollar could strengthen against other currencies, lowering the price of imports, but making U.S. exports less competitive.

Immigration restrictions could also push up prices, particularly on goods and services from businesses that rely heavily on the labor of immigrants. Goldman Sachs estimates that the share of workers who are unauthorized immigrants is about 13% in the construction industry and 16% in the animal-processing and slaughtering industry, for example.

Some of the things that might push inflation higher in the new year could be transitory. Prices might rise in response to tariffs, but that would presumably be a one-time increase.

But one problem with a fresh bout of inflation is that people and businesses might do more to try to get in front of it than they did a couple of years ago—which could be inflationary in itself. Inflation is, after all, a movie that Americans have now seen before.

As the economists Milton Friedman and Edmund Phelps pointed out in the late 1960s , inflation expectations matter for future inflation. If workers, for example, think prices are heading higher, they will demand bigger wage increases. The rising labor costs that result will then be pushed through into higher prices.

Already, there are signs that inflation expectations could be shifting. Some retailers’ holiday-shopping pitch to shoppers is to buy now, before tariffs hit . And in the latest University of Michigan survey of consumers, there was a surge in the share of people who said it was a good time to buy major household items, such as furniture, refrigerators and televisions, because they think prices are going up .

Write to Justin Lahart at Justin.Lahart@wsj.com