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he Federal Reserve raised interest rates another quarter-percent Wednesday, citing the “solid rate’’ of economic activity­ as a reason for its widely expected move to tap on the monetary brakes.

Looking ahead, though, Federal Reserve board members have widely differing views on what to do next — everything from zero further rate hikes in 2018 to five.

The tricky thing about the US economy is that it seems to be in an impossibly paradoxical state: growing too fast, and not fast enough.

Unemployment is nearing historic lows, for instance, but somehow that has not led to accelerated wage growth or higher inflation.

Then there’s the uncertain effect of the Republican tax bill, set to provide an oversized hit of stimulus, regardless of whether we need it.

Here are key puzzles the Fed needs to solve if it’s to keep the economy on track in the months and years ahead.

#1: What happened to inflation?

The Federal Reserve has two basic tasks: Make jobs plentiful and keep inflation under control.

For decades, managing these tasks has been seen as a kind of trade-off, or a balancing act. A little stimulus was essential to help people find work; too much risked driving up inflation.

Somewhere in the middle is the supposed sweet spot, the ideal unemployment rate, with jobs abundant but inflation still tame. Economists call it the NAIRU, for Non-Accelerating Inflation Rate of Unemployment.

But this concept has come under serious strain because the unemployment rate has dropped below current estimates of NAIRU — roughly 4.6 to 4.7 percent — without triggering any noticeable rise in inflation. What’s going on?

Maybe the unemployment rate is the wrong indicator to focus on, or perhaps there’s a more fundamental issue with the whole idea that having lots of jobs means higher inflation.

It’s not yet clear, but according to Wednesday’s official statements, Fed members still expect inflation to approach 2 percent “over the medium term.’’

#2: Where’s the wage growth?

Inflation isn’t the only thing that’s supposed to go up when jobs abound — so are wages.

Think of it this way:

During a recession, when unemployment is high and people are desperate for work, companies don’t have to pay much to attract employees.

But when the economy is strong and most people are working, then companies need to poach — which means paying a premium to get the best workers.

Plus, to keep poachers at bay, businesses have to fight back by raising salaries.

The result is higher wages all around.

Except for some reason, that hasn’t happened.

Despite years of economic growth and historically low unemployment, average wages are growing by about 2.5 percent per year — well below the 3.5 to 4 percent growth you’d hope to see in a strong economy.

Here, again, the problem could be that we’re focused too narrowly on the unemployment rate, when other indicators suggest jobs aren’t quite so easy to find. Alternatively, it could be that machines and robots are slowly pushing workers out of high-productivity jobs and into the lower-paying service sector.

#3: ill-timed tax cuts

There’s a serious macroeconomic problem with the Republican tax plan. It provides a substantial amount of tax-cut-related stimulus in 2019 and 2020, when there’s no guarantee such stimulus will be needed. Deficit spending is supposed to be carefully timed, landing in people’s pockets when they need an extra boost. Otherwise, it’s either unnecessary or dangerous.

Remember, the Fed already believes the economy is growing as fast as it can — that’s the reason for rate hikes. Should we remain at this maximum, tax cuts could push the economy into unsustainable bubble-land.

So the Fed needs a plan to offset the tax cuts, at the risk of angering the cuts’ Republican sponsors. One approach would be to raise rates more quickly in preparation for the tax reductions, which would create room for stimulus (albeit at the risk of triggering a recession.)

Projections released Wednesday do suggest a slightly speedier pace of rate hikes after 2018, but the effect is relatively small. And the more likely approach is for the Fed to set clear expectations about its willingness to act quickly at the first sign of overheating.

The greatest risk of all

Behind all these puzzles lies the one calamity the Fed is most eager to avoid: recession. And given that our current recovery now ranks as the second-longest one since World War II, you can be sure it’s out there somewhere, just waiting for the opportunity.

Yet there is still room for hope. If the Fed can somehow figure out the best medicine for an economy with such contrary symptoms as low unemployment, low inflation, and low wages, ours may be remembered as the longest sustained period of economic growth in American history.

Evan Horowitz digs through data to find information that illuminates policy issues facing the United States. He can be reached at evan.horowitz@globe.com.