John C. Williams, the president of the Federal Reserve Bank of New York, thinks that the central bank’s push to cool the economy is near its peak and that he expects that interest rates could begin to come down next year.

In an interview on Aug. 2, Mr. Williams said that inflation was coming down as hoped, and that while he expected unemployment to rise slightly as the economy cooled, by how much was unclear.

The upshot is that interest rates are unlikely to rise much further than the current range of 5.25 to 5.5 percent. Fed officials could also consider cutting them soon: Mr. Williams did not rule out the possibility of lowering rates in early 2024, depending on economic data. His comments are a sign that moderating inflation could pave the way for a shift in policy approach. After months of focusing single-mindedly on bringing inflation under control, officials are increasingly focused on not overdoing it as they try to ease the economy through a gentle cooling.

Below are edited highlights of the interview. (Read the full transcript here.)

I wonder if there is anything that is on your mind that you want to talk about?

We’re seeing continued strength in the economy. At the same time, a lot of the indicators are moving in the right direction. We’ve seen the job openings and other indicators are telling us that supply and demand are moving closer together.

On the inflation front I definitely think that the data are moving similarly in the right direction, but I think that similarly, the only way we’re really going to achieve the 2 percent inflation on a sustained basis is really to bring that balance back to the economy.

Clearly we’re not in a recession, or anything like that — but we need to see that process of getting supply and demand, from both sides, coming back into balance.

Do you think additional rate increases are necessary to achieve that?

I think that’s an open question, honestly.

I think we’ve got monetary policy in a good place, it is definitely restrictive, but we have to watch the data. Are we seeing the supply-demand imbalances continue to shrink, move in the right direction? Are we seeing the inflation data move in the right direction, in order to decide that?

Of course, there is another question, which is: How long do we have to keep the restrictive stance of policy? And that I think it’s going to be driven by the data.

Are we talking about one more rate increase or more?

Given what I see today, from the perspective of the data that we have, I think — it’s not about having to tighten monetary policy a lot. To me, the debate is really about: Do we need to do another rate increase? Or not?

I think we’re pretty close to what a peak rate would be, and the question will really be — once we have a good understanding of that, how long will we need to keep policy in a restrictive stance, and what does that mean.

When you say “what does that mean,” what do you mean by that?

I think of monetary policy primarily in terms of real interest rates, and we set nominal rates.

[Note: Real interest rates subtract out inflation, while nominal rates include it. Estimates of the so-called “neutral” rate setting that neither heats nor cools the economy are usually expressed in inflation-adjusted, real terms.]

Assuming inflation continues to come down, it comes down next year, as many forecast, including the economic projections, if we don’t cut interest rates at some point next year then real interest rates will go up, and up, and up. And that won’t be consistent with our goals. So I do think that from my perspective, to keep maintaining a restrictive stance may very well involved cutting the federal funds rate next year, or year after, but really it’s about how are we affecting real interest rates — not nominal rates.

My outlook is really one where inflation comes back to 2 percent over the next two years, and the economy comes into better balance, and eventually monetary policy will need over the next few years to get back to a more normal — whatever that normal is — a more normal setting of policy.

Could you see a rate cut in the first half next year?

I think it will depend on the data, and depend on what’s happening with inflation. The first half of next year is still a ways off.

I don’t think the issue is exactly the timing, or things. It’s really more that if inflation is coming down, it will be natural to bring nominal interest rates down next year, consistent with that, to keep the stance of monetary policy appropriate for an economy that’s growing, and for inflation moving to the 2 percent level.

Is inflation falling faster than expected?

I do think that overall P.C.E. inflation for the year will probably come in at 3 percent, that depends on a lot of different things, and I expect core inflation to be above that, based on all the information we’re seeing.

I do think that we are moving to an environment already where the underlying inflation rate has come down quite a bit. Mainly because — or not mainly, but in large part because the shelter inflation has come down so much. That’s been such a big driver of core inflation over the last couple of years.

Is it coming down as expected, or quicker than expected? How has this compared to what you would have forecast three months ago?

The data have surprised me and everybody a lot the past couple of years, because of the pandemic, the war, Russia’s war in Ukraine, all the things that happen. Surprises in data have become more the norm. For me, personally, the inflation data have been coming in as I had expected — and also hoped.

What do you see as that sustainable pace of job growth?

A lot of the labor force growth we’ve seen over the past year or so has been a rebound, and a return to a strong labor market conditions after the pandemic. That can’t continue every year forever: I mean the high labor force participation can continue, but it can’t continue to grow and grow and grow forever.

Like a 100,000, or 150,000, gain in monthly employment?

I’m not sure exactly, but it’s more in that 100,000 range than where it is today. We can’t be really precise about what exactly that means.

What about wage growth? How much do you think you need to get wage growth down in order to feel confident that inflation is going to come down?

I view wage growth, in terms of your question, as more of an indicator, rather than a goal or a target. So I don’t sit there thinking: We need to see wage growth do one thing or another in the next year or two.

We’re still in an economy where demand exceeds supply, it’s a strong labor market, clearly, and wage growth has been very strong and it’s higher than inflation.

Now, in the longer run, when you think about — over the next five years or something — you would expect real wages, wages adjusted for inflation, to grow consistent with productivity trends. Right now, I don’t think that’s exactly what I’m focused on. I’m more focused on: what are all these indicators, all the different data telling us about the overall balance or imbalance between supply and demand and what that implies for inflation.

Would you be comfortable skipping a rate increase in September?

We get a lot of data between now and the September meeting, and we will have to analyze that and make the right decision. I personally don’t have any preference of what we need to do at a future meeting.

From my perspective, we have gone from a place — a year, a year and a half ago, where the inflation was way too high, not moving in the right direction, and the risks were all on inflation being too high, to one where the risks are on both sides.

We have the two-sided risks that we need to balance, making sure that we don’t do too much, and weaken the economy too much — more than we need to in order to achieve our goals — and at the same time make sure that we do enough to make sure that we convincingly bring inflation back to 2 percent.

Do you think that unemployment needs to go up in order for inflation to come down?

Right now the unemployment rate is below many people’s view of a long-run normal unemployment rate, but not by a lot. A few tenths or so. From that perspective, I would expect the unemployment rate would move back to a more normal level. Will it rise above that, in order to really get inflation back to 2 percent? I don’t know the answer to that, in my own projection, my own forecast, I expect that the unemployment rate will rise above 4 percent next year, but I can’t say with any conviction how much will that need to happen.

What do you think the criteria will be for cutting interest rates next year?

To me, I think the main criteria that I’m thinking about in my forecast, is that really about with inflation coming down, needing to adjust interest rates with that so that we’re not inadvertently tightening policy more and more just because inflation is down. That is my baseline forecast — obviously, if the economic outlook changes, or other factors happen, there are other reasons why you’d change interest rates.

A risk that people are talking about right now is this possibility of not just no landing, but re-acceleration. It’s possible that the economy takes back off and you guys have to do more down the road. I wonder how you think about the possibility?

It’s a possibility. Being data-dependent means that if we see the data moving in that direction, we’ll need to act appropriately, as we have in the past.

To me I guess if that risk were to materialize, it probably would be more that, demand is a lot stronger than I had been expecting, and we probably need more restrictive policy to bring supply and demand back into balance.

A question we get from our readers all the time is: Are mortgage rates ever going to go back down to where they were before the pandemic disruptions? And I wonder what you think of that, as the person who’s done all of the research on interest rates?

My expectation is that over time, over years, real interest rates will actually come back down from the levels they’re at.

I haven’t seen really any strong evidence that neutral rates have yet risen much beyond what they were, say before the pandemic.

If there’s a risk of going back to very low neutral rates, which obviously carries this inherent risk of ending up back at zero, why not just raise the inflation target now? It seems like you could deal with two problems at once, both giving yourself more headroom and making it easier to hit the inflation target.

I think the experience of the past few years has taught me that 4 percent inflation is not considered price stability — it has not felt like price stability by the general public, or quite honestly, by policymakers; 4 percent inflation seems very high in the modern world. 3 percent seems high; 2 percent was already the compromise, of saying: Why not go all the way to zero? And there’s some technical reasons that you might not want to go all the way to zero, but 2 percent was to provide a buffer.

[When the Fed reviewed its approach to setting policy in 2020] I personally felt comfortable that a 2 percent target, along with a commitment to achieving 2 percent inflation on average over time, positioned us well to achieve those goals.