The Federal Reserve has met one part of its legal mandate: Unemployment is low enough that most people looking for a job can usually find one. Yet interest rates in the United States remain at historic lows. The reason is that inflation remains below the central bank’s target of 2 percent per year, and the Fed is reluctant to raise rates quickly until policymakers are confident that inflation will return to its desired level.

So the key question facing both Fed policymakers and anyone else interested in the future of interest rates is: When will inflation rise? Both conventional wisdom and the Fed’s official communications emphasize two main factors that drive inflation. First, there is un- and underemployment, what economists call “labor market slack”: When more people are out of work, it’s harder for employees to demand higher pay. This suggests that more slack results in lower inflation because when wages stagnate, so do prices. The second factor is the expectation of future inflation: The more inflation people expect, the more workers will demand raises and businesses will raise prices in anticipation. That is, higher expected inflation results in bigger price increases.

But in a report released Friday as part of the U.S. Monetary Policy Forum in New York, we argue that the focus on these two factors is too narrow. We find that the strongest predictor of what inflation will do in the near future is what it has done in the recent past. In statistical jargon, we find that inflation is highly persistent, fluctuating around a slow-moving trend. This long-term trend is not sensitive to unemployment or to inflation expectations.

This finding has significant implications for Fed policymakers. It suggests that they should put less faith in traditional models of inflation and should both think and talk about it differently. Furthermore, it means that achieving their long-run 2 percent objective could very well require that policymakers overshoot their target for at least a short time.

The chart below shows one of the most closely watched measures of inflation, the “core” Consumer Price Index, which tracks the cost of common items but excludes food and energy purchases because those prices have historically been volatile. The orange line shows our estimate of the long-term trend, which is calculated using only past information and is updated as each new observation becomes available. (In other words, our calculation of the trend isn’t based on any information that people setting prices wouldn’t have had at the time.)

As the chart shows, inflation typically sticks pretty close to its recent trend. In fact, once we account for that trend, neither labor market slack nor expectations help forecast inflation — they provide little information that isn’t already accounted for by the trend. The low predictive value of unemployment has been noted before, but the fact that expectations are also irrelevant is more surprising.

Why is this such a surprise? The chart below helps explain why many observers consider expectations to be a good predictor of inflation. It shows the level of core inflation on the vertical axis and forecasts from one year earlier on the horizontal axis. The relationship is fairly strong: Higher inflation does follow higher inflation forecasts.

But this picture turns out to be misleading. To see why, consider that as the long-term trend in inflation moves, both current inflation and expectations of future inflation move with it. If inflation has been about 2 percent in recent years, most forecasters will expect it to remain in that neighborhood — and they will probably be right. So instead of looking at the absolute level of inflation, it is more revealing to compare changes in predictions to changes in the rate of inflation. The next chart shows what happens when we do this. The result is striking: Changes in expectations tell us almost nothing about changes in future inflation.

Our findings don’t mean that the trend is the only thing that matters for understanding inflation. Our research suggests that other factors help explain the trend, including the exchange rate (the Fed’s broad trade-weighted dollar index), the growth of the money supply (specifically growth in the so-called M2 money supply), total nonfinancial credit growth, and U.S. financial conditions more broadly. We conclude that policymakers should pay attention to a broader array of factors rather than just focusing on expectations and slack. If inflation expectations move away from the Fed’s target but other measures remain stable, policymakers should be less concerned. If several indicators shift simultaneously, on the other hand, the Fed should expect inflation to move and take appropriate action.

Our findings also have implications for one of the most hotly debated questions among Fed policymakers and observers: Should the Fed allow inflation to “overshoot” its 2 percent target? We find that the answer to this question is yes — but not by much and not for long. The logic underlying this conclusion comes from the fact that the long-term trend of inflation closely follows an average of the past few years of inflation. Right now, inflation is less than 2 percent, so to reach that target, it will need to overshoot that number temporarily, which will raise the recent average. The size of the required overshoot depends on how quickly the Fed’s actions influence inflation and how quickly the central bank wants it to return to target. However, because inflation isn’t far below the Fed’s target — less than half a percentage point — it wouldn’t need to rise much above 2 percent or stay at that level for very long to bring the trend to its target. The temporary overshoot would also be less than half a percentage point.

We conclude that the Fed needs to remain vigilant. Movements in slack and inflation expectations can be misleading, so policymakers should closely monitor a broader set of indicators. While a modest overshoot may be appropriate, if inflation continues rising, policymakers will need to act. Allowing inflation to rise too much could lead to a prolonged period of inflation above 2 percent. If that happens, the Fed could be forced to aggressively raise interest rates to bring inflation under control.