How Inflation Helps Locate Slack: The Level-and-Speed Test

This chapter explains how economists use inflation and wage behavior to infer a benchmark that cannot be observed directly. The Federal Reserve framework does not look only at whether output or unemployment is high or low; it also asks how quickly the gap is changing and whether prices and wages respond in a way consistent with cyclical pressure. That level-and-speed test gives the model a way to distinguish a movement in the cycle from a movement in capacity, while still leaving room for uncertainty.

A gap has a level and a direction of travel

A single unemployment reading tells us where the labor market is. It does not tell us how the market got there or where it is going. An unemployment rate of 4 percent could represent a stable condition, a rapid decline from a much higher rate, or the end of a period in which the rate has been unusually low. Those situations can have different implications for wages and prices even if the final number is identical.

The Federal Reserve paper builds this distinction into its Phillips curves. In the price-inflation relationship, inflation depends on the level of the output gap and on the change in that gap. In the wage-inflation relationship, wage growth depends on the level and change of the unemployment gap. The level term asks how far activity is from the relevant capacity. The speed term asks how quickly that distance is changing. Together they allow the model to represent both the current position and the history carried by recent movements.

The speed term is not simply a second way to say “the economy is strong.” It is informative because a capacity that responds to past cyclical conditions changes as the gap changes. If a period of weak demand pushes output below its supply-driven path, the subsequent movement of that gap contains information about whether the economy is merely returning to its old capacity or whether capacity itself has been altered. A model with no scarring can use only the cyclical component to explain the persistence. A model with scarring can let the trend absorb part of it.

The wage equation adds a related labor-market check. Wage growth is compared not just with unemployment but also with trend labor productivity and trend inflation. That matters because nominal wage growth can be high for different reasons: labor demand may be strong, prices may be rising, or productivity may support higher compensation without the same inflationary pressure. A model that treats all wage movement as evidence of excess demand would confuse those channels.

Price inflation provides another check. If output moves sharply but inflation and wages respond only modestly, the observation is harder to reconcile with a large purely cyclical demand gap when the Phillips curve is steep. It may instead point toward supply-driven movement or a capacity path that has absorbed some of the persistence. Conversely, a rapid inflation response to a relatively small cyclical movement can support a different allocation of the data. The signals are not self-interpreting; the model connects them through restrictions.

Those restrictions are what turn several time series into evidence about a hidden benchmark. Output and unemployment describe real activity.