This issue’s syllabus · Issue No. 17 · August 23, 2026
Extra Credit Series · Fixed Income · Part 2 of 2The Math Behind the Echo.
How much of a price shock actually survives. You already have the core distinction from the Foundation piece — now here’s how to actually check it against the numbers.
You already have the core distinction. A first round effect fades on its own. A second round effect feeds itself through wages and expectations. But how would you actually tell the difference between the two? Well there are three questions worth asking.
What share of current inflation comes from the original shock itself, versus from wages and other second round prices?
The useful framing is what fraction of the current reading is still attributable to that shock, and whether that fraction is rising or falling from month to month. A falling share, even during a period of high headline inflation, means the shock is behaving like a first round effect. A rising share is early evidence of a second round taking hold. The cleanest proxy most people can actually follow is the gap between headline inflation and core inflation. A wide gap generally means the shock is still sitting in the volatile categories where it started. A gap that keeps closing means the increase is migrating into everything else which is an early sign of a second round.
Is nominal wage growth running ahead of, in line with, or behind inflation, and has that relationship recently flipped?
This is the checkable version of asking whether a spiral is actually happening, rather than simply feared. A common mistake is treating falling real wages, meaning wages adjusted for inflation, as proof that no spiral is occurring. It can mean the opposite is true. Workers have not yet caught up to the prices they are facing and are still trying to close that gap. What matters is the trend in the gap between nominal wage growth and inflation over time, not the level of either line on its own.
Are long run expectations still anchored near target, or have they started drifting?
Consumer expectations are captured through surveys that ask households directly what inflation they expect over the coming year and over the next five to ten years. Market based measures exist too, most notably the gap between ordinary government bond yields and inflation protected bond yields, which reflects what investors are collectively pricing in for future inflation. When either measure drifts meaningfully away from a central bank’s target, that is what officials mean when they say expectations have become unanchored.
Let’s start with the arithmetic question. Take a price index that is equal to one hundred. One category inside it jumps ten percent in a single month and then never moves again. Here is what the twelve month inflation rate for that category looks like along the way.
| Month | Index | Vs. a year earlier | 12-month rate |
|---|---|---|---|
| Month 0 | 100 | — | Before the shock |
| Month 1 | 110 | vs 100 a year earlier | Up 10 percent |
| Month 6 | 110 | vs 100 a year earlier | Up 10 percent |
| Month 12 | 110 | vs 100 a year earlier | Up 10 percent |
| Month 13 | 110 | vs 110 a year earlier | Up 0 percent |
The price never came back down. The category is still ten percent more expensive than it was, permanently. But its contribution to the yearly inflation rate falls to exactly zero in month thirteen, because the comparison month now already contains the increase. That is the whole of what a first round effect does mathematically.
Fighting near the Strait of Hormuz has repeatedly disrupted the flow of crude, and gas at the pump has followed it upward. That is a textbook first round shock, and the question worth asking is not whether it happened. It obviously did. The question is whether it stays a first round shock or starts migrating into the second round.
Run question one against it using the framework above. Watch the gap between headline and core inflation in the months ahead. If that gap holds roughly steady or widens, the shock is behaving the way a first round effect is supposed to, sitting in energy prices and waiting to age out of the twelve month comparison. If core starts climbing to meet headline while energy itself levels off, that migration is the tell.
Run question two against it by watching whether wage growth accelerates in the months following the spike or stays roughly where it was. A shock that never shows up in wage negotiations has a much harder time becoming self-sustaining because nothing is refilling the loop.
Run question three against it by watching the gap between near term and long run inflation expectations. It would be unusual for near term expectations not to move at all when people are watching gas prices rise in front of them. What actually carries information is whether the long run number moves with it or holds where it was. A near term jump paired with a steady long run number is a very different signal than both numbers moving together.
None of this requires a forecast. It requires watching three specific relationships over the months ahead rather than reacting to a single headline print, which is precisely the discipline the Foundation piece was building toward.
The next time an inflation headline lands, whether it involves oil, a tariff, or something else entirely, the same three questions apply. What share of the number is pass through from the original shock, and is that share rising or falling. Is nominal wage growth gaining on inflation or losing ground to it and has that trend recently turned. And are long run expectations, whichever way you choose to track them, still sitting close to target or starting to drift.