Why do people dislike inflation?

Matt Yglesias thinks that if people knew that wages were the biggest component of the price level, they wouldn't be as freaked out by inflation:

[T]he most important price in the economy is the price of labor and the price of labor is equal to workers' incomes, so a general increase in the nominal price level is necessarily a general increase in nominal incomes. But nobody seems to believe that. Instead people are convinced that gasoline and milk are the main prices in the economy, and that a general increase in the nominal price level is necessarily a general decline in real incomes.

This is a pretty common idea: People dislike inflation because of money illusion. They mistake their nominal incomes for real incomes, and mistake consumer prices for the real cost of living. Seems plausible. And it provides a parsimonious explanation for other phenomena, such as downward nominal wage stickiness.

Except that I see a problem with this explanation. Money illusion explains why people dislike hypothetical or prospective inflation, but it does not explain why people are unhappy when inflation actually happens. Suppose real prices and real wages are unchanged, but inflation spikes to 10%. People who suffer from money illusion will tend to be upset when consumer prices rise, but happy when their nominal wages rise. So in this scenario, it seems that their elation at rising "incomes" would at least mostly cancel out their dismay at rising "costs of living". Instead, it seems that actual inflation causes a lot more dismay than elation.

Here's an alternative explanation: Maybe people think that inflation lowers their real wages. Why would they think that? Well, because inflation tends to correlate with lower real wages! Check out this graph, courtesy of Pau Rabana of NYU, which shows the historically observed correlation between inflation and real wages in the U.S.:

This graph clearly shows that when inflation goes up (at time 0), real wages tend to go down over the next few months. That means that inflation really is correlated with an increase in the cost of living for the average American.

Now, of course, correlation does not equal causation, but mistaking correlation for causation seems like a lot easier of an error to make than money illusion. If people see a spike in inflation, they are logically justified in saying "Oh no, here comes an increase in my cost of living!" They are not necessarily justified in saying "If we had taken steps to prevent that inflation, my cost of living wouldn't have gone up." But it is a very short leap of illogic to go from the first statement to the second. 

It's easy to to see how the correlation in this graph could be misleading. People instinctively think that causes precede effects in time, but this is not always the case. For example, what if expected inflation leads actual inflation, and a spike in expected inflation causes real wages to rise, through a forward-looking Phillips Curve kind of effect? 

But on the other hand, maybe inflation really does cause real wages to fall. How would this work? I don't know, because the wage bargaining process is not well-understood. There are a lot of puzzles and mysteries. One possibility, just off the top of my head, is that inflation allows employers to cut real wages more easily without violating implicit contracts. That could be caused by money illusion too, or it could be caused by people thinking that their coworkers might have money illusion. Anyway, that's just a conjecture.

The basic point is: Maybe people don't dislike inflation because they're stupid. Maybe people dislike inflation because they know it's correlated with falling real wages.