Thanks. Have you thought about doing something similar with wages? In other words, if the Calvo thing was ever going to make any sense, it feels like it would make a little bit more sense with wage setting. You know, you get your raise once a year. So I don't know if there was some scope for that. I wonder if we show up there.

I would like to comment on the list of reasons why one wanted to have low inflation. I believe that something has been missing for the sixth

reason, and I think it is the most important one. My background is German, so we have German history. And the great inflation in the 20s destroyed the Weimar

Republic. And so there is a feedback between the political system and price stability. In particular, now that people live 20 years longer than they leave the

labor force, which means somebody has to provide for their living after having left the labor force, which is by either Social Security provision or other government measures, or by individual saving. And if you rely

completely on the government to provide for the living of the old generation, the government would be overwhelmed, and this would probably would mean that the

society in a democratic way would no longer be able to operate. So we need the reliance on individual provision for one's own future. That is, we need to

rely on saving, individual saving. And therefore it is particularly important from the political economy point of view that you provide a simple way of providing for the future. And this is basically price stability. I think you

mentioned that cognitive limitations of people in providing for the future may also be a reason to provide for price stability, and I believe this is a very important point. This is a much more practical suggestion relating to Jordi's

comment about the changes in prices are not equivalent to the cross-sectional variance. So why might this go wrong? Because you might have a bunch of small changes, period after period, but if they're persistent, then prices can slowly drift apart, and so the changes might look small and the dispersion high,

and this might be plausibly what happens in an inflation. So my suggestion would be to correct with autocorrelation. That's something you probably could measure with your data, because I get that doing cross-section directly is really hard, because we've got a lot of different products, but the autocorrelation within each product is something that you could compute, and then changes over one minus autocorrelation is the

cross-sectional variance of a stochastic process that has that variance in the innovation, has that autocorrelation. Does it solve all the problems? No, but would it get, you know, bring us a lot closer to narrowing that gap between changes and dispersion? Yeah, I think it would help. So two reasons inflation was costly in the 70s. One,

capital income taxation is nominal. That's true now, too, so if you increase steady-state

inflation, you increase the capital taxation, which you may or may not like, but it has that implication. Second, with constrained financial markets, where banks

essentially only showed annuity loans, high inflation meant that you had to repay that debt really fast. With that cost, it's probably not so large now, given financial innovation. It's much easier to get around that particular cost of inflation, but I feel capital taxation should

not be forgotten. And by the way, it would be nice if you emphasize beyond, besides steady-state inflation for central banks, given that you basically showed that

we should trash the implications of the Calvo model and go with the new cost model, what should central banks think about in terms of the transmission mechanism there or the policies?

Well, thank you very much, Jordi. I mean, basically I agree with everything you say. Let me talk a little bit about this relationship between absolute size and measures of inefficient price dispersion. It's absolutely right that this is an indirect link. This is

something Laura also mentioned as well. The reason that this is so challenging is that I think a very convincing conclusion of the empirical literature on pricing in recent years is that you have to consider idiosyncratic shocks. The model just doesn't work at all in terms of fitting the data if you don't allow for some kind of idiosyncratic shocks

to firms' desired prices, because average price changes are something like 10% per year. There must be a lot of unobserved reasons why firms want to change their prices that aren't related to average inflation. Once you allow for the fact that there's a lot of unobserved reasons for why firms want to change their prices, then it becomes much more difficult to

tell whether they have the right price or the wrong price. For example, if you didn't have these idiosyncratic shocks, you could just look at how far the current price was from some kind of long-term average, like a fixed-effect regression or something, and that would give you some sense of inefficient price dispersion. But if you have these idiosyncratic shocks, then when the firm changes its price, it might be because they really wanted to,

because something happened that made it want to change its price. And so our approach of using these absolute size of price changes is kind of like a revealed choice approach. The idea is that if you did decide to change your price by a lot, then that indicates that your initial price before you adjusted was far off. So that's kind of the idea, that we're using

this kind of revealed preference approach. But it's absolutely true that this relies on some structure. So in particular, it relies on the notion that is true in many of these models but not universally true, that your difference between your current price and your desired price would be related to how much you adjust conditional and adjustment.

So for example, in a world where you always change your price by 5% no matter what, no matter what, then our method really wouldn't work. Because even if you're super far from your desired price, you still change it by just 5% per year or whatever per period every time, and it just doesn't work. So that I think is an important assumption in what we're

doing. More generally, I think this role of idiosyncratic shocks is a huge difference between this class of models and the earlier generation of models. So the earlier generation of models, which didn't have these idiosyncratic shocks, there is an earlier generation of menu cost models where in fact the SS bounds themselves were pretty sensitive to steady-state inflation.

And that was basically because there weren't these idiosyncratic shocks. But I think it is a genuine challenge of how to come up with a measure, and so this is sort of a semi-structural approach to doing it. I totally agree with the idea that there are other things like, for example, cognitive costs and political concerns and so on that we need to think about.

It's important to recognize that there are other potential upsides of higher inflation. Like, for example, if there are sticky wages, there's this idea that having higher inflation might sort of grease the wheels of the labor market, and that could be a potential upside. On this issue of whether the Calvo model already sort of generates essentially nothing at low

inflation rates, it's worth recognizing that the axes on that graph make the changes at low inflation rates look really small, but they are something like, even at low inflation rates, half a percent of steady-state consumption. So depending on how you specify things, that could play a role. I'm very sympathetic to what you said about your model suggesting

that these costs were small relative to the potential costs of hitting the zero lower bound, but there is other research where the costs of hitting the zero lower bound maybe is parameterized to be smaller, and so even this half a percent of steady-state consumption actually makes a difference. Thank you. Thanks a lot. You want to say?

Lunch.