 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 put up by Tony Ghani I Believe that something has been missing. So there's a six 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 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 they 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 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 Jordy'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 auto correlation That's something you probably could measure with your data because I get that like doing cross-section Directly is really hard because we've got a lot of different different products But the auto correlation within each product is something that you could compute and then changes over one minus auto correlation Is the cross-sectional variance of a stochastic process that has that variance in the innovation has that auto correlation? 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 Was costly in the 70s was one Capital tax capital income taxation is nominal That's true now too. So if you increase Stabilized inflation you you increase the capital taxation Which you may or may not like but it has that implication second within with constrained financial markets with banks Essentially only should and with the loans high inflation meant that you have to repay that debt really fast with with That cost is 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 if you emphasize Beyond besides steady-state inflation For central banks. What are they given that you you basically show that we should Trash implications of the Calvary model and and go with them and a new cost model what should Central banks think about in terms of the transmission mechanism there or the policies Well, thank you very much Jordy, 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 it's absolutely right that this is an indirect link, you know, this is you know 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 prices are 10% average price changes or something like 10% per year And so there must be a lot of unobserved reasons why firms want to change their prices that aren't related to average inflation And then 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 Like 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 kind of like a revealed choice approach The idea is that if you if you did decide to change your price By a lot then that indicates that your initial price before you adjusted was 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 you know your your 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 five percent 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 five percent per year, you know or whatever per period every time and it just doesn't work So that that I think is is 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, you know 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 bands themselves were pretty sensitive to steady-state inflation And and that was basically because there weren't these idiosyncratic shocks But I you know I think it is a genuine challenge of how to come up with a with a measure And so this is sort of a semi structural approach to doing it I totally agree with the idea that there 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 might be 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 Caval 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 are like half a percent of Steady-state, you know consumption so depending on how you specify things that could play a role And I I mean I'm very sympathetic to what you said about your model suggesting that these costs were small relative to the potential cost of hitting the zero lower bound But there is other research where the cost 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