Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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# Are State- and Time-Dependent Models Really Different?

Authors:   
Discussant: None  
Video: https://www.youtube.com/watch?v=Asf4Eki6FCU&t=0s


## Talk (00:00:00 – 00:19:53)

[00:00:02] so what this paper does is to develop an analytic comparison of two of the main frameworks that are used to model sticky prices in macroeconomics the first framework is one in which  
[00:00:16] firms monitor economic conditions that determine their state like markups or profits on a continuous time basis so firms have all the information um and you know they're presumably reacting  
[00:00:30] to those conditions when shocks occur so that's why these approaches is called the state dependent approach second approach is one where firms are assumed to behave differently they're subject to spells of inattention so to  
[00:00:44] say for reasons that i'm going to discuss so that when the news arrive say an aggregate track or something they cannot be expected to react on impact sometime needs to elapse for some special times  
[00:00:57] to arrive when the new observation is retrieved and processed and decisions are made so the question we want to ask is whether the type of rule that one uses to model  
[00:01:10] stickiness matter for the response of the economy to an aggregate nominal shock and we're going to do this with a simple analytic model and the contribution is going to be partly theoretical and a little bit of  
[00:01:25] evidence concerning the theory we'll show that if one focuses on small shocks the ones that are typically at the center of our of many of our exercises and if the two approaches are used to  
[00:01:39] model the same key moments of an economy think of these key moments like the frequency of adjustment and something else i'm going to discuss then the two approaches are going to give you exactly the same kind of propagation so there is no difference  
[00:01:54] now for large shock instead the two approaches will differ and we'll try to use such predictions concerning different reactions depending on the size of the shock to collect some evidence um  
[00:02:09] on state dependent behavior so let me give you a little bit of the flavor of what's in our theory it's a simple framework so we consider a profit maximizing firm that is uh  
[00:02:26] you know has some constant markup over marginal cost p star is the profit maximizing prices that the firm would be charging ups and frictions and this ideal price moves around because of shocks to marginal costs which are  
[00:02:39] idiosyncratic to the firms in particular we assume they will follow a random walk or brownian in continuous time now the firm is profit maximizing and we'll con we'll consider a second order approximation to the profit function of  
[00:02:53] the firms where essentially the firm's decision can be summarized by one single state variable this g variable is a price gap that will measure the distance between the current price charged by the firm pt and these  
[00:03:05] uh static profit maximizing prices p star and the law of motion of g is going to be a diffusion with a drift pi that you can think of that like a drift in productivity or or inflation and those  
[00:03:20] idiosyncratic innovation sigma dw now for uh this paper we let's assume that pi over sigma is a small number you can think of focusing on a word of zero inflation or just a world where idiosyncratic shocks  
[00:03:34] are large relative to the drift which is a good approximation for most developed countries now the paper is more broader than the simple formulas i'll be able to show here but given time that's the only thing i can do now but so the paper has  
[00:03:48] firms selling many products not just one the shocks to these products could be correlated between them there could be different elasticities between the substitutability of goods within the bundle that the firm is selling and  
[00:04:00] across bundles of different firms those generalizations are useful to account for several features of the micro data but as i said they're in the paper so let me provide a little bit of  
[00:04:14] context you know what we mean by each of these frameworks the classic state dependent case emerges with the menu cost model so it's assumed that a firm has to pay a fixed cost psi  
[00:04:26] to reset the price so firm is monitoring g at every any point in time but adjusting g to the optimal place it's costly so that this gives rise to an ss rule that is the state space  
[00:04:40] is split into two regions one region where in action is optimal so the firm will just not adjust prices as long as these deviations are not too large that's an interval that is labeled here g lower bar the upper bar and as soon as  
[00:04:54] the state hits one of those boundaries will be reset to the interior of this of this set the important object to think about impulse responses in this framework is a cross-section distribution of those gaps you want to know where firms are in a  
[00:05:08] steady state to answer how this economy will respond to a shock you know how long it will take until all firms have adjusted to the news the news will be a once and for all  
[00:05:21] increase in the or change in the nominal marginal cost so this f of g is going to be an important object for our analysis in the tank dependent decision rules  
[00:05:34] one way to rationalize is that firms processing information is costly i mean ricardo rice who sitting here was one of the kind of founders of this view that firms need to process and gather the information and  
[00:05:47] and this is a costly activity so there are some special times when the firm's pace is caused psio at those times the new observation is learned okay so we were talking about this second form of uh decisions  
[00:06:02] so-called time-dependent decisions and i was telling you that here the essential cross-sectional element to to think of of the propagation of the shock is this a distribution function q of t that will tell us in a cross-section you know how  
[00:06:17] long until a fraction uh queue of the firms has learned of the news so at the center of our analysis is an impulse response we want to think of a steady state  
[00:06:31] and hit the steady state with the unanticipated and permanent shock delta this black line and see how long it takes until the cpi this curly p reacts to that and eventually converges to delta  
[00:06:45] so the response conceptually is made of two pieces there's a big theta of delta an impact effect you know the moment the shock arrives you could have a reaction and impact that's what you get with flexible prices and then there's a cumulative you know  
[00:06:59] there's an integral flow of adjustments that will arrive gradually because maybe firms were not paying attention or they were well inside their inaction region and they didn't adjust on impact so we're now going to characterize how this thing looked like in some  
[00:07:14] cases first of all in term dependent models there's no impact effect that's easily seen because the number of adjustments the timing of the adjustment is assumed to be orthogonal to the state so the moment the shock  
[00:07:28] arrives nobody changes his decision if you want to see it more clearly think of using a calvo model in a month you got a fraction lambda of adjustment you do it weekly you get lambda divided by four you do it daily eventually at the in the instant the shock arrives nobody's  
[00:07:43] responding and more than that actually the whole profile of the impulse response is linear in delta because just because those decisions to adjust are unrelated to data so if you look at a delta shock or a two data shock you're just  
[00:07:57] rescaling the vertical axis but you get the same profile in state dependent models instead there may be an impact because the moment delta arrives some agents may be pushed out of their inaction region and  
[00:08:11] react now one result that we you know that we provide in the paper is that if you're thinking of frameworks where those sigma shocks those idiosyncratic shocks are important this impact effect of delta is going to be a second order effect there is going to be  
[00:08:25] no first order effect and that's why it's actually quite easy to see so this now you see my object f of g is there in blue that's this distribution the density of how firms are distributed in a steady state  
[00:08:39] before the shock arrives everybody's in the blue density now the shock delta rise so this density shifts left by an amount delta and the red triangle is the mass of agents that adjust on impact because  
[00:08:52] they're pushed out of in action now that triangle is as an area as a mass proportional to delta square and why is that well you see the density is zero the boundaries and the reason is zero is that boundaries are exit points in this type of model where sigma is positive  
[00:09:07] agents get there and they leave so you don't pile up any mass there so when you do the algebra you know for computing who responds notice how different this is from the old like shachinsky and wise type models or coupling and spool there where the density is uniform and you do  
[00:09:22] have a first order effect on impact but um so here this this area you know that's more or less like the the height and the base so that's an object small so you know that's the first proposition  
[00:09:36] says okay on impact the two models will look the same because one is zero impact the other one is the second order impact so they're going to be very close notice this is not a statement about the continuity of the function sigma delta of course there's continuous statement  
[00:09:50] about the elasticity it has a zero derivative now the second result shows that this similarity for small shocks is not an oddity of the impact it's not that after the impact they behave very differently so the second result  
[00:10:04] shows that if you focus on the notion of some you know of the whole profile of the impulse response what i'm focusing on is this big is this area this uh shaded area on top between the delta shock and the  
[00:10:17] price response so this mass every vertical distance is proportional to some real variable like the output response that follows the nominal shock because prices are not catching up so the distance between delta and p is a  
[00:10:31] measure of say how real wages increase so we have a result that shows that if you compute the accumulated you know the error so the community output following a shock the two models are going to give  
[00:10:44] you exactly the same number provided that they have the same frequency of adjustment and the same kurtosis of the size distribution of price adjustment now it's kind of complicated to explain the  
[00:10:57] frequency is obvious i mean you take an economy that adjusts twice as often obviously everything is going to go twice as fast so effects are going to be smaller kurtosis what i can tell you here is that it's basically a summary statistic of how much selection these  
[00:11:11] firms will have say in a goalless of lucas a model versus a calvo model so that if two models have the same quartos is even very different in their foundations they will kind of have the same amount of selection and will give rise to the same  
[00:11:24] kind of accumulated propagation now the third result is kind of obvious if you consider big shocks then the two models differ just think of my triangle if you push it completely outside in action then you get flexible prices  
[00:11:37] the blue line is the same one we saw before that one does not depend on delta and okay so so the  
[00:11:50] to recap the theory so the theory basically suggests that time-dependent models are models where there's a zero impact of any shock and state-dependent models are models  
[00:12:04] where the impact is small when shocks are small so they will look like time dependent but this the reaction is actually non-linear as the delta shocks become large they may give rise to large responses  
[00:12:19] so we thought what type of evidence could one use to go and see whether there is anything in the data to kind of identify or test whether any of this is going on so the  
[00:12:33] the we we decided we looked at propagation of shocks from nominal exchange rate innovations to prices uh we're aware of the many limitations the one reason three reasons why we like these nominal  
[00:12:48] shocks is that number one they're close to random walks exchange rates are innovations are hard to predict so the theory was focusing on a once and for all nominal shocks so that's you know one plus for for for the exchange rates they're available at high  
[00:13:03] frequencies so what we want to analyze really is an impulse response and our results tell us that only you would see differences on impact now not only on in fact maybe if you you know go back to this picture and extend to the first period those differences  
[00:13:17] persist but eventually they wash out so you want to folk you want to have high frequency data and so that's another plus of the exchange rate data and you want to condition  
[00:13:32] for the size of the shock we want to be able to tell apart responses to small and large shocks so we need lots of observations so uh you know we need many countries and uh to to try to do something also we focus on a sample of small  
[00:13:46] inflation countries because as i mentioned before the theory is developed for a small pi over sigma ratio so here's what we did we ran some  
[00:13:59] regressions of a pass-through from the bilateral exchange rate vis-a-vis the u.s for about 60 countries and and the cpi of of these countries i think we focus on countries whose mean  
[00:14:14] inflation and moving average is below eight percent um and we split the sample in two groups we keep countries on a fixed exchange rate separate i mean we do the full sample but we also our prefer regressions are  
[00:14:28] those where we exclude countries on a fixed exchange rate because of this assumption that we'd like those exchange rate innovations to be exogenous and unanticipated and in many fixed exchange rate regimes there are episodes that you know maybe the real exchange is appreciating  
[00:14:43] and then you expect the countries to devalue so it's easy to think of episodes in which causations could be going the other way around but you know i'll raise my hands there's nothing deep about causations here we're just running a regression hoping that  
[00:14:55] you know the right hand side variable is sort of orthogonal so here's the type of regression we run we run inflation at different horizons so we construct an impulse response by a  
[00:15:08] series of local projection we run the regression for you know the the response in the first month in the third month and so on and each of these regressions has a linear term the one that is usually appearing in in past regressions and a  
[00:15:23] nonlinear term here is the quadratic specification we tried uh different ones this was linear cubic etc uh so that you know if the gamma h coefficient was to be significant it would be evidence of a nonlinear  
[00:15:38] response to those shocks okay so so this is our baseline regression outcomes  
[00:15:52] is as i mentioned is from a sample that excludes the fixed exchange the countries on a fixed exchange rate regime maybe i should have mentioned we use uh to classify countries in a fixed or or non-fixed exchange regime we use  
[00:16:06] the classification several classifications one by levy and sturzenegger another by reinhard rogoff and a recent update of that and the results are kind of robust to that it seems so  
[00:16:20] each column is a different regression so on impact for the one month we see that um so in the first on one month and three months the nonlinear coefficient appears to be statistically significant  
[00:16:34] here you see the coefficient multiplied by a hundred which you know is useful to do a back of the envelope calculation because the regression was at the had the de squared so if the de is ten percent this would be how much  
[00:16:48] impact you get out of a 10 shock okay so if b is small you get nothing out of this term but if it's 10 it basically doubles the impact of the compared to the small shock you keep seeing some differences some  
[00:17:02] non-linearities at the three-month horizon but then the differences disappear from the six-month horizon on um i the tables also report 12 and 24 but here just i just wanted to focus i am  
[00:17:16] using a few numbers and and when we repeat the exercise for the sample where we have all the countries we see something similar on impact and  
[00:17:28] then we don't see anything uh later on okay so what did we do we asked this question we tried to do a systematic comparisons  
[00:17:42] between state and time dependent models are they different so what we find is that for small shocks we think the nature of the friction is irrelevant the models give rise to the same propagation  
[00:17:57] provided that's important that the two models have the same frequency and currencies operating changes i mean that they have the same amount of flexibility as measured by the frequency of adjustment and selection this important  
[00:18:09] feature of models that is captured somewhat magically by kurtosis uh so we could give you examples of models that you know accented you wouldn't think that they're the same we could take a  
[00:18:23] nakamura steinson calvo plus model with certain features and and a a time dependent model with a certain distribution of adjustment times at face value they would look to me as very different models yet they will produce  
[00:18:37] if they produce if their parameter tries to replicate the same moments from an actual economy about these two two statistics they will behave the same also i didn't mention it in the presentation so the results in the paper  
[00:18:51] are also then extended to models that combine elements of state dependent and time dependent like the calvo plus model that i just mentioned so what do we make of this finding well in some sense we think it may be  
[00:19:04] reassuring for most applications that we do say for policy exercises or so we focus on small shocks so it's not so important it seems the nature of the underlying friction there's some things that are important  
[00:19:18] like those moments but that's it for large shocks the propagation is different between the two classes of models we think we provided some evidence that  
[00:19:32] there are traces of state dependence we see this work as the empirical work is very preliminary i mean kind of we hope to spawn maybe some more ideas for how one could test that more  
[00:19:46] rigorously and i'll leave it at that thank you