tag:blogger.com,1999:blog-2499715909956774229.post1907022867702195541..comments2022-08-10T04:21:42.420-07:00Comments on Stephen Williamson: New Monetarist Economics: Summers in WinterStephen Williamsonhttp://www.blogger.com/profile/01434465858419028592noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-2499715909956774229.post-75524891543476026122016-01-04T06:31:19.941-08:002016-01-04T06:31:19.941-08:00Always in the mood to learn Stephen...
If you cal...Always in the mood to learn Stephen...<br /><br />If you call yourself a New Keynesian (not me by the way), then yes its important to know what Keynes meant, if not you better call yourself a new something else.Anonymoushttps://www.blogger.com/profile/00953651130070799720noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-22504453534488400152015-12-30T13:47:11.075-08:002015-12-30T13:47:11.075-08:00Hopefully Jose is in a mood to learn something. Bu...Hopefully Jose is in a mood to learn something. But learning usually happens in small steps. I don't want to overwhelm him with too much information.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-29783042883729641662015-12-30T10:59:38.966-08:002015-12-30T10:59:38.966-08:00Jose seems not to understand what equilibrium mean...Jose seems not to understand what equilibrium means, and also seems to think that "what Keynes meant" is somehow important.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-12860770897779184502015-12-30T07:19:47.787-08:002015-12-30T07:19:47.787-08:00I certainly agree that NK models have much more to...I certainly agree that NK models have much more to do with Prescott's work that Keynes's, but this is the state of the art now among people who call themselves Keynesians.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-78227118933322712292015-12-30T02:38:47.101-08:002015-12-30T02:38:47.101-08:00OK I understand. But IMHO this is all but a Keynes...OK I understand. But IMHO this is all but a Keynesian model, since it fails to understand what Keynes saw in the first place.<br /><br />There is a tendency to see aggregated Demand and Supply like normal Supply and Demand curves, which they aren't and Keynes was very conscious of that, that leads models to have a huge "neo-classic" behaviors, namely the equilibrium adjustments, which Keynes firmly disbelieved , and its IMHO the fulcrum of his General theory.<br /><br />IMHO, any model that ignores the effect of the increased risk aversion in a depression, cannot be called Keynesian, and the "ZLB" can only be achieved in liquidity trap conditions, i.e. once you reach zero you will stay at zero, the model doesn't go back to equilibrium by itself.Anonymoushttps://www.blogger.com/profile/00953651130070799720noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-29986497591887118752015-12-29T09:04:56.243-08:002015-12-29T09:04:56.243-08:00"...why would Cochrane model work in the firs..."...why would Cochrane model work in the first place?"<br /><br />I'm not endorsing the model, and I don't think Cochrane is either. It's just a baseline New Keynesian model.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-59754680005584801042015-12-29T07:25:03.809-08:002015-12-29T07:25:03.809-08:00Humm, sorry nut why would Cochrane model work in t...Humm, sorry nut why would Cochrane model work in the first place? If indeed there is a relation between interest rate (expected and real) and output, we wouldn't be living in this conditions in the first place, would we?<br /><br />We have to account to the liquidity trap conditions, that due to the changes in liquidity preferences, monetary stimulus alone doesn't work since all liquidity will be absorbed and interest rates will remain at the zero lower bound.<br /><br />Actually if you think about it, the ZLB can only be explained by an horizontal LM...<br /><br />Ergo, it doesn't matter what the Monetary Authority does, rates will remain at zero, and if they move its not because the Monetary policy is successful, its because they lost the riskless character.<br /><br />All and all, why wouldn't monetary authorities raise rates when facing liquidity trap conditions? At least they would be giving themselves room to lower them after regaining monetary traction<br />Anonymoushttps://www.blogger.com/profile/00953651130070799720noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-75330731127992147392015-12-28T04:07:45.052-08:002015-12-28T04:07:45.052-08:00OK. Well, I’m happy to carry on. It’s an interes...OK. Well, I’m happy to carry on. It’s an interesting discussion (for me at least).<br /><br />So, yes, this is about mathematics. But it’s not just about the solution to equations. It’s also about the choice of what problem we specify. And that’s where I think we may be differing.<br /><br />Take my equations (1), (2) and (3) together with the boundary conditions on b, and consider an announcement of a change in future taxes. It’s also useful to think of actual inflation, that appears in (2) and (3), as made up of expected inflation and unexpected inflation.<br /><br />The normal way to specify this problem is to take unexpected inflation as zero (or at least a random exogenous shock), even following an announcement. This means that (3) and the boundary condition do not give us complete freedom to set taxes. Taxation in at least one period must be set at a level which ensures the boundary condition is met.<br /><br />In this case, equation (3) has no bearing on output or inflation. This is the way the problem is usually specified, because when we have a central bank reaction function, it generally has to be done this way. And this is what I think you have in mind.<br /><br />However, I’m talking about a different problem (one that works fine here where we have an interest rate peg). I’m saying that we set taxes for all periods, but let unexpected inflation for the period of the announcement be determined endogenously. So I’ve simply swapped the status of a couple of variables. I’ve changed the nth tax charge from endogenous to exogenous and done the reverse for the announcement-period unexpected inflation.<br /><br />Given this, it should be fairly clear that equation (3) determines the level of unexpected inflation and since unexpected inflation also appears in equation (2), then we can conclude that tax policy will impact the solutions to (2) and (3). (Incidentally, the inflation tax due to unexpected inflation here is an exact substitute for the “missing” nth tax payment). <br /><br />Now, as you say, the maths part of this is not in question. What is perhaps at issue is whether this is a reasonable problem to specify. But, I’m pretty sure that this is equivalent to what Cochrane is doing in using the government budget constraint to choose between equilibria. <br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-80603562736274104032015-12-27T09:52:01.904-08:002015-12-27T09:52:01.904-08:00This isn't a disagreement, as we're just d...This isn't a disagreement, as we're just discussing mathematics. In an actual disagreement, there is no right and wrong. Yes, there are multiple dynamic solutions to (1) and (2), but (3) is irrelevant to those solutions.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-48651862821125361372015-12-27T01:21:05.547-08:002015-12-27T01:21:05.547-08:00I disagree. There are multiple equilibria which m...I disagree. There are multiple equilibria which meet (1) and (2), provided we allow for unexpected changes in output and inflation immediately following an announcement. However, if we consider equation (3), all but one of these equilibria result in the real stock of bonds rising or falling indefinitely, implying either that households are not maximising or they are engaging in a Ponzi-game. Exactly which equilibrium path avoids this depends on taxation policy.<br /><br />I'm grateful to you for engaging on this, but maybe we're never going to agree here?<br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-83601181438382488382015-12-26T11:19:36.449-08:002015-12-26T11:19:36.449-08:00The way you've written it down, (1) and (2) so...The way you've written it down, (1) and (2) solve for inflation and output given the nominal interest rate, which is determined by policy. Then (3) is just the tail on the dog, essentially. There's no effect of the stock of bonds or taxes on output and inflation.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-20394252979620941762015-12-26T10:00:04.808-08:002015-12-26T10:00:04.808-08:00Fiscal policy comes into Cochrane's model when...Fiscal policy comes into Cochrane's model when he talks about selecting between multiple equilbria. He has real primary surpluses, which I'm just equating to real taxes, because I'm assuming no government expenditure. This is pretty relevant to what I'm saying, because I'm suggesting a fiscal policy rule that forces us onto an equilibrium path that starts from a low point (post-announcement). It looks a bit like his paths D or E in Fig 15 (even though we're talking about a reduction of rates here.)<br /><br />It's pretty difficult to describe what I mean without charts, so I've set it out in more detail here: http://monetaryreflections.blogspot.co.uk/2015/12/fiscal-policy-in-neo-fisherite-versions.html<br /><br />Feel free to tell me what you think, but likewise don't feel obliged to humour me.<br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-78381778679223921482015-12-26T07:49:21.099-08:002015-12-26T07:49:21.099-08:00In the reduced form that Cochrane writes down, not...In the reduced form that Cochrane writes down, note that taxes do not appear anywhere. That's because, in the underlying model, government finance is irrelevant. As I mentioned above, it's a Ricardian world. Government spending on goods and services of course matters, in ways that people have studied in this class of NK models. What you're talking about is another - seemingly non-Ricardian - model. I can't tell from your description whether or not you have the ideas right.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-76868775873438717952015-12-26T03:49:49.392-08:002015-12-26T03:49:49.392-08:00I agree that it would look as you describe, but on...I agree that it would look as you describe, but only if we assume the fiscal policy rule is to keep lump sum taxes constant (and I'm assuming no government expenditure here).<br /><br />However, what is happening between periods -10 and 0 in that chart is that the real value of outstanding government bonds is rising. This is easy to see. The change in debt is equal to the actual real interest on outstanding debt less taxes. The real interest rate is rising between periods -10 and 0 and we're assuming taxes are constant.<br /><br />I am talking about a fiscal policy rule that would not allow this. Under my rule, the government has to raise lump sum taxes at this point to prevent the real debt rising. The impact of this is to cause a shock fall in both GDP and inflation at period -10, when the announcement is made. But the shock fall in inflation itself increases the real value of debt, so the tax increase needs to be even higher to compensate. It turns out the (only?) way to resolve this for all future periods is when both output and inflation fall by enough on the announcement that they then strictly only rise to reach their long-term equilibrium levels.<br /><br />This does not violate the inter-temporal government budget constraint. The absolute amount of future taxes goes up, but the present value stays the same, because future real rates have also increased.<br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-49357928629803806372015-12-25T10:01:23.122-08:002015-12-25T10:01:23.122-08:00"I was thinking of a scenario where the cut i..."I was thinking of a scenario where the cut in rates is announced at the time that rates rise in the first place ..."<br /><br />Me too. I'm basing this on the fact that, in the first chart, you can see that the nonneutrality dies out quickly. Probably better to choose 40 rather than 35. At 40 you can see that you're roughly back to where you are in period -10. So if we announce a policy in period -10 under which the nominal interest rate goes back to zero at period 40 (everything else the same), output should increase in period 40, with response that looks pretty much like period 0. Cochrane gives you the solution, so it would be straightforward to compute.<br /><br />"As to Ricardian Equivalence, it's not really that the timing of tax matters. It's rather that the total amount of tax is increased, but driven by a real time rule that looks at the debt level in each period."<br /><br />If you increase taxes in present value terms, then government spending has to go up. That's something different altogether. Now we're not talking about monetary policy.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-38536229738606130022015-12-24T13:56:42.433-08:002015-12-24T13:56:42.433-08:00If we are out at period 35, everyone expects inter...If we are out at period 35, everyone expects interest rates to stay up, but it is then announced that interest rates will be cut to zero, then no - that is not what I am saying. In that case, the surprise cut must lead to a period of expected declining inflation which implies a positive GDP gap.<br /><br />I was thinking of a scenario where the cut in rates is announced at the time that rates rise in the first place (probably not what Summers had in mind admittedly). The only time that output goes down in my scenario is when the announcement is made. From then it continually rises, back to its original level, even when the expected rate cut takes place.<br /><br />The problem here with the 35 period horizon is having output rising continually from the time of the announcement through the time of the actual change. Furthermore because inflation is also rising from an initial downwards shock, so is the real interest rate. This means that when we have 35 periods until the actual rate changes are complete, the initial drop in output and inflation has to be implausibly large. (I would probably interpret this as implying that my supposed fiscal policy rule is unrealistic in this case.)<br /><br />As to Ricardian Equivalence, it's not really that the timing of tax matters. It's rather that the total amount of tax is increased, but driven by a real time rule that looks at the debt level in each period.<br /><br />Incidentally, I'm basing all this on looking at data sets that I find using iteration algorithms and that conform to the model equations (including the forward looking aspects) and converge to long term steady states. I know this does not amount to a rigorous proof, but it helps me get a sense of what solutions might look like under assumptions (like my fiscal rule) which are difficult to solve analytically.<br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-81560531175105277382015-12-24T11:16:32.625-08:002015-12-24T11:16:32.625-08:00The underlying model - i.e. Woodford's - that ...The underlying model - i.e. Woodford's - that Cochrane is working with, is Ricardian. So, the timing of taxes is irrelevant, and you cannot get the kinds of effects you mention. You could of course write down a model where tax policy matters, and work it out. But you seem to be suggesting that, if you are out at period 35 on the chart, and the nominal interest rate goes back to zero, that output will go down. Is that correct?Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-59366742406028656102015-12-24T10:34:29.432-08:002015-12-24T10:34:29.432-08:00I understand what it means.
I was thinking in ter...I understand what it means.<br /><br />I was thinking in terms of something like John Cochrane's model. We have a standard NK IS curve and Phillips curve, but we replace the central bank reaction function with an interest rate peg. We also have single period government bonds. I'm then suggesting a fiscal policy rule whereby lump sum taxes are the sum of: a) a fixed real amount; and b) any additional amount required to ensure that the real value of debt does not exceed a specified level (which we can take as the opening level).<br /><br />We can then consider what happens when rates are raised and then lowered again, on the assumption that this whole path of rates going up then down is announced at the time that rates start going up.<br /><br />In that scenario, I believe that you can get an immediate negative output gap which then reduces over time but never goes positive. Inflation follows a similar path. Critically, inflation only falls by surprise in response to the announcement - a fall in expected inflation being only possible in the event of a positive output gap. <br /><br />This scenario requires that deviations in inflation are strictly negative, which is possible here because the fiscal policy rule results in a drain of nominal bonds giving a permanent reduction in the equilibrium price level (determined here by the FTPL). Without this, a period of reduced inflation has to be followed by a period of higher inflation which then implies a positive output gap when the period of higher inflation ends.<br /><br />I'm not saying you're wrong to pick Summers up on this because I'd agree that many models will do exactly what he says they won't. I'm just suggesting one way that a model might do what he says. <br />Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-40605798446165188892015-12-24T07:34:50.623-08:002015-12-24T07:34:50.623-08:00"Positive output gap" in this case means..."Positive output gap" in this case means output higher than it would have been if prices were flexible. That is, if the nominal interest rate stays at zero, output stays the same. If interest rates go up gradually, and then go back down, then output goes down temporarily, and at the time interest rates go down again, output goes up.Stephen Williamsonhttps://www.blogger.com/profile/01434465858419028592noreply@blogger.comtag:blogger.com,1999:blog-2499715909956774229.post-89489030522576348722015-12-23T16:08:22.922-08:002015-12-23T16:08:22.922-08:00"Then the output gap will indeed be positive ..."Then the output gap will indeed be positive for a period of time. So, Summers is incorrect. Indeed, I think it would be difficult to find a model with a non-neutrality of money where this is not the case."<br /><br />I think this depends on what you assume about fiscal policy. If you assume that it acts to prevent higher debt service raising the level of debt above its opening level (but not preventing debt going below this level), then I think you can get the result where a temporary rise in rates does not result in any positive output gap. Anonymoushttps://www.blogger.com/profile/15342983814699700396noreply@blogger.com