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where are you going to be in England? If in South West and with free time, do email.

If I unerstand, the key is rational expectations. But I use to think that neokeynesians were based on NO rational expectation. I thought They have discarded it, because the menu cost and so on.
NK with RE, that is a new form of NK unknown for me.
On the other han, RE is a catchall box were any form of expectation is possible.
In any case, good post Nick, have a good travel.

If anything about Keynesian economics makes sense to you, then you shouldn't be sitting there at your computer. Get out there and start burying bottles full of banknotes in coal mines! Better yet, burn your house down and invite everyone for a barbeque! And if you really want to rev up the economy, crash some jets into the Trade center!

About assumptions.

1. You cannot assume a representative agent for your NK model or heterogeneity with spreads like Woodford. Reality is more imperfect and complex than that.
2. You cannot assume that every agent has the same knowledge set implying that all other agents will have the expectation that their behavior will be Pareto optimal at each period over time/space. Reality is more imperfect and complex than that.
3. You cannot assume that all agents live for ever and their behavior is not mismatched. Reality is more imperfect and complex than that.
4. You cannot assume that the CB can control the ST "real" rate only the nominal rate. The feedback effects to the reaction function of the CB are more imperfect and complex than that.
It is time for alternative models based on reaction functions that embed imperfection(asymmetry,heterogeneity,disintegration,dispersion) and complexity(entanglement of the tropies of the mechanisms of reaction such as the entropies of reduction,inertia and disclosure). These models are at work and are trully dynamic with motion generated by 'surprise".

Let's make the assumption that somehow you knew what the equilibrium interest rate was.
Why would you want to artificially set it to that rate? If market transactions are what ultimately decide what % clears the market then shouldn't we be more focused on allowing those transactions to take place? I mean the interest rate is an intangible number, a magical model that crunches out correct equilibrium rates is insufficient by itself because you cannot convince every market participant to believe you. So we fall into this paradox of if you announced what you knew to be true, you would have to endogenize your announcement in your model, creating a one equation, two unknowns scenario.

I guess my point is this:

invisible hand market transactions (desired) => equilibrium rate (natural)
equilibrium rate (set by CB) =/=> desired market transactions

What about Post Keynesian Models?

Has anyone done a cost/benefit analysis of employing the Bank of Canada vs. Tinkerbell to achieve full employment?

I would say even the idea of full employment is ill defined. Moving from subsistence societies without much employment or unemployment, to single breadwinner households, to two or more worker households, and partially back, from fewer hours with higher pay to more hours of lower pay, full employment may only be what we become accustomed to. As discouraged workers no longer seek employment, they no longer become unemployed and the level of full employment declines to meet reality.

To say that discouraged workers are not unemployed is fallacious. The issue is "if presented with a job suitable to your skills and experience, and with your desired level of pay, would you take it?" We know wages are sticky, so you shouldn't take issue with a pay constraint. A person used to living on $45,000/year can't go down to $20,000 without significant costs both to themselves and to society.

The paradox of economics to me is that employment is a micro cost and a macro benefit. In my experience, firms treat employment as a cost, additional employment especially so.

Nick: you didn't solve anything. You're back at tinkerbell.

Need a production technology and household labour supply right?

Representative household gains utility from consumption which is funded from wages, disutility from work which provides wages. So they work until the marginal benefit of consumption per hourly wage is equal to the marginal cost of an hour of work. The loss during a shock comes from a relative "misallocation" on the back of price stickiness - given the difference between relative prices of goods and labour and the actual technologically determined value of the two.

That is my impression of how New Keynesian stuff works - essentially I think your description above is just missing the production technology and labour supply (so the supply side), which is why income doesn't appear to be determined.

Matt: "essentially I think your description above is just missing the production technology and labour supply (so the supply side), which is why income doesn't appear to be determined."

yes, that's exaclty right. I covered this on the tinkerbell thread.

As we move from low productivity to higher productivity and a domestic to global labor force, we are politically forced to rely upon a policy choice to maintain domestic workers hours/aggregate demand. It has been a failed policy to solely depend upon new products to employ unemployed resources.

The policy choice to counter the negative effect of higher productivity can lead to a change in the price level, employment, or monetary base.

With the opening of a global manufacturing platform, technological innovation (new product creation) has not kept pace with the increase in technical efficiency (productivity gains) and expansion of the global labor market sufficiently to maintain full employment.

As we move from consumers/innovators to monetary savers/efficiency gainers/labor pool expanders, policy can be used to maintain the velocity of money and aggregate demand.

Monetary policy can only mask the mismatch between changes in savings desires/technology given its short-term effectiveness of 30 years as rates drop from 20% to 0%. The global manufacturing platform is still in its infancy and the Fed is out of ammunition.

Fiscal policy is needed to bridge the mismatch.

"Perhaps he should lower the real interest rate to 4%, and hold it at 4% until the economy returns to full employment, then raise it to 5% again. What happens if he announces this policy?"

I don't know if the rest of the analysis holds up, but here is at least one problem. NK models generally adhere to the Taylor principle, while here you're assuming a 1-for-1 reaction to inflation (since you are keeping the real rate constant).

You missed one of the key ideas in Woodford. It is not about which rate is set now. It is about how interest rates would have been set given alternative states. It is about how the interest rate will respond dynamically to the state of the world -- to deviations from full employment and the target path for inflation. As you note, there DO exist an infinity of RE equilibria (indeterminacy) if you don't have a sufficient reaction function specification. This is one of the central ideas of his book and a huge chunk of it is devoted to the issue of indeterminacy.

You are correct if you define a NK model as a model without such a sufficient interest rate rule. However, that is not the standard definition of the NK model. Reread Woodford.

Nels, everything you say is perfectly correct but it does not address, as I understand it, the question Nick is asking.

Basically Nick is asking about the transmission mechanism from real rate changes to the consumption path. That is, suppose we are at less than full employment and so the central bank cuts the real interest rate. Nick wants to know why it can't be that agents satisfy their Euler equations by reducing their expected future consumption instead of increasing their current consumption since generally the Euler equation only pins down the ratio. (I'm getting this from his tinkerbell post).

This may seem a strange reaction from the agents but we do need to rule it out because after all, all the indetermincies you refer to are situations where expectations some how co-ordinate to allow nominal explosions with no real effects. How do we know it can't happen?

The answer is basically from two properties of the model (along with the CB reaction function as you mention). The first thing is that wages are flexible in the canonical version of the model and so the labour market always clears.

The second thing is that just the first order condition does not entirely characterize the solution to an optimization problem. There is also the condition that says you are on, not inside, the constraint set. In the intertemporal utility maximization problem this basically says that all income is eventually spent, none is wasted. (Otherwise you could have higher consumption in some period without reducing consumption in any other period and this would be a better consumption path, so the original path wasn't the optimal one).

Together these two things prevent agents from reacting to lower rates by lowering future consumption forever. This works by the following chain (I'm doing this in detail for Nick, not you):

1)Suppose the interest rate is reduced at time t and agents respond by lowering consumption plans for time t+1. This means that at t+1 there must be savings because we enter period t+1 at a level of employment that supports a higher consumption level by assumption.

2) Now, the central bank lowers the rate again and again agents respond not by consuming more at t+1, they don't spend the savings. Instead they plan to consume even less at t+2.

3) Suppose this continues forever (when rates hit zero consumption just stays fixed forever). The savings where never spent, thus agents were not on an optimal consumption path.

Thus, by lowering the interest rate the central bank can always manage to have consumption demand eventually go up. And if there is less than full employment the sticky prices combined with the labour market that clears will always translate that into increased employment and output.

It occurred to me "what is labour markets don't clear?" ... A quick Google search reveals:

http://www.crei.cat/people/gali/pdf_files/bgu08.pdf

Which is WAY over my head, but the last sentence of the conclusion is interesting:

"Optimal monetary policy implies some accommodation of infation, and limits the size of the fluctuations in unemployment"

Now I'm depressed.

@Adam P:

"This means that at t+1 there must be savings because we enter period t+1 at a level of employment that supports a higher consumption level by assumption."

Hmm...I don't believe that's right. A very basic model (like the one assumed here) would have zero net savings rates, because there are complete markets -- basically a representative consumer. It's not possible for everyone to save, but everyone wants to do the same thing. That is, loans/borrowings are allowed, but in equilibrium, they are in zero net supply. No?

Your correct it doesn't happen, I'm explaining why it doesn't happen. It implies non-maximizing behaviour.

Nick was the one claiming it could happen in the equilibrium of this model.

Yes, assuming optimization, you need the transversality condition.

Eh... I don't know that that -- by itself -- implies that behavior is suboptimal. You seem to be arguing that the agents are not utilizing all lifetime resources. But the idea (at least how I understood it) was that everyone consumes their wage every period (which means that all lifetime resources are indeed consumed) -- but, somehow, falling demand implies that real wages fall over time. I'm not sure this story holds together in whatever model is being imagined, but it's not necessarily the case that resources are being left on the table.

I'm sceptical about the story, but I don't think the lifetime resource constraint is the essential problem.

If everyone consumes their wage each period without attempting to save then how does demand fall? This model has no capital, no investment demand. Consumption demand is the only demand in this model.

What I'm saying is, if agents act as Nick suggests they might, by reacting to a reduction in interest rates by reducing future demand instead of increasing current demand, and they continued this forever then they would be throwing away some resources.

Nick, This is just a wild guess, because I don't understand these models, but here goes:

1. It is assumed that nominal aggregates don't fly off to zero or infinity. (No indeterminacy) I am not sure how this assumption is justified, but I think it is made.

2. In that case the money market anchors nominal aggregates. Once that's done, the only important piece of information in the money markets is the interest rate, or the expected path of interest rates over time. This tells us what we need to know about money supply and demand.

3. Monetary policy ties down the rate of inflation. Once inflation is tied down, the flexibility of wages and prices insure that we always move back toward full employment after a shock.

As I said I assume this is partly wrong, but perhaps there's something accurate in my account.

Adam,

"If everyone consumes their wage each period without attempting to save then how does demand fall? This model has no capital, no investment demand. Consumption demand is the only demand in this model."

With only a single agent, they can buy bonds sold to them by firms, and that is the only way they can save. But then the assumption must be that firms invest the proceeds of the bond sale into increasing the capital stock, and adding to the capital stock *should* also require labor and generate wage income (but now you are pushed into an endogenous growth model). Again, this model makes no sense without investment -- it's only half a model.

Your attempt to convince Nick is hopeless, because he will come back to you and (rightly) point out that agent will not actually save anything by spending less -- he will just receive less income. In a consumption only model, in which you insist that "real" income is equal to real units consumed, then it is impossible to save.

RSJ, you've missed the point. You can't take my response to someone else out of context and claim I'm mistaken.

The issue is that Nick claims that agents can respond to a decrease in the real interest rate by reducing their future consumption demand instead of increasing their current consumption demand. Further he claims that they can repeat this response forever.

This model does include one period nominal bonds so although it's physically impossible for agents in aggregate to save, they can all attempt to save by buying bonds instead of the consumption good. The result is that some of the consumption good is thrown away and this is always possible.

The shift from consumption into bonds then has the usual effect of falling prices and employment and income, but it does all start with agents in aggregate holding a stock of nominal bonds. But if Nick's story continues forever the bonds are rolled over forever, the savings are never spent. Thus the effect is that agents have simply thrown away some consumption without getting anything in return, this violates their transversality condition.

I should add that conditions like income = consumption is an equilibrium condition, it needn't hold out of equilibrium.

My whole point is that Nick's story is not an equilibrium exactly because it implies consumption < income.

Adam, I agree with you!

But I am saying that Nick won't agree with you, because he hasn't specified any investment in the model, and therefore attempts to save result in consumption being thrown away *rather* than any bonds being purchased.

If your model has a single representative agent and no investment, then the model must have bonds = 0 at all periods. Therefore the transversality condition is not violated.

This is because the representative household, when it tries to save, is unable to do so, and therefore does not have the income to purchase the bond.

What is violated is the assumption that "real" output is not thrown away. I.e., that all income is transformed into either consumption or investment. In this model, real income is destroyed -- it just vanishes -- which makes it a nonsensical model.

If you add investment to the model, or if you add have an overlapping generation model, then your argument would go through.

The simple NK model without investment exists because it seeks to model the inflation process, and adding just investment to the model doesn't change its inflation dynamics hugely. It can be thought of as modeling investment as a type of consumption. So in a sense the distinction is irrelevant in the model. Think of it as being blind to which fraction of output is "investment" versus "consumption". It isn't meant to explain investment dynamics, but that doesn't imply that it imposes no aggregate savings per se -- in a sense savings/investment is latent in the model. Adding investment is simple, see the various vintages of the Smets Wouters and Christiano et al papers.

"The simple NK model without investment exists because it seeks to model the inflation process"

Absolutely! That is my point. If you only have consumption, then savings is impossible and therefore any change in nominal income results in increasing or decreasing prices, _because_ as all income is spent. So you can only model inflation.

It is not possible to acquire bonds in such a model, unless you bring in overlapping generations or have multiple agents with differing preferences or endowments.

Right, plus it is easy to extend and, in my opinion, performs well. So why doesn't modern GE modeling make sense?

"So why doesn't modern GE modeling make sense?"

IMHO, it is because they get the income flows all wrong.

I know nothing about new Keynesian models (well I know about old New Keynesian models from around 20-25 years ago). So consider this a totally fresh look.

In your example, everything is real. How odd since nominal rigities are central. I think the key is that in new Keynesian models, the central bank can't set the real interest rate to any level it wants. You quickly moved from setting nominal to real interest rates. Now one might imagine that a central bank can forecast inflation (they have rational expectations too) and then add say 5%. However, since private sector agents have rational expectations, their behavior depends on the central banks policy. It's not like there is an inflation rate which is given no matter what the central bank does. The question becomes, is there a Nash equilibrium in which the Central bank gets r=5% (presumed to be its only goal) and private agents maximize their utility given the monetary policy rule, tastes, technology and nominal rigidities (or menu technology if you insist). I think the answer is that there is one and only one such equilibrium and that is the tinkerbell equilibrium with production equal to production in the flexible price steady state.

Now the economy can be elsewhere with, say, output below that level (because prices are too high because ... well I just assumed they are at the beginning of time cause no way am I gonna model any uncertainty). I think that, in that case, the central bank cant achieve r=5% always. That there is no Nash equilibrium. In other words, for any nominal interest rate rule, the real interest rate will not be 5%.

I think the contradiction is between new Keynsian models and your assumption that the central bank can achieve any real interest rate which it wants.

I will try to invent a simple new Keynesian model on the spot.

Producers are self employed. Their marginal cost in units of consumption is the marginal disutility of work divided by the marginal utility of consumption. T.his declines if they work less and consume less (disutility of work convex utility of consumption concave).

They make different goods with a constant elaticity of substution (all consumers have Dixit Stiglitz preferences) so their utility is maximized if they set a price equal to one plus a constant markup times their marginal cost.

OK a nominal rigidity. They are on a circle and a clock hand goes around say once a month. When the hand points at me, I can adjust my price. Otherwise it stays the same.

Is there an equilibrium with r = 5% and consumption less than the flexible price consumption (for a steady state with r = 5%) ? It seems that if I am working less and consuming less than in the flexible price steady state, then I want to lower my relative price, that is set a price lower than the average price over the next month. So there can't be an equilibrium with a constant price level.

I will assume that my loss from having other than the best price is quadratic in log price (just cause I want to and new Keynesians always do stuff like that)

How about one with a constant deflation rate of 1% per month ? Well then I forecast the average log(price) will fall 1% over the month so will be on average 0.5% lower than when I set my price. so I set my price *below* the current average price minus 0.5%. Prices as set fall 1% a month, so, when the hand pints at me, my price is 0.5% higher than the average price (I am making a linear approximation to an exponential here). so I cut my price by more than 1% so deflation is more than 1%.

So if I assume that deflation is 1% per month, then it is more than 1% per month. There is no equilibrium with r=5% and consumption below the flexible price steady state.

I haven't proved it, but it seems to me that this happens for prices being any function of time.

One last example (here the r=5% actually matters). If the deflation rate is
exp(-(constant)t) so it goes to zero exponentially. Then if I lower my price according to the deflation rate it will be lower than the average over the next month (since later price adjustments will be smaller than mine). So I do get a price lower than the average over the month of my average competitor's price. However, this difference gets smaller and smaller
(it shrinks just like exp(-(constant(t))). This is only optimal if my consumption is getting closer and closer to flexible price steady state consumption. So there are equilibria, but in those equilibria consumption grows till it converges to FPSS consumption (what you call full employment consumption).

This can't happen if r=5%, because r=5% implies constant consumption. I think this means there is no sticky price equilibrium with consumption below FPSS consumption and r=5% always. There is no way the central bank can make r=5% always no matter what it does with nominal interest rates.

To repeat maybe.

I think this means that if current consumption is below the flexible price steady state, then the central bank can't keep r=5%. I think it means that the economy has to converge to the flexible price steady state (which means r must be greater than 5% if consumption is now below flexible price steady state consumption)

The basic mechanism is that lowering real-rates below the natural always contracts the future full-employment production-possibilities curve and stimulates present consumption.

Nick, I think I've figured out where you're coming from.

To set the context up again, the question Nick is asking is, consider the following two scenarios:

1) consumption demand falls in the current period due to a rise in the real rate
2) consumption demand falls in the following period due to a fall in the real rate

Why is 1 allowed but 2 is not? For the answer you actually need to combine what I said on the tinkerbell thread (my first comment @2:42am) with what I've been saying on this thread and the assumed form of the central bank reaction function that is in the standard NK model.

Let's assume today is time t.

So, case 1 is allowed without having people throw away consumption at time t because the fall in demand causes output and employment to contract, thus reducing output to match demand.

Why can't we say, in case 2, that the fall in demand at t+1 causes output and employment to contract (at t+1) and so the t+1 output matches the t+1 demand?

well, 2 things:

a) The CB reaction function is specified such that the real rate is only lowered when inflation is already lower than steady state. Further, inflation below steady state ONLY happens if the economy is at less than full employment at time t.

b) The fact that prices are already falling (relative to steady state) translates in the labour market (via the mechanism I described in the tinkerbell thread) into higher employment and outuput at t+1. As I explained on that thread, the labour market will tend towards full employment.

And thus, if consumption demand at t+1 has been reduced by the time t real rate reduction we have a contradiction. This can't be an equilibrium of the model because at t+1 supply and demand will be mis-matched, the supply side will expand output from t to t+1 (due to the structure of the labour market and the demand elasticities that firms are assumed to think they're facing) but the demand side will contract.

You could say it this way Nick:

If agents respond to a falling real rate at t by reducing t+1 consumption then the demand elasticities firms thought they are facing (and are assumed in the model) will not be the demand elasticities that are actually realized.

"so I cut my price by more than 1% so deflation is more than 1%."

You would expect that at any point in time, the actual price cuts are greater than the average price movement, because the average price movement is the sum of those firms that cannot cut prices and those that can.

In this case, the integral is tricking you. Work it out for just 2 firms, and you will get (with a CES) a (non-constant) rate of deflation, but nevertheless employment is not increasing, as those firms that cut prices take labor away from those that cannot, and then in the next round, the situation is reversed. At each point in time, the average price cut (for those firms that can cut prices) is larger than the average price movement.

According to Krugman, IS curve and money supply jointly determines output in this kind of model.

In normal times, reducing price increases demand, but I don't think we can always say it does. If the expectation becomes prices will be even lower in the future then demand may be deferred causing prices to fall further. Demand can't be deferred forever and prices can't fall to zero, but it can be deferred until they stop falling, and that is what happens during deflation. Higher real wages do not lead to its end but its prolongation in this case. It is a disequilibrium that grows until the expectation of lower future prices is dashed.

" The actual price cuts are greater tha the average price movement....."

Nonsense! THe actual price movement is a dynamic path and this is not sustainable as only the firms that can cut prices will survive! CES and dynamics?!? Be careful!

P, we were describing how this particular model works. CES ensures that if one firm cannot cut prices, then it will still survive. It will merely lose market share for that period, and the other firm will gain market share. Because of that, the average price will not fall as much as the magnitude of price cuts for those firms that can cut prices.

If output expands between t and t+1, income is higher and it can sustain a higher demand at t+1 without altering demand elasticities.The supply and demand at t+1 occurs simultaneously. If you introduce imperfection with heterogeneity of agents, mismatches, etc., (see Brock, Hommes 1997, 1998) and the literature on complexity from CANDEF, University of Amsterdam) then you have a multiple equilibria and possible instability in NK models.

P, I was addressing the proof provided by R. Waldman -- his toy model.

Robert's argument is that because each firm has to cut prices more than the general rate of deflation, that this is evidence of a contradiction -- i.e. that the general rate of deflation is less than itself. And the conclusion is that the assumption of the real rate being X must be false.

My argument was that the reason why the firm is cutting prices faster than the general rate of deflation is because some other firms are not cutting prices. Because of the elasticity of substitution, those firms that cannot cut prices do not see their sales fall to zero, and therefore the average price level always falls by less than the decline in prices made by those firms that can cut prices. In other words, there is no contradiction.

I do think it would be impossible, with CES, to get a constant rate of deflation each period. But Nick's argument does not require a constant rate of deflation.

himaginary @4:24:

Krugman is not talking about "this kind of model". That his he is not talking about the standard NK model. Just because he has an Euler doesn't mean it's the canonical NK model, ALL macro models, including IS-LM in its modern incarnation, have consumption Euler equations.

This does bring up another point though. In his book Woodford does in fact work out the model with and without money. The results are unchanged if you have the central bank operate through the supply and demand for money, this really just shows that Nick doesn't know what he's talking about here. He should at least try to understand the model before saying it doesn't make sense.

Lord @7:14:

You're correct that falling prices don't always increase demand, the increase in demand here comes first of all from the CB lowering the real rate (this part I took to be implicit in the tinkerbell thread). Falling prices then has two roles:

1) On the demand side to increase the real wage so their is sufficient purchasing power to support the higher consumption demand

2) To allow individual firms to expand output and thus employment (without having to understand that there will be higher aggregate demand, they only need to know they, individually, will see higher demand). Thus the supply side will expand to provide the extra output.

Now, the model does allow for nominal explosions, a situation where despite full employment prices explosively inflate or deflate but these can only happen in such a way that the real interest rate and real wage never changes, nothing real changes. But that would be a situation where falling prices caused no change in demand, in fact it would cause no change in any real quantity.

This does however bring me to a response to the last sentence of RSJ@8:49pm. I believe you're correct that any permanent inflation or deflation must be explosive, there is no constant rate of deflation that the CB can never correct.

RSJ,

All I was trying to tell you as I have done before is to tell you that statements should be clarified. Assumptions must be stated and the argument must follow. You generalize although what you assume is that in certain industries firms face inelastic demand and have persistent market power. This is not a general case but a special one so It should be stated.Furthermore, it is not clear what you mean about elasticity of substitution. For example, a general facility to substitute across firms and industries with a general equilibrium model it will force firms to cut prices in order to compete. (Arrow-Debreu), As about CES it is a static construct. I DO NOT DISAGREE with you if you are talking about firms in certain monopolistic industries sheltered from substitution pressures.

Adam P,

Not all macro models have consumption Euler equations. Post Keynesian models that are specified with stock-flow consistent financial accounts do not have one and are not specified in intertemporal optimization terms. What is a "period"? Is it a time concept or a complete adgustment to an equilibrium stasis? For mathematicians like my self this is important!

My answer to Lord just now does bring up something Nick said on the tinkerbell thread that I never explained why it's wrong. The comment was Nick Rowe | June 09, 2010 at 05:40 PM.

Here is the part I want to address:

I had said: "The falling P, with W not falling, means higher real incomes and so higher demand(this is the demand elasitcity again), so THERE IS SUFFICIENT DEMAND TO BUY THE EXTRA OUPUT AT THE LOWER P!"

Nick responds: "Disagree. That's the microeconomist's fallacy. For a given aggregate level of output and employment, a rise in real wage income means an equivalent fall in real profit income, so no change in total income, and no change in demand (unless you bring in distribution effects). Income always equals output, regardless of W/P."

But the whole point here is that the aggregate level of output is not given. The whole reason prices are falling is that those firms that are allowed to adjust their price are doing so and moving from a sub-optimal price to the optimal (profit-maximizing) one.

And again, the demand elasticities are such that this increases aggregate firm revenue. Part of the increase goes to labour in the form of a higher real wage, part to higher firm profits. But total income does go up.

As I said in my first few comments on the tinkerbell thread these demand elasticities are the key to everything here because they ensure that when firms adjust prices the result is higher total income and NOT just that firms who can change prices steal income from those who can't without a change in the aggregate.

Thus, this market structure (combined with the other stuff like CB reaction function and a labour maket that always clears) ensures that the real side of the economy always tends to full employment.

Panayotis, you can always work in continuous time, as many of these models were originally formulated. We just tend to use discrete time for verbal discussion.

Adam P,

This exactly the confusion of many economists. Moving from one period definition to another as if they make no difference. This is not correct!

The individual form that cuts its relative price increases its total revenue (and hence the income of its workers and shareholders. (Assuming elasticity greater than one, which it must be of course, for profit-maximisation). But if half the firms cuts their relative prices, then by definition, that must raise the relative prices of the other half of the firms by an equal amount. So it's a wash. I agree with RSJ @8.49

But this micro stuff is skirting round the macro question. There must be a better way for me to convey my point. I am really surprised that others can't see my point on this thread, and are misunderstanding NK macro. (Others are naturally equally surprised that I can't see their points, and am misunderstanding NK macro!)

A little thought experiment: Take all the imperfectly competitive firms and dixit stiglitz demand functions form NK. Then add a very old Keynesian consumption function. Namely, C=a+bY. What happens? I say that Y=a/(1-b), the old Keynesian demand side determines Y, regardless of all the NK stuff. No tendency to full employment whatsoever.

Happily jet-lagged and worn out from excessive gardening on the old family farm. Not thinking about econ much at all!

Nick, RSJ was not addressing my point. That has nothing to do with what I'm saying.

It's also not correct what you're saying, the issue is the aggregate price level as it relates to aggregate demand. The firms that don't cut prices do see a rise in their own relative prices but the issue is that the aggregate price level is falling, it's not a wash.

"A little thought experiment: Take all the imperfectly competitive firms and dixit stiglitz demand functions [from] NK. Then add a very old Keynesian consumption function. Namely, C=a+bY. What happens?"

That's not a thought experiment, it's a cop-out. The only way to justify C=a+bY, apart from Keynes's own approach which was simply to announce it as a psychological law, is to assume that jobs are rationed. Nobody really formalised that until Clower tackled it. (Personally I prefer Hahn's treatment but that's another story.) If you want to go that route that's fine but that's Old Keynesian or Post-Keynesian thinking, not NK.

I'm struggling to understand you, but what I think you're getting at is that the NK model rules out Old-K-style involuntary unemployment by means of a kludge. I suspect you're right (don't know NK well enough to be sure) but I think the kludge has a name: Rational Expectations.

Nick, I'll try this one more time. I'm only rephrasing what I've already said but whatever, I'm doing this for myself as much as for you but feel free to explain where you disagree. So...

Let't take your example where potential output is 100 and the real rate that supports it is 5%, then somehow we find ourselves with output of 90 and the central bank responds by reducing the real rate to 4%. You claim:

"Suppose the central banker finds himself in one of those states of persistent unemployment. Output is at 90, and everyone expects it to remain at 90 in future. What should he do? Perhaps he should lower the real interest rate to 4%, and hold it at 4% until the economy returns to full employment, then raise it to 5% again. What happens if he announces this policy? To keep the math simple, assume that D(4%)=(1/0.99).

One possibility is that people expect that the economy will never return to full employment, so the interest rate remains forever at 4%. And they expect income and consumption to go from 90 this period, to 89.1 the next, to 88.2 the period after, and so on, with the economy falling by 1% each period. This is a rational expectation. If that's what people expect to happen, that's what will happen."

You are wrong here Nick, even if everyone expects that to happen that is NOT what actually will happen.

Let's suppose everyone, firms and workers/consumers expect this decline in consumption and income. Fix P as the price level that is expected and W the nominal wage that is expected next period. Further, notice from the production technology that if everyone expects falling output then everyone MUST also expect falling employment.

Consider a firm that has the ability to change its prices, if it reduces its price RELATIVE TO P it can sell more output at the lower price. Further, its demand elasticity implies that selling more at the lower price will increase its profit (this is also true at full empoyment). Thus, all firms that can adjust prices will lower them relative to P.

Now, what about firms that can't lower their prices. Is it a wash? Does the amount of sales they lose exactly equal the total gained by the cohort that can asjust prices? NO. Those demand elasticities again. Total output and employment will (try) to expand. (Again, so far all this would also be true at full employment).

So, my claim is that ANYTIME the economy is at less than full employment the process in the preceding two paragraphs moves us towards full employment but if we are already at full employment then it does nothing.

So where is the difference? At full employment the firms can't hire anybody without offering a higher wage. Further, that wage would need to be so much higher as to negate the increase in profit from the higher sales, this condition is what characterizes full employment. Understanding this firms don't lower their price relative to the expected price level in the first place.

At less than full employment firms CAN hire extra workers without offering a higher wage. Knowing this they will attempt to lower their price (relative to P) and increase their employment. Thus, the realized aggregate price level ends up less than P (our first contradiction) and employment ends up expanding (2 paragraphs up I showed it won't all be a wash, aggregate employment will expand).

This repeats the supply side part of the argument in my comment at June 11, 2010 at 02:01 AM, combine it with the argument there about not throwing away ouput and you conclude that even if falling output/income is expected by everyone it is not an equilibrium. THEIR IS INCENTIVE TO DEVIATE FOR ALL FIRMS WHO ARE ABLE TO ADJUST THERI PRICES!! It is not an equilibrium!

Nick, I went back and actually looked up the derivation of the model, here are a few more details.

1) The labour supply problem of the consumer implies that the real wage that clears the labour market is an increasing function of consumption.

2) As usual, the marginal product of labour increases when employment falls.

3) The profit maximizing pricing problem of the firm implies an optimal (target) markup of price over marginal cost (here marginal cost is just the wage).

Thus, we get that at less than full employment the firm finds that their marginal product of labour exceeds their real wage by more than the target markup (that is, marginal revenue exceeds marginal cost) and that makes it profitable to reduce the price and increase employment for any firm that can adjust the price.

At full employment the real wage will already have been bid up (from the labour supply equation) so, at the full employment real wage firms won't want to decrease price and increase output. Slightly different from what I said just above. Otherwise the logic of my last comment goes through.

My critique is that there is not one but two demand elasticity curves. That during deflation, elasticity negates so reducing prices reduces output and the conventional story doesn't apply, but a sufficiently aggressive CB can prevent deflation, righting the ship.

NIck Rowe,

Regarding your comment @9:42.

Are you saying that if half of firms lower their prices the other half will sit around and not respond assuming some gross substitution? If this is what you say it is nonsense!

Food for thought.

1. The definition of the time period for intertemporal models is important. There can be an operational period where all adgustment is completed and calendar time whose arbitrary choice depends on your selection of the variable set of relations you analyse. Discrete vs. continuous intervals can also make a difference.
2. NK models are based on the general equilibrium hypothesis with gross substitution, all economic units are internalized and the sources of imperfection are non existent. I have mentioned these sources and that they lead to multiple equilibriain a previous comment in this post, among other things not elaborated here.
The state authority has a role as a) social planner and b) distributor of resources. As a social planner it sets prices based on relative preference and technical parameters subject to a) knowing these parameters, b)being neutral and c)making no errors. As a distibutor, due to friction, it shifts resources but for optimal conditions net of transaction costs it needs a theory of how relative preferences and technical parameters change. Are these assumptions realistic? If not, how are rational expectations are formed in NK models?

If you think that these points are trivial, then I suggest with all due respect that you need to check your a) assumptions, b) logic and c) math.

Nick is in England and likely cut off from blogging until he returns on June 18.

Food for thought.

NK models are based on the General Equilibrium Hypothesis (GEH). GEH requires gross substitution and market competition to adjust in operational time (not in calendar time) and an external state apparatus of control as a)social planner and b) distributor in the presence of friction.
However,GEH cannot survive with market imperfection whose sources (asymmetry,heterogeneity,disintegration,dispersion) bring complexity during adjustment (entanglement of the tropies of adjustment)imposing entropies (reduction,inertia,illusion) and the GEH system breaks down and is not sustainable. Thus price regidity induced and mantained by market imperfection cannot be compatible with GEH. So, NK models with price rigidity as specified with GEH are inconsistent (οπερ εδει δειξαι).

"But this micro stuff is skirting round the macro question. There must be a better way for me to convey my point."

Just a wild guess... :
IS is basically a demand-side model. It doesn't involve labor-wage relationship. So, maybe what Nick is trying to say is that NK-IS model does not have tendency to achieve full-employment output level by itself. It needs working on supply-side which involves labor-wage relationship to achieve it, just as Adam P repeatedly explained.
On the other hand, ISLM does have tendency to achieve full-employment output level by itself: if there is demand shortage, price falls, real money stock increases, and output-gap is filled. Labor-wage relationship is not involved in this process (at least, not explicitly). If you want to make similar process in NK-framework, you need to add money as exogeneous factor to NK-IS model, as Krugman did (which I linked in my previous comment).

Question for Nick: consider the special case (in the NK model) where all firms are free to revise their prices in every period, so that output and the real interest rate are always at their natural levels. Does your objection to the model hold in that case also?

Nick, I hope you had a nice trip to England!

I also hope you'll answer Kevin's question above and I'd like to add another question:

why do you think that IS-LM models don't have an Euler equation underlying the IS curve? How else do you justify the shape of the IS curve?

Thanks Adam. I had a good time in England. Trying to get my mind back from thinking about old farm buildings (must do a post on that) to NK macro.

Despite (because of) the good comments on this post, I am feeling frustrated. Somehow I'm not getting my point across.

Let me start with Kevin's question (2 comments above): "Question for Nick: consider the special case (in the NK model) where all firms are free to revise their prices in every period, so that output and the real interest rate are always at their natural levels. Does your objection to the model hold in that case also?"

Short answer: Yes.
Long answer: Your question begs the question: will output necessarily be at the natural rate, even if the real interest rate is at the natural rate, and even if each firm can adjust price every period (and even if they correctly anticipate shocks)? My assertion is that price flexibility does *not* create any tendency towards the natural rate when aggregate demand is driven by a consumption-Euler equation.

Let me try to work with Adam's comment @June 12 2.26: (Please excuse MY CAPITALS)

"1) The labour supply problem of the consumer implies that the real wage that clears the labour market is an increasing function of consumption. AGREED.

2) As usual, the marginal product of labour increases when employment falls. AGREED.

3) The profit maximizing pricing problem of the firm implies an optimal (target) markup of price over marginal cost (here marginal cost is just the wage). AGREED

Thus, we get that at less than full employment the firm finds that their marginal product of labour exceeds their real wage by more than the target markup (that is, marginal revenue exceeds marginal cost) AGREED and that makes it profitable to reduce the price AGREED and increase employment THIS IS THE CONTENTIOUS POINT for any firm that can adjust the price.

At full employment AND ONLY AT FULL EMPLOYMENT, AS I AM SURE ADAM WOULD AGREE the real wage will already have been bid up (from the labour supply equation) so, at the full employment real wage firms won't want to decrease price and increase output AGREED"

What's so contentious about the point I have labelled "CONTENTIOUS"? Each firm will *want* to increase employment, output, and *sales*, but will it be *able* to increase *actual* sales? Clearly, if it can't increase *actual* sales, it won't want to increase employment. (Think of the hairdresser model, for example, with no inventories, for simplicity).

The *individual* firm knows that if it cuts its price, *relative to other firms' prices* it can take sales and employment away from other firms. But if all firms cut prices (by the same amount) at the same time, does the individual firm have any reason to believe that actual sales will increase?

If we had an old-fashioned ISLM model M/P=L(Y,r), Y=Y(r) (I'm ignoring the difference between real and nominal interest rates) then a cut in all firms' prices would increase total output demanded and increase actual sales. So firms would have reason to believe that actual sales would increase. (And even if they were pessimistic, and didn't increase output and employment, they would be pleasantly surprised to find an excess demand for output, so would increase output and employment in response).

But if we have a NK model of AD, why would firms have reason to believe that a fall in the general level of prices would increase the aggregate demand for output? If they were pessimistic, and did not increase employment, would they find that pessimism confirmed?

Yes, at less than full-employment, each individual firm will *want* to cut price and increase sales. They *can* cut price, and will do so. But *can* they (collectively) increase actual sales by collectively cutting prices? Will a fall in the general price level increase aggregate quantity of output demanded? If it doesn't, then actual sales will not increase.

Put it another way. I am asking essentially the same question that Keynes asked in Chapter 19 of the GT. If we are at less than full employment, money wages (and prices) will fall (let's assume). But this will only increase employment if the fall in W and P causes an increased *demand* for output. It's not enough that firms *want* to increase sales of output. They won't actually increase employment and output unless they can sell the extra output, which requires an increase in demand.

But Nick, it's in the structure of the model.

You ask, "But if all firms cut prices (by the same amount) at the same time, does the individual firm have any reason to believe that actual sales will increase?" and you imply, correctly, that the answer is no.

But the structure of NK models rules that out, all firms can't cut prices in any given period. It's exactly this fact that makes it work, the firms that can cut prices know they'll have the extra sales materialize exactly because most firms can't cut their prices. Like I said above, If agents respond to a falling real rate at t by reducing t+1 consumption then the demand elasticities firms thought they are facing (and are assumed in the model) will not be the demand elasticities that are actually realized.

Thus, the co-ordinated pessimism fails to be an equilibrium because there is incentive to deviate.

Thus, when you ask "why would firms have reason to believe that a fall in the general level of prices would increase the aggregate demand for output?" you are asking the wrong question. Firms don't need to ask that question because the ones that can lower prices, relative to what was expected remember, know (because they know the demand curves they face) that they, individually, will be able to increase sales and profit. They can do this exactly because the other firms are constrained from matching them (the ones that can't change their prices that is).

Now, just follow the chain of reasoning I was giving on the tinkerbell post where I explained that the increased employment/output of the subset of firms that can adjust prices is, in total, greater than the (total) decrease in output and employment from the constrained firms. Thus the income is available to support the higher demand.

Another way to say it.

You point out: "If we had an old-fashioned ISLM model M/P=L(Y,r), Y=Y(r) (I'm ignoring the difference between real and nominal interest rates) then a cut in all firms' prices would increase total output demanded and increase actual sales... (And even if they were pessimistic, and didn't increase output and employment, they would be pleasantly surprised to find an excess demand for output, so would increase output and employment in response)."

The same thing happens here, the firms that cut prices find increased demand for their output regardless of whether or not they expect it. All that you need is that the firms that can decrease prices do so, just like in the old keynsian model.

Thus, you don't need to say "incentive to deviate" like I did (I phrase it that way because I'm assuming the firms know the demand curves they face). You could just as easily say they are simply cutting prices because they expect their competitors to, just as in the old keynsian model. After all, in your model you still need them to cut prices.

"Put it another way. I am asking essentially the same question that Keynes asked in Chapter 19 of the GT. If we are at less than full employment, money wages (and prices) will fall (let's assume). But this will only increase employment if the fall in W and P causes an increased *demand* for output. It's not enough that firms *want* to increase sales of output. They won't actually increase employment and output unless they can sell the extra output, which requires an increase in demand."

But you have to remember that implicit in everyting I'm saying is that the central bank lowered the real rate. This is what causes the increased demand.

Now, in order to be sure that the lower real rate does in fact cause an increase in demand we need to rule out this pessimistic equilibrium and that what I've been doing. I repeat, if agents respond to a falling real rate at t by reducing t+1 consumption then the demand elasticities firms thought they are facing (and are assumed in the model) will not be the demand elasticities that are actually realized.

BTW Nick, this part of your post, on why the old Keynsian models automatically return to full employement:

"wages and prices would eventually fall, cause the real money supply M/P to rise, cause the LM to shift right, cause interest rates to fall, cause investment and consumption demand to rise, and cause output and employment to rise"

After all, the part "interest rates to fall, cause investment and consumption demand to rise" is something that you are assuming (that is, the fact that the IS curve slopes down in (Y,r) space is an assumption).

So, can you justify this assumption without reference to the intertemporal optimization problem of consumers/investors?

Further, if you are willing to assume interest rates falling causes investment and consumption demand to rise for the old model then why not the new one?

Adam @5.01: "BTW Nick, this part of your post, on why the old Keynsian models automatically return to full employement:"

That's not a "BTW"; that was the key part of my post. Now we are getting to the key issue I wanted to draw attention to.

Old Keynesian models just *assumed* that the IS curve sloped down in {Y,r} space -- that a fall in r would increase the level of output demanded. New Keynesian models *derive* the IS relationship.

But it's a very different relationship. It's not a *negative* relation between r and the *level* of Yd. It's a *positive* relation between r and the *growth rate* of Yd. Nobody seems to have noticed that this difference has very big implications for the mechanisms by which OK and NK models tend towards full employment. They aren't the same.

I must have really screwed up writing that post. Because this was they key point that all the comments seem to have ignored, until now.

Leave aside the difference between OK and NK in that OK assumes and NK derives. Leave aside the difference between OK and NK in that NK has a formal model of price-setting by imperfectly competitive firms, and OK doesn't. Leave aside the LM curve difference, where OK has the central bank setting M, and NK has the central banks setting i. Leave aside the difference between i and r.

OK gets to full employment (if it does) because a fall in r increases the level of Yd. NK gets to full employment because a fall in r......ummmmmm.....reduces the growth rate of Yd???

And yet everybody seems to talk as though NK is basically just the same as OK, but with better microfoundations. It's not.

Ok, a couple of things. First of all, yes in a NK model a fall in r reduces the growth rate of Yd but as I've repeatedly explained the structure of the model is such that the lower growth rate must come from higher current Yd and not from lower future planned Yd, so where's the difference? You haven't told me why you don't accept my explanation.

Now, I suppose the reason you don't accept the explanation is that it's not entirely a demand side explanation. Essentially the co-ordinated pessimism equilibrium from the demand side can't be matched by the supply side, (that is, the supply side is assumed not to be pessimistic) because of the demand curves firms are assumed to believe they face. Thus, my claim is that when tomorrow arrives consumers find themselves with income in excess of what they planned to spend. So why don't they just save it?

I've actually addressed this several times, it's the transversality condition that says consumers always choose consumption paths that have zero savings in the limit as time approaches infinity. However, in all those times I was connecting it to the supply side because to me the point was that the savings would have to exist in the first place.

Now, what about the intuition from OK models that if Yd is defficient then income falls to match and so excess saving is ruled out because income falls and the savings ceases to exist? In NK models that does happen but only in current period. Furthermore, firms always infer that the reason there wasn't enough demand for their output was that their price was too high. Basically you could say that fimrs are always optimistic and so they never co-ordinate with consumers on the pessimistic expectations.

Adam: Let me start with the transversality condition. Essentially, that's playing the same role as the intertemporal budget constraint (satisfied as an equality) in a finite-horizon model, right? (As you know, I'm shaky on technical stuff).

Suppose that C=Y=100 for all periods, and r=5% for all periods, satisfies the Euler equation for all periods, and transversality, and is full employment for all periods.

Assuming exactly the same fundamental parameter values: why can't my pessimistic scenario, in which C=Y=90 for all periods, r=5% for all periods, with less than full employment, also satisfy the Euler equation *and* transversality, with less than full employment? (Sure, firms will be cutting prices like crazy, with each one trying to undercut all the others, so firms aren't in equilibrium, but consumers are, it seems to me, in equilibrium. Since C=Y in each and every period, the budget constraint, and transversality, is satisfied trivially. No?

Just to be explicit: in my pessimistic scenario, consumers expect their future income to be 90 today and in all future periods, and plan to consume 90 today and in all future periods also.

"Essentially, that's playing the same role as the intertemporal budget constraint (satisfied as an equality) in a finite-horizon model, right? "

Yes.

"Since C=Y in each and every period, the budget constraint, and transversality, is satisfied trivially. No?"

That's why I bring up the supply side, at less than full employment firms find the real wage has fallen (from the labour supply equation) and thus they are at greater than their desired markup. They make INDIVIDUAL decisions to expand employment expecting the demand to be there (this is from the assumptions about the demand curves they face). There is nothing in the structure of the firms problem that allows them to co-ordinate on the pessimistic expectations except for their choice of price and if they expect low outut then they expect even lower real wages, thus they just lower price even more (the incentive to deviate).

One thing though is that through all of this we've had the implicit assumption that the real rate also fell yet the supply side story appears independant of the real rate. So what happens if the CB does nothing? Well, in this case we can have less than full employment forever but the way it happens is that the deflation means that the real rate has gone up causing a further decline in demand. But at each step you need a new increase in the real rate, that is you need accelerating deflation, hence the point that RSJ made that in the face of a passive CB you don't get a constant rate of deflation forever (just like a passive CB can't give a constant inflation rate). If the CB does nothing then the inflation or deflation must eventually be explosive.

But, since we do assume a CB that follows the actuallly reduces nominal rates far enough that the real rate is reduced the supply side argument will go through and firms won't end up dissapointed.

If tomorrow comes and consumers, in aggregate, want to have positive net savings this will push the interest rate down relative to where it was set. The CB will keep on lowering the real rate until the savings market clears.

"Just to be explicit: in my pessimistic scenario, consumers expect their future income to be 90 today and in all future periods, and plan to consume 90 today and in all future periods also."

No, that won't work as the real rate is continually reduced by the CB. You actually need the scenario where conumption plans keep falling, and as the CB lowers the real rate consumers react to each decrease in the real rate by lowering future consumption plans still further. You had this right in the post.

If you try for the steady state of C=Y=90 then you have the real rate falling and so one of current Y or future Y has to move away from away from 90. My whole thing has been to explain why having future Y go below 90 is not an equilbrium of the whole system (even though it does satisfy one equation of that system).

Adam: Good. We are much closer to being on the same page now. I will reflect some more about the supply-side.

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