WARNING: this post is not quite ready for prime-time. But I can't figure out how to re-write it before I leave to England this evening. And we were arguing about this stuff in comments on my Tinkerbell post, so I'm just going to post it anyway.
Old Keynesian macroeconomics makes sense. It might be right, it might be wrong, but at least it makes sense. I used to think that New Keynesian macroeconomics made sense. Now I think it doesn't. I think it's internally inconsistent. Not quite a full-blown logical contradiction, but very very close. New Keynesians effectively assume full employment (on average), even though there is absolutely nothing in their model that would warrant that assumption, even with good monetary policy. Somebody help me out! Tell me why I'm wrong. Or tell me I'm right.
[Just before posting: OK, I think I've got it figured out now. But man is it weird! You need to assume something like static expectations of future income to get it to work, even though the model formally assumes rational expectations.]
One of the oldest questions in macroeconomics is this: "Does the economy tend towards full employment, and can good monetary policy help it get there?" Old Keynesians gave an answer to that question, and that answer was consistent with their model. It might be right, it might be wrong, but the answer made sense.
New Keynesians give essentially the same answer to that question as the Old Keynesians. But their answer is not consistent with their model. It does not follow from their model. Their model actually gives a different answer. So the New Keynesian answer does not make sense.
The Old Keynesian answer was that there is a force that will normally make the economy move towards full employment. But that force will operate slowly, and may be weak, and may be offset by other forces. Good monetary policy will nearly always help the economy get to full employment more quickly, and help it stay closer to full employment.
The Old Keynesian model was the textbook ISLM, plus some sort of Phillips Curve. If the economy was at less than full employment (less than the NAIRU, or natural rate, or whatever you want to call it), 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. But this "real balance/Keynes effect" might be slow, weak, and offset by other forces. Good monetary policy would increase the nominal money supply, and so make M/P increase by increasing the numerator rather than waiting for the denominator to fall. The same process could then operate more quickly with central bank assistance than without it, and also leave less opportunity for deflationary forces to work in the opposite direction.
The Old Keynesian answer is consistent with the Old Keynesian model. It is not consistent with the New Keynesian model.
There are two differences between the Old Keynesian and New Keynesian models that matter for this post: the LM curve difference; and the IS curve difference.
New Keynesians replace the LM curve with a central bank's interest rate reaction function. Obviously, this makes a difference to their answer to the question. New Keynesians have replaced an invisible hand causing interest rates to fall with the visible hand of the central banker, who chooses to lower interest rates when the economy is at less than full employment. That's not what concerns me here. I'm also not concerned here by the distinction between nominal and real interest rates. Lets just assume the central bank can set the real interest rate, and can and will lower it, and keep on lowering it, if the economy is at less than full employment.
With an Old Keynesian IS curve (except in pathological cases like a vertical IS curve due to zero interest elasticities of consumption and investment) this would be enough to get the economy moving towards full employment. The answer to the question of whether and why the economy eventually gets to full employment would be basically the same, making due allowance for the replacement of the invisible by the visible hand lowering interest rates.
The difference that does concern me is the IS curve difference. The New Keynesians replace the IS curve with an Euler equation. Take the simplest possible case: no investment, no government expenditure, and no exports or imports. All demand is private consumption demand. Assume a utility function such that the marginal rate of intertemporal substitution between present and future consumption depends on the ratio of present and future consumption. (This is a standard simplifying assumption in New Keynesian models). The consumption Euler equation then asserts that C1/C2 = D(r), where D'(r)<0. A fall in the one period real interest rate will increase the ratio of current consumption demand to currently planned next period's consumption demand.
New Keynesian models assume imperfect competition, so firms have P>MC in the neighbourhood of equilibrium, so with prices sticky, firms will produce just enough to satisfy demand, so long as output does not get so much bigger than the natural rate that P<MC. Income equals output, which is demand-determined, and demand is consumption demand.
Assume full employment output is 100 each period (nothing ever changes on the supply-side of the economy). Assume that a real interest rate of (say) 5% in each and every period is compatible with full employment in each and every period. In an Old Keynesian model, monetary policy would be very easy, because nothing ever changes. Just hold M constant, and let the invisible hand bring the real interest rate to 5%, or else use the visible hand to set the real interest rate at 5%, and leave it there forever. At a 5% real interest rate, the Old Keynesian IS curve says that demand will equal 100, which gives you full employment.
In the New Keynesian Euler equation, a 5% real interest rate being compatible with full employment means that D(5%)=100/100. Every year, the representative agent has an income of 100, consumption demand of 100, expects to have an income of 100 next year, and plans to consume 100 next year.
But in the New Keynesian model, that very same 5% real interest rate is also compatible with any persistent, permanent, constant level of output less than full employment. D(5%)=100/100=90/90=80/80=…etc. Setting the right real interest rate is consistent with full employment, but is also consistent with any level of unemployment whatsoever, provided it is expected to be constant over time. And those expectations can be fully rational, or model-consistent.
In other words, even if the central bank sets the real interest rate is at the right level, there is zero tendency towards full employment in the New Keynesian model.
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.
A second possibility is for consumption to jump to 100 immediately, and the central banker to raise the real interest rate to 5% immediately. This is also a rational expectations equilibrium. If that's what people expect to happen, that's what will happen.
And there are many other things that might happen, that are all rational expectations equilibria.
Let's ditch rational expectations. Assume instead that people think that future income will be exactly the same as today's income. Current income is permanent income. With permanent income at 90, permanent consumption must also be at 90 (otherwise the "No-Ponzi" constraint will be violated). But current consumption must be greater than permanent consumption, because people must plan to decrease consumption over time, if they expect interest rates to remain at 4%. So current consumption and hence current income could jump immediately to 100, which is what the central bank wants. And in the next period, people revise their expectations of permanent income up to 100, and the central bank raises interest rates back to 5%. And the economy stays at full employment thereafter.
OK, I think I have it figured out now. With static expectations of future income (or something similar), a good central banker can adjust interest rates to get the economy to move towards full employment. But it's not enough for the central bank to set interest rates at the right level. He has to be prepared to move them down, and then back up again.
Alternatively, just ask Tinkerbell to move the economy from the C=Y=90 for all time equilibrium, to the C=Y=100 for all time equilibrium, and leave r=5%. Tinkerbell works just as well as monetary policy, if we believe her. "We have nothing to fear but fear itself, let's all fly to full employment!"
Worthwhile Canadian Initiative 
“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.