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"Assume that nifty new goods don't take any more labour (or other inputs) to make than the old goods. It takes the same amount of labour to make one gadget; it's just a niftier gadget."

What if making the niftier gadget requires less labor?

Awesome post.

Could you go more into this (I ask out of curiosity),

Assume prices are a constant mark-up over wage costs. That means monopolistically competitive firms maximise profits and the elasticity of demand for an individual firm's gadget is independent of niftiness, and is the same in odd and even years. (Dodgy assumption, that.)

I wonder if we have any historical evidence about nifty gadgets and aggregate demand. My first thought was that maybe the latter half of the 19th century was the heyday of nifty gadgets. I checked out the etymology of both words and it seems that "nifty" entered the language in the 1860s and "gadget" came into writing in the 1880s, but had been in use for some time before that. Were there a lot of nifty gadgets made during that time? Did they stimulate the economy?

Related question: Are Pet Rocks harbingers of inflation? Too much money chasing too few goods and services?

Jonathan: Thanks!

Let E be the own-price elasticity of an individual firm's demand curve.

Then marginal revenue is given by:

MR = [1-(1/E)].P where P is its price

Profit maximising firms set Q where MR = MC.

Assume a simple production function Q = L - F , where L is labour input and F is some fixed cost amount of labour, so the Marginal Product of Labour = 1 everywhere.

Since MC = W/MPL where W is wage, we get:

W = [1-(1/E)].P

Rearranging we get:

P = [E/(E-1)].W (if I got the math right)

This only strictly works if MPL is a constant and it's a constant elasticity demand curve. Otherwise MPL and E are both functions of Q. And of course you need E > 1.

My guess though is that E would be lower for a new good than an old good. Because other firms will generally produce closer substitutes after a lag. Which is why I said it was a dodgy assumption.

TMF: that would just accentuate the effect. But it isn't very plausible.

What if the periods were, say, decades, and we defined "niftiness" to mean that consumer goods were unlikely to become technologically obsolete in the near future?

Then decades with nifty gadgets would be periods with a lack of technological innovation and decades without nifty gadgets would be periods of high levels of technological innovation.

Throw in the central bank incompetence and then what you get is decade-long consumption recessions during periods of high rates of authentic technological innovation (e.g. the Great Depression), alternating with decade-long consumption booms during periods of low rates of substantive technological innovation (e.g. the annual stylistic ditherings of the Populuxe era).

Min: I don't know the empirical evidence. I guess someone else, like Mark, would know much better than me.

"Are Pet Rocks harbingers of inflation? Too much money chasing too few goods and services?"

Hmmm. Makes me think of: "Cocaine: Nature's way of telling you you have too much money"!

Dunno. Need to think about that one. Pet Rocks were 1975, IIRC. Works OK empirically.

Mark: so say in even decades n is high (N is growing), and in odd decades n is low (N stays the same). If r is constant, we would get booms in odd decades and recessions in even decades. Yep.

(And it's incredibly ironic you give me that example, because you have just hoisted me on the same petard that I have been hoisting all the New Keynesian fiscalists on in my last few posts. It's all about the difference between continuous and discrete time, N and Ndot !)

"But if you expected gadgets to get much niftier next year than this year, you would postpone some consumption until next year. What matters is the expected growth rate of niftiness, n."

If I buy now I get a return of gadget_life * utility_of_gadget(t). This assumes I use the gadget until it has negligible resale value.

However there is an opportunity cost of utility_of_gadget(t), so it depends on whether gadget_life * n * utility of gadget > utility_of_gadget(t) or

This seems right intuitively.

I'm not discounting, since I have no idea what the discount rate would be for niftyness, but if I did it would discount the Δ and make the relative utility of purchasing now larger.

Nick:
"Min: I don't know the empirical evidence. I guess someone else, like Mark, would know much better than me."

My favorite proxy for the rate of technological change is total factor productivity (TFP).

The BLS maintains a database of annual TFP for the US back to 1948. A good source of information on TFP growth prior to that is a few of papers by Alexander J. Field: “US economic growth in the gilded age”, “The Most Technologically Progressive Decade of the Century” and “The origins of US total factor productivity growth in the golden age”.

Average annual TFP growth is as follows:
1835-1855-0%
1855-1869/1878-(-0.5%)
1869/1878-1892-2.0%
1892-1919-1.1%
1919-1929-2.0%
1929-1941-2.8%
1941-1948-0.5%
1948-1973-1.9%
1973-1995-0.5%
1995-2005-1.5%

The first thing that should grab your attention is that TFP growth was at its most rapid during the Great Depression. (Hence my hypothetical example.) The second thing you should observe is that TFP growth was at 1.9% or higher from the 1870s through 1973 with the exception of 1892-1919 and 1941-1948. TFP growth has picked up since 1995 (but has slowed since 2005).

Now, why was TFP growth faster during the periods mentioned?

Well, Field analyzes the growth by sector and sector size and comes to some interesting conclusions. TFP growth was fast from the 1870s through 1892 because of railroads (which peaked in track mileage in 1916) and to a much lesser extent because of the telegraph. Almost all growth in TFP in the 1920s can be accounted for by manufacturing and that probably fed that decade’s stock market boom. Why did manufacturing TFP explode in the 1920s? According to Field it was due to the widespread electrification of factories (which had started in the 1880s). In the 1930s manufacturing TFP, although still relatively fast, slowed down. (He also points out that private R&D quintipled from 1929-1941.) But transportation TFP soared from 1929-1941 mainly due to the five fold increase in the share of tons-miles hauled by interstate trucking and its interaction with railroad transportation. (The US built its first interstate highway system in the 1930s.) And he argues that transportation TFP was largely responsible for the growth seen from 1948-1973, as manufacturing TFP actually went negative for part of that period. (And recall the Interstate Highway System, built on top of or paralleling the US Route system of the 1930s was largely completed from 1956-1973.) TFP growth was negative from 1855 to the 1870s primarily because of the Civil War.

Recent work by Bart van Ark shows that TFP in the distribution sector was the main source of the surge in growth from 1995-2005, and he argues that was due to the widespread adoption of ICT technology by that sector. (Think big box Walmarts.)

But this description barely scratches the surface of the breadth of technological change that took place during the periods of rapid TFP growth. For that I would read Field's papers.

Nick Rowe:
"And it's incredibly ironic you give me that example, because you have just hoisted me on the same petard that I have been hoisting all the New Keynesian fiscalists on in my last few posts."

I've been reading your last few posts and comment threads with fascination, although I did not comment myself. It's quite possible I unconsciously immitated you, as it surely wasn't intentional.

Mark: I would really like your opinion on my other posts, particularly on the math technique I use in my hybrid model. Is it right? Is it original? Because it is very simple, compared to solving out the model the usual way, where you start from an assumed monetary and fiscal policy rule and solve for Y. I keep hoping one of the New Keynesians, like Simon Wren-Lewis, will respond, but no sign yet.

Mark: If TFP growth was high during the 1930s, mostly because of transportation improving, that might tend to increase elasticity of demand for an individual firm's output, because it's easier to buy from competing firms (spatial competition), leading to falling markups of prices over marginal costs. Increasing real wages, but also deflationary pressure, if nominal wages are sticky. I wonder...

Interesting data. Thanks.

Hi Nick,

(Really off topic)

I just had a look at one of your old posts on the national debt being a burden on future generations, which someone gave me a link to:

I think your argument is wrong for a very simple reason: money. The debt is a promise to pay a specific amount of money, yet in your example you assume that it is a promise to pay a specific quantity of goods. This makes all the difference, I think. The short explanation of why is as follows:

In your example the government buys 100 apples from cohort A for a certain amount of money, let’s say \$100. It gives cohort A a \$100 bond and promises to pay 10% interest on that bond in the future. Then when the bond matures the government pays it off by giving cohort A \$110 in money. Cohort A then uses that \$110 to buy apples from cohort B. However, in your example the total supply of apples does not increase over time, as there is no real growth. As such there is an increase in nominal spending on apples but no increase in the quantity of apples available to buy. This means that the price of apples has to rise. As such cohort B sells 100 apples to cohort A for \$110 instead of \$100. So no one is worse off. Cohort A gets as many apples as they originally sold to the government, but no more because there is no real growth in the supply of apples, so the interest on the bond simply results in inflation.

Alternatively, if the government taxes cohort B \$10 to pay the 10% interest, then cohort B receives a total of \$100 overall for the 100 apples it sells to cohort A. Again, no one is worse off. In both cases cohort B can then buy 100 apples from cohort C, cohort C can buy 100 apples from cohort D, etc, etc.

The key here is that the supply of apples does not grow, so the interest on the initial bond can't be paid in real goods. The interest is purely nominal. This is due to the fact that the initial \$100 was spent on consumption, not investment. If the initial \$100 had been spent on investment, then productive capacity would have increased, the supply of apples would have grown, and cohort A could potentially have bought 110 apples from cohort B with the \$110 they received when the government bond matured.

What do you think?

If you read someone like Schumpeter, the reason innovation boosts growth is that capital goods are specialized. A shift in the direction of demand -- when some substantial class of goods gets replaced by something niftier -- in effect reduces the value of the capital used to produce the old goods. Gross investment is higher for a while as the obsolete capital is replaced by capital specialized for the nifty new goods.

So I think your model abstracts away from the real story.

Well, I guess you've got to ask yourself, why is the economy growing at all, if not for invention of new _____. And if it is driven by the invention of new _____, then what is the mechanism for that getting into the economic numbers?

A key assumption your analysis makes is in "But if gadgets suddenly got niftier this year, you would expect gadgets to be at least as nifty next year too". Is that really how people behave (remember lines overnight outside Apple stores...)? Some do for sure, but you're representing broad measures of an economy. I suppose that the inclination to buy an iphone could have been matched by an equal and opposite dis-inclination to buy everything else, but everything else includes things like food, etc. So I guess I just don't buy the formulation.

On a side note, I'm glad I've discovered your blog. It's an excellent study on current economic theories. I read your mix-of-old-and-new-keynesians post, and for the life of me couldn't understand why the "r" was in the numerator not the denominator, now I get it (the C's aren't consumption, they're marginal utility of a given level of consumption...).

In any case, I still think you've got a problem in that one in that, it just can't be right if the addition of one new keynesian to a group of 1000 old keynesians changes all the rules.

Nick,

"An increase in n, the expected growth rate of niftiness, for a given interest rate r, will reduce consumption demand today, as people save more because they are waiting for the niftier gadgets that will be in the stores next year."

That's all well and good except that people and most goods don't last forever. You need to adjust n by some factor representing finite life individuals and goods.

JW: At the macro level, that would be equivalent to random destruction of bits of the capital stock. Yep, that's a different story.

Philippe: did the people who bought the bonds see the inflation coming? If they had, would they have bought the bonds? If not, isn't inflation like a tax on them?

Define the real rate of interest r as the nominal rate minus the inflation rate. Let g be the real growth rate of the economy.

If r > g, then if you borrow to pay the interest on the debt, the debt will grow at rate r, which is faster than the economy, so debt/GDP will rise, which is unsustainable. So eventually you will have to increase taxes (or inflate) which burdens some future generation.

If r < g, however, you can keep on borrowing to pay the interest, and debt/GDP falls over time, so there need be no burden on future generations. All generations can be better off.

I went into all this in various posts that followed up the one you read.

Andy: "n" is a forward-looking variable. If people know the new Apples will arrive next month, n is very high. On the day when the new Apples actually hit the store, and don't expect any newer Apples for many months, n is very low.

C is consumption. MU(C) is marginal utility of consumption. The two are inversely related. If r goes up, you cut the *level* of C, and increase the *growth rate* of C (Cdot).

Frank: I "need" to adjust for the weather as well. Because people won't go shopping for a new car when it's cold and wet. Plus 1,001 other things too. The whole point of a *model* is that you *don't* do that. You pick out the few parts of reality you think might be important.

Nick Rowe:
"I would really like your opinion on my other posts, particularly on the math technique I use in my hybrid model. Is it right? Is it original? Because it is very simple, compared to solving out the model the usual way, where you start from an assumed monetary and fiscal policy rule and solve for Y."

I don't think there is anything wrong with the math technique you used, but I don't think it is original either, although offhand I have nothing to support my assertion.

I think the seemingly strange results you derived in those posts (e.g. slower expected growth in government spending means higher output in the present) all goes back to your observation in September ("New Keynesians just assume full employment without even realising it") that New Keynesian models simply assume the economy converges to full employment even though there is nothing in the models that says that it should.

Nick Rowe:
"I keep hoping one of the New Keynesians, like Simon Wren-Lewis, will respond, but no sign yet."

Yes, it's a little strange those posts didn't get more attention from other bloggers. I noticed a parade of very thoughtful commenters come through and nobody found any major errors. In my opinion Cochrane's posts were far less damaging than yours were, but he received much more attention because, I suppose, he's, well, Cochrane.

It's almost as though the New Keynesian true believers, such as Simon Wren-Lewis, are hoping nobody notices you pointing out that the emperor has no clothes.

Mark: thanks. That's roughly my perspective too.

Nick,

“Define the real rate of interest r as the nominal rate minus the inflation rate. Let g be the real growth rate of the economy.
If r > g, then if you borrow to pay the interest on the debt, the debt will grow at rate r, which is faster than the economy, so debt/GDP will rise, which is unsustainable. So eventually you will have to increase taxes (or inflate) which burdens some future generation.”

In my interpretation of your example the real rate of interest has to be zero because cohort B sells 100 apples to cohort A for \$110 dollars. The interest is purely nominal, because there is no real growth. Cohort B has no incentive to sell more than 100 apples to cohort A for \$110.

In your example you seem to assume that cohort A somehow extracts real interest from cohort B, but you don’t explain how or why. You avoid this issue by assuming that the government bond promises payment in a specific quantity of real goods, but in reality it does no such thing.

Also, in the example it doesn’t matter whether the government borrows to pay the interest, or if it taxes cohort B \$10 to pay the interest – the real result is the same. Cohort B sells 100 apples to cohort A, and either receives \$110 without taxes (in inflated dollars) or \$100 after taxes (in non-inflated dollars).

Philippe: I disagree. My little model was a world without money, so there's no such thing as inflation, which is a falling value of money. Bonds promise to pay apples. If you want to talk about inflation, you must talk about money and monetary policy. Assume there's a central bank that targets 0% inflation, by adjusting the money supply to keep it there. And assume lenders won't lend unless there's positive interest rates to give them the incentive to postpone consumption.

But this is too off-topic for this post. I spent too much time already convincing people that what they said about the impossibility of debt burdens on future generations is wrong. One counterexample is all I need, and I gave it. Assume no money, and that bonds promise to pay apples. End of discussion, for now.

Nick: Ignore me if I'm missing something fundamental (I'm piecing together the theory from reading a flurry of recent blog posts...) but - my understanding is that NK theory seeks to explain disturbances away from a (generally) upward trend in output and consumption; the trend is taken to be exogenous. Your trouble here is that you're trying to explain something with a theory which takes the thing you're analyzing as exogenous (well actually, the thing you're trying to explain is causing the thing which is taken to be exogenous). So it's not going to work.

Let Y(t) be the speed of the car, G(t) the position of the gas pedal, and S(t) some shock (like hills). Let Y*(t) be the speed limit.

Assume Y(t) = aG(t) - bS(t)

Assume Y*(t)=100kms/hr

Where do I need to put the gas pedal to drive the speed limit?

Assume Y(t)=Y*(t)=100km/hr for all t. Solve for G(t).

Y(t) is now exogenous, and G(t) endogenous.

Nick,

"I spent too much time already convincing people that what they said about the impossibility of debt burdens on future generations is wrong. One counterexample is all I need, and I gave it. Assume no money, and that bonds promise to pay apples. End of discussion, for now.'

The problem is that you tried to prove that government debt is a burden on future generations by assuming that the government debt is a promise to pay a specific quantity of goods rather than a specific amount of money.

I agree that it is possible for debt, under certain circumstances, to be a burden on future generations. But your model does not - as far as I can see - prove that government debt is a burden on future generations.

In order to make your argument you had to assume all sorts of things which are not relevant to the issue. Your statement "assume no money" seems to encapsulate this approach.

I was arguing against people who were saying it was *impossible* for debt to be a burden on future generations, in a world with no investment, distorting taxes, or foreigners. My counteraxample proved they were wrong.

Sure, if the future generations default on the debt (via inflation or whatever) then of course it isn't a burden on them. Jeeez.

Nick: "Assume no money, and that bonds promise to pay apples."
As Abba Lerner said :"It's magnificient but it's not war." Or at least, "It's modeling, but it's not economics"

Nick:

"I need to adjust for the weather as well. Because people won't go shopping for a new car when it's cold and wet. Plus 1,001 other things too. The whole point of a *model* is that you *don't* do that. You pick out the few parts of reality you think might be important."

If we are using an assumption of New Keynesian theory (nominal GDP growth will eventually go back to trend just because) then aren't you using two conflicting assumptions? With infinite life people and goods there is no reason for nominal GDP growth to revert back to any trend. Seems pretty important to me if we are using two conflicting assumptions.

Jacques Rene: I didn't know Abba Lerner was at the charge of the Light Brigade? Introducing money into the model matters for some questions, but not for others.

Frank: NK macroeconomists just assume that people expect Y to revert to Y*. Trend Y is just an empirical proxy for Y*, it is not the same thing.

"It's almost as though the New Keynesian true believers, such as Simon Wren-Lewis, are hoping nobody notices you pointing out that the emperor has no clothes.

Posted by: Mark A. Sadowski | November 22, 2013 at 11:14 AM

Mark: thanks. That's roughly my perspective too"

They're using the same idea that they used on Keen's criticism of DSGE models. They took particular criticisms and applied the logic that because they had seen a DSGE model somewhere for which the criticism was incorrect, the criticism was incorrect in general.

There are certainly Models which people call NK models to which your comments don't apply, and it looks very like critics are citing those models.

Without some sort of meaningful taxonomy of models, this is what you're going to get. The same thing is true, of course, with Cochrane.

If you employ this technique and also apply Friedman's defense of unrealistic models, you can defend almost any model against all but the most comprehensive and rigorous criticisms. Those you can always ignore as the work of cranks, which is at least somewhat right, as most ordinary people wouldn't think such a thing was worth the effort, particularly given the likely outcome.

Of course, if you discard all bathwater vigorously and systematically, you're going to lose some very cute babies. OTOH sieving tons of bathwater takes time that could be devoted to something more rewarding, like a new DSGE model.

Peter N: (if I understand you correctly). But my model here (for k=0) is exactly like the simple textbook NK model. (I did it in continuous time, and used slightly different math, but that didn't ought to make any substantive difference to the results, it only lets you see them more clearly. (Same with Cochrane).

But Cochrane's critics mostly didn't address hid arguments, they just either cited models to which they didn't apply or gave arguments that the results weren't realistic.

DeLong:

[Cochrane quote]"These are just the beginning of the strange predictions new-Keynesian models (or modelers) make. "Fiscal stimulus" is the prediction that even completely wasted government spending is good for the economy. "

He then goes on at some length objecting to conclusions and many statements Cochrane has made (like Scott Sumner, he will often overstate his case for effect. You're just painting people a bullseye). DeLong goes back to 2009 and maybe beyond. I lost interest since I was looking for a direct mathematical refutation.

"Let's roll the videotape, from March 2009: John Cochrane:

'[T]he danger now is inflation. And I would say it's a greater danger than most..'"

This is Simon Wren-Lewis

" Basic NK models employ the construct of the (possibly infinitely lived) intertemporal consumer. To explain, these consumers look at the present value of their expected lifetime income, and the income of their descendents if they care about them (hence infinitely lived). This has two implications. First, temporary shocks to current income will have very little impact on NK consumption (it is a drop in the ocean of lifetime income). The marginal propensity to consume out of that temporary income (mpc) is near zero, so no multiplier on that account. Second, a tax cut today means tax increases tomorrow, leaving the present value of lifetime post-tax income unchanged, so NK consumers just save a tax cut (Ricardian Equivalence), whereas OK consumers spend most of it. However NK consumers are sensitive to the real interest rate, so if higher output today leads to higher inflation but the nominal interest rate remains unchanged, then you get a multiplier of sorts because NK consumers react to lower real interest rates by spending more.

So far, so different. But the NK consumption model assumes that agents can borrow whatever they need to borrow. There are good theoretical reasons why that is unlikely to be true (e.g. asymmetric information), and even better empirical evidence that it is not. Empirical studies that look for ‘natural experiments’, where agents obtain an unexpected increase in post-tax income which is likely to be temporary, typically find a mpc of around a third (even for non-durables), rather than almost zero as the basic intertemporal model would predict. (For just one recent example: Consumer Spending and the Economic Stimulus Payments of 2008, by Parker, Souleles, Johnson, and McClelland, American Economic Review 2013, 103(6): 2530–2553.)

So if mainstream Keynesian theory wants a more realistic model of consumption, it often uses the (admittedly crude) device of assuming the economy contains two types of consumer: the unconstrained intertemporal type and the credit constrained type. A credit constrained consumer that receives additional income could consume all of that additional income, so their mpc out of current income is one. [1] That credit constrained consumer is therefore rather Old Keynesian in character. But there are also plenty of unconstrained consumers around (e.g. savers) who are able to behave like intertemporal maximisers, so by including both types of consumer in one model you get a hybrid OK/NK economy."

Much better, but still a direct confrontation of the model.

Here's an example from Facts and Other Stubborn Things of the "nobody believes that old stuff" genre. He seems to agree with Cochrane's model results, as far as it goes, but it's hard to tell.

It's an interesting post but I disagree with him on (at least) four counts:

(1.) Nobody really thinks (well, maybe Cochrane does) that the NK consumption function is exactly right. We bring in intertemporal optimization because people do plan for the future, but people still think that current or at least near/medium term income matters for psychological/behavioral reasons if nothing else,

(2.) so with MPC = 0 if government spending doesn't crowd out you've still got a case for government spending. The problems only come in if government crowds out. Insofar as government commits to major investment programs, and insofar as we think investment is governed by expectations of future demand, you get positive multipliers again (of course, by a different mechanism than the Old Keynesian multipliers).

(3.) The whole MPC/income thing goes out the window when we consider credit constrained, paycheck-to-paycheck people, which leads me to

(4.) It's true politicians talk like Old Keynesians. I think economists do this less - they focus on my (2.). When we do talk about MPC it's almost always with reference to something like (3.).

So it's a good post laying out the issues, although I don't buy all the "you silly Old Keynesian" implications. I agree with Krugman that the Old Keynesian intuitions hold up surprisingly well, even if the mechanisms do change."

So people claim these aren't the models people really use. Their only for teaching and Friedman model simplification purpose. I saw the phrase "setting metes and bounds somewhere" IIR.

I could find more examples, but this is probably long enough.

"still NOT a direct confrontation", Sorry.

and their for there and hid for his, no less. Maybe I should learn to proofread!

Yes. People go into debt to buy goods/services and subsequently work more.
Other than blocking carbon pricing/cap, the main error of the CPCs has been cutting and continuing to cut upper tier corporate and upper tier income taxes too deeply. The 2012 Bilir paper, "Patent Laws..." tables on page 31 a median estimate of 9 yrs 9 months as the lifecycle of a product. Based on how long a product patent continues to be cited by subsequent patents.
This suggesting the manufacturing industry at least, and probably alot of the high end service industry, need about 12% of their revenues devoted to new product generation whether or not the product is considered R+D on a financial statement. Finance gives as a few new products....petro maybe a few new drilling techniques; alot of their technologies spinoff off to aid carbon sequestration and even archeology. But still, these are not the industries that should be channelled surplus cash and certainly we should not go into federal debt to dole out this mindless 1930s prairie rhetoric.
We are now dependant on technologies made in the USA, China, Germany, and offering nothing in return but future AGW. The correct RW policy is raising taxes to Chretien rates, running an immediate surplus, and building up university schools in the West, in rural/suburban (R.Ford friendly 905) ridings, and switching over petro to pterochemical product through the federal subsidizing of refineries. It has been correctly pointed out it is hard to forecast refinery economics. Even easier is to point out, there won't be a petro/coal market for power generation, home heating oil, nor auto gasoline/diesel. Within two decades, the RWers will have slit their own throats at present trajectory, and everyone will move away from the West, presumably to Ontario and the (young Asian) West coast.

At least Americans will spend money anyway. Dude up the house...you can spend serious money doing that, using 1950s technology too. Have any of you guys ever been married? I never met a women yet who did not like restaurants, the fancier the better....new hairdos and clothes doesn't matter how much they cost...will guys ever get tired of ballgames? \$100 seats? Las Vegas baby!

Aggregate demand can be soft if you hit zero bound, and people are saving anyway, as they save for retirement, college, to buy land or a house, to start a business etc. Some cultures are savings oriented...

New gadgets have little to do with it, besides there are probably more new gadgets now than ever...in your car, on your head, on your desk, in your hand....3-d printing and who knows what all....we live in the age of innovation...

The solution to weak aggregate demand at or near ZLB is...printing money baby.

Nick,

"Sure, if the future generations default on the debt (via inflation or whatever) then of course it isn't a burden on them."

In my interpretation of your model (i.e. including money) no one defaults on any debts. The government pays what it promises, but cohort B sells 100 apples to cohort A for \$110 instead of \$100, because there is no real growth. Cohort B and cohort A's transaction is voluntary. Overall cohort A loses nothing, and cohort B loses nothing. Cohort A just doesn't receive any real interest, but they don't lose any value over time either. In fact they are all better off. No debt default occurs at all.

Nick,

I've studied the old post on OK and NK, and here's where I think your issue arises. It's in your assumed relationship between Cdot(t) and r(t).

In the NK equation, a change in r(t) would cause the following to happen: and I wish I could draw right now, but imagine a "v", with the left side vertical, and the right side taller than the left, and with a line connecting the left to the right. The top line now represents the undisturbed growth in consumption (C(t)). The bottom "v" represents the consumption given an increase in r at time t. Note that Cdot(t) has increased just like your equation. But that's not the only thing that happened - there was an immediate "hit" to consumption. And this immediate "hit" is nowhere reflected in your equations. That's why you are getting counterintuitive results. I think.

For example, here:
"Set r(t) to ensure that output is at potential, given G(t) and T(t). This means that r(t) must respond positively to n(t) and to Y*dot(t), and negatively to Gdot(t) and positively to Tdot(t). (Look at the equation!)"

This is correct given you equation, but the equation ignores the immediate "hit" to C of this change in interest rate.

Andy,

I am guessing that Nick's response is that this requires you to assume the ending points of the two paths are the same, but there is nothing in the model to make this happen. I.e the immediate hit isn't in Nick's equations because it isn't in the NK model either.

Andy: I think JW gives a good guess of how I *should* respond. (He understands it as well as I do.)

An NK agent maximises discounted sum of utilities, subject to permanent consumption equaling permanent income. Permanent income is exogenous to an individual agent, so if r goes up he cuts C(t) and increases Cdot(t). But in aggregate, permanent income is endogenous, and equal to permanent consumption, so it's indeterminate.

At present, the main reason for the slow introduction of goods that raise quality-of-life of boomers, and not just what dumb women want with their deviation away from utility and instinct to nest, and not just what dumb men want with their over-reliance on religion and inability to permit their children to form intellectual bonds with intellectual peers ratehr than inferior nearby community and family units, is the slow rate of FDA testing for new medical products and treatments. There are moral concerns, non-pandemic health concerns, and pandemic health concerns. The second main technology sector that would increase boomer quality of life is robotics. There is a lack of good robotic software. This may be a good thing else the machines would take over and begin nuking cities, civilian infrastructures, asassinating the chains of commands and potential leaders of the resistance....in the uSA in particular there is way too much money spend on building giant community churches which is bad for innovation.

Nifty stimaultes AS too as much of the low cost goods from China originate from computerized inventory.
A comment by N.Rowe or S.Gordon about 2% inflation being an achievement has stimulated me to read my "Two % Target" book. Stable inflation is a nice achievement but it seems like there wasn't much experimentation until the Cold War ended. I believe central bankers can act as a check on the power of uneducated leaders and sheep democracy voters. Leaders from petro or finance or defense sectors may not be as econo-worldy as a Central Banker.
Of all the effects of raising or lower the interest rate, the one that is a most useful lever is the stimulation or r3tardation of exports. Domestic manufacturing is closely proportional too. Two main pitfalls of progress are pandemics and robotics/AI gone bad. The basket of goods and services that lead to harnessing the upside of these technologies and/or successfully outlawing them (and other sci-fi type risks), is probably more important than is the rest of the economy combined. Nations that enact the basket or plan to very shortly, should lower their interest rates. Nations that don't, should raise their interest rates to stimulate imports.
I'm still not sure how much of the basket is basic human capital to prevent terorists and enact good gvmt, and how much is dependant on getting responsible police/military actors, or surrogates. The surveillence functions like the existing NSA, but is more intrusive; intrusive upon many actors able to destroy little fake insects.
The smartest people in the USA agencies also give serious consideration to this conclusion. Probably there is a valley of death in learning multi-disciplinary expert knowledge; it takes long enough that people would rather get the earnings of the single discipline over-specialization. I like a core curriculum maybe even in HS, but the Ivy School swimming is not part of it.

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