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Niveditas98 .
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Ralph, I don't mean that full-reserve "banks" will have failures -- I mean that other entities will spring up to perform the economic function that fractional-reserve banks currently do, and they will create the same issues. It is fantasy to believe that the failure of these entities will not cause problems because they are funded by "equity". Fractional reserve banks when they originally arose did not have deposit insurance. Deposit insurance was created to mitigate the economic stresses caused by their failures, and it has worked quite well. Fractional reserve banking serves a useful economic function, which is why it exists. I think of it as essentially providing insurance: after all, why do people want to hold their savings as deposits? It is because of uncertainty around when they will need money. Just as it is more efficient to pool resources in an insurance company to provide fire insurance, rather than each homeowner attempting to self-insure, it is more efficient for depositors to pool their deposits together and lend out the excess -- their money needs are uncertain, but pooling reduces the uncertainty of how much money the depositors in aggregate will actually withdraw at any point in time.
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Full-reserve banking is an oxymoron. Full-reserve banking is not banking. It is a storage/payments service. Credit intermediation and maturity transformation will be done by entities which will not be called "banks" because they won't take deposits, but will have exactly the same issues as existing non-full-reserve banks. We will then proceed to reinvent the entire structure of regulation that deposit-taking fractional-reserve banks are subject to, and end up with the same system that we have today.
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Jon, in the model without money, the central bank can't actually influence the interest rate by trading the bonds, since there's no money, and the bank doesn't have apples or any other real goods. So it would appear this has to be set by law. Would this have an impact on real interest rates? In the model with money, the assumption is that when the central bank changes the nominal rate, in the short run inflation expectations don't change, and the change in the nominal rate flows through into a change in the real rate, right? Is this still a plausible model in the absence of a medium of exchange?
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Nick/Jonathan, I would like to clarify something very basic in your discussion on bonds in the absence of money. First, what does "bond" mean in this situation? Since there's no money, I assume it must mean something like "give me 100 apples today in exchange for my promise to give you 105 apples next month". Now there could be orange bonds and pineapple bonds in addition to apple bonds, with possibly different rates of interest, but let's focus on the apple bonds. Assuming this is what is meant by "bond", how would the central bank set the interest rate on these bonds -- is it by government edict, saying the only apple borrowing and lending allowed is 100 apples today for 110 apples tomorrow? Second, Let's make this more concrete. Assume in the previous equilibrium, 100 apples were produced by lenders and exchanged for promises of 105 apples next month. With the higher interest rate for apples, notional demand for apple bonds rises to 120, say, which represents 132 apples next month. Meanwhile notional supply of apple bonds falls to say 90, representing 99 apples next month. Here Walras's law applies to the notional demands, with the excess demand of 120-90=30 for apple bonds matched by an excess supply of 30 apples today. Now let's follow Nick's argument -- 120 apples can't be lent, since there is only demand for 90 apples of borrowing now. Fine, so 90 of the previous lenders continue to lend, the extra 20 new lenders find they can't lend, so they do whatever they were doing before with their apples. What happens, however to the 10 old lenders who can no longer lend? What do they exchange their apples for? What happens to the 10 old borrowers who no longer exchange next month's apples for apples today? Also, next month, previously 105 apples were produced and given to the lenders to pay off the debt. Now there are only 90 borrowers, who pay off their lenders with 99 apples. What happens to the remaining 6 apples of production?
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Remember that this is still a barter economy -- you cannot say you want to buy apples without specifying what you want to sell in exchange. If given the constraint all other markets were clearing, your statement that you want to trade pears for apples, is equally a statement of excess demand for apples and excess supply of pears.
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Nick, I don't understand your comment about jobs and cars. My point is that you are comparing an unconstrained excess demand for apples with a constrained lack of excess supply of pears, which makes no sense. You have to pick one or the other for all the goods. Either say that because you say you would trade pears for apples if given the chance, there is both excess supply of pears and excess demand for apples; or say given the constraint, you are not trying to buy apples, nor are you trying to sell pears. You can't have it both ways, saying you want to buy apples, but you don't want to sell pears because you recognize the apple constraint.
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To put it another way, once you've hit your constraint, apples are no longer meaningfully part of the market. This is entirely clear in the case of unobtainium -- if you are accounting for the fact that it is in zero supply, there is no meaningful sense in which there is an unobtainium market -- everything is the same as it would be if there were no such good.
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Nick, I think my point is that you're defining excess demand in one way for the apples, but excess supply in a different way for pears. i.e. if I were to ask you, "at these prices, would you want to buy apples and sell pears", you would say yes to both those questions. If I asked you, "at these prices, knowing that you cannot buy more than 60 apples, would you want to buy more apples and sell pears", you would answer no to both questions.
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I read this post and some other unobtainium posts, and I must confess I don't understand the "unobtainium" controversy over Walras's law. Walras's law says that if there is an excess demand for unobtainium, there must be an excess supply of other goods. This is true when agents reveal their notional demands, since they wish to sell other goods and purchase unobtainium at any price vector that includes a finite price of unobtainium. You say that well the agents are smart, realize that unobtainium has no supply, and hence do not demand unobtainium and instead plan to purchase other goods with their production. But if this is the case, then there is no excess demand for unobtainium: the demand (zero) equals the supply (also zero); and hence there is no reason to expect excess supply in the other goods. The other argument, that in the presence of money, there is not one price vector for n goods that agents see, but rather n 2-price vectors (for each good vs money), and this can result in an excess supply (or excess demand) of all n goods, makes sense. In this context, though, I don't understand the distinction that some people draw between a medium of account and a medium of exchange. It seems to me that anything that is to have value as a medium of exchange, must also have value as a medium of account (or be instantly convertible into the medium of account, which amounts to the same thing). If you had scrip that only had value as a medium of exchange, but could not be "stored", it would be useless in solving the coincidence of wants problem, since you would only accept scrip in return for a haircut if you simultaneously had arranged to exchange that scrip for a manicure, and the manicurist would only accept the scrip if she had simultaneously arranged to exchange that scrip for a massage, and the masseuse would only accept that scrip if she had simultaneously arranged to exchange it for a haircut. The scrip adds no value whatsoever over a pure barter economy in this case.
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Didn't we agree a few weeks ago that if the interest rate is zero, there is no cost to additional government debt?
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In the trading book p&l view, interest income is not really income unless it exceeds your cost of funding, by the way -- that's why we subtract funding.
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Is there no standard definition of income? I'm sure someone has thought about this before :) I initially thought income should be defined as what you can consume, regardless of what you actually do consume. This looks like it would work nicely for 1-4 in the first period. Assuming all are price-takers, and 1 apple = 1 leisure-hour = 1.05 bananas = 1.05 apples tomorrow, they all can consume 100 apples today, so their income is 100 apples. This does not seem to work very well in succeeding periods once you introduce savings. If #4 saves all his apples today to get 105 apples next year, and also produces 100 apples next year, we surely don't want to say his income next year is 205 apples. Should we subtract 100, what he saved; or 105, the future value of his savings, or something else? What if he did have a secret technology, so he could produce 110 apples, is his income in the first period 110/1.05, or do we count the extra 5 apples as his second-period income? These sort of issues look pretty similar to the issues of income accounting for a firm. What sources of income should be accrued, what should be marked to fair value etc. From my biased point of view (working in finance), fair-value accounting together with the definition of profit & loss for a trading book would be the easiest to make consistent. For 1-3, initial wealth = 100+100/1.05. When we go from year 1 to year 2, p&l = 100 (realized) + 100 (unrealized) - (100-100/1.05) (funding) - (100+100/1.05) (yesterday) = 0. For #4, assuming he produces 100 apples next year the same as #2, in addition to the 105 coming from his investment, the breakdown is a little different, but he has the same initial wealth and p&l: 105/1.05 + 100/1.05 wealth, p&l = 105 + 100 - (205-205/1.05) - (105/1.05+100/1.05) = 0. This does lead to the odd result that if everything is deterministic, income is always zero.
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Is this just saying that with perfect competition (i.e. no secrets), all forms of capital must have gross returns equal to the rate of interest, and hence on net can generate no income (to the individual capitalist)? Same as in perfect competition, no firm can make economic profit?
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Why is it so important to "own" capital? The trend in many industries if anything is towards not owning capital. Eg, neither of the two leading graphics chip companies own the capital necessary to manufacture their chips. Most of the parts that go into a GM car are probably not produced by GM, etc. Why is hiring a semiconductor fab to manufacture your chips different from hiring a bunch of PhDs to design your chips? "Wealthy people's incentive, in maximizing their return on assets they have or could trade into, is very heavily tilted toward maximizing the return to capital other than human capital. If anything they are incented to hold down the return to human capital since it is in competition with their slice of the pie." But returns to skills are increasing, and they are regularly invoked as an explanation for rising inequality. This doesn't jive with the notion that there are strong pressures trying to hold down the returns to human capital.
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Nick: "But it takes me (almost) no labour or land to write "IOU 100 apples next year signed Nick Rowe" on a bit of paper." I think the point was that presumably you made that promise because the person to whom you gave that IOU gave you, say, 75 bananas in exchange for it. That is, his asset (the IOU) was earned by his labour expended in producing 75 bananas with which to buy the asset. Or perhaps even more directly, he was employed by you for 40 hours, and you paid him in 100-apple IOU's. I think the distinction which you want to make between "real" capital and financial capital might be that while financial capital might look like real capital at the micro level, to individuals, from society's perspective, it does not directly increase production. That is, if I work, and exchange my labour for an IOU that yields 100 apples a year from now, from my perspective that looks like working and building a machine that will produce 100 apples a year from now. If I had actually done the latter, society actually will have 100 more apples next year. My buying an IOU from you, though, does not create 100 more apples.
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Nick, yeah, I get the same result if I work it out in scenario #4 (working out details, since I don't yet trust myself to see the intuition). The incremental (throw-away) tax on the young that is equivalent in disutility terms to additional dB debt is 2B/(Y+B) dB. The interest rate is 2B/(Y-B), so the burden is r/(1+r) dB, which is basically the same as what you get (our dB's are different by a factor of (1+r)). The tax T that produces the same total utility as debt B is just given by solving ln(Y-T) + ln(Y) = ln(Y-B) + ln(Y+B) which gives T = B^2/Y To express this as \int r/(1+r) dB, I'd have to work out what the interest rate is in the presence of both taxes and debt, I think, and then integrate along the curve of constant utility from (0,B) to (T,0). This doesn't seem to be an easier way of figuring out the equivalent tax burden?
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Nick, in my example, I think Paul has to issue a consol. After period 0, both of them want to keep their consumption constant, and their production is constant, so the only possible payments between them must also be constant. Have to run to work, so don't have time to read your question in full just now, but here's a calculation of debt impact in scenario #4. Assume lifetime utilities of log c_y + 1/(n+1) log c_o. Suppose there is debt of B/(1+r), interest of rB/(1+r) (and hence taxes of the same amount), and assume B changes by a small amount dB. Assume the young are the ones who pay taxes. Then c_y = Y-B, c_o = Y+B for flows to balance. Reduction in utility from the additional debt is dB/(Y-B) - 1/(n+1) dB/(Y+B) = ( Y+B - 1/(n+1) (Y-B) )/(Y^2-B^2) dB = ( Y n/(n+1) + B (n+2)/(n+1) )/(Y^2-B^2) dB If n = 0, this is 2B/(Y^2-B^2) dB This doesn't seem to depend on what interest rates or taxes actually are, only on what the time rate of preference is and the amount of existing debt (as long as you measure debt by its maturity value rather than face). I think this makes sense, in that it shouldn't matter whether the government chooses to call your payments "debt" or "taxes". This would all work through exactly the same if the entire B were just called taxes: the government taxes you B when you're young and gives it to the older generation, and there's no debt.
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Nick, thanks! Now I won't try to break my head working out an impossible problem. I'm a maths guy.
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Ok, thanks. I tried to work out a detailed example in a slightly different model: Suppose there are just two infinitely long-lived people, Peter and Paul, and no government. Normally, they each brew 100 beers per period and consume it themselves. What will happen if in one period, something goes wrong with Paul's brewery and he produces no beer in just that period? Assumptions: their utility function is log c_0 + 1/(1+n) log c_1 + 1/(1+n)^2 log c_2 + ..., where n = 1/9 (to make numbers look nice), and Paul's income is zero in period 0. Assuming my math was worked out correctly, I conclude that Paul will borrow 45 beers from Peter in the first period, and will in each subsequent period pay 10 beers in interest, rolling the debt over indefinitely. In general, I get that the interest rate will be 2n, and the sum borrowed will be 50/(1+n). I have to dig into this a bit more though -- my method was to assume that some amount B is borrowed and interest rB is paid on it forever, then maximize (individually) Peter and Paul's lifetime utility assuming a fixed rate of interest r, then note that the two optimum B's are equal only for a certain value of r, which ties down everything. However, if instead I try to do it assuming a sum B is borrowed and then in each period B1 is paid back (with no assumption on the relationship between B1 and B), I can't see how to get a unique solution.
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Or do you mean that the interest rate was negative before the issuance of debt, not after?
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Nick, right I was talking about case #3, which you said works out because interest rate is negative. But how do I interpret my example numbers to see that the interest rate is not 5 on 45, which looks positive, but some negative number?
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Nick, thanks for the kind encouragement :) I don't see any obvious arithmetic error. To put concrete numbers in, say the young pay 5 beers in taxes, and buy bonds with 45 beers, and consume the remaining 50 beers. When they're old, the bonds mature at 50 beers, which they consume (the old aren't taxed). The flow of beer balances out in each period. These people are clearly better off than if the government simply taxed the young 5 beers and threw them away. The interest is apparently positive, with a 45 beer investment yielding 50 beers. But if you forget that 5 of the beers that you gave up when young were labeled "taxes", then you give up 50 beers when young and get 50 beers when old. That's a zero rate of return.
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Nick, re economics I know -- formally nothing beyond a couple of undergrad courses a long time ago. I just read up on topics that interest me. I don't "recognize" the Euler equation, I read other posts that called it that, and then looked it up on the web :) I set the bonds to mature at 50 because that's how much the old people need in order to consume, and it seemed more natural to tax the young, rather than tax the old, which effectively just reduces the interest rate they get. I think I see what you mean by a negative interest rate -- the young would clamor to lend funds even at r < 0. But on the other hand, isn't the natural rate of interest supposed to equal the rate of time preference, for equilibrium? I do see a paradox in my example though, since effectively all I've done is take 50 from everyone when they're young and give it back when they're old. At a positive rate of interest, that should be equivalent to destroying value. Yet everyone appears to better off.
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From your previous post, why don't we consider model #3 instead of model #4? It seems more realistic, and better suited to the existence of debt -- in model #4, everyone is producing what he himself would like to consume, so introducing debt moves you away from optimality, because no-one actually wants to lend. Whereas in model #3, everyone is better off with the existence of debt. In the long run, you get taxed 50r/(1+r) when you're young, you buy 50/(1+r) bonds when you're young, and you consume 50. When you're old, the 50/(1+r) bonds mature at 50 -- financed by taxing the next generation 50r/(1+r) and selling them 50/(1+r) bonds -- and you consume 50. Debt stock is constant at B = 50/(1+r), each cohort pays rB in taxes, and they're better off than if there were no debt but the government just taxed the young rB?
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Nick, thanks for the pointer to the other post. There are definitely some interesting ideas here to think about, and I think I am learning something. Regarding your question, I can't help but feel that any model that implies that the two societies in your question (i.e. one has debt of B and taxes itself rB to pay itself bond interest, the other taxes itself rB and throws away the tax) are even approximately equally well off, must have some flaw, because resources are only redistributed in the first instance, while they are destroyed in the second. I have some issues understanding the Euler equation referred to in the other post -- as I understand it, the equation relating marginal utility of consumption in the two periods to the rate of interest is derived assuming that non-investment income and the interest rate are fixed. Doesn't the equation have to change form if the interest rate is not exogenous but determined in a market? I am not familiar with these concepts, so that might be a dumb question. But I feel like something is missing here -- in the real world, the young don't just buy debt because they have to in order to maintain some equilibrium in the government debt market. They want to invest money so they can consume more than they produce in retirement. Savings and investment should arise even in the absence of the government -- if they didn't I'm not sure how the government would be able to issue debt in the first place.
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