Saturday, December 7, 2013

The Interest Rate, the Interest Rate, and Secular Stagnation

In the previous post, I argued that the term "interest rate" is used to refer to two basically unrelated prices: The exchange rate between similar goods at different periods, and the yield on a credit-market instrument. Why does this distinction matter for secular stagnation?

Because if you think the "natural rate of interest," in the sense of the credit-market rate that brings aggregate expenditure to a desired level in some real-world economic situation, should be the time-substitution rate that would exist in a model that somehow corresponds to that situation, when the two are in fact unrelated -- well then, you are going to end up with a lot of irrelevant and misleading intuitions about what that rate should be.

In general, I do think the secular stagnation conversation is a real step forward. So it's a bit frustrating, in this context, to see Krugman speculating about the "natural rate" in terms of a Samuelson-consumption loan model, without realizing that the "interest rate" in that model is the intertemporal substitution rate, and has nothing to do with the Wicksellian natural rate. This was the exact confusion introduced by Hayek, which Sraffa tore to pieces in his review, and which Keynes went to great efforts to avoid in General Theory. It would be one thing if Krugman said, "OK, in this case Hayek was right and Keynes was wrong." But in fact, I am sure, he has no idea that he is just reinventing the anti-Keynesian position in the debates of 75 years ago.

The Wicksellian natural rate is the credit-market rate that, in current conditions, would bring aggregate expenditure to the level desired by whoever is setting monetary policy. Whether or not there is a level of expenditure that we can reliably associate with "full employment" or "potential output" is a question for another day. The important point for now is "in current conditions." The level of interest-sensitive expenditure that will bring GDP to the level desired by policymakers depends on everything else that affects desired expenditure -- the government fiscal position, the distribution of income, trade propensities -- and, importantly, the current level of income itself. Once the positive feedback between income and expenditure has been allowed to take hold, it will take a larger change in the interest rate to return the economy to its former position than it would have taken to keep it there in the first place.

There's no harm in the term "natural rate of interest" if you understand it to mean "the credit market interest rate that policymakers should target to get the economy to the state they think it should be in, from the state it in now."And in fact, that is how working central bankers do understand it. But if you understand "natural rate" to refer to some fundamental parameter of the economy, you will end up hopelessly confused. It is nonsense to say that "We need more government spending because the natural rate is low," or "we have high unemployment because the natural rate is low." If G were bigger, or if unemployment weren't high, there would be a different natural rate. But when you don't distinguish between the credit-market rate and time-substitution rate, this confusion is unavoidable.

Keynes understood clearly that it makes no sense to speak of the "natural rate of interest" as a fundamental characteristic of an economy, independent of the current state of aggregate demand:
In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest — namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of Wicksell’s “natural rate of interest”, which was, according to him, the rate which would preserve the stability if some, not quite clearly specified, price-level. 
I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate of interest for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. I had not then understood that, in certain conditions, the system could be in equilibrium with less than full employment. 
I am now no longer of the opinion that the concept of a “natural” rate of interest, which previously seemed to me a most promising idea, has anything very useful or significant to contribute to our analysis. It is merely the rate of interest which will preserve the status quo; and, in general, we have no predominant interest in the status quo as such.


EDIT: In response to Nick Edmonds in comments, I've tried to restate the argument of these posts in simpler and hopefully clearer terms:

Step 1 is to recognize that in a model like Samuelson's, "interest rate" just means any contract that allows you to make a payment today and receive a flow of income in the future. It would be the exact same model, capturing the exact same features of the economy, if we wrote "profit rate" or "house price-to-rent ratio" instead of "interest rate." Any valid intuition the model gives us, applies to ALL asset yields, not just to the the credit-instrument yields that we call "interest rates" in every day life.

Step 2 is to think about the other factors that enter into real-world asset yields, besides the intertemporal exchange rate Samuelson is interested in -- risk, liquidity, carrying costs and depreciation, and expected capital gains. Since all real-world asset yields incorporate at least one of these factors, none correspond exactly to Samuelson's intertemporal interest rate.

Step 3 is to realize that not only are credit-instrument yields not exactly the Samuelson "interest rate," they aren't even approximately it. The great majority of credit market transactions we see in real economies are not exchanges of present income for future income, but exchanges of two different claims on future income. So the intertemporal interest rate enters on both sides and cancels out.

At that point, we have established that the "interest rate" the monetary authority is targeting is not the "interest rate" Samuelson is writing about.

Step 4 is then to ask, what does it mean to say that some particular credit-market interest rate is the "natural" one? That is where the dependence on fiscal policy, income distribution, etc. come in. But those factors are not part of the argument for why the credit-market rate is not even approximately the intertemporal rate.

14 comments:

  1. People waste so much time trying to understand interest, when there is nothing to understand except the need to abandon a reliance on it. The wisdom I share with you is divine in origin. Interest is un-natural, and everything related to it is as well. You write well, but when you write about non-sense as your subject, your well crafted composition still sounds uninformed. Interest is flawed, is man-made, and is destructive to economies. You are not supposed to make money from money, instead when you invest you are supposed to share in profits of ventures. That way growth is always linked to natural levels, as allowed by the sun, the land and man's efforts in measured steady amounts. Interest on the other hand grows without bounds and quickly becomes detached from what nature can support. All of interest is wrong, trying to separate one form from another is a waste of time. There is no need to try to unlock some kind of secret meaning to interest. It's not magical in any way, it rubbish, disregard it and use your brain power for something better.

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  2. "Came not by usura Angelico; came not Ambrogio Praedis,
    Came no church of cut stone signed: Adamo me fecit.
    Not by usura St. Trophime
    Not by usura Saint Hilaire,
    Usura rusteth the chisel
    It rusteth the craft and the craftsman
    It gnaweth the thread in the loom
    None learneth to weave gold in her pattern;
    Azure hath a canker by usura; cramoisi is unbroidered
    Emerald findeth no Memling
    Usura slayeth the child in the womb
    It stayeth the young man’s courting
    It hath brought palsey to bed, lyeth
    between the young bride and her bridegroom
    CONTRA NATURAM
    They have brought whores for Eleusis
    Corpses are set to banquet
    at behest of usura."

    Welcome to the blog. Just one request -- could you use some kind if handle, rather than Anonymous? Thanks!

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  3. Very interesting. I have found it rather puzzling recently the different ways the idea of a natural rate of interest seems to be used.

    I am not so sure that the interest rate in a model like Samuelson's is so far removed from the rate which would serve as a policy tool. The things you mention like the fiscal position, income distribution, trade propensities do not appear in Samuelson's model. In fact his result, concluding that the rate of interest must equal the growth rate, depends on the absence of those complicating factors. As soon as we introduce these things, we find we have a situation where the interest rate that will achieve the desired level of income, depends on current circumstances.

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    1. I am not so sure that the interest rate in a model like Samuelson's is so far removed from the rate which would serve as a policy tool.

      Then I have not done a very good job explaining! Tho on the other hand, there are a lot of layers of confusion to unravel.

      Step 1 is to recognize that in a model like Samuelson's, "interest rate" just means any contract that allows you to make a payment today and receive a flow of income in the future. It would be the exact same model, capturing the exact same features of the economy, if we wrote "profit rate" or "house price-to-rent ratio" instead of "interest rate." Any valid intuition the model gives us, applies to ALL asset yields, not just to the the credit-instrument yields that we call "interest rates" in every day life.

      Step 2 is to think about the other factors that enter into real-world asset yields, besides the intertemporal exchange rate Samuelson is interested in -- risk, liquidity, carrying costs and depreciation, and expected capital gains. Since all real-world asset yields incorporate at least one of these factors, none correspond exactly to Samuelson's intertemporal interest rate.

      Step 3 is to realize that not only are credit-instrument yields not exactly the Samuelson "interest rate," they aren't even approximately it. Because the credit market transactions we see are exchanges of two different claims on future income, not an exchange of present income for future income.

      At that point, we have established that the "interest rate" the monetary authority is targeting is not the "interest rate" Samuelson is writing about.

      Step 4 is then to ask, what does it mean to say that some particular credit-market interest rate is the "natural" one? That is where the dependence on fiscal policy, income distribution, etc. come in. But those factors are not part of the argument for why the credit-market rate is not even approximately the intertemporal rate.

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    2. I think I understand what you're saying, but let me just expand on what I meant.

      I'm not sure how important Samuelson's interest rate is as an inter-temporal substitution rate. Whatever assumption you make about household time preference, including assuming that there is zero elasticity of substitution, you still get the same interest rate.

      In my opinion, it's role is more relevant in relation to the household budget constraint. It's what allows households to spend more over their lifetime than their income (in a growing economy) even though aggregate spending is always equal to aggregate income.

      Samuelson assumes only one asset. If you have a similar model with more assets, the rate you need to use is the (after-tax) weighted average return, because that is the figure that matters for the budget constraint. It's this return that I think of as the "interest rate" in Samuelson's model.

      When the monetary authority change the policy rate, clearly they are only directly changing one particular rate on one particular asset class. However, this is likely to affect all other asset returns to a greater or lesser extent. Therefore, we should expect some correlation between the policy rate and Samuelson's "interest rate".

      A couple of further points of note. The fact that Samuelson's model has no public or foreign sector makes a significant difference to the relevance of the interest rate, as there are no inter-sectoral income transfers. Also, the return on the asset has to exclude any transfer payments between households. For example, if you adapted Samuelson so that all saving took the form of land holding, you would need to exclude rental payments from the return, in order to get the same result.

      Anyway, I don't think any of this contradicts what you are saying in your post and I agree that the interest rate in Samuelson is not the same thing as actual policy rate.

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    3. I'm not sure how important Samuelson's interest rate is as an inter-temporal substitution rate

      There is a problem of terminology here. Samuleson's interest rate IS the intertemporal exchange rate. It is the rate at which a good in period one can be exchanged for a good in the following period. That's just what he means by interest rate.

      You are right, that is different from intertemporal *preferences*. Samuelson explicitly assumes no pure rate of time preference. Now, in equilibrium, this rate will be equal to households' intertemporal substitution rate; but this is an equality between two conceptually distinct rates. When I say the interest rate is the intertemporal exchange rate, that's not a statement about equilibrium; these are two interchangeable labels for the same thing.

      That is why I have been scrupulous to refer here to the intertemporal rate of **exchange**, not rate of substitution.

      When the monetary authority change the policy rate, clearly they are only directly changing one particular rate on one particular asset class. However, this is likely to affect all other asset returns to a greater or lesser extent. Therefore, we should expect some correlation between the policy rate and Samuelson's "interest rate".

      No, I don't think so. What the monetary authority is doing is changing the liquidity premium. That is, they are changing relative prices among assets all of which are equally correlated with Samuelson's interest rate.

      Thanks for the comments. It is hard to think clearly about this stuff and the back and forth helps.

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    4. Thank you for your reply. I'd agree that the terminology is problematic. And in Samuelson, we have equilibrium and only one asset, so the "interest rate" is various things at once.

      A few points if I may, again not necessarily countering what you are saying, but interesting in the context (I hope).

      The interest rate in Samuelson is certainly the rate at which future consumption is in fact being exchanged for current consumption. However, in that model, it is not in general equal to the household substitution rate. The easy way to see this is to note that the equilibrium rate must always be equal to the growth rate, whatever the substitution rate. This is obviously completely different to the standard result. It reflects the fact that the interest rate in Samuelson is important not so much for its substitution effect as for its income effect, albeit that the "income" is arguably fictitious bubble income.

      If you change the interest rate in a Samuelson type model, the impact on spending arises because of the redistributive effect between generations (there might also be substitution effects as well, but they're not essential). In my view, this redistributive effect is what mainly matters in the real world - not inter-temporal substitution. If the monetary authority change the policy rate, it will affect other rates in a way that causes redistributive effects, between young and old, but also between rich and poor.

      May I ask a question about your analysis, which might help me clarify what you are saying. Your equation 4 (in the previous post) looks like an LM type relationship, if we assume that the liquidity premium on money and bonds is a function of the quantities of each relative to NGDP. But, as I understand it, the natural rate of interest is usually described as being reflected in an IS type relationship - the rate of interest that would deliver the level of spending necessary to remove any output gap. Does that distinction relate to what you are saying?

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    5. You are right. Samuelson is not the best example for my argument. I've been using because I read it recently, and it's come up a lot in these discussions, and because it's a very good article. (And also, frankly, because I don't know the current NK stuff as well as I should.) But it would be better to take a more standard model where the interest rate refers to the intertemporal substitution rate. (Or exchange rate -- which do you think is clearer?) There's no shortage of them.

      All the equations are LM type relationships, in the sense that they are all asset market equilibrium conditions. You are right, they don't have anything to do with the natural rate.

      The problem here is that I am making two different arguments. First, I am saying that the credit market interest rate and intertemporal interest rate are two different prices with no particular relationship to each other, so we shouldn't use language that mixes them up. And second, I'm arguing that the credit-market rate that brings GDP to its target level (the "natural rate") shouldn't be seen as a fundamental characteristic of the economy, but depends on lots of factors that are just as accessible to policy as the interest rate itself, including the current level of unemployment. The first argument is sort of ground-clearing for the second, but they are two different arguments. I tried to make this distinction clearer by separating what I'd originally written as a single post into these two, but I'm sure it's still not clear enough.

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  4. J.W,

    I am still confused as to the distinction you are trying to make.

    We have a symbol for the intertemporal rate of substitution, Beta. That is purely a preference.

    We have a symbol for the nominal and single period "real" interest rate that obtains in the market at any period of time.

    By definition, this is the cost of transferring consumption from one period to the next.

    We have a concept of a "natural" interest rate which corresponds to price stability.

    The observation that the "market" interest rate need not correspond to the hypothetical natural rate is agreed upon by almost everyone who believes that Central Banks have a role to play in forcing the market rate to be the natural rate. Plus, there is the historical record of large swings in prices and output when interest rates were set purely by the market and not by any central authority, leading to the creation of larger and larger reserve banks which eventually were superseded, or in the case of the UK, became "the" government reserve banks.

    All of the above assume that this natural rate is a function of many other factors -- e.g. tax policy, preferences, how productive the nation is, the global trade environment, etc.

    So, are you introducing a new rate, distinct from the above, or are you making some other claim -- e.g. that we can achieve price stability with multiple levels of employment, and so a different definition of natural rate is required.

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  5. Rereading these posts I see a referred consistently to the intertemporal substitution rate. That was a mistake. I should have written intertemporal exchange rate.

    By definition, this is the cost of transferring consumption from one period to the next.

    This is the issue. Yes, economic theory normally defines the "interest rate" that way. But in that case, the yield on a bond or bank loan is generally NOT an interest rate. But this is very confusing, since in most contexts the yield on a bond or bank loan is precisely what people mean by an "interest rate."

    Most credit transactions do not involve any transfer of consumption from one period to another.

    So, are you introducing a new rate, distinct from the above, or are you making some other claim -- e.g. that we can achieve price stability with multiple levels of employment, and so a different definition of natural rate is required.

    Both. This is one reason these posts are not very clear -- there are two different arguments mixed up here. But the main point is that credit-market transactions as such do not involve any transfer of consumption from one period to another, so we should not use the single term "interest rate" to refer to both the yield on a credit-market instrument and the premium on current as opposed to future consumption.

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    1. Yes, this is an argument against loanable funds -- one that I have been trying to make over at worthwhile, to no avail. But because the supply and demand for transporting consumption across the future are not what causes the market price for loans, nevertheless that is the price, by definition, of transporting consumption across the future.

      One can make a similar analogy for any other good that can be re-sold. The concept of supply and demand curves as commonly used have an implicit assumption that the purchasers of goods will immediately consume the good. This machinary breaks down when goods are purchased in order to be re-sold at a later time in addition to being immediately consumed.

      Take for example, wheat, which may be stockpiled. Is the price of wheat high because there is a demand to consume wheat, or because people are purchasing wheat to re-sell later? Is the price of wheat low because people do not want to eat wheat or because existing stockpilers are "dumping" the wheat on the market. In this type of environment, you can no longer tie the market price of wheat to some fundamental production function driven by real transformation processes interesecting with a fundamental consumption function driven by preferences.

      Nevertheless if you want to buy wheat, you have to pay this price, regardless of how it is set.

      In short, I don't think its helpful to say that you have discovered a "new" interest rate of some sort. From my reading, you are making an argument against the loanable funds model -- you are making an argument that market forces will not cause the natural rate to be obtained on their own.

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    2. My goodness. I certainly don't claim to have discovered anything! I'm not a crank. What I claim to be doing is explaining an old argument, made by Keynes and others, which I think would be helpful in current discussions.

      You are right, it might be better to present this as an argument against loanable funds. Probably that would be clearer. You are right, a great many prices have an intertemporal component. My argument is that the yields on credit market instruments (which, again, are what is referred to in most contexts as "interest rates") are NOT one of those prices. In fact, the normal function of credit contracts is precisely to avoid the need to shift expenditure between periods.

      So I don't think we disagree at all.

      The only point where I might object to your comment is the last sentence. I do think that (1) the loanable funds model is wrong, and (2) there is no tendency of market forces to adjust the price of credit to the "natural" (or full employment) rate. But I don't think claims 1 and 2 are equivalent, or even very closely related. For instance, my impression is Krugman does believe in the loanable funds model, but does not believe there is any tendency for unregulated credit markets to move toward the natural rate. So he disagrees with us on 1 but agrees with us on 2.

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  6. @rsj

    "This machinary breaks down when goods are purchased in order to be re-sold at a later time in addition to being immediately consumed. "

    The point is that there is a lot of stuff that is sold, but is never consumed. The main example is land.

    If I pay 100$ for a piece of land, I can let some sharecropper work on it, have a nice rent of, say 2$ a year, and 10 years later resell it for 100$, then use the 100$ to buy a lot of ice cream. This is delayed consumption, and the 2$/year is in some sense the price (for others) of my delayed consumption.

    But, I could also keep the land for ever and ever, and just enjoy my 2$/year rent forever.
    In this case, 100$ is just the cost of a flow of cash of 2$/y, there is no way to say that this is delayed consumption.

    Financial goods, if I understand correctly what JW is saying, beahave very much like the land in my example (for some reason, it is usually said that 2$/y is the price of money [100$], whereas it would be better to say that 100$ is the price of a cash flow [2$]).

    I think that there is a problem in most economic models, because those models imply that all economic activity is driven by "consumption".
    But as a matter of fact, a lot of people just accumulate a lot of wealth without consuming it.

    For example, a lot of people accumulate a lot of financial goods (or other assets). According to the normal assumption of economic rational behviour, once they realize they are getting old, they should sell everything and consume tons of ice cream, as in my first example of landowning; that's because their behaviour is supposed to be motivated by a drive for consumption, they have no reason to die rich.

    But in reality, most people dont spend everything before their death, because they are not just motivated by a drive for consumption, but also by a drive for accumulation: everyone wants to be rich! Rich people are respected, succesful, salt of the earth that create jobs for others, while poor people are suckers and moochers that have a job just because rich people are goodhearthed, not because the losers are useful or something.

    So in pratical terms many people try to accumulate assets, such as land or financial assets, and enjoy the cash stream that comes from it: the price that they pay is not a form of delayed consumption, but just the price of the cash stream (that can, in certain conditions, be used to purchase new assets instead of consumption goods).

    The wheat example you made is a bit misleading: suppose that I'm a wholesaler. I buy 100$ of wheat today, because I expect to sell them at 102$ one year from now. At the end of this period I have my 2$/y cash flow, so this is not very different from land or bonds. It is true that the wheat is consumed, but not by me: from my point of view wheat is just inventory, I could keep roses or bullions for sale as long as I expect to make money from them. From the point of view of the consumer, however, it is very different, because they need bred to eat, and not roses or bullion; but it is not them who refrained to consume at t1 and want to consume at t2, so there is no intertemporal preference for them; and also there is no intertemporal preference for me, since, once I sell them the 102$ of wheat, I won't spend those 100$ on consumption but to buy other inventory for the next year (so this is really a slightly more complex case of the guy who buys some land and sits on it forever).

    From this point of view, the interest rate has nothing to do with intertemporal preferences and everything to do with the "equalization of the rates of profit".

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  7. Josh, It's good to see that the RWE site picked up on this post. I made a criticism of the (somewhat friendly) accusation in the comments that your point (and Keynes) is muddled but that argument seem to be fairly muddled itself trading so heavily on counterfactuals.

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