Thursday, April 3, 2014

The downward trend in real interest rates

I saw this [1] today (on global interest rates) and decided to look at what the old model shows for real interest rates in the US where we take 1 + i = (1 + r)(1 + π) where r is the real interest rate, i is the nominal interest rate and π is the inflation rate. Here's the fit to the price level and the 10-year interest rate:

And here is the resulting real interest rate:

The downward trend since the 1980s appears here as well. If this model is successfully describing that trend, then we can trace it to the diminishing impact of changes in the monetary base on the price level. In fact the global data in the link [1] above seems to imply that this diminishing impact is widespread, implying many developed countries are moving towards the right on this diagram:

The diminshing impact of monetary expansion shows up as a negative (downward) curvature as you move to the right on the graph.


  1. Well, this is rather rude of me, posting an off-topic comment 1st thing, but it seems you read Nick Rowe sometimes, right? Glasner too? They have a bit of a disagreement in David's latest post... with perhaps another commenter (Nick Edmonds) taking a middle position. Do you happen to have an opinion, or an idea how you could possibly sort out which person is closest to the truth by examining data? Thanks.

    1. No worries Tom. And I have been following that discussion. Their disagreement seems to be about how many markets there are in Walras' law [1] (which says the sum of excess supplies in all markets must be zero) and how the excess supplies and demands net out to zero.

      The original Walras argument is that there are N goods markets, so there can never be a "general glut", an excess supply that isn't countered by an excess demand (deficient supply) in another market.

      I think it was Keynes, but I may be wrong, who said that there is an additional market: money. So there can be a general glut as long as there is excess demand for money.

      Nick Rowe says that there are two money markets: α (monetary base -- I think) and β (commercial bank or M2, approximately) -- Glasner puts their disagreement as whether an excess supply of β money can be withdrawn from circulation without impacting "the real economy" of goods and services, vs Rowe who thinks the excess supply must have a "real" effect.

      I've wanted to try to see if I could model M2 (the models I've put together so far all depend on the monetary base) ... I'll see what I can do there. It appears M2 is basically proportional to NGDP, which would mean that the "money multiplier" M2/MB would have some direct relationship to short term interest rates (since log r is proportional to log NGDP/MB). I might be able to rephrase the question as to whether there are differences in the implied interest rates in terms of aggregate demand vs M2 as a measure of the demand for commercial money. I'll think about it some more.

      Walras' law, on the other hand, requires some assumptions in the information transfer model [2] that are not always true except under ideal information transfer. So the overall argument from Walras' law may not hold during recessions (which seem to coincide with non-ideal information transfer [3]). Actually in [3], I showed that the information transfer efficiencies are not necessarily related across markets.

      Sorry for the long comment reply. I'll see if I can turn it into a post.


    2. Jason,

      "so there can never be a "general glut""

      I thought that was Say's Law?

      "A modern way of expressing Say's law is that there can never be a general glut."

      "(commercial bank or M2, approximately)"

      I think of M1 as being demand (checkable) deposits, and thus a medium of exchange (MOE), but M2 includes time deposits. It also includes something called "reservable deposits" which used to mean that banks were required to hold some reserves against them, but that requirement on the fraction of M2 which is "reserveable" was dropped to 0% in the early 1990s (I just learned today actually!):

      I actually think the information in the 1st table here is accurate:

      I've been assuming that the money multiplier is M1/MB, but I guess it can be any broad sense money in the numerator. We also have this:

      money multiplier = (1+c)/(r+c)

      c = (currency in circulation)/deposits
      r = reserves/deposits

      "deposits" could work for either M1 or M2 in the numerator. A similar type formula came up in a Fed paper that JKH found, except they used "reserveable deposits" which sound to me like M1+(some things in M2 but not in M1)... so like a M1.5 maybe?

      Here's Sadowski:

      So actually the Fed paper divided up r into a new "required reserves only" r and an e. Here's the paper:

      Your ideas about how to attack the problem sound very interesting!

      I'm not sure I understand/agree with this characterization though:

      "Nick Rowe says that there are two money markets: α (monetary base -- I think) and β (commercial bank or M2, approximately) -- Glasner puts their disagreement as whether an excess supply of β money can be withdrawn from circulation without impacting "the real economy" of goods and services, vs Rowe who thinks the excess supply must have a "real" effect."

      It sound in Glasner's latest:

      Like he's saying that he and Nick agreed to look at a situation where:

      1. MB is fixed
      2. Interest rates banks charge for loans is fixed
      3. Checkable deposits are an imperfect substitute for currency and therefore banks must increase the interest rate they pay on it to induce people to hold more of it

      Since interest rates banks charge are not lowered, in order for banks to increase deposits they must induce people to deposit their currency. He then goes on to claim that this will necessarily decrease MB, so the CB must perform OMPs to compensate for that.

      That's where I disagree with Glasner (in my two long comments below that). So we'll see what he says to my comments.

      Meanwhile, I'm not sure why it's important that the rate of interest banks' charge for loans should remain fixed for Glasner to say this is a "fair" comparison. He loses me a bit after that.

      Basically I boil down Glasner's overall argument to be a "Strong Law of Reflux" and Nick's to be a "Weak Law of Reflux."

      In Nick's world, bank deposits don't reflux for the banks in aggregate. For individual banks attempting to increase deposits they do, but not in aggregate.

      Glasner doesn't see why this would be (he uses Tobin as a source for this opinion). Nick Edmonds seems to be in between those two. So far I'm favoring Nick Edmonds approach... but I have nothing to back that up with!...

    3. I think Nick Rowe thinks of commercial bank money as checkable deposits, so that's a smaller set than M2. I don't think that Nick considers savings deposits (or time deposits in general), which are part of M2 to be a medium of exchange (MoE) and thus they are not a substitute (imperfect or otherwise) for MB.

    4. So basically for Nick, M1 (checkable deposits + currency in circulation) is an MoE and is therefore money. M2 includes stuff which is not an MoE, and thus is too broad to be called "money."

      Sumner's easy: for him just MB (currency in circulation + reserves) is money.

    5. This was interesting from Nick Edmonds:
      Notice how he has separate "Savers" and "Borrowers." Two groups which could very well overlap, but they either needn't completely overlap, or there may be a heterogeneous mix of those who are primarily borrowers and those who are primarily savers.

    6. The general glut interpretation of Say's law is implied by Walras' law if all the markets are for goods (not including money). Say says that people make stuff with the hope of selling it for money with which to buy other stuff. Walras' law is a bit more subtle, but if you assume there is just one generic "goods" market, then Walras' law is Say's law. Walras said that a glut of goods in one market could be offset by a deficit of goods in another.

      And you are correct about M1; my mistake.

      Regarding the quote from me, I was characterizing Glasner's statement

      "Our disagreement concerns a slightly different, but nonetheless important, question: is there a market mechanism whereby an excess supply of commercial bank money can be withdrawn from circulation, or is the money destined to remain forever in circulation, because, commercial bank money, once created, must ultimately be held, however unwillingly, by someone?

      ... [Glasner believes the] Law of Reflux works to eliminate excess supplies of bank money, without impinging on spending for real goods and services."

      I think Glasner is basically saying Nick's got some new idea, citing Tobin as the established literature that says the law of reflux holds. Your characterization as a battle between a "strong" interpretation and a "weak" interpretation is a good one.

    7. Thanks Jason, that makes sense. Now I'm trying to figure out what jt26 wrote:'

      Glasner conceded my point BTW: OMOs are not necessary to keep MB fixed.

    8. Jason, one time tried my hand at summarizing good monetary policy in one sentence in a manner in which Nick Rowe would approve. I failed, but he offered his own one line summary (which I could dig up for you, but I'll just paraphrase instead):

      "Good monetary policy should endeavor to make Say's Law true in practice if not in theory."

      He says he stole that from Brad DeLong, and indeed he did (although we might be able to add to Brad's statement "and fiscal"). Brad says that a lot. Sumner say the comment and said he wrote something similar in a post. Sadowski didn't give his view directly, but implied he agreed by pointing out that Keynes himself said something similar. I also found a similar comment by Lars Christensen, except he referred to RBC rather than Say's Law, again paraphrasing:

      "Good monetary policy would make RBC true, even though we know it's not true."

      David Glasner was the lone hold out (of those I asked in the MMist world), saying something I still don't understand, but he did a whole post on it (mentioning me in the post actually, as part of the inspiration). Basically he said "Well, it's complicated." IIRC Krugman commented on that post... but I don't recall what he wrote.

      Why am I telling you all this? Because I'm wondering if Walras' law is one of those things (Like Say's Law or RBC) that in a monetary economy might not be actually true, but could be ideally made to look as if it was true given the right policy. What do you think?

      BTW, Rowe went so far as to claim that Say himself later refuted his own Law (I suppose for monetary economies) later in life, but I've never tried to verify that.

    9. Walras' law being true seems to be the problem with bad monetary policy. The excess supply in the labor market is offset by an excess demand for money (liquidity, safe assets, depending on who you talk to). You might want good monetary policy to make Walras law false! :)

    10. Ah... interesting. Thanks. Is that doable?

    11. Jason, it seems that the excess demand for money can be eliminated (by printing more money, for example) thus letting the excess supply in the labor market return to 0. So Walras' Law could still hold, at all times, and yet the problem of involuntary unemployment could be fixed. True?

    12. I think that is the point of demand management through monetary policy ... Stimulate aggregate demand by "printing money" (depends on the theory) making people not want to hold it (Sumner's hot potato effect).

    13. Sure that sounds right. What I was worried about though was the universal correctness of Walras' Law. I think Say's Law depends on people being "rational" and not having an excess demand for money... because that wouldn't be rational, would it? Well, it happens, so there goes Say's so-called "Law." In the same way the existence of sticky-prices and wages kind of undoes the logic of RBC (from what little I understand of it).

      But so far, it looks like Walras doesn't have that limitation, so it's more like a universally true thing? Like an uncontroversial accounting identity almost?... or do some people dispute it? The Wikipedia article wasn't entirely clear to me.

    14. Actually I guess sticky prices & wages and the existence of an excess demand for money are kind of the same thing, right? I always hear that w/o stickiness then nominal shocks would cause wages & prices to adjust immediately w/ no real effects. I didn't mention sticky debts... but they should be listed too in general shouldn't they? The fact that debts are denominated in nominal amounts and mostly at nominal interest rates.

    15. Walras seems more like a conservation law (in fact, when I derived it in the information transfer framework, it is related to the conservation of mass in fluid dynamics).

      I think sticky prices is the reason adjustment happens through a winding down of an excess demand for money (through e.g. expansionary monetary policy). If prices weren't sticky, then an excess supply would be immediately eliminated by a falling price for goods. In Walras, it is the sum of the values (price times quantity) of the supply Σ p·s = 0, so it can fall if the p's fall (deflation).

      As an aside, Krugman also has a bit on Tobin and Walras that is relevant to the Glasner/Rowe debate:

    16. Hi Jason,

      I tried answering a question about Walras' law regarding a super simple example (pretty much simultaneously with me reading the Wikipedia article on it)... I don't know how well it came off. When you do eventually get a chance, you might take a look (it starts about half way down this short set of comments... I don't seem to be able to obtain a link to the specific comment though):

    17. Jason, also when you get a chance, you're way more mathematically sophisticated than I am, but I had a thought about the terms "endogenous" and "exogenous" in economics. I don't know if they come up in other fields much... I haven't heard them outside of econ, but sometimes I think people use those terms as if they are yes or no propositions: binary and mutually exclusive states. I had an idea that perhaps we can assign a degree of endogeneity (which would be the complement of exogeneity) on a scale of 0 to 1. Thus if something is 0.3 on the endogenous scale wrt something else, then it is also 0.7 exogenous wrt that same something else. I even proposed a simple scheme for measuring co-exogeneity of one variable wrt another in terms of the magnitude of the correlation coefficient between them (|rho|). I'm sure that scheme has lots of problems, but I lay out how I'd go about trying to do that here:

      Here's a little back ground material justifying the appproach (basic vector differential system equations):

      I threw the bit in about chaotic systems, but I know almost nothing about that so that was a bit presumptuous of me... I don't dwell on it though.

      So it's not a practical thing perhaps (as a real method of measuring endogeneity/exogeneity), but I'm wondering if you have had a similar thought at one time, or ... more precisely, just how far off base do you think I am there? :D

    18. Regarding your comment about Walras' law above -- I don't seem to be able to find the relevant comment. The link goes to a forum page with one post on it.

      Regarding exogenous/endogenous: there can easily be feedback effects that make an exogenous cause have "endogenous" effects. The first example that comes to mind is global warming -- exogenous CO2 production can create enough warming to make permafrost melt or clathrates release methane to cause more warming. The separation is not clean in a cause and effect sense. However if you think of it in the econ model sense -- a variable is exogenous if it is a model input and endogenous if it is not -- then it's a bit clearer. In quantum electrodynamics, the electron mass is exogenous, except that it is renormalized "endogenously" ... but it's still an input parameter to the theory. So I'd still call it exogenous.

      I did do a post on the terms awhile ago:


Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.