Home > Uncategorized > JW Mason on ´Money, the interest rate and the ´intertemporal rate of substitution´´

JW Mason on ´Money, the interest rate and the ´intertemporal rate of substitution´´

On this blog, people occasionally take the trouble to debunk neoclassical macro-models. Look for instance here, here, here, here, here, here, here, here, here, and here

These posts discuss the neoclassical take on unemployment (assumed away), consumption (goes up when incomes go down), rationality (people know everything and supposedly even speak french and mandarin), gross-substitution (there is only one good, which means that you can eat your car) etcetera.

Interest rates have however escaped our attention. Fortunately, JW Mason on the Slack Wire blog makes up for this. He restates the Sraffa/Keynes position that:

* The money you own is a claim on future production (mind that I write: ´the money you own´, not ´money´)’

* But so are bonds

* Money does not yield interest but bonds do

* People own bonds as well as money

*Which means that the interest rate on bonds, which are bought with money, is not some kind of ‘savings’ interest rate. People do  not sacrifice present consumption for future consumption when they buy a bond but they sacrifice money-claims on the future for bond-claims on the future. The interest rate might be a reward for foregoing liquidity and whatever – it’s not the neoclassical intertemporal substitution rate incorporated in the DSGE models).

Mason goes on to argue that any kind of interest rate targeted by central banks and even the, at this moment, in the Eurozone negative Wicksellian ´natural rate´ which is supposed to bounce us all back to prosperity without any need for higher government expenditures is a kind of bond rate. While the ´intertemporal substitution rate´ is closer to house rents and the like (net of maintenance costs).

Two excerpts, the first from his second post and the second from his first post.


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

The second excerpt


So the value of an asset costing one unit (of whatever numeraire) will be 1 + y – r – c – d + l + g – i. In equilibrium, you should be just indifferent between purchasing and not purchasing this asset, so we can write:

1 + y – r – c – d + l + g – i = 1, or

(1) y = r + c + d – l – g + i

So far, there is nothing controversial.

In formal economics, from Bohm-Bawerk through Cassel, Fisher and Samuelson to today’s standard models, the practice is to simplify this relationship by assuming that we can safely ignore most of these terms. Risk, carrying costs and depreciation can be netted out of yields, capital gains must be zero on average, and liquidity is assumed not to matter or just ignored. So then we have:

(2) y = i

In these models, it doesn’t matter if we use the term “interest rate” to mean y or to mean i, since they are always the same.

This assumption is appropriate for a world where there is only one kind of asset — a risk-free contract that exchanges one good in the future for 1 + i goods in the future.
The problem arises when we carry equation (2) over to the real world and apply it to the yield of some particular asset. On the one hand, the yield of every existing asset reflects some or all of the other terms. And on the other hand, every contract that involves payments in more than one period — which is to say, every asset — equally incorporates i. If we are looking for the “interest rate” of economic theory in the economic world we observe around us, we could just as well pick the rent-home price ratio, or the profit rate, or the deflation rate, or the ratio of the college wage premium to tuition costs. These are just the yields of a house, of a share of the capital stock, of cash and of a college degree respectively. All of these are a ratio of expected future payments to present cost, and should reflect i to exactly the same extent as the yield of a bond does. Yet in everyday language, it is the yield of the bond that we call “interest”, even though it has no closer connection to the interest rate of theory than any of these other yields do.

This point was first made, as far as I know, by Sraffa in his review of Hayek’s Prices and Production. It was developed by Keynes, and stated clearly in chapters 13 and 17 of the General Theory.

For Keynes, there is an additional problem. The price we observe as an “interest rate” in credit markets is not even the y of the bond, which would be i modified by risk, expected capital gains and liquidity. That is because bonds do not trade against baskets of goods. They trade against money. When we see a bond being sold with a particular yield, we are not observing the exchange rate between a basket of goods equivalent to the bond’s value today and baskets of goods equivalent to its yield in the future. We are observing the exchange rate between the bond today and a quantity of money today. That’s what actually gets exchanged. So in equilibrium the price of the bond is what equates the expected returns on the two assets:

(3) y_B – r_B + l_B + g_B – i = l_M – i

(Neither bonds nor money depreciate or have carrying costs, and money has no risk. If our numeraire is money then money also cannot experience capital gains. If our numeraire was a basket of goods instead, then we would subtract expected inflation from both sides.)

What we see is that i appears on both sides, so it cancels out

  1. BC
    December 27, 2013 at 5:14 pm

    The value of debt-money is the imputed compounding interest accrued to the creator/owner in perpetuity in its varying substitutable forms or proxies, e.g., stocks, bonds, leveraged real estate, etc. The creators/owners today are the top 0.01-0.1% owners of the TBTE banks, their largest creditors and borrowers, and the central bank the owners of the TBTE bank own. The next 9.9% hold subordinate claims on ~40-45% of debt-money claims, whereas the bottom 90% own nothing, i.e., they own no debt-money rentier claims to wages and production; they/we only borrow the debt-money at compounding interest and circulate it for subsistence, if we’re fortunate.

    Debt-money growth, at a minimum, must increase at a rate sufficient to service the existing debt-money claims outstanding.

    If the rate of debt-money exceeds the rate of growth of investment, production, and labor returns, inflation occurs; less than that, and deflation occurs, i.e., liquidation/consumption of excess value of assets representing an onerous claim on labor and production that cannot be serviced.

    In the US today, total imputed rentier claims, i.e., “rentier taxes”, from credit market debt outstanding is an equivalent of 100% of private value-added output of the US economy. Rentier claims plus total gov’t receipts now far exceed wages and salaries.

    Real GDP per capita cannot grow under these conditions, which are characteristic of a debt-deflationary regime.

    Moreover, total deposits/debt-money supply (M2+ and large time deposits) less bank cash assets are contracting yoy for the first time since 2009-10, 1993 (effect of sweeps), during the US Treasury’s “gold sterilization” in 1937-39, and in 1931-33. The US is experiencing incipient debt-money deflation despite (because of?) unprecedented central bank reserve expansion and ZIRP.

    Equities are currently priced for no real total returns for 10-20 years, implying little or no revenue and earnings growth and liquidation of assets hereafter for cash flow.

    As such, debt-money growth will not exceed the 2% range, which implies nominal GDP growth of 2% or slower, the 5-year rate of wages decelerating from the current 1.5% rate, and the 10-year yield eventually back below 2%.

    Too much private debt to GDP and wages will continue to drag on real GDP per capita for years to come until, or if, debt to GDP and wages is defaulted on, paid down, or restructured, or a combination, so that debt to GDP and wages again permit growth of wages to GDP.

    Falling debt to GDP and wages by definition means lower asset prices to GDP and wages, which historically has meant a Shiller P/E of 8-10 (vs. 25 today), Q ratio of 0.30-0.35, and market gap to GDP at 30-35%.

    As debt-money supply after bank hoarding of cash continues to contract or not grow, assets will be liquidated by firms and households to make up for the lack of growth of bank lending, deposits (after bank cash), debt-money, investment, production, employment, and wages.

    Fed reserve expansion and ZIRP will eventually be perceived for what it was always meant to be: liquefy bank balance sheets and to provide incremental primary dealer liquidity to fund record deficits to GDP to prevent nominal GDP from contracting. “Stimulus”? No, not in a debt-deflationary regime.

  2. December 28, 2013 at 5:52 pm

    Interesting post. But I think the whole thing is slightly muddled (as it was in Keynes too). Here is an extended response:


    • wallflower
      December 28, 2013 at 6:39 pm

      Okay, I’ll bite. Why does the existence of “objective probabilities” mean that there is no “uncertainty” (and hence no sensible way to talk about risk premia).

      • December 29, 2013 at 1:52 am

        If everyone was able to determine what happened to yields based on objective probabilities then they could hedge amongst assets in a perfect manner and would not need a buffer of liquidity. At the same time cash would be neutral because all future events would hedge out perfectly and everything would run smoothly. There would be no need for a buffer of safety because every future event was already known… through objective probability estimates and the hedging strategies that would accompany them.

    • wallflower
      December 29, 2013 at 5:52 am

      I don’t know why that follows unless I am not understanding what “objective” means (is that just a way of saying Knightian uncertainty is zero). 1) You are assuming a hedge position exists for every investment
      2) If a generic hedge mechanism for any investment exists (e.g., an options market) where the expectations are known by all players the price is determined by the competitiveness of the hedge markets (in a oligopoly situation, the price of the hedge approaches the profit from the investment). In a competitive situation the price of the hedge tends to the supply cost which is really the cost of maintaining enough capital to cover all bets (some variety of a interest rate) but then why does anyone make a market or why does capital flow into the industry.
      3) There is still gambler’s ruin, just because the hedge will cover the 1 of 10 investments failing, as a random process the investment could fail much more frequently in the short term, that’s the nature of random variables, so you can’t assume there is never a zero preference for a safety margin. Point 2 also implies the potential for gambler’s ruin also applies to hedge market makers as well.

      From the argument in your blogpost, you seem to imply that an objective probability (which I will take to mean a precise estimate of the distribution underlying the random process) means freedom from an uncertain future (and hence, zero liquidity preference). This is only true in the case of an infinite regress of hedge/insurance markets, or some other unrealistic claim (e.g., infinite pools of investment capital). People (including professionals) don’t deal with precise estimates of randomness but rather estimates where they believe the error in their precision is bounded. I don’t see how at least two premises (precise estimation of probability takes away uncertainty resulting in no liquidity preference; the non-existence of precise estimates precludes the act of investment based on some calculation of risk) of your argument hold.

      • JW Mason
        December 29, 2013 at 1:54 pm

        Interestingly, Brad DeLong had the same reaction as Phil — that there is no reason to think of both a risk premium and a liquidity premium. Of course for the opposite reason — DeLong thinks risk is sufficient where Phil thinks it’s meaningless. But I still find it useful to think of yields as incorporating both kinds of premia.

      • December 29, 2013 at 2:50 pm

        Yes, I mean something like Knightian/Keynesian uncertainty is zero.

        1) Yes. There is a hedge for everything. People can carry perfectly balanced portfolios.

        2) I don’t really get your point here. Perhaps you can be clearer.

        3) In the long-run this should all net out and it shouldn’t be a problem. Even if peoples’ perfectly balanced portfolios underperformed in the short-run because they know the objective probabilities they would be comfortable to continue to hold them going into the long-run.

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