28 Sep 2019

Deep Thoughts on Capital Theory

Bob Murphy Show, Business cycle, Capital & Interest 4 Comments

In the latest Bob Murphy Show I talk to Nicolas Cachanosky about his work (often with Peter Lewin)…

4 Responses to “Deep Thoughts on Capital Theory”

  1. Tel says:

    Interesting episode. I’ve noticed that most economists are not familiar with how accounting practice works, so there’s probably lots of useful things out of accounting textbooks that economists have never bothered learning about.

    For example “Stock Turns” are well known in the retail trade. High stock turns means you only keep small inventory and it sells briskly. Low stock turns means you keep large inventory of items that only sell occasionally. It’s a measure familiar to anyone keeping a warehouse (or writing inventory software) but seems to mean nothing to economists. The units of Stock Turns is “per annum” which happens to be the same physical unit as interest rates (assuming you measure accounts in years which is normal). Weird huh?

    Here’s another one: interest rates map onto the half-life concept that Physicists use (because it’s the same exponential decay formula). You can make a little reference table:

    0.5% per annum is a half-life of 139.0 years
    1.0% per annum is a half-life of 69.7 years
    1.5% per annum is a half-life of 46.6 years
    2.0% per annum is a half-life of 35.0 years
    2.5% per annum is a half-life of 28.1 years
    3.0% per annum is a half-life of 23.4 years

    This is not trickery … nor depending on any economic theory, it’s pure units conversion … the two sides of the table mathematically mean the same thing.

    Consider I have $100 in my wallet and price inflation is at 2% per annum then the real purchasing power of my wallet reaches half it’s original value in 35.0 years … hence the half-life concept. No different to radioactive decay. The reverse concept (typically from biology) is known as the “doubling time” and the same lookup table applies. Hence I have $100 in a bank account paying 2% interest and it nominally doubles to $200 after 35.0 years (i.e. 1.02 ^ 35 = 1.99989).

    Now come over here, just take a step through this looking glass and we can do it all backwards.

    I have $100 in my wallet and prices are deflating at 2% per annum so the real purchasing power of my wallet will be double after 35.0 years. My bank account is paying negative interest of 2% so therefore the $100 I put in there has a half-life of 35.0 years and ends up as $50. There’s a growth/decay symmetry as the positive rates flip over to negative rates.

    Of course, we know that could never really happen … but in case it ever does, the math has you covered.

    • Harold says:

      The half-life, or doubling time is a much more intuitive way to think about interest rates and inflation. I wonder why is it not used more?

      • Tel says:

        This happens in many disciplines.


        The philosophy of only accepting “approved sources” makes this much worse. Suppose a student refuses to read any textbook other than exactly those recommended by the teacher. At first glance this might seem quite efficient, the reasoning being something like this:

        Student: “I don’t know enough to know what is good, so I am better off depending on the wisdom of my teacher, who knows a whole lot about this stuff.”

        Troublemaker: “If you admit to ignorance, how can you figure out whether your teacher is any good?”

        Student: “I trust the college who hired the teacher.”

        Troublemaker: “That’s turtle stacking. What makes your college worthy of trust?”

        Student: “They sent me a lovely brochure!”

        Troublemaker: “How did you go about evaluating the brochure?”

        Student: “The college has government approval!”

        Troublemaker: “Does government ever make mistakes?”

        Of course this all comes back to argument by authority. If you are too lazy to figure things out yourself, then deferring to authority might save time, except that you are left with the task of choosing which authority to trust. Generally people end up inside a recursive thought loop where they believe something because it reinforces what they already believe. They have forgotten why they started believing that in the first place.

        The only thing that can save you is having basic principles that you have carefully considered. One such principle is consistency: if you believe that somewhere in the universe are rules of nature then it would be reasonable to conclude that more than one group of researchers would come across the same rules of nature, although they might call it by a different name. If the rules of nature worked differently for economists as it did for other people, that would violate the principle of consistency.

        If you have basic principles, you can keep applying that over and over … is this politician a hypocrite? Can I find real world examples that match what’s in the textbook? Is this researcher following the scientific method?

        • Harold says:

          Also known as the silo effect, which can be a real problem, hence the growth of “multidisciplinary” teams to try to counteract this.

          In one sense this is slightly different. It is OK for economists to use whatever they find useful, and interest rates are fine for them because they have a deep grasp of what they mean through exposure to the concept. It is more of a problem for the general public. If we say interest has gone from 2 to 2.5% it means very little, but of say doubling time has gone from 35 to 28 years we have a more immediate grasp of what that means. Financial journalists may find it useful to have a table such as yours to hand so they could readily convert interest rates to make their articles more readable.

          “Suppose a student refuses to read any textbook other than exactly those recommended by the teacher.”

          Maybe things have changed, but in my college days we were expected to use different sources. Basic textbook stuff would get you a pass, but higher grades required more.

          It is certainly a good idea to read the recommended sources as a student, but it is not a good idea to only read those. I doubt lecturers recommend that-maybe Bob could help? Do economics lecturers recommend wide reading and research?

          “Of course this all comes back to argument by authority. If you are too lazy to figure things out yourself, then deferring to authority might save time, except that you are left with the task of choosing which authority to trust.”

          It is not just a matter of laziness, but it is literally impossible to be an authority in everything. We are forced to accept authorities, or go live in a cave. The fallacy “appeal to false authority” is not the same as an appeal to genuine authority. We tend to accept that doctors have genuine authority and trust them to an extent. We also recognise that authority is not absolute, so we may seek a second or third opinion. If all agree, we generally go with the opinion. But, as you say, how do we recognise an authority? We certainly use stuff like qualifications and employment history as guides, which, while useful are not perfect.

          ” Is this researcher following the scientific method?”
          We do have shortcuts that are very useful, again if not perfect. One such is has this been published in an academic journal? This is not a perfect filter, but it does mean that there has been some quality control. It does depend on the academic area of study, but for the “hard” sciences, if it is in a reputable journal then the researcher very likely followed the scientific method. At the very least, the work will be put into context of the wider field with a decent review of the current state of knowledge of the area.

          If something is published on a blog or a book, we really don’t know if the scientific method has been followed.

          “is this politician a hypocrite?” Yes, of course. Not just a joke – we are all hypocritical to some extent, and politicians probably more so than most because they are forced to make pronouncements on so many topics. We need to ask if they are hypocritical over important things. Similarly with lying. Everyone is a liar, without exception. The question must be concerned with what we lie about and how much we do it.

          “Can I find real world examples that match what’s in the textbook? ” Sometimes this would be very bad test, as common sense can lead us astray. Quantum mechanics and relativity are examples. We cannot find examples personally that match what is in the textbooks. In fact, our everyday world directly contradicts what is in the textbooks. But this can be useful in many other cases – “back of the envelope” type calculations can show that many “kickstarter” type offerings are pretty much doomed to failure.

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