Savings

I have just come from a very spirited discussion of savings that started on Mises.org and carried over onto Robert Murphy’s blog.  Apart from some distractions which dominated much of the conversation there are some important questions raised about savings.  Foremost among them is the issue of whether the interest rate is a payment for foregoing consumption or liquidity.  This goes back to Keynes (and probably before, I haven’t done all the required Austrian reading).  I think I can clear up the issue though.

The thing most people seem to miss is that the prices of goods are dynamic.  They can change over time.  For instance, if there is a stock of oil on Earth (assume we know what it is and how to get at it) the price of oil (in a dynamic equilibrium) will evolve over time to equate the discounted marginal value of it at all points in time.  Owners of the oil will have to decide at any given time whether to sell or hold their oil.  The decision will come down to whether they expect the price of it to increase by more or less than the rate of profit from some alternate investment.  This means they will sell oil until the price is expected to rise at the rate of interest (assuming no difference in risk etc.).  In this way the owners of oil receive a payment for holding it in the form of a price increase.  Note that the oil does not physically grow it is its value that grows because of the change in price.  This of course is a partial equilibrium analysis, it doesn’t explain why the interest rate is what it is.

The same is true of money in a natural (free market with commodity money) economy.  People who hold gold or silver are rewarded or punished by the change in price level.  Price (from now on I will suppress the term “price”) deflation means they receive a “payment” for holding money (the value of the money increases), inflation means they are charged for doing so.  What does this have to do with interest?  Well first you have to say which interest rate you are talking about.  The nominal interest rate is the nominal payment for lending money.  Therefore, if people hold other investments the return will be the rate of deflation + the nominal interest rate (approximately).  The reason people save is so they can consume later.  If people have no preference between holding their savings in money and, let’s say a corporate bond, then they would hold it in whichever one paid the highest return.  Since the rate of return on holding cash is determined by the rate of deflation/inflation, any positive nominal interest rate would cause all savings to be held in bonds rather than cash.  However, this does not appear to be the case.  The observation of a positive nominal interest rate indicates that people prefer holding some amount of cash to other investments for some reason at an equivalent rate of return.  This is because money is more liquid than other assets and people don’t have certainty about when they will want to spend it.  This “liquidity preference” drives a wedge between the rate of return on money (the deflation rate) and the rate of return on other investments (the deflation rate + the nominal interest rate).  This wedge is the nominal interest rate.

So that’s liquidity preference but how does time preference factor into this?  The classical theory of interest rates basically says that the interest rate is determined by people’s willingness to substitute consumption in one period with consumption in some future period.  This is still the case here.  This can be seen by deriving the real interest rate via the Fisher equation:

r=i-π

where r is the real rate, i the nominal rate and π the inflation rate.  Note that this economy would likely (but not necessarily) be characterized by deflation not inflation so we could rewrite the Fisher equation as:

r=i+d

where d is the deflation rate.  When written this way it is easy to see that the real interest rate, which is the “payment” for foregoing the ability to consume until some point in the future is equal to the payment for foregoing the actual consumption (d) and the payment for foregoing the ability to change your mind at some point along the way (i).  Or you could look at it another way:

d=r-i

The payment for foregoing consumption by holding cash (d) is equal to the real rate minus the premium for giving up liquidity (i).  And finally:

i=r-d

The premium for giving up liquidity is the payment over and above that which is required to postpone consumption (r) which is required to induce holding wealth in the less liquid asset.  So as you can see, it all works out, liquidity preference and time preference can coexist.  You just need to have 3 prices: 2 interest rates plus inflation rate.

 

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  1. Dan(DD5)
    July 22, 2011 at 2:58 pm

    ” liquidity preference and time preference can coexist.”

    I’ve been saying this all along! Coexist is the key word here. But it is not the former that dictates interest rates but only the latter.

    Look, it is like this: What determines the price of a good in real terms? Say there are only apples and oranges. Obviously, the price of apples is determined by the demand for apples relative to oranges. Whatever the money supply will be, the relative prices will be the same. If reservation demand for cash is increased, this does not in any way affect the relative prices of apples and oranges.

    The same applies for the interest rate which is basically the relative preference for present over future goods. People can hoard or dishoard cash, allowing less or more cash to be spend to present and future goods (oranges and apples), but what ultimately determines the interest rate is the only the allocation of spending between present and future goods, i.e., time preference.

  2. Dan(DD5)
    July 22, 2011 at 3:03 pm

    By the way, the following quote: “This is because money is more liquid than other assets” is nonsensical. The liquidity of an asset is basically its convertibility to money, so how can money be “more liquid then….”. Money is not more liquid, it is liquid!

  3. Free Radical
    July 22, 2011 at 5:08 pm

    “what ultimately determines the interest rate is… only the allocation of spending between present and future goods, i.e., time preference.”

    Yes but you have to specify which interest rate you are talking about. As long as you are talking about the real rate this is correct. But time preference doesn’t explain the nominal rate (unless there is no liquidity preference then the nominal rate would be zero and the deflation and real interest rates would be equal).

    “‘The liquidity of an asset is basically its convertibility to money so how can money be “more liquid then…..’ Money is not more liquid, it is liquid!

    I disagree with your definition of liquidity. This is probably how an investment banker would define it but it is not the most useful way for our purposes. A better way of defining it is to say that it is its convertibility into other assets. Obviously this is what people are interested in. Howver, (it’s probably a mistake to open the door to this argument but what the hell) even if you want to define it your way isn’t already being money the maximum amout of ease in convertibility tomoney? This doesn’t seem to contradict the point of my argument in any way.

    About real prices: Remember I said at the outset that I am talking about an economy with commodity money. So money is a real good the price of apples is determined by the demand for apples relative to oranges and also pickaxes and also gold (money). Change the money supply and, yes the relative prices of apples and oranges will be the same but their money prices will change. I’m not saying anything about their relative prices. The important thing is that the rate of change in money prices is important for determining the demand for cash balances. This is why you need 3 rates because you can’t just say that it depends on “the interest rate” and that this is also determined by time preference.

    P.S. Thanks for the comment, my usual readers are so agreeable (=

  4. June 21, 2013 at 3:43 pm

    What’s up every one, here every person is sharing these experience, therefore it good to read this blog Savings | Free Radical, and I used to visit this blog daily.

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