## A Note on the “Real” Rate of Interest

In my Mises Canada post walking through problems with the typical neoclassical approach to capital & interest, I came up with a simple thought experiment in which there are capital goods (nets) that have a positive marginal product–the workers can catch more birds with nets than without. This explains why the nets can earn a positive rent, and why workers would pay a positive spot price for the nets if they wanted to buy them outright.

However, I deliberately designed the example so that the consumption good (birds) trades at par across time periods. This is because the quantity of birds that the workers catch declines each period, perfectly offsetting the natural tendency for positive time preference.

The point of the example was to show that in this contrived setup, where capital goods had positive marginal product but the real interest rate was 0%, the capitalists would earn no net financial return from investing in nets. For example, someone buying a net at the start of period 9 would pay 20 birds for it. During the period, he could rent the net out and earn an income of 10 birds (which is the net’s marginal product for one time period). But the capitalist wouldn’t have earned a net (no pun intended) return on this operation, because the market value of the net would have fallen by exactly 10 birds during the period as well. So his original investment of 20 birds in buying the net, would land him at the end of the period in possession of 10 birds and a net worth 10 birds, i.e. for total wealth of 20 birds which is what he started out with.

I didn’t get into money prices because I wanted to keep things simple, and mainstream neoclassical economists think in terms of simple models like this. (My model is actually more complex than theirs; they usually think in terms of a one-good economy, whereas mine had two–birds and nets.) But I captured the essence of Bohm-Bawerk’s critique of the “naive productivity theory of interest.”

Now in reality, interest payments accrue in the form of money. (Indeed, my dissertation chides even Mises and Rothbard for adhering to a “real” as opposed to a monetary theory of interest.) Let’s think through how we normally correct for price inflation (or changes in “the price level”) when contrasting the nominal versus real rate of interest.

Suppose the nominal interest rate is 10%. So you lend someone $100 today, and get paid back $110 next year. Ah, but in the meantime, “prices” have risen by 3%. So, we say that the “real” or “inflation-adjusted” interest rate is actually only about 7%. More specifically, most economists would look at a basket of consumer goods to gauge the “price level” and say that it has risen 3%.

So if you step back and consider, what we’re ultimately doing is figuring out how many more units of consumption goods people get, if they are willing to postpone consumption for a year. For example, if we start with something that had a price of $1 originally, then the consumer gives up 100 units of consumption by lending out the money. Then next year the lender gets paid back $110. You might think he can buy 110 units of the consumption good, but nope, he can’t get that many, because instead of $1 each now they are $1.03 each. So if he spends the whole $110 on them, he can buy 106.8 of them. (Notice it doesn’t equal exactly 107.0 units; that’s the vagaries of dealing with percentage growth like this. It’s why I said “about 7%” above.) This simple numerical example shows that the person was able to “sell” 100 units of present consumption and “buy” 106.8 units of future consumption. Thus what it *means* to say “the real rate of interest is about 7%” is to say that units of real consumption trade at 100 units today for (about) 107 units one period later.

Now notice in the discussion above, I didn’t have to specify what was driving the increase in the “price level” and the nominal rate of interest. I didn’t have to explain what the utility function or preference rankings were. If you took my report at face value, namely that the nominal interest rate was 10% and that the price of consumer goods rose 3%, then that was all you needed to conclude that the real interest rate was (about) 7%.

That’s what’s going on with my bird and net example. I cut right to the chase and deliberately designed it so that 1 bird in period 1 trades exactly for 1 bird in period 2, etc. Thus the real rate of interest is zero.

If you want me to give you a story about money prices, I can certainly do that, but it doesn’t affect the essence of the thought experiment. For example, you can suppose that the birds have a price of $1 in period 1, and that the nominal interest rate is 10%. But then the price of birds rises to $1.10 in period 2. So a capitalist who starts out in period 1 with $100 can lend it out to receive $110 next period. That means he sacrifices 100 birds he could have eaten in period 1, in order to have the ability to eat…100 birds in period 2. The real rate of interest is 0%.

Only if you ignore depreciation in the capital value of the net. Once that is accounted for the result is a 0% gain for the “capitalist” who owns the net. So what the example shows is that capital asset values are part of the equation. One bird gain less one bird capital depreciation gives 0% return.

There’s plenty of real examples… what happens in the housing market when government interference drives down interest rates on loans? The rents can’t easily change, so it goes into asset prices instead. For a while you have rising asset prices and falling interest rates and it looks brilliant because you are making a capital gain, plus rent in a falling interest rate environment. It seems like capital can outgrow its own marginal productivity.

That’s just temporary while the system finds a new equilibrium under the low interest rate regime. Interest rates go down, and as a percentage of the asset price, capital productivity also goes down, and those capital gains won’t keep happening forever so when the dust settles the three-way link between asset prices, interest rates and capital productivity remains.

Thanks. I had a hard time following the initial statement of the bird market because the cost of the net was not given and I missed the 100% interest part of the story.

“If you want me to give you a story about money prices, I can certainly do that, but it doesn’t affect the essence of the thought experiment. For example, you can suppose that the birds have a price of $1 in period 1, and that the nominal interest rate is 10%. But then the price of birds rises to $1.10 in period 2. So a capitalist who starts out in period 1 with $100 can lend it out to receive $110 next period. That means he sacrifices 100 birds he could have eaten in period 1, in order to have the ability to eat…100 birds in period 2. The real rate of interest is 0%.”

Bob,

That doesn’t seem to be what’s going on in your model.

In your model the ‘bird’ interest rate is zero.

I.e. I lend you one bird in period 1, and ask you to repay me one bird in period 2.

However the cost of birds is increasing over time as they are becoming scarcer.

The supply of birds is decreasing over time, but demand for birds remains constant, so their value goes up.

So in money terms, in period one 1 bird costs $1, and in period 2 one bird costs $1.10.

This means that if I lend you one bird in period 1, and you repay me one bird in period 2, the real rate of interest is positive (because a bird in period 2 is worth $0.10 more than a bird in period 1).

the above comment is a bit unclear.

“if I lend you one bird in period 1, and you repay me one bird in period 2, the real rate of interest is positive (because a bird in period 2 is worth $0.10 more than a bird in period 1).”

What I mean here is that if, for example, the rate of inflation is 0%, but there is a relative increase in the price of birds, then if I lend you one bird in period 1 and you repay me one bird in period 2, then I make a real return on the loan.

Like for example if I lend you an ounce of gold, and you repay me an ounce of gold when the price of gold has doubled.

However, rather than talking about the money price of birds it’s clearer to think about the birds in your example as being money.

If I lend you $1, and there is deflation (so that the purchasing power of a dollar increases), if you repay $1 at a later date, I make a real return on the loan. Even though the nominal rate of interest is zero in this case, the real rate of interest is positive due to the deflation. This is what is going on in your model.

However in your model there is no money – only birds, nets and labor.

The cost of the birds in terms of labor is increasing over time. As you say: “over time it gets more difficult to catch birds per hour of labor”.

So say, for example, that it takes one hour in period 1 to catch one bird, and two hours in period 4.

This means that the cost of one bird in period 1 is one hour of labor. And the cost of one bird in period 4 is two hours of labor.

So if I lend you one bird in period 1, and you repay me one bird in period 4, the bird you give me is worth more than the bird I gave you. So the real rate of interest is positive.