## Real Interest Rates, Hoarding, and the Zero Lower Bound

A line at the end of a recent post by David Andolfatto got me thinking.

I want to stress, however, that while getting inflation and inflation

expectations back to target (and firmly anchored to target) may be a solution to

one problem, it is unlikely to be a solution to every problem currently facing

the U.S. economy. To put it another way, suppose that the current real interest

rate of -1% is too high relative to the current “natural” rate of -x%. Somehow

driving the real return on bonds to -x% may then help things a bit, but it does

nothing to address the more pressing question of why the “natural” rate is so

low to begin with.

I believe the theory I have tried (somewhat crudely) to lay out on this blog explains why real rates are below zero. However, rather than try to give a complicated theoretical explanation for this phenomenon here, I will simply discuss some of the implications of this. The difference being that interest rates, which are prices, are “caused” by more than one force (supply and demand), and are therefore complicated and elusive, especially when these forces are derived from expectations of variables at various points in the future. Nonetheless we can look at investment supply in isolation and identify some things which must be true if the market rate is below zero, and I think noticing these things will help put this phenomenon into perspective.

Negative Real Interest Rates

If credit markets are in equilibrium, then the real interest rate must be equal to lenders’ marginal rate of substitution between consumption now and consumption in the future. In other words, lenders must be willing to give up 1 unit of consumption today for 1+r (where r is the real interest rate) of consumption in the future. There is pretty much no getting around this fact. However, since utility functions are subjective, theory cannot tell us what they “should” look like, it can only assert certain shapes for them and see what those assertions imply. Usually, they imply a positive real interest rate.

One way to imply a positive real interest rate is to assume a positive discount factor. For many macro models, this is assumed to be constant, and therefore, implies a fixed (by assumption) real interest rate. In a more realistic model, marginal utility is decreasing in consumption each period but agents are assumed to prefer consumption today over consumption tomorrow at a given rate (the discount factor). This means that if consumption is constant over time, the real interest rate will be equal to this discount factor, but the real rate can be higher if people are expecting to be richer in the future since higher consumption then will mean lower marginal utility relative to today. If they are expecting to be poorer in the future, they will be willing to transfer consumption to the future at a premium, since lower consumption implies higher marginal utility of consumption.

There is no economic reasoning which proves that people prefer consumption today to consumption in the future. There is however a long history of observation to justify this assertion. This observation being positive real interest rates in the face of rising consumption. Similarly, there is no economic reasoning for assuming that people prefer consumption in the future to consumption today and since there is no significant history of observation that implies this there are few, if any, models which assume this.

So if people don’t arbitrarily prefer consumption in the future to consumption today, there is only one explanation for a negative real interest rate: people expect to be poorer in the future than they are today. When this is the case, their marginal utility of consumption in the future (relative to today) will be higher because expected future consumption is lower. Therefore, people will be willing to pay a premium to transfer some real wealth from today to some point in the future. The negative real rate is implying that the market for investment reaches equilibrium before consumption is perfectly smoothed out between periods (with a positive discount rate, this could be the case even at a positive real rate, so long as it is below that discount factor). In other words, this amounts to a market prediction of a recession.

Lower Bounds

It is widely recognized that there is a zero lower bound for nominal interest rates. This is because negative nominal interest rates always open the door to arbitrage. If the nominal interest rate is -1%, then (if possible) I could take out a trillion dollar loan, put 990 billion dollars under the mattress (metaphorically speaking) to pay it back in a year and go spend the extra 10 billion on whatever I wanted. In other words, demand for loanable funds would be infinite. It’s not so much that interest rates couldn’t be made negative but the market could not function in such a case, it would require an entirely different system of rationing. There is no such lower bound with real interest rates, because they don’t allow for such arbitrage. But there is a considerable amount of inertia around the zero level. To see why, we must examine why the potential for arbitrage doesn’t exist as it would for negative nominal rates.

If the rate of inflation were uniform across all goods, then there would be potential for arbitrage with zero real rates. Imagine that inflation were expected to be 5% and the nominal rate is only 3%, implying that the real rate is -2%. If inflation is uniform across goods, then you could make a profit by taking out a loan at 3% and buying a durable good like gold and holding it for a period, then selling it after its price increased 5% and repaying your loan. The reason this doesn’t work is that ~~everyone ~~enough people recognize this potential that they drive the price of gold up today and down in the future to the point where this arbitrage is no longer possible. This point will be when the real return on gold is equal to the real return on other investments which is -2%. If the price of consumption goods is rising at 5%, then the price of gold will have to rise at only 3% (the nominal interest rate). This will be the case no matter how high inflation rates are expected to be. If inflation is expected to be 100% and nominal rates are 3%, then gold will have to find a price where the expected increase is still 3% (assuming the real rate is still -2%). Thus gold cannot be used to cash in on *expected* inflation.

Of course, if one happens to be holding gold when inflation expectations increase, the price will rise sharply. But this rise should not be interpreted as a sign that it will continue to rise rapidly, *even in the face of high expected inflation*. On the contrary, it should be seen as a sign that the price will rise more slowly. Listen up all you Austrians, libertarians, and other gold-jockeys.

The effect of this is that a fixed quantity of gold will become more valuable in both nominal and real terms and therefore, it will take up a larger portion of peoples’ portfolios. This reduces the quantity demanded of other financial assets which imposes some inertia on real interest rates. Or to put it another way, people will take money out of bonds and other financial assets and put it into gold which will put upward pressure on the rates of those assets and tend to raise real interest rates.

But gold is not the only durable asset. In a world of negative real interest rates, if you can buy consumer goods today and save them, you benefit. If the price of canned food is expected to increase 5% and nominal rates are only 3%, then you are better off to buy the food today and store it than to invest the money and buy it in the future. This of course, imposes additional costs such as taking up space and rotating stock that gold does not because canned food is bulkier and less durable than gold. Nonetheless, this type of “hoarding” is a perfectly rational response to negative real interest rates. The lower the rate, the more effort people will be willing to devote to this type of activity. The result will be increased demand for canned food today and decreased demand tomorrow which means higher prices today and lower tomorrow. Although the rate of increase will probably be greater than gold, it will be less than the rate for haircuts.

Goods which are not durable like haircuts, vacations, and nights on the town, cannot be stored so there is no way of mitigating inflationary effects on them. The price of these will rise the most.

Summary

1. Negative real interest rates imply that people expect to be poorer in the future than they are today (assuming no negative discount rate).

2. Inflation is not uniform, it will be more severe the less durable/storable a good is.

3. “Hoarding” is a predictable economic response to negative real interest rates.

4. The ability to convert wealth holdings into real assets that can be stored, exerts considerable inertia on real rates once they fall below zero. The greater the ability to do this, the more inelastic the demand for other financial assets will become and the stronger the inertia will be.