Paradox of Thrift, Savings and Investment

There was such a great comment by reader "es" on a post about the paradox of thrift at Paul Krugman's blog that I just have to copy it here verbatim.

Krugman:

The story behind the paradox of thrift goes like this. Suppose a large group of people decides to save more. You might think that this would necessarily mean a rise in national savings. But if falling consumption causes the economy to fall into a recession, incomes will fall, and so will savings, other things equal. This induced fall in savings can largely or completely offset the initial rise.

Which way it goes depends on what happens to investment, since savings are always equal to investment. If the central bank can cut interest rates, investment and hence savings may rise. But if the central bank can’t cut rates — say, because they’re already zero — investment is likely to fall, not rise, because of lower capacity utilization. And this means that GDP and hence incomes have to fall so much that when people try to save more, the nation actually ends up saving less.

"es":

Okay, I admit I don’t really understand this. I always seem to get hung up on S = I (Savings equals Investment). What would happen if you worked from the hypothesis that S = I + W, with W standing for Waste? Sure it muddies things, because it’s hard to weight whatever you are measuring as to its true productivity. But this is reality. When the old paradigm doesn’t work, or leads to paradox, you have to question your basic assumptions. Not all savings lead to purposeful investment. Witness the proverbial gold under the mattress. Witness wheat put by for a bad harvest and then mouldering in a badly maintained storage facility. Check out the over-elaborate plastic toys that over-stimulate and maybe poison our already hyper-active children. Especially pertinent, witness a population underfed and under educated and inadequately protected from disease to guard against the future possibility of debt.

Already in your columns I see you speaking of saving and investment as different entities, and then when you get “wonkish” (I guess you mean mathematical) you fall back to S = I.

I recommend that you assign a graduate student to work on the need to incorporate more variables into the S=I axiom. It might get him a Nobel prize, or save the world, or something.

I just love the snark in that last paragraph.

Of course, the identity of savings and investment doesn't make any common sense, but since when such a thing has been expected of economic theory?

I'm not sure either if it makes any sense to think of this identity in terms of any units of currency, but in addition to the waste term on the right, there should at least be a term for credit expansion on the left. I would also amend the equation to

S + C = I + W,

where C is the net amount of credit creation. Of course this equation is not a real equation. There are severe time lags in all the processes that are part of it. It can only be discussed in a statistical sense:

E[S + C] = E[I + W],

where E denotes the expected value. In addition to a temporal sense for this statistical dependence, one must also think about the ensemble statistics to account for people with different concepts for value, etc.

Credit has the ability to create investment without any net savings. Somebody gets into debt, which is equivalent to negative saving. Somebody else gets the loaned sum of money, and decides to save it. The net savings are zero.

However, there would have possibly been an investment that was made with the borrowed money. All is well, as long as the debtor pays the money back. Credit is a form of delayed savings. Investment is made first, then come the savings, little by little.

Problems occur when too much credit is extended. What if there is no income from which to save? People default on their loans. Oops... Now (nominal) investment has been much higher that the "savings" from which it was supposedly made. Savings are actually smaller than investment.

This is where the identity asserts itself with a lag. The value of savings increases while the value of investment decreases. Result: deflation.