S = I ?

16 Jan, 2012 at 11:09 | Posted in Economics | 1 Comment

For those still having problems with understanding the nuts and bolts of what’s wrong with textbook versions of the savings and investment nexus, perhaps this little lecture might help:


Q: If consumers spend less and save more, does this mean investment must increase? 

A: Absolutely not. Someone increasing their saving does not automatically imply that some firm will decide to buy more capital goods.

Q: But surely savings equals investment by identity in the national accounts.

A: Indeed. Total output = total income = total expenditure = Y. In the most simple model of a closed economy without government, income (Y) = consumption (C) + saving (S), but also expenditure (Y) = consumption (C) + investment (I). So S=I by definition. But here investment includes what is called ‘stockbuilding’ or ‘inventory accumulation’, which includes goods that firms wanted to sell but could not. To make this clear, lets split measured investment (I) into these two components: I=DK (buying new capital goods) +DS (stockbuilding). So if people consume less (C falls), but investment in new capital (DK) stays the same, measured investment rises because firms accumulate inventories of the goods that consumers did not buy (DS rises).

Q: But this situation cannot continue, as firms may be losing money.

A: Exactly. They will cut back on their output, incomes will fall, consumption may fall further, and savings will also fall, cutting back on the initial increase that we started with.

Q: When will this process stop?

A: When firms stop accumulating inventories i.e. when DS=0. Then, and only then, will S=DK.

Q: But how can this be? We have assumed that DK stayed the same, and we started with an increase in S?

A: You have not been paying attention. Each time firms reduce their output to match lower demand, incomes and savings fall. Eventually the initial rise in savings is reversed, because overall income has fallen.

Q: Got it. But textbooks make a big thing about aggregate savings equalling investment. If it is just an accounting identity, why is it important?

A: What the textbooks really mean is that we eventually end up with a position in which S=DK. And that is important, for the reasons we have just discussed. It is called the paradox of thrift. A desire by consumers to increase savings ends up just reducing output, and savings do not increase at all. (Of course they are still saving more of their income: S/Y has gone up, but because Y has fallen, not because S has increased.)

Q: But I thought with all this ‘just in time’ production stuff, firms did not hold many inventories any more.

A: Well we could short circuit the story by forgetting about inventories and having firms accurately forecast what demand will be, and therefore what their output should be. In practice what we call involuntary inventory accumulation can still be important when looking at quarterly movements in national output.

Q: But is it realistic to assume investment – I mean DK – stays the same if savings are initially higher? If there are more savings around, it becomes cheaper to borrow, which will encourage investment, right?

A:  It might, but it might not. In particular, if output is falling, firms may be reluctant to add to their capital stock.

Q: But won’t interest rates keep falling until they do? After all, the asset market has to clear.

A: Savers have an alternative, which is to just keep their savings as money.

Q: But they will put the money in a bank, and the bank will lend it.

A: Maybe, but the bank may just decide to hold on to the cash.

Q: It seems to be really important what people do with their additional savings.

A: Perhaps. But I think the key point is that, most of the time, the person doing the saving is different from, and has different motives to, the person doing any investing. A highly complex financial system links the two. And in that system, there will be lots of opportunities for the additional savings to be parked as money.

Q: Money seems very important here. It is why the extra saving does not have to find its way into more investment.

A: I think that’s right.

Q: If people hold the extra savings as money, will that not increase money demand. What happens if the central bank keeps the money supply fixed?

A: People hold money not just as a way of saving, but also to buy and sell things. And if less is being consumed, there is less need for money on this account. It is difficult to predict what will happen to the total demand for money, which is why central banks nowadays focus on determining short term interest rates rather than the money supply.

Q: That’s not what it says in my textbook. It says the central bank fixes the money supply.

A: Yes I know. I’m afraid it’s a bit out of date. Don’t ask me why.

Q: So if the central bank determines the interest rate, why don’t they ensure the interest rate is low enough to encourage firms to buy more capital goods?

A: That is what they would like to do. There are two problems. First, it may take some time for the monetary authorities to work out what is happening, and what the right interest rate is. (I could talk about real and nominal rates here, but let’s leave that for another day.) Second, nominal interest rates cannot go below zero, and maybe we would need negative interest rates to persuade firms to raise investment enough.

Q: My textbook also says that the classical model assumes interest rates adjust so S=I, by which I assume they mean S=DK. Does that mean the classical model is wrong?

A: Only if you think it applies at all times, and that there is no other reason why output cannot fall. However if we assume that the monetary authorities eventually are able to chose the right interest rate, then the classical model is fine when thinking about economies over a long enough time horizon.

Q: This all seems like common sense. I feel a bit stupid not to have understood this before.

A: Don’t worry, you are not alone.

Simon Wren-Lewis: Savings Equals Investment?

1 Comment

  1. Reblogged this on LARS P SYLL.

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