Saturday, 14 January 2012

Savings Equals Investment?

This post is for first year undergraduate students (and the occasional blogger) who appear confused.

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.

35 comments:

  1. Yawnish.

    "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."

    Just assume everyone is saving until they either buy or invest.

    A dollar (or one of your weird pounds) saved (in a piggy bank) this year is spent or invested next.

    You don't need the complex bank in the middle to riddle out the math.

    You attempts to start talking about inventory make you suspect.

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    1. Morgan, I do believe that economics at its fundamental principle (at least from what I know) is the general redistribution of resources? Allocative efficiency is the goal of economics is it not? And allocative efficiency at its most basic level is the redistribution of economics, not simply 'socialism'

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  2. Morgan? Whats your point? In the long run savings are invested or spent? That doesn't prevent income falling this year such that S=I, and you know what they say about the long run...

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    1. The point is Simon's goal is the re-distribution of wealth, from that goal he starts talking. That is NOT, CANNOT BE, economics. That is a social agenda that actually pits him directly against economics.

      To your question, the long run is not that long:

      1. Savers of any size quickly get to a large purchase or an investment. This is what I advocate, we should actually use words in economics that encourage people to saved and spend, save and invest - credit be damned. One thing is better than the other, our semiotics should reflect that.

      2. Savers of little size don't have any effect.

      3. Follow the 80 / 20 rule, what matters is what the top 20% are doing, and they are not piling cash endlessly into a piggy bank.

      The moment someone tries to introduce banking into the equation, the answer is policy that limits leverage. End of discussion.

      As I note below to Nick, inventory discussions are silly, the far bigger shift is around digital consumption and distribution.

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    2. Morgan, you don't understand the very basics, yet despite your complete ignorance you have very strong opinions.

      I believe that in your country people like you are normally referred to a "jackasses".

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    3. "You're ignorant" is not an argument. I think Morgan does know the basics, and has not lost common sense in a sea of socialism disguised as "complexity".

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    4. "The point is Simon's goal is the re-distribution of wealth, from that goal he starts talking. That is NOT, CANNOT BE, economics. That is a social agenda that actually pits him directly against economics."

      Morgan are you unaware that economics is a social science-no matter it's pretensions... It's not physics. As economics is a 'science of society' where would a social agenda be more appropriate?

      You too from what've you said on many occaisons clearly have a social agenda. You've hear of the Immaculate Conception? Well this conservative definition of economics is the Immaculate Economy

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  3. Two genuine questions:

    Q1: would macroeconomics be fundamentally different if all goods were services, or produced to order, so there were no inventories?

    Q2: would macroeconomics be fundamentally different if the economy consisted of yeoman farmers so savers and investors were the same people?

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    1. Dear Nick

      Q1 – I think it would not be different: that was what I was trying to convey with the Q &A involving 'just in time' above, which in turn was inspired by your post that I linked to later. The models in the literature typically make the implicit assumption that firms forecast demand accurately, so you only tend to find the inventories story in the text books. However I instinctively feel it is easier to get the point across to first year students if we do talk about inventories – do you think this is wrong?

      Q2 –Less sure on this, which was why my link to you was ‘Perhaps’. What I think is important in the real world is that the decision to save (postpone consumption) is not automatically a decision to invest (buy machines). That seems to be self evident when we have consumers and firms. I guess my question would be why you wanted to have the same agents taking both decisions, when I feel the key point is that they are different decisions.

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  4. P.S. Don't worry about Morgan. He is the tame troll who hangs out on Scott's blog, trying to convince Scott to join the Tea Party.

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    1. Dear Nick, worry about me very much! Remember Scott's entire policy approach has to change - thats our bet - if Obama loses. He's only been right IF Obama gets to stay in office, if the GOP can pin the economy on him, the the GOP strategy since 1980 is a winner, winner, chicken dinner.

      Note: As a serious study on 3D printing, so glad you are not a Luddite, but still the real issue is that inventories are a gas, they have shrunk and continue to shrink the deeper the Internet wraps itself into the real world.

      The FAR MORE INTERESTING part the economy 2.0, is that the digital isn't scarce, and every year we are buying and receiving more of our lifestyle from the digital.

      That's a bigger shift than no longer caring about inventory on economics.

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  5. @Nick Rowe

    A1: Macro would not be fundamentally different. Instead of a story in which brewers accumulate excess inventories in a slump, we would have a story in which barbers do crossword puzzles while waiting for customers to show up. You could, if you liked, call it involuntary accumulation of solved puzzles.

    A2: Macro would not be fundamentally different if the harvest went to market. (If all crops were grown for home consumption there would be no Keynes and no Ricardo either.) The farmers would sow their seeds based on anticipated market sales and if they were pessimistic they would grow less than if they were optimistic.

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  6. Excellent post, but I think it could have been clearer on a couple of points, which I spell out below:

    According to the classical view, output (Y) is fixed at the natural rate, because wages and prices are assumed to adjust to eliminate unemployment. So, if Y=C+DK, an increase in C necessarily implies a fall in DK. This ensured because the interest rate (r) is assumed to adjust so as to equate savings and investment, i.e. S=DK, where saving is assumed to be a positive function of r and investment a negative function of r. In this model, we can apply the story of an increase in savings driving down the interest rate, as savers compete to find willing borrowers, thus causing higher investment.

    Now, most economists would (to a first approximation) agree that the model above holds in the long run, and before Keynes it was the orthodox view of how the economy worked in the short run.

    According to Keynes, the classical model is incorrect. The Keynesian view is the, in the short-run, Y is determined by aggregate expenditure (essentially, because Keynes assumes wages and/or prices are fixed above the market-clearing level, so there is unemployment). Also, for the reasons Simon points out regarding the importance of money, Keynes rejects the idea that interest rates are determined by the market for loanable funds. Instead, interest rates are determined by the supply and demand for money. So, according to this view, E=C+DK determines Y, with DK fixed because there's no reason for r to change. Thus a fall in C (rise in S) reduces C and hence reduces Y. The condition S=DK is achieved not by changes in r, but by assuming that S depends positively on Y, that is output adjusts to ensure S=DK.

    So, there's a fundamental difference between the two approaches. In the first, Y is a constraint on E, so changes in consumption (or government spending) must lead to an offsetting change in investment. In this case the accounting identity S=I can be interpreted in a straightforward manner. In the Keynesian case, I provides a constraint on S, and S=DK is ensured by the adjustment of Y. Hence we have the paradox of thrift, whereby an increase in desired saving causes output to fall.

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  7. Simon and Kevin: I tend to agree that the answers to both questions are "No (to a first approximation)". But the sheer prevalence of the "unintended inventory accumulation" and "savers and investors are different people" memes makes me wonder sometimes.

    In a symmetric Cournot-Nash game (which is essentially what this is if we assume savers and investors are the same people) and there are no inventories, it is very hard to make sense of the original question:

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

    We know this is supposed to mean a shift in the reaction functions, so that they *would* all save more *if* (counterfactually in this model) income stayed the same. But interpreted literally, and not as a counterfactual conditional, then if people *do* save more then investment *must* increase.

    Best never to use the S-word!

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  8. econojon: there is no Paradox of Thrift. There is a Paradox of Hoarding Money (the medium of exchange). Could an increased demand for saving in the form of antique furniture cause a recession? Everybody decides they want to buy old chairs instead of new chairs. That's by definition an increased desire to save (or a reduction in desired investment in consumer durables) in standard terminology. But since everybody is trying to buy old chairs, they must all fail, or else the price of old chairs rises so high they give up. So they all go back to buying new chairs again.

    Keynes was wrong on this; Silvo Gessel was right.

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    1. Nick,

      If people decide to save, they are looking for a certain return. If the price of antiques goes up, the relative return goes down, so they would switch to different assets, which pay a higher return. They wouldn't start buying new chairs unless they needed to sit down. It's true that some consumer goods are bought as investments, but these are the exception and don't negate the paradox of thrift.

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    2. econojon: OK, suppose they switch to a different asset, call it X. Then I repeat my question again. Either X is a newly-produced good or it isn't. If it's a newly-produced good (or can be created as a paper claim on a newly produced good), then there is no recession. If it isn't a newly-produced good, and the total supply is fixed, then either they can't buy it because nobody wants to sell, or else the price goes up and they decide to buy something else instead. In which case I repeat my question...

      Ultimately, if everyone decides to try to save more, either they buy newly-produced goods, or they try to hoard money.

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    3. They try to buy existing assets but the supply is fixed, as is price. The excess demand is eliminated by a reduction in income, which reduces desired savings.

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    4. Quote:

      there is no Paradox of Thrift. There is a Paradox of Hoarding Money (the medium of exchange).........Keynes was wrong on this; Silvo Gessel was right.

      This leads me to ask the question. What happens when financial institutions "invest" in other financial assets while at the same time leveraging the money (medium of exchange) they have - I am thinking CDO's SIV's etc. which were like a stack of cascading bets of increasing size, based on a very small "real" asset base.

      How does this work in the National Income macroeconomic accounts?

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    5. econojon: there is this material called "unobtainium". It is really really neat stuff, that everyone wants to spend part of their income on. The only problem is....., unobtainium is...not obtainable. You can't actually buy any. Therefore, if everyone ever thinks of buying unobtainium, and wants to spend part of their income on buying some, and they can't, and so everyone's income must drop to zero so they stop wanting to buy any unobtainium.

      For God's sake, I hope word never gets out about unobtainium, because if it does, global GDP will drop to zero.

      http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/12/unobtainium-and-walras-law.html

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    6. Nick,

      I think you are confused on a couple of points. First, when we talk about demand for a particular good, say unobtainum, we are talking about exchanging one good for another. That is, we have to satisfy a budget constraint, or else people would demand limitless amounts of goods. Now, if a good isn't available for exchange it's meaningless to talk about demand for it, people will still exchange real goods for real goods because not doing so won't help them obtain unobtainium. Walras's Law still applies because there is no market for unobtainium, there are no sellers to provide the opportunity for exchange.

      Now, the above is only slightly relevant to your initial claim, because the Paradox of Thrift concerns macroeconomics, whereas the demand for a particular good (unobtainium) is microeconomics. In macro, we have broad areas of spending, essentially just consumption goods and investment goods, plus a role for money, the government, etc. Walras's Law still applies, but has a different interpretation: we say excess demand in these aggregate markets must be zero, so equilibrium in the goods market and in the capital market implies equilibrium in the money market, for example.

      The question at hand is: what happens if there is a change in desired saving (i.e., disequilibrium in the capital market). If people could only save by purchasing unobtainium, then there would be no possibility to invest, and all income would have to be consumed. However, in practice an imaginary material makes a poor store of wealth, and there are plenty of real investment goods available. If demand for these increases, but supply is fixed, then we have the paradox of thrift.

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    7. econojon: you didn't like my unobtainium example? I thought it was cute!

      OK, here's a more "realistic" example: start in equilibrium, then suppose the government imposes binding rent controls on all apartments, so there's an excess demand. Assume everyone rents (to keep it simple). Assume everyone wants to spend 40% of their income on renting an apartment, but because rent controls halved rents, everyone is only spending 20% of their income on renting apartments. Does this mean the level of income must fall by half to restore equilibrium in the market for rental apartments?

      Obviously not. OK, then why is it different if there's an excess demand for (say) land? Why does an excess demand for land not cause income to fall until people don't want to buy more land?

      (I don't believe in Walras' Law, by the way. I think it's wrong.)

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    8. Nick,

      Again you seem to be thinking in microeconomic terms. If the only consumption good is apartments, then yes, if people decide to spend less on apartments their income will fall (assuming fixed prices and interest rates) because their income must come from selling/renting apartments.

      You seem to have in mind a model where income is fixed, and if people don't spend on one good they must be spending on something else. But this is macro, we are talking about aggregate spending, not particular goods.

      As for Walras, I hope you appreciate the irony in basing your critique of Keynesian macro on a rejection of Walras's Law. Many people would claim (wrongly, in my view) that Keynesian macro violates Walras's Law. Maybe Simon could give us a post on Walras (or persuade one of his micro colleagues to do so) because there seems to be some confusion on the topic.

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  9. "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."

    Banks don't lend out money, that's not how it works. Just throw out the stupid textbook, they don't know what they are talking about.

    Banks clear and settle payments with reserves. It doesn't matter if the check they are clear and settling is a loan check or a private check. The FED will always insure that there are sufficient reserves to clear and settle payments. Banks only need sufficient capital to underwrite the loan default risks and creditworthy customers asking for a loan to lend. It does not lend out deposits!

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  10. I have a very basic question (expressed in non-Keynesian terms).

    When savings increase people spend less and have more cash. In your model then I stays equal to S by breaking I into DK+DS. Is DS just assumed to be equal to the increase in savings to make the maths work - with no actual money flows involved ? In other words: increase in savings = decrease in consumption spending = increase in inventories to exactly match the fall is consumption ?

    I can't see what else it could mean but just wanted to confirm.

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  12. I commented on your post, Mistakes and Ideology in Macroeconomics, essentially raising the point that this post is discussing, to say that if saving=investment then consumption smoothing does not imply that government spending financed through taxation will increase aggregate demand.

    My issue with your post is that ignorance of consumption smoothing is not the mistake that Lucas and Cochrane are guilty of committing (as you implied), since in the general equilibrium models with which they work consumption smoothing is the optimal response to a tax increase. Their mistake more likely is in the multitude of other assumptions that underlie their models.

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  14. Having extra money that was saved earlier is particularly ideal for people who want to retire early since it gives them alternative options to think about.

    

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  15. High I am studying the basic relationship between Output, Investment and Savings.

    This is what I understood so far but there are still some sections that are unclear and would be very thankful for you to explan them for me, Thanks.

    To derive a relation between output and investment we must make 3 assumptions.

    First..since economy is closed therefore I = S + (T-G)
    I is Investment
    S is Saving
    T is Private Saving
    G is Public Saving

    Second..to focus our behavior between Investment and Saving, we assume that (T-G)=0, so by definition the previous equation now is I=S.

    Third..we assume that Saving is proportional to Income so S = sY
    where s = the saving rate (being from 0 to 1)
    So therefore since I=S and S=sY We get I = sY also.

    so I believe I understand correctly when I say that higher output implies higher saving and therefore higher investment. Good?

    But still I am a little bit Confused on mainly assumption number 2 were we say that T-G = 0 ... Why exactly?

    Thank you! found the post very helpful.

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  16. alternate way of thinking is Investment savings, please i need someone to give a detailed analysis for this

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  17. Yes. There is a difference between saving and investing. And it is not as subtle as you might think. The key to successful financial planning is to do both as much as your personal situation allows.

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  18. In the context of the saving-investment balance and purely as an accounting identity, which variable or variables are directly affected and what would happen to gross private domestic investment (I) if:

    a) Domestic saving by households was to decrease, everything else remaining the same?

    b) U.S. net tax receipts were to increase, everything else remaining the same?

    c) There was a sudden increase in exports from the U.S., everything else remaining the same?

    d) Pre-tax business profits were to increase, everything else remaining the same?

    e) Federal grants to state and local governments were to disappear, everything else remaining the same?

    Recall the saving-investment balance is given as:

    S + (M-X) = I + (G-T) where S is domestic saving by households and businesses, M is U.S. imports of
    goods and services, X is U.S. exports of goods and services, I is private domestic investment in capital
    goods, G is total federal, state and local government spending on goods and services, and T is the net
    receipt of tax revenues by federal, state and local governments

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  19. Could somebody answer the questions above and explain the logic behind it?

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  20. Dear all,
    I am struggling to understand the IS curve so please check my notes regarding conditions that have to be met and let me know if I got it right:
    - Based on fact that aggregate expenditure equals aggregate income is the requirement that planned expenditure equals actual (or realized) income. The idea is that no-one would produce in excess of consumption, if he does not want to either exchange it or invest it. Any overproduction in the consumer goods sector (investment in inventories), necessarily implies that profits of entrepreneurs will have to fall (since they are not capable of selling). This will itself lead to a fall in investment - reducing capacity accordingly. Resulting reducement in output will reduce future incomes based on which savings and consumption will be reduced. The same is true if consumers start this cycle by decreasing the consumption in favour of savings which would lead to increase in business inventories and the whole process repeates. Decrease of incomes and consequently consumption and savings would continue until the surpluses in inventory are depleted, so in the long run investments are made only to capital goods without increase in inventories.

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