Over any period of time, in any nation, the total quantity of investment that takes place must equal the total quantity of savings that are generated.
In the simplest case, where there are no inventories, depreciation, government, or foreign trade, it is trivial to prove that “savings equal investment.” It starts from the premise that all income is earned by producing something, so that the total of everyone’s income equals the total value of everything that gets produced. That “income equals output” (at the national level, though technically only when net foreign income is zero) is a very basic truism in macroeconomics. (As I recall, by the time I had attended my third class in the subject, I had already forgotten that there was a conceptual difference between output and income, and even today, outside occasional spells of lucidity, I labor under the delusion that the two terms are synonyms.) Everything produced is valued either for benefits it has in the present (“consumption”) or for benefits it will have in the future (“investment”). Thus “output equals consumption plus investment.” Savings are defined as unconsumed income. Thus “savings equal income minus consumption.” You do the algebra.
It’s pretty straightforward to add inventories, depreciation, government, and foreign trade and show that the algebra still works. But I don’t find the algebra very enlightening. The algebra shows what must be the case, but it doesn’t explain how it gets to be the case. I mean, people make decisions about how much to save, and other people (businesses, mostly) make decisions about how much to invest. Does the Good Fairy come along with a magic wand and make sure that one side is deciding the same number as the other side?
I’m going to try to avoid exceeding my snark limit here, but the conventional explanation does seem to me, at least under today’s circumstances, to be more a fairy tale than an enlightening description of reality. The Good Fairy in this story is called the Loanable Funds Market, and her magic wand is called Market Clearing. Savers (households with income to save) bring their funds to market, and investors (firms with potential capital spending projects) bid on those funds until they are used up. If the firms are really determined to invest, maybe they can offer an interest rate so high that it will induce households to save more. If households are really determined to save, and firms aren’t very interested in investing, then the households can offer to lend at lower and lower interest rates, until they find one that clears the market.
Many economists enjoy telling their students this fairy tale. I gather that some economists even believe it almost as if it were literally true. But as a description of how savings actually do come to equal investment, it has some problems. First, as a theoretical point, what happens when households are willing to accept a zero interest rate and still can’t unload their savings? In a normal market, when it cannot clear and there is excess supply, the suppliers are out of luck. (The classic example is a worker who is willing to work for less than minimum wage but can’t get a job.) Is that how the loanable funds market works? Do households have to take those extra potential savings and go home and consume them instead, whether they like it or not? Does the Good Fairy force them to consume?
And more generally, empirically, do the institutions of the real world of saving and investing bear any resemblance to the abstract loanable funds market? In real life, funds can be saved but not lent (as when banks decide to use new deposits to increase their excess reserves). In the real world, funds can be lent without ever having been saved (as when the Fed makes loans with newly created money). What does the Good Fairy do to make sure that these discrepancies offset each other?
Even when the funds lent are exactly the same ones that were saved, there can be a substantial time lag between the saving and the lending, and an even longer lag until the actual investment of the borrowed funds. Nor are these just banking issues. When a company issues stock, it is also acquiring “loanable funds” (in the relevant sense), though not in the form of a loan. And just like banks, nonfinancial companies can sit on the cash rather than making immediate use of it. The Good Fairy may be busy forcing reluctant households to consume, but as the end of the quarter approaches, she will have to excuse herself and grab her cattle prod, so she can force businesses to invest quickly. Otherwise the investment may not take place until next quarter, and savings will not equal investment for the current quarter.
If I were the Loanable Funds Market, I would hand in my resignation as Good Fairy. It’s obviously quite an impossible job. (OK, I give up on the snark limit.) And yet, as a matter of algebraic certainty, over any time period, investment must equal savings. If this good fairy quits, we’ll have to hire a new one.
And so we will. Her name is the Definition of Saving, and she’s both more powerful and more subtle than I made her out to be in the second paragraph.
What does it mean to save? It could mean “to set aside part of one’s income for the future.” Only, that definition is deceptive, because it implies a positive act of “setting aside.” There can be positive acts – purchasing a certificate of deposit, for example – that represent the commitment to save, but the act of saving is itself entirely passive. If you get paid in cash and put all the cash in a box without spending it, your are saving. It is no different if you get paid in cash and put all the cash in your wallet without spending it. Like “to rest” or “to fast,” the verb “to save” is defined not by what you do but by what you don’t do. “To save” means “to receive income and not to spend it.”
Bearing in mind the passive nature of saving, think about the old joke where the tourist asks, “Lived here all your life?” and the crusty local replies, “Not yet.” By definition, you have saved if you have received income and have not spent it. Suppose that, a few seconds ago, you received your pay in cash and put it in your wallet. Have your received it? Yes. Have you spent it? Not yet. Like the crusty local, economics is precise. You may intend to spend every single dollar of your pay, but for now the answer to the question, “Have you spent it?” is “No.” Therefore, as soon as you receive your pay, you have already saved it. It has become part of your savings. When you do spend it, you will be dis-saving, taking money out of savings.
The New Good Fairy thus presents us with a bizarre but indisputable fact: all income is saved. If you make the time period short enough, the savings rate (out of newly earned income) is always 100%.
And that’s half the reason that savings always equal investment. The other half has to do with the source of the income. Whoever pays the income must be either making an investment (in which case the amount of that investment exactly matches the amount of the receiver’s new savings) or taking money out of their own savings (in which case that dis-saving offsets the receiver’s new savings, and there is no net change in either savings or investment).
How do we know that the payer must be either dis-saving or investing? The payer is purchasing something, and it must be either for consumption or for investment. If it is for consumption, then the payer is taking money out of savings to pay for it. If it is for investment, then the payer is investing.
To take a simple example, suppose you’re a freelance software developer, and a company pays you to develop some custom software for long-term use. From the company’s point of view, that’s investment. As soon as they pay you, they’ve made an investment, and you have saved the exact amount of the investment they just made. Savings equal investment.
And what happens when you spend the money? To take another simple example, let’s say you spend some of it on a haircut. You are taking money out of savings, so your savings are reduced by the cost of the haircut. But the payment is income for the barber, and all income is initially saved, so the barber is putting into savings the same amount that you are taking out. Total net savings are unchanged, and since there was no investment involved, net investment is unchanged.
The Loanable Funds story tends to give the impression that saving determines the amount of investment. (It’s not the only possible interpretation, but when I hear the story, I tend to think, “Savers decide how much to save, and that is the amount that can be invested.”) In the immediate time frame, however, it is the other way around: investment determines the amount of savings. In general, saving occurs whenever someone receives income. Net saving occurs whenever someone receives income that is not offset by the payer’s dis-saving. That can (and will) happen only when the payer is investing.
In the slightly-longer-than-immediate time frame, people make decisions about how much to save, but it is still investment that makes that saving possible. Suppose, for example, that all investment were to stop for an entire year. Suppose everyone completes or cancels any investment plans by the end of 2009 and nobody makes any new investments in 2010 – no new houses or factories built, no new equipment or software created, no net purchases of foreign securities, and so on. (Because inventories are a form of investment, you also have to imagine – and I’m being a bit tricky here – that manufacturers start 2010 with inventories at some kind of maximum and refuse to produce anything new except to replenish those inventories.) In that case, there can be no net saving in 2010. People will receive income, presumably, but only as the result of dis-saving by others, so the most net saving that can happen is zero.
And just as the decision not to invest can prevent net saving from taking place, so the decision to invest can force people, collectively, to save. Consider the converse thought experiment, where everyone resolves not to save in 2010. "Any income I get in 2010,” everyone says, “I'm going to spend before the end of the year." Then someone comes along and decides to build a factory (financed, let's say, with money that the builder was holding in a safe at the beginning of the year). So the builder hires construction workers to build the factory, and the workers now have income, which they have resolved to spend before the end of the year. So they spend it. Now someone else has income, which they have resolved to spend. When they spend it, yet someone else has income, which they have resolved to spend. And so on. The money keeps getting passed around like a hot potato. Or like a game of musical chairs. At the end of the year, someone will have the money and will not yet have spent it. Someone will have unspent income. Someone will have saved.
I grant you, I've left out a lot of details that could become important. In particular, I've ignored inventories, and I’ve ignored imports, and there are some possible loopholes there that might allow people to avoid saving the invested money in the last paragraph. But I think I’ve made a pretty good prima facie case that the causation normally runs from investment to savings.
You may object, however, that my assertion doesn’t make sense. There must be causation running from savings to investment, because an economy has limited real resources. If people choose to save less, more of those resources will have to be used for consumption, and fewer will be available for investment.
That’s a valid point, as far as it goes, but now you’re not talking about saving income; you’re talking about saving resources. Resources have to be “saved,” in the sense of “not used up by consumption,” in order for investment to take place. You could say, perhaps, that a certain part of our potential real income – the income we would have if we made use of our resources to the greatest sustainable extent – has to be “saved,” in that sense, to make possible a given amount of investment.
But it has become painfully clear that actual income can fall far short of potential. As of today, according to typical estimates such as that of the Congressional Budget Office, the US is (in the relevant sense, though not in the terminology the CBO uses) “saving” about a trillion dollars extra of its annual potential income, over and above any actual income it saves. The US is “saving” that potential income in the sense that, if there were another trillion dollars worth of investment to be done, the resources to do that investment would be available. Those “savings” aren’t being used for investment; they’re being more or less thrown away – held in reserve, if one may speak euphemistically. The unemployed, the idly-self employed, the discouraged workers, the involuntary part-timers, and everyone else who would be doing something more productive in a better-functioning economy – they are the human counterpart of banks’ excess reserves. In real terms, they represent the idle portion of our national savings.
That’s certainly a coherent way of thinking about savings, and it is one in which savings put a constraint on investment. But it doesn’t conform to standard semantics. In practice, nobody counts those extra “savings” as savings. If you want to increase the savings that count, you have to find a way to increase investment.
DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management.
Paul Krugman: The Piketty Panic
1 hour ago