Please help me understand: personal savings rate

I know the dictionary definition is something like personal income minus personal spending.

But isn’t it also true that spending is always equal to income? (Every transaction has a buyer and a seller - the sum of all spending by all buyers is therefore always exactly equal to the income of all sellers.)

I like to use simplified examples, so consider:

Suppose there’s two people on an island, Abel and Bart. In the morning Abel goes to Bart’s house and buys $10 worth of bananas. In the evening Bart goes to Abel’s house and buys $10 worth of oranges. The GDP of the island is $20. The savings rate is 0, because each spends all of his income.

So an economist comes to the island and explains to Abel and Bart that they need to save more, to grow their economy. Abel and Bart each commit to saving 10% of their income. So the next day Abel cuts his banana purchases to $9, and Bart does the same.

You can work it out yourself, but the net result is GDP shrinks by 10%, as well as personal income, and the savings rate remains the same - 0.

It’s the same result no matter how much Abel and Bart try to save, all the way down to 0 GDP, 0 income, and 0 spending.

So where is the savings?

I know it’s a stupid question, but I can’t find the answer. Thanks.

You’re ignoring the leftover apple and orange. Presumably they are still capable of harvesting at least 10 each. Therefore, they have some extra to stockpile in case of a bad harvest or to invest in paying the local lemur population to catch groundbirds.

I was afraid of that - can that really be it? That savings is just unsold inventory?

How do you square that with the idea that savings are a good thing, or something we should be upset about not having?

And what about the popular idea that savings means having more money in the bank, or wherever, than what you had before?

It’s true.

All you need to add to your scenario for savings to make sense is a fruit picking machine that doubles one’s labor productivity. And it costs 20 oranges and 20 bananas to buy it.

The problem with simple economic examples like yours is that they don’t account for the infrastructure improvements that are the ultimate end goal of having a net savings rate.

I’m not sure I understand what you’re saying about the fruit. For one thing, wouldn’t the guy selling the fruit picker want money? For another, why would the fruit sellers invest in a machine when sales were falling?

Anyway, I’m not sure it changes the equation.

Suppose Abel and Bart go to Cain and offer to give him unsold fruit for a machine that picks fruit faster. Abel and Bart have gotten rid of their excess inventory, but still don’t have more money.

What I’ve always wondered is what is included in the personal savings rate that economists talk about.

If I get paid $1,000 on payday and I immediately spend $900 of it, is the other $100 “savings”? What if I buy gold with it? What if I put it in my savings account and then spend it next month?

What about investments and 401(k)s? Unless you are maxing out your Roth IRA and 401(k) there is no point in saving money using other methods. If I put $10,000 into a 401(k) but don’t have anything in my savings account am I “saving” for purposes of this metric?

If you earn a flat income of $1,000 a month, then during the first month your savings rate is 10%. If next month you take the $100 you saved and spend that in addition to your salary, then during that month your savings rate is -10%.



It seems very odd to conflate the two in this way. I think of my own finances as “saving” when I contribute to something that I won’t dip into for decades. 401(k), IRA, 529 plan, etc.

Spending vs putting in my account isn’t a metric that seems like it has any value in being tracked. One month I might spend thousands more then I make because the tuition bill and insurance bill and tax bill all came in at the same time. The next month might be light and I’ll be way in the black.

Economically there’s no difference, and therefore no distinction. Economists do have ways to measure aggregates savings in different classifications, but that’s because the timeframe involved is different (i.e., short temporary bankroll intended for relatively near consumption, medium-term savings for significant purchases,. long-term investments for retirement etc.).

People don’t “save” money. It’s always intended to be consumed at some point. That’s the sole purpose of wealth. Economists know this, and ignore the distinction you draw because it doesn’t matter to the macroeconomy.

Stop right there, chief. You created the scenario without money, so the response did not deal with money in all its complexity. You can’t go back now and add money in abitrarily and expect it to make sense.

The whole point of my response (and Zerial’s) was to show that investment is intended to create additional value, of which money is only a symbol. You started out by dealing with the value directly (i.e., fruit). Dont’ confuse things by trying to add the symbols later on. At the end of the day, if the pair save up and buy the machine, they get more fruit - more value for their labor.

That’s investment, and that’s all investment is. Savings is the means you use to get that investment: skip consumption now so you can have even more later, or at least a safety net in case of bad times.

It has nothing to do with money.

The classic formula for income is consumption plus savings. So savings is basically income minus consumption. You now have savings that you can use for consumption in the future. Bart and Abel might not always be able to produce 10 apples and oranges each but with enough savings they can continue to eat long after they can no longer pick fruit.

In a modern economy, savings is also the source of capital, which is necessary for the growth of an economy.

Not sure why you say I created a scenario without money. The symbol $ means dollars. I’m also not talking about value. I’m talking about money. You say, “At the end of the day, if the pair save up and buy the machine, they get more fruit - more value for their labor.” You say that as if it’s obvious that spending less helps them buy the machine. How, exactly?

It can be helpful to look at the identities first, the stuff that we define to be true. We define our savings, right from the beginning, as our income minus what we consume. This is how we’ve deliberately set up the meaning. Here are other important identities.

GDP = G + C + I + NX
Total expenditure/income is government spending plus consumption plus investment plus net exports. For our purposes, though, we can cut out government and international trade. We’re left with:

Y = C + I
Income is consumption plus investment. Rearrange that.

Y - C = I
Income minus consumption is investment. Oh? What was our previous identity?

Y - C = S
Income minus consumption is savings. Same thing. There is one more relevant identity then.

S = I
Savings is investment. They are the same thing. That’s not some miracle of algebra, but rather how we deliberately set things up to be. Why? Your own island example gives us our justification, if we work through it.

GDP is bigger than $20. You haven’t mentioned personal consumption. In the hallowed ideal, GDP isn’t defined by how many dollars change hands. Consumption is a factor of GDP. If we consume our own production, then it counts.

Abel goes to Bart’s house and buys $10 worth of bananas. Okay. But how many dollars worth of bananas did Bart pick and eat himself? Another $10 worth? That extra production absolutely must count toward GDP for this island economy or we are leaving important info out of the reckoning. I’m going to assume that they both pick $20 worth of fruit, and trade half their output with each other. Then? They consume all of the fruit. GDP is $40.

Y - C = S
40 - 40 = 0

Notice that their trading isn’t really affecting anything so far, because they’re eating all that fruit at the end of the day.

You’re still not looking at production, so nothing has to change here.

Let’s say they’re still creating 20 dollars of fruit each. Now they’re trading 9 instead of 10. But if they continue to consume what’s left, then they’re still eating the whole production. It’s just that they’re eating 11 dollars worth of fruit they picked themselves, and 9 picked by someone else. GDP is still $40 and it’s still being consumed in its entirety. That isn’t savings at all. To save means to invest.

If they absolutely must have 20 dollars worth of fruit every day in order to survive, and they are at the limit of their productive capacities, then the process is done. There’s nothing else to talk about, no investment/savings possible. However, if one of them is good at building tools, and they can go on a diet or work harder, then we can have a different story.

Abel picks $20 worth of oranges, as usual, while Bart starts a new company, Fruit Picking Machines, Inc. Abel gives Bart $10 worth of oranges and keeps $10 worth for himself. They consume that to live. Abel accepts an IOU from Bart, rather than cash. GDP so far, $20. At the time time, Bart spends $20 of his time building his fruit picking equipment every day trying to make their future lives better. (We know it’s $20 worth of time because that’s the opportunity cost of not picking bananas.) The island’s GDP is still $40, but the composition of that has changed. They’re exerting the same amount of effort but only eating half as much fruit: they are saving. The extra effort that previously went to making them fat is now going into machinery. They are cutting back on how much they’d like to eat, and that reduction in present consumption is being directed toward the future. That is savings. That is investment. Same thing.

After two weeks, the machine is done. It now takes Bart one tenth the time to get bananas. That makes his work more productive, which through trade is going to increase the leisure time of both of them. Bart can easily repay the debt, and they can both spend more time surfing the waves or the internet. Or, if there are other little niceties that they’d like to have, like a boat, they can invest in those things, too. Investment means saving their efforts for future gain instead of consuming the entire fruit basket the same day they pick it.

Economies that grow have enough people investing efficiently in the future, not just consuming everything today.

As far as calculating GDP goes, it can be a little bit fuzzy in real life. If real people produce anything that they personally consume, then that doesn’t normally get counted toward GDP, though technically it should be. Do you have a garden? Grow vegetables? That’s real effort you’re exerting, for real reward. It should technically be included in the GDP calculation. That would be a supreme hassle, though, so we skip that and mostly only count our measurable incomes/expenditures. Much easier. For the island scenario, though, you can’t ignore that stuff because personal consumption is such an overwhelming percentage of total production.

In the case of the modern economy, our savings must ordinarily be channeled by financial intermediaries into useful investment. If the financial intermediary can’t be trusted, then our savings won’t come back. It’s like giving 10 oranges to Bart, and instead of building the machine, he practices building sand castles on the beach on the other side of the island. We might think we have a nice cushion, but when the future happens, we’ll find out that we’re significantly less rich than we anticipated. This very thing has, in fact, happened to a few people. Might’ve been in the news in the last several years.

There’s no money in your scenario. You assign an abritrary value to the fruit, but it’s the fruit which matters. Same in the real-world economy.

Investment also doesn’t create money. It can create additional value, but it doesn’t create money.

In practice there’s a lot of ways they can do so. Here are several to continue the analogy:

(1) Use the leftover fruit to train lemurs to catch ground birds
(2) Use the leftover fruit to bait some fishtraps and crabtraps
(3) Use the leftover fruit to save up a stockpile, so they can take time off to build some useful gadgets and make future fruit collection easier.

In the first and second cases, they consume less resources today in order to get other resources tommorow. In the third, they consume less today in order to get even more of the same resources. It’s the resources, not the arbitrary number you assign to them, which matters. And investment adds resources, not arbitrary numbers.

Looking back, it seems that Hellestal looked at it from the more academic PoV.

Hi Hellestal. Thanks for your response.

You said:

Would it be better to say either “what we produce minus what we consume” or “income minus income spent on consumption”?

Otherwise we’re confusing things with money, which is a problem (at least for me) because money can’t be used up, or consumed. Things can be.

In the first case, it’s clear that “savings” includes unsold inventory, because inventory isn’t consumed. In fact, by the first definition, food rotting in the fields is “savings” because it is not consumed. To go back to the hypothetical, if $18 worth of oranges and bananas are sold, and $2 go to waste, then GDP is $20, and savings are $2, which gives you a savings rate of 2/20, or 10%. On the other hand, if none of the food goes to waste - if it all gets sold - your GDP is still $20, but your savings rate would be 0%. So by cutting back on spending, you create savings in the form of inventory that doesn’t get sold.

In the second case, the income of Abel and Bart (after they start saving) is $9 each. Their spending is also $9 each. (In a closed economy, spending and income are always the same.) Since, in this case, Abel and Bart eat all the fruit they buy, there is no savings. GDP is $18 (The rotted fruit did not produce any income for anyone, so it is therefore not part of GDP) and the savings rate is 0%.

Anyway, that’s my understanding of the difference between “stuff produced minus stuff consumed” vs. “income minus income spent on things that are consumed.”

Spending is always the same as income, but the amount of stuff produced is not always the same as the amount consumed.

You said:

To my understanding, GDP is not the total amount of spending, but the value (market value) of everything that is produced. Or, at least, it’s an *attempt *to get at that number.

But G, C, I and NX are not production values, but estimates of spending. So, for example, G is government spending, C is (nongovernment) spending things that are consumed, and I is (nongovernment) spending on things that are not consumed.

So unsold inventory (since it’s unsold) is not part of C or I, initially. But it’s added back in, right? They estimate the value of unsold inventory, and treat it as part of I. The inventory has not actually been sold, so it’s not actually income or an expense for anybody. But it’s added to the “I” column.

So, in the hypothetical, initially you count the amount of money that changed hands in exchange for fruit ($18). Then you look to see if there’s any fruit that didn’t get sold, and add that in as an investment.

You said:

This is where it gets confusing. In some cases savings is defined as “money not spent” and in others it’s defined as “things not consumed”. Here we’re talking about things produced, but not consumed.

But when people complain about the supposedly low American savings rate, for example, they’re almost always thinking in terms of “money set aside for later”, not “things we’ve built or made, but haven’t finished using yet.”
**I’m out of time, but… continued.

What I gather from this is that saving has nothing to do with spending or not spending, but is a function of whether you consume what you produce. Whether Abel and Bart spend some of their income, all of their income, or none of it makes no difference in terms of the islands savings rate. What matters is whether they produce something that they don’t consume right away (like the fruit picking machine, for example, or a house, or a can of preserved fruit that can be eaten later).

So if I buy a shovel that lasts ten years, I’ve consumed 1/10th of a shovel, and invested 9/10ths of a shovel.

Putting money in a savings account, on the other hand, is not saving.

This part, I think, is wrong.

The banking sector, in general, doesn’t care whether I spend my paycheck or not. That money is in the banking sector somewhere, whether I leave it in my account or transfer it to someone else’s. Spending money doesn’t make it disappear. It just changes who owns it.

The former.

Fruit picked and left in the warehouse is a form of savings/investment, even if it’s left to rot. That is, of course, an inadvisable form of savings/investment.

The amount of stuff produced is the same as income.

Again, identity. That is how it is defined.

GDP in its ideal form is both the total amount of spending on new goods and services, and also the total market value of everything that is produced.

They are the same thing. Our measurements aren’t perfect, but by measuring spending on new goods and services, we are in fact attempting to measure production and income. Same same same.


Unsold inventory is counted as investment. If inventories increase unexpectedly, then that is unexpected investment.

You asked for the economic definition. You said an economist goes to the island and suggests that they save move.

Okay then. You’re getting the economist’s core definition first.

It is confusing, yes. That’s why I start with the identities. Once we’ve got those well hashed out, we can go on to other definitions.


Did you know the Greeks work longer hours than the Germans? The Germans have the benefit of having built more machines in the past (savings/investment), which helps them do their work more efficiently in the present. That means today they can put less effort in and still have a high standard of living and more time for summer trips to Majorca.

Again correct, economically.

Yet it is measured as savings in other more familiar contexts. Why?

Because we have a limited amount of resources available to us. You work. You are given a paycheck. That paycheck is money, but I don’t care about the money in itself. What I’m concerned about is the full extent of your buying power which the wage represents. You can use the full extent of your buying power today, right now, and other people will be working as busy little bees trying to get you the consumer goods that you’re demanding. And? All of those people who are sweating away to give you consumer goods are not sweating away building investment goods. Do you see?

That money isn’t valuable in itself. It’s a claim ticket on resources. There’s a limited amount of resources. We’re all producing, producing, producing. What do we end up producing? If people are spending the entirety of their paychecks, then we end up producing consumer goods which vanish tomorrow. However, if we’re sticking our paychecks in the bank, then we are not claiming those resources as personal consumption. We’re all producing, producing, producing but we’re not consuming all that we produce. So what do we end up producing in that context? Hopefully, investment goods. And hopefully, these are efficiently produced investment goods. That is unfortunately not always the case. The USSR had an stupendous savings rate, but most of that savings was the equivalent of fruit rotting in the warehouse.

Why do some people measure the amount of our paycheck put into the savings account as savings, even when it’s not invested? Well, it’s an intuitive guideline. It’s a useful indicator that says, hey, these people are quite possibly not consuming the entirety of what they produce. That means they should, hopefully, be producing investment goods.

And there you have the gulf between the pure enlightened economists’ definition and the slapdash everyday definition. Happens all the time. On the one hand, there are the identities we use to try to untangle in our minds what’s important in the economy, and on the other hand, there are the definitions that are commonly used because they so readily fit our personal experience.

It’s not that one or the other is correct. They are both correct.

Just different contexts. We have to deal with that, just as we have to deal with the fact that there are at least three commonly used definitions of investment. Naturally, I care most about the economic definitions because I think they cut to the heart of the matter. Now I’m obviously biased on this, but I genuinely believe it’s easier to start with the economic identities, and from there try to see the sense in other formulations. Our future prosperity is based on real investment goods, not digits on bank computers. If we begin with a very physical understanding of these things, it’s easier to see later how money fits in.

I wasn’t intending to talk about banking, I was talking about resources.

This is, by the way, why I have a mild dislike for MMT. The jargon of the thing, even when it’s correct, tends to distract away from the underlying issue of resources.

The only way to clear our heads on this, in my experience, is to think about resources first and then add money later. Yes, money is significantly weirder than the average economics textbook indicates. It doesn’t work like those little myths that are taught to undergrads. I don’t support teaching those myths to undergrads. At the same time, though, I’d still like to talk about resources before bringing banking into the process. It makes things conceptually cleaner.

I like explaining to people that money exists only in their imagination. Many people will get this weird look of stunned partial disbelief when they realize that their money is a bit of sturdy cloth or even mere electrons, and it actually represents a debt for somebody else.

So everyone should these worthless debt notes to me. I will be happy to dispose of them in an environmentally friendly manner.

Here’s the problem with that. In a coherent example, fruit doesn’t spoil in a day.

It doesn’t even spoil in a week. So if either participant can produce enough enough fruit such that they can save enough to eat one day a week on slightly old fruit, then they can invest that time they would have spent picking into something else, ideally something that will increase their infrastructure (ability to produce more goods with the same amount of work).

That’s what savings IS, ultimately.

The dollars are ultimately an agreed-upon measure of what something is worth. They don’t have value in and of themselves except in the willingness of other people to treat them as though they are an nonperishable intermediate store of value. Going back to your island analogy, this is a reason why fruit makes poor money–it doesn’t store value indefinitely, and does go bad eventually. So our heroes are constrained in their actual ability to save by the propensity of the fruit to go bad. By the same token, this is a reason why gold often makes good money–it is nonreactive enough to remain uncorrupted in storage for an effectively unlimited period of time.

If you want to posit an economy where the fruit DOES rot every day, and cannot be stored in some meaningful way, then you have both an economy where savings is nonsensical AND an analogy that is too far removed from reality to tell us anything meaningful.

Hellestal, I want to take this chance to thank you for all your posts on economics over the years; I teach AP Macro and Micro and, as I’m an English teacher by training, am pretty much entirely self-taught. Your posts have really helped me.

I have a couple questions:

This year, I had a brain flash and started telling kids that dollars are our unit of measurement, but not what we were measuring: we care about the distance from A to B, not the number of miles, but miles is what we have. ( and 2006 miles are not the same as 2012 miles). Is that accurate enough for an intro course? It’s not a phrasing I’ve seen in any of the major textbooks, but it makes sense to me.

And the reason they are producing investment goods is because that money is, one assumes, available in the loanable funds market, right? One problem I’ve found over the years is that my kids think that “real” savings is money in a coffee can, and bank savings is a less perfect type of savings, and stock even less so, and owning an apartment building is not savings at all. But it seems to be that from an economists point of view, a coffee can full of money is the worst sort of savings–inflation is rotting it away–and can hardly be called savings at all. Whereas any financial asset, be it a bank account or a bond or a stock, is savings and, because of how the system is set up, represents money available for investment spending.

Which myths? AP economics is basically 101 for majors, and while that demands stripping it down to the basics, I try really hard not to teach anything that’s actually untrue.

I spend a lot of time reminding kids that no one wants money just so that they have something to go home and roll around in. They’ve heard about businesses “raising capital” their whole lives and it’s left them with a vague sense that the financial markets are places where fat white dudes with monocles collect vast piles of cash, which then multiplies itself.

That’s great for an intro course or any course. That is exactly how I describe it myself.

Shame that that description isn’t in your textbooks. It’s the best, most accurate way of thinking about it.

That’s the conventional explanation, so you should probably stick with it. The AP people aren’t about to change their test, anyway.

However, it is… not fully accurate. I wouldn’t call it a myth, though.

The thing is: banks make money. Literally. They don’t have to wait for loanable funds. If they see a highly advantageous loan opportunity, they personally create the funds that are loaned. They print a check, credit their deposit liabilities, make a loan or purchase a security (i.e. debit assets) and that’s it. Most money is private bank money, and up pops more private bank money at the click of a mouse. Now obviously, they have way more short-term obligations than they can possibly fulfill at one time. The depositors can’t all get their money at once, and there are regulations, too. There are limits in place, it can’t go on forever. So they would really like you to deposit your check at their super happy fun bank, not the evil competitor across the street. Our deposits give them breathing room, allow them to stretch out their loans a little faster, which affects future profitability.

You see how there isn’t any clear dividing line? Banks can create money, but they’re dependent on their depositors. Banks make investments by just crediting an account, but attracting new funds helps them do it more securely. And then there’s the difference between the banking system as a whole, and individual banks. Gah.

I don’t particularly like “loanable funds”, but the students have got to start somewhere, and the truth in this particular case is just hideously complicated.

Is the money made available? Or is it created? I mean, we know loaned funds are personally created by private banks, and we also know it’s easier to invest if more money is tossed their way.

I’d like to be able to throw out a few paragraphs that clears it up, but I can’t. All I can say for sure is that if all of our workers are busy producing consumer goods, then they’re not busy producing investment goods. Putting it in the terms of actual resources, of actual people doing jobs providing consumption or building factories, makes the concepts a little cleaner. Saving is building a factory. Anything else is just pushing paper around.

The conventional story of the money multiplier is a myth. It can happen that way, but generally doesn’t. The story has the advantage of being fairly simple. The bank regulations are clear. The rules of the game are distinct. It is very vivid in clarifying the difference between the monetary base and broader forms of money. All of this is to say that it’s easier to teach than the truth. If you look below that section at Wikipedia, you see the loans-first model. This relates to endogenous money theory. It gets one paragraph. It also happens to be generally correct. It deserves at least twenty times as much explanation, but that would take a lot of class time.

Prehistoric barter exchange is also a myth. Hunter-gatherers have elaborate systems of interpersonal obligation. They don’t wait for the perfectly weighted exchange opportunity to make a barter trade. They give gifts to each other, and these gifts instill obligation on the receiver, who will eventually gift back. The whole barter thing makes it easier to see the usefulness of money, but the funny thing is, it’s a complete straw man for ease of money explanation. History wasn’t actually like that. Again, the story is easier than the truth.

I would prefer if econ education didn’t take little inaccurate short cuts.