Scott Sumner  

There's no point in arguing over definitions

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Economics textbooks define savings as being equal to investment:

S = I

This means savings is defined as the funds used for investment. It's derived from another identity, which says that in a closed economy with no government, gross domestic product equals gross domestic income:

GDI = C + S = C + I = GDP

David Glasner doesn't like these definitions, but for some reason that I haven't been able to figure out he doesn't say that he doesn't like the definitions, but rather he claims they are wrong. But the economics profession is entitled to define terms as they wish; there is no fact of the matter. In contrast, Glasner suggests that my claim is only true as some sort of equilibrium condition:

Scott begins by discussing the simplest version of the income-expenditure model (aka the Keynesian cross or 45-degree model), while treating it, as did Keynes, as if it were interchangeable with the national-accounting identities:
In the standard national income accounting, gross domestic income equals gross domestic output. In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.


David's characterization of my views is simply incorrect. And it's easy to explain why. I hate the Keynesian cross, and think it's a lousy model, and yet I have no problem with the national income identities, and believe they occasionally help to clarify thinking. The quote he provides does not in any way "discuss" the Keynesian cross model, just as mentioning MV=PY would not be "discussing" the Quantity Theory of Money.

David continues:

Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal.

The equality of these three variables can be thought of as a condition of macroeconomic equilibrium. When a macroeconomic system is not in equilibrium, aggregate factor incomes are not equal to aggregate expenditure or to aggregate output. The inequality between factor incomes and expenditure induces further adjustments in spending and earnings ultimately leading to an equilibrium in which equality between those variables is restored.


I can't imagine how anything important is affected by whether output is retained by the firm, or sold. In national income accounting any inventory accumulation is counted as investment. More importantly, it seems to me that David should not be focusing on me, but the broader profession. If economics textbooks define S=I as an identity, then it's clear that I'm right. Whether they should define it as an identity is an entirely different question. I happen to think it makes sense, but I could certainly imagine David or anyone else having a different view.

David is also still confused about an earlier post I did:

About three years ago, early in my blogging career, I wrote a series of blog posts (most or all aimed at Scott Sumner) criticizing him for an argument in a blog post about the inefficacy of fiscal stimulus that relied on the definitional equality of savings and investment.
I have never in my entire life made any sort of causal claim that relied solely on an identity. In other words, I never did what David claims I did. Like all economists, I may use identities as part of my argument. For instance, if I were to argue that rapid growth in the money supply would increase inflation, and that this would increase nominal interest rates, and that this would increase velocity, I might then go on to discuss the impact on NGDP. In that case I'd be using the MV=PY identity as part of my discussion, but I'd also be making causal arguments based on economic theory. I never rely solely on identities to make a causal claim.

David continues:

Scott begins by sayings that Keynesians don't deny that (ex post) less saving leads to less investment. I don't understand that assertion at all; Keynesians believe that a desired increase in savings, if desired savings exceeded investment, leads to a decrease in income that reduces saving. But the abortive attempt to increase savings has no effect on investment unless you posit an investment function (AKA an accelerator) that includes income as an independent variable.
I'm not sure why David is confused. The term "abortive attempt to increase saving" is pretty much the exact opposite of ex post increase in saving. So there is no contradiction.

Bill Woolsey also has a post on the subject. He agrees with me that David is wrong about the identities, but then accuses me of doing something that I most definitely did not do.

And so, while income equals output equals expenditure is true enough, and I can never understand why Glasner says they are not, I don't think it matters much. And so when Sumner seems to think it does matter, I find it puzzling.
Once again, and identity cannot show that group X is right and group Y is wrong about the causal relationship between A and B. Rather identities are merely useful to help clarify thinking. I plead innocent. Here's Bill:
In a closed private economy, saving must equal investment. This is a matter of definition. Saving is defined as income less consumption. All output is defined as either being consumer goods or capital goods. Consumption is spending on consumer goods and investment is spending on capital goods. All expenditure is either on consumer goods or capital goods. Since income equals expenditure, and consumption is itself, then income less consumption must equal expenditure less consumption. By the definition of saving and investment, saving and investment are always equal.

I guess someone might think that is all insightful, but it comes down to saying that purchases equals sales.


Yes, it boils down to that, but since neither David nor millions of other people agree with Bill and me, it's worth pointing out every so often.
To say that at the natural interest rate saving equals investment is like saying at the equilibrium price quantity supplied equals quantity demanded. To say that savings always equals investment is like saying that purchases always equals sales by definition.

Not just at the natural rate of interest, but always, every nanosecond, even when we are not at the natural rate of interest.
What about Sumner's argument? Suppose nominal (and real) income falls. Households don't want to cut consumption and so reduce saving. That makes sense. It is based upon what households choose to do.

Now, investment must equal saving by definition, so investment must fall more than in proportion to nominal income?

Well, no.


I wasn't just assuming that saving falls, I assumed it fell as a share of national income. Bill agrees that S=I is an identity, so I presume he agrees that if saving falls as a share of national income, so will investment.

Now of course I might be wrong about saving. I was relying on a theory, the permanent income hypothesis, which might be wrong. But if I am right that saving would fall as a share of national income, then so would investment.

If my post were addressed to professional economists, I would have stopped at the point where I claimed that the share of income saved would fall. I'd assume they would naturally draw the inference that investment would fall as well. I only brought in the identity because in the past some commenters did not follow that last step. They'd say, "suppose people saved less but investment didn't fall?" But that's impossible!

HT: TravisV


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CATEGORIES: Macroeconomics




COMMENTS (29 to date)
Kenneth Duda writes:

Scott, if S=I by definition, then if I work and earn wages and stuff them in a mattress, am I "investing" in US currency, planning to earn a 0 nominal return?

Steve Y. writes:

First, thank you for your explanation of S=I. I understood the concept 40 years ago when I took a couple of economics courses but now I couldn't explain it to save my life.

Every field of study, not just economics, has to define its terms precisely to reduce misunderstandings and advance the field. I am struck by the wisdom of your earlier post:

Macro uses a lot of terms like money, saving, interest rates, investment, income, demand, unemployment, inflation, exchange rates, debt, deficits, etc., that seem to correspond to things in our everyday experience. And we obviously do have opinions on things in our everyday experience. And we are entitled to those opinions. But in fact almost none of these terms mean the same thing in macro as in everyday life.
In my own field of accountancy, for example, the definition of "depreciation"---the allocation of cost across time periods---is not the first meaning that would come into people's minds. Depreciation expense is popularly conceived as "wear and tear" or "reduction in value with age", and "allocation of cost" usually attracts blank stares. However, this definition is necessary to make progress across a whole range of accounting matters, e.g., M&A and accounting for income taxes.

I will never achieve a master's level of understanding in economics (or biochemistry or string theory), but thank you for providing a window into your world.

Keith E. writes:

Another headache with such an identity is that GDP = C + I is just a distribution statement (or source statement) at a point in time. At any point in time (any snapshot), GDP = C + I.

Such an identity says nothing about how things change over time: what causes/enables a change in GDP or C + I. There seems to be much confusion in the world on that front too.

Andrew_FL writes:

I think it would be helpful to refer to, instead of "savings" or "saving" two separate things:

Deferred Consumption-The intuitive meaning of the word "saving."

The Supply of Loanable Funds-The Macroeconomic definition of S.

Hoarding money is deferring consumption. It is not supplying loanable funds, unless hoarding of bank liabilities allows banks to safely expand their investment loans.

E. Harding writes:

The I=S definition (I think) only applies to a closed economy; in open economies there are typically substantial levels of net lending or net borrowing.
http://research.stlouisfed.org/fred2/series/W994RC1Q027SBEA

Mark V Anderson writes:

I am really confused by this second posting now that says I=S. I thought there was an important economic graph called the IS graph that compares savings to investment, which is determined by the interest rate. So that as interest rates go higher then more savings goes into investment.

Also I thought that was the whole point of people arguing that aggregate demand was too low -- people's savings are just sitting there and not being used for either consumption or investment. In fact Obama has constantly complains about corporations saving too much money and not investing it.

Actually this has always been one of my biggest beefs about macro-economists -- in my mind S=I has always been mostly true, but the powers that be make it sound like it is not true and that it matters greatly. It sounds like this is one of those areas where I simply don't understand what you professional economists really mean.

BC writes:

@Kenneth Duda, I believe that wages stuffed in your mattress are savings for you and investment by *your employer*. (When your employer paid you, those wages were investment.) So, over the whole economy, savings and investment increased by the same amount, S=I.

Alternatively, if a consumer paid you for some service and you stuffed the cash in a mattress, then that consumer's savings decreased by the amount that your savings increased. Thus, there is an increase in C, no *net* change in S, and no net change in I. Again, S=I.

In a previous post [http://www.themoneyillusion.com/?p=28620], Scott linked to this post by Harless [http://blog.andyharless.com/2009/11/investment-makes-saving-possible.html], which I think does a good job in explaining why S=I. The key seems to be to consider the whole economy, recognizing that a dollar received by one person is paid by someone else. That's why S=I is an identity.

Miguel Madeira writes:

"I thought there was an important economic graph called the IS graph that compares savings to investment, which is determined by the interest rate. So that as interest rates go higher then more savings goes into investment."

IS does not compare savings to investment - it is a list of possible combinations [income, interest rate] where saving=investment.

bill woolsey writes:

Ken:

Investment is spending by firms on capital goods and really has nothing with what assets you accumulate or the return you expect to make.

If you choose to spend less on consumer goods and stuff U.S. currency in your mattress, the the investment that would match that is the accumulation of consumer goods that are not sold by the firms that would have sold them to you.

Yes, not spending on capital goods, really, but acccumulation of unsold inventories of consumer goods counts as inventory investment.

Of course, things might work out better than that. It could be that your decision to spend less on consumer goods and stuff currency in the mattress will be matched by some firm buying new capital goods.

Having additional U.S. currency created and the right interest rates would help that work out.

Rob Rawlings writes:

Scoot,

Can you clarify 'I'm not sure why David is confused. The term "abortive attempt to increase saving" is pretty much the exact opposite of ex post increase in saving. So there is no contradiction.'

He quotes you as saying that:

'Keynesians don't deny that (ex post) less saving leads to less investment'

While he states that in the Keynesian model :
'the abortive attempt '

These seem like alternative views so I'm not sure how your statement clarifies your differences. Can you explain ?

Kenneth Duda writes:

Bill, thanks for the answer but I am still confused.

Scott says S=I as a matter of definition. But say I work, stuff cash in my mattress, and give a clear advance signal to producers that I will not spend, and that signal propagates up the supply chain so that there is no inventory accumulation, and people who would have been employed to make goods for me wind up unemployed instead. Is my savings matched by the imputed value of the unemployed workers' leisure? Because that is a very dissatisfying "investment".

-Ken

Scott Sumner writes:

Ken, If you put cash under a mattress then you may personally be saving, but the person you got the cash from is dissaving an equal amount.

Thanks Steve.

Keith, That's right.

Andrew, You can have a loanable funds market in a country with zero investment.

E. Harding. That's right, of course it works at the global level.

Mark, Unfortunately, there is a lot of misinformation about saving and investment.

Rob, In the Keynesian model the public may attempt to save $500 billion, but end up saving only $450 billion ex post. So the level of investment ($450 billion) is less than the attempted saving, but equal to the ex post actual saving.

Ken, You said:

"Scott says S=I as a matter of definition."

Just to be clear this is not my opinion, but rather the official definition in economics textbooks.

Market Fiscalist writes:

'But if I am right that saving would fall as a share of national income, then so would investment'

Well, if I=S then, yes , (by definition).

But in the Keynesian model I is an exogenous variable, from which S is derived (via the multiplier). So if I is assumed to be exogenous, and the saving function changes, it is S that has to do the adjusting.

So:
Y changes due to a change in the consumption function
I stays the same as its exogenous
S is adjusted via the multiplier to match the exogenous I.

But (as I think David points out): We need a process to get from the change in C to the new I=S (this is provided by the multiplier). During this process I will NOT = S until we reach the new equilibrium. Initially S falls but I remains the same.

So something has to give. Either the definitions don't match the reality of this model, or there is a logical inconsistency in the Keynesian model.

I suspect that the difference maybe between planned and unplanned investment (and inventory build-up) but can't quite think it through.


(Please forgive the "thinking aloud" nature of this post - I'm genuinely trying to understand this discussion).

Andrew_FL writes:

@Scott Sumner-I meant, not counting consumption loans. Which would just be someone deferring consumption, and someone else engaging in consumption instead.

vikingvista writes:
the person you got the cash from is dissaving an equal amount.


How can that person be dissaving, unless dissaving equals consumption?

Rick Hull writes:

Hm, this whole dissaving thing seems awfully suspect. If I put that money under the mattress, then the guy who paid me those dollars (i.e. my employer, most likely) is dissaving. But if, alternatively, I go and spend the money, either for consumption or maybe a financial asset, then would we really change the category of my employer's action (paying me for my labor)? If so, this type of explanation is unsatisfying at best. If not, then it seems like the dissaving happens when I get my paycheck, not when I decide what to do with it.

Kevin Dick writes:

@vikingvista:

I think this is pretty much the entire point. In a closed economy with no government, dissaving does in fact equal consumption. That's what the identity says.

NGDP = C + I
S = I

NGDP = C + S

So at a given level of NGDP, every dollar that you dissave _must_ be defined as consumption.

If "D" is the number of dollars dissaved, then:

NGDP = (C + D) + (S - D)

Again, this is simply definitional.

BC writes:

Rick, when you spend the money, your savings goes down but the recipient of the money increases his or her savings. Total savings remains unchanged, so no change is necessary to your employer's category. Again, I would recommend reading Harless [http://blog.andyharless.com/2009/11/investment-makes-saving-possible.html].

The identity is just an accounting of how a dollar received (saved) by you is spent by someone else. The other party can be
(1) a consumer (offsetting decrease in S) or
(2) a business (increase in I).
If we add government and foreigners, then the payer could also be
(3) government (offsetting decrease in public saving) or
(4) foreigner (increase in net exports).
Then, we get private+public saving equals investment + net exports.

Rick Hull writes:

BC, thanks, and I don't disagree, but your response seems tangential. My concern regards Scott's reply to Kenneth, where Kenneth questions whether money under the mattress is an investment. My intuition says savings has occurred without any corresponding investment. Scott counters that my paycheck is dissavings by my employer, implying net savings and investment are both zero.

OK, but what if I alternatively buy a financial asset. Now savings are negative and investment is positive, just looking at me and my employer and my paycheck action. Someone else has my paycheck money of course, but maybe I just bought a stock share from my own employer.

If S=I just says that cash is always held by *someone*, fine. But I do not see how the definition holds above, or in common economic policy analysis. Are we just assigning different names (S and I) to the same variable?

EB writes:

Rick Hull,

We have to distinguish stocks and flows. If we are analyzing what happens at a point in time when John hides a one-dollar bill under the mattress, so we are talking about the stock of currency and we are assuming that the stock of currency doesn't change. Now if John had the bill in his pocket, it doesn't matter at all. If John sold anything to get the bill, then someone else has handled him a one-dollar bill and he hided it under the mattress. Indeed, totally irrelevant to the understanding of the macroeconomy. Scott is talking about irrelevant situations and therefore you can ignore what he says.

Now let us assume that John sold his collection of old cars to the government and he was paid one trillion dollars for his collection. Then he hided these dollars under the mattress (a big one), then we are talking about a large increase in the stock of currency but as long as John keeps all his dollars under the mattress there has been a matching increase in the demand to hold currency and nothing happens. This is the case that usually Paul Krugman has in mind. But please take note that the purchase of John's collection amounted to an increase in government expenditure that has been financed by seignorage.

Now let us assume the same sale of John's collection but John's spends all the revenue in new cars. But if we assume that the purchase of John's collection of old cars was an excuse for government to give away a trillion dollars in order to stimulate the economy, then we are talking about Milton Friedman's helicopter. Again government expenditure has increased by the amount of the transfer to John and it has been financed by seignorage. But this time, since John spends the new dollars, private consumption will increase (you can also assume that John saves part of the gift and invest in bonds, so the macro effect will depend on how the seller spends the revenue). Whenever we talk about government expenditures, consumption, investment and saving we are talking about flows (and remember that some flows imply corresponding increases or decreases of stocks over time).

Scott writes:
S = I is a definition. Savings is defined as the funds used for investment. (*1)
GDI = Consumption + S = Consumption + I = GDP
In national income accounting any inventory accumulation is counted as investment.

Bill Woolsey writes, and Scott agrees:
"Saving is defined as income less consumption. All output is defined as either being consumer goods or capital goods. Consumption is spending on consumer goods and investment is spending on capital goods (*2)."

Scott: Ken, If you put cash under a mattress then you may personally be saving, but the person you got the cash from is dissaving an equal amount.

[AMG: So, income is immediately savings, offset by the dissaving of the employer. Income is a transfer of savings. Any consumption reduces savings, leaving the rest of income as savings by definition. ]

Rob, In the Keynesian model the public may attempt to save $500 billion, but end up saving only $450 billion ex post. So the level of investment ($450 billion) is less than the attempted saving, but equal to the ex post actual saving. (*3)

---
(*1) It seems incorrect that savings is "the funds used for investment". From the other statements and definitions, savings is whatever is not consumed, whether it is cash put in a mattress or cash exchanged for other investments.

(*2) Again, investment is not "spending on capital goods". Anything not spent on consumption is savings = investment. No spending is needed.

(*3) If savings = investment by definition, then how is it possible to attempt to save $500 but end up saving $450. When you start with $500 in cash, that is already savings = investment. You have saved it, whether you put it in the mattress or buy an asset.

It seems to me that given these definitions, one can say very little about savings and investment in an economy, by definition. One can define things as one wishes, but is this definition of savings = investment useful for discussion? It seems to produce endless confusion.

vikingvista writes:

Kevin Dick,

Thanks. That clarifies it. I wasn't presuming to argue economic jargon with an economist.

But just as economists define "perfect competition" as a state in which competition is impossible (and any degree of competition is referred to as a degree of "monopoly"), the notion that you can be "dissaving" something you've completely relinquished, or that you are only "saving" of your deferred consumption contributes to loanable funds, certainly flies in the face of how those terms were used prior to economic jargon, or how they are used outside of economics today.

I'm sure the question is moot, but I do wonder why economists would redefine existing terms in such odd ways.

Scott Sumner writes:

Market Fiscalist, You said:

"During this process I will NOT = S until we reach the new equilibrium. Initially S falls but I remains the same."

Not so, S=I during every single nanosecond, that's what it means to be an identity.

Andrew, OK.

Vikingvista. These equalities only apply at the macro level. If one person saves more it is not necessarily true that aggregate investment rises.

Regarding the odd definitions, unfortunately common sense definitions are not at all useful in macro, due to the fallacy of composition. What's true for the individual is not true for the group.

Rick, You said:

"If not, then it seems like the dissaving happens when I get my paycheck, not when I decide what to do with it."

That's right, I should have made that clearer.

Andrew Garland, I certainly agree that the distinction between planned and actual saving is not very useful. But it's not wrong. I may start the year expecting to save X amount, and then lose my job. I'll end up saving less than I planned to.

Regarding your other point, in this simple model all goods are either investment or consumption goods.

vikingvista writes:
These equalities only apply at the macro level. If one person saves more it is not necessarily true that aggregate investment rises.

Instead of S=I being a *definition*, then isn't it *derived* from the microeconomic definitions by applying closed system aggregation?

Fralupo writes:

Let me see if I can reach back into my intro to macro memory.

S≡I. This means that for every quantum of investment there is an equal amount of saving somewhere in the economy. If this weren't the case it would mean that the economy was either spending more than its income (i.e consumption + investment somehow was greater than the total amount that everyone had to spend) or spending less than its income (i.e. someone earned income without someone paying it to them). Neither make sense, because in the economy spending equals income.

Right?

J.V. Dubois writes:

Fralupo: that is one way to think about it but it really does not make sense. I will try another example of identity:

2 + 3 = 5

If two plus three does not equal 5 it means that 5 - 3 is either greater or lower than 2. Technically correct but not particularly enlightening. In reality there may never even be the case wher 2 + 3 is not equal 5 or 5 - 3 is not equal to 2.

The magic bullet in all these discussions is DEFINITON OF SAVING. Saving is income not spent on consumer goods. That is all there is.

Ricardo writes:

"I never rely solely on identities to make a causal claim."

Indeed, you even praised Nick Rowe for making the reason for this clear:
http://econlog.econlib.org/archives/2014/07/nick_rowe_on_fi.html

M. writes:

S = I is an equilibrium concept.

"Not so, S=I during every single nanosecond, that's what it means to be an identity."

Then there is no AD or AS...

S = I is an equilibrium result, just as supply = demand.

S = supply of funds / demand of debt
I = demand of funds / supply of debt

Just think of this: there's a shock to the discount rate, people discount the future much more than before. Savings fall. Why would investment? Because the interest rate increases. Prices adjust to restore equilibrium.

M. writes:

Sorry for the double post.

S = I ex-post for sure (in the data). As supply = demand ex-post.

But not ex-ante (before exchanges are realized). If prices do not adjust, there is rationning at the equilibrium (or disiquilibrium), that's what David Glaesner means.

And the whole of macro. is concerned with why S = I ex-ante (liquidity trap etc.).

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