There's no point in arguing over definitions
By Scott Sumner
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.
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.
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?
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!