Savings and Investment: Sorting Out Confusion Over Definitions

A Bit More on Savings and Investment

by Steve Randy Waldman,

Steve Roth (1, 2), Scott Sumner (1, 2, 3), Bill Woolsey, and Matt Yglesias have been debating questions of saving versus investment and paradoxen of thrift. See also JW Mason in the comments here, and Simon Wren-Lewis a while back. Cullen Roche reminds us that, even under conventional definitions, the accounting identity S≡I only holds for a closed economy without government spending, and of JKH’s useful tautology S=I+(S-I). [See Update below.] I think the recent recrudation of these issues owes something to Garett Jones’ and my conversation on capital taxation, which Jones has continued and on which Matt Bruenig has weighed in.

As is often the case, I think that the protagonists agree more than we think we do. Our various allegiances — to schools or tribes or policy ideas — exploit the ambiguity of language to manufacture conflicts, through which we reassure ourselves that we are right and they are wrong. (And no, math doesn’t help much, because we must map it arbitrarily to the same ambiguous language for it to be of any use.) Now I will reassure myself that I am right and they are wrong.

I think we have all agreed, one way or another, that the K in a Ramsey model does not map easily to the financial investment whose (non)taxation we debate in the real world. If new cash or government debt can be understood as a kind of capital good, it’s not obvious that it behaves similarly to the physical capital in an aggregate production function. It might, but you’d have to do some work to persuade us. If the conjunction savings supplied, investment demanded, and “at potential” total expenditure depends upon interest rates or other financial variables that may vary independently, there is no reason to believe that privileging saving will unconditionally promote investment, qua Chamley-Judd logic. Savings supplied may not be the bottleneck.

Update: Ramanan (1, 2) and Hellestal say I’m wrong to write that -

“even under conventional definitions, the accounting identity S≡I only holds for a closed economy without government spending”.

They make a very good case! But in doing so, they remind us of the ambiguities and limitations of this “conventional” framework. In the current conversation, we are most immediately confronted by an ambiguity surrounding the letter S. When people say that S ≡ I, they mean total savings equals total investment. But in many of the conventional equations used to discuss this stuff, S is refers only to private savings. That leaves tiny fragile minds like mine liable to confusion. Stealing a lot from Ramanan and Hellestal, in conventional accounting, savings are defined simply as the residual between what is produced and what is consumed (both by private parties and by government). Let’s consider a closed economy:

Equation 1 says production is comprised of the resources that we consume (C by definition), that the government consumes (G by definition), and whatever is left over, which is evocatively but perhaps misleadingly designated I for investment. But, as commenter Eric L emphasizes, in these accounts I is just a residual. It refers to whatever resources are not consumed (either by private parties or by government).

Equation 3 is most easily understood as a decomposition of claims on the resources produced. We choose to decompose these into the claims made by government (T), the claims of private consumers to precisely the resources they consume (C), and the claims of private parties on production extinguished by neither taxation nor private use (S). We reconcile the disposition of claims with the disposition of resources in equation 4. This tells us that private savers’ claims to production (at the moment of production, before any real investment outcomes have a chance to muddy things up) include the resources no one used (I by definition) and the resources the government used in excess of the taxes the government claimed.

To keep things clean, let’s adopt, um, a convention. When we use the word “savings” we should refer to claims. When we use the word “investment” we should refer to real resources. Let’s then separate “savings” from “investment”, claims from resources, in Equation 5:

Equation 6 is what we should really mean when we say S ≡ I (even though algebraically it doesn’t because we mean different things by S). That is to say that total claims on unconsumed resources must equal the quantity of unconsumed resources. I, by definition, for a closed economy, represents unconsumed resources. (T - G) represents the claims government has made on resources by taxation in excess of the resources the government has actually consumed. S represents the claims on resources left to private parties after consumption and taxation. If we call the claims of the state “government savings”, the claims of private parties “private savings” and unconsumed resources “investment”, then we can write:

So, yay! This is true by definition. It is just a way of saying that balance sheets must balance. It says that total claims on resources must always be equal to the total quantity of resources to be claimed.

But before we get all triumphalist, let’s emphasize how unhelpful this mostly is. First, it is simultaneously conventional to claim that S ≡ I and to write equations in which S refers to private savings, which is not equal to I. It is conventional to claim that the letter I represents “investment”, when in fact it represents any resources that are unconsumed. In a hypothetical, instantaneous sense, unconsumed resources mean resources available for consumption. In an actual sense, much unconsumed production (as vlade emphasizes) goes to waste. I is not “investment”, in the ordinary meaning of the word. It is simply resources that are not consumed in a certain period, regardless of what befalls them. Cars produced and not consumed become “inventory investment”. That’s fine. But electricity produced and not consumed? It dissipates as heat. Bread produced and not consumed grows moldy. The product of a university, when left unemployed, becomes less employable. Trees cut and “invested” in unsellable desert homes get accounted as investment, but fail to contribute to future production.

So we can argue. Maybe stuff that’s wasted should get embedded in C, which keeps “investment” more accurate by doing violence to the commonsense meaning of consumption. But we can’t really embed “bad investment” in consumption, because we can’t know which investment is bad. The letter Y usually gets mapped to “gross domestic product”, but if we want to sum across periods and keep our stocks and flows consistent, when we do our Period 2 accounts, we must define Y as a net product, and include any losses and misadventures that befell our old “investment” in the new period’s I. (We refer to this as a “valuation adjustment.) Again, the use of conventional mappings between letters in the equations (“Y”) and real-world referents (“GDP”) will mislead us. Alternatively, we can keep the periods separate and let Y ≡ GDP, but then we will need to impose valuation adjustments when summing savings and investment across periods to account for actual investment outcomes.

The framework grows shabbier still when we consider an open economy. Equations 1 and 2 become

But now we’ve really mixed up our treatment of resources and claims. Equation 2 defined resources unconsumed as total savings, but equation 9 redefines it as the resources we have failed to consume, but that may have been consumed by others. Hmm.

Equation 10, the open-economy analog of equation 5, is a very useful decomposition of private savings. It stands at the core of MMT-ish intuitions about how a putatively savings-hungry private sector might be accommodated, and inspires JKH’s very clean reminder that private savings represent claims on domestic investment plus some other claims that can’t be mapped to domestic investment. But it might suggest to the incautious that all exported goods are matched by domestic claims, and that those claims against foreigners are good and stable and should be valued at par. In real terms, that is almost never true. The NX component of “investment”, like the I component, is unstable, and if we carry these accounts forward in time, we’ll have to include valuation adjustments there as well.

None of this is to say that this is a “bad” accounting framework. The only thing that’s really terrible is the inconsistent conventions, under which S sometimes means total saving and sometimes private saving. The deeper difficulties would be shared by nearly any accounting framework. In the accounting of private firms, it is not easy to classify “expenses” vs “capital investment”, just like it’s hard to distinguish consumption and investment in national accounts. In corporate accounting, there are valuation adjustments and statements of “other consolidated income” to reconcile differences between values between period t and period (t+1) that cannot be accounted for by current period undistributed profits. The real world is unruly, yet accounts must be defined. The accounts must find ways to track the unruliness of reality rather than expect the world to conform to simple definitions.

However, whenever anybody tries to make a substantive point by quoting S ≡ I, they are offering no insight at all into any nontrivial question. They are saying nothing more or less than balance sheets must balance. They reveal nothing whatsoever about how. It certainly doesn’t mean that the production of new claims (“savings”) is necessarily matched by the production of new resources (“investment”). It just reminds us that, if the new claims are not matched by real resources, we shall have to devalue the claims of others if we wish to keep our accounts straight.

This whole conversation started with questions about whether the S ≡ I identity somehow implies that real-world savings vehicles are necessarily matched by investment in the Ramsey/Chamley/Judd sense. The answer to that question is unequivocally and irrefutably “no”.  Real-world savings vehicles need not be matched by any investment whatsoever.  Suppose I purchase shares in a mutual fund which then lends it on as consumer loans that finance vacations.  In a macroeconomic sense, there is neither savings nor investment, my saving is matched by vacationers’ dis-saving, resources are consumed and none are invested.  S ≡ I = 0 Nevertheless, my shares in the fund would yield returns in forms like dividends, interest, and capital gains. No matter how hard you squint at accounting identities, nothing in the logic of Chamley and Judd suggests that these “investment returns” should remain untaxed. Lending to finance private and government consumption represents a significant fraction of gross financial savings, even though it contributes nothing to net savings or the aggregate investment Chamley and Judd presume.

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