David Glasner and Scott Sumner are arguing about whether saving = investment is an identity or an equilibrium condition. So I thought I would step in and resolve this dispute. Instead of using textbook accounting identities, let’s consider a framework everyone is familiar with — a two-period consumption model.

1. Consider a Robinson Crusoe economy. There is one guy on an island with production opportunities, but no market opportunities. For simplicity, think of a two-period model. In the first period, the individual receives an endowment, Y. The individual can invest that endowment to generate future production or consume the endowment. The individual transforms Y into P1, production now, and P2, production later. It follows that investment is defined as I = Y – P1. Savings is defined as S = Y – C1, where C1 is consumption in the first period. Since there is only one guy on the island, it must be true that P1 = C1. These decisions are both determined by the individual’s rate of time preference. Thus, S = I is an identity.

2. Consider the same guy on an island, but who now has market opportunities. Now we have the same definitions for saving and investment. Saving is

S = Y – C1

I = Y – P1

Note that with exchange opportunities, it is very unlikely that C1 = P1. Thus, at the individual level, savings probably doesn’t equal investment. Combining these conditions, we get

S = I + P1 – C1

for the individual. Now sum across all terms and we get

Now in equilibrium, market-clearing requires that total production equals total consumption. Thus, market clearing implies that total savings is equal to total investment:

Saving = Investment is therefore an equilibrium condition.

3. Finally, David’s issue is that he doesn’t think that gross domestic income and gross domestic expenditure are the same thing. Empirically, he’s correct. This is why we have GDP Plus.

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It is neither an identity nor an equilibrium condition, for the obvious reason that the total inputs and outputs to both sides of the entities of this over-simple model are insufficient to properly represent anything like the true situation. Were all of these entities properly included (there are at least 6, see model below) then the input = output equation for each entity is indeed an identity. Equilibrium is when the exchanges between the entities are in balance (demand money = supply goods value) and more correctly when they tend to reduce the magnitudes of the remaining differences. A suitable model may be seen as FuncDiagMacroSyst.pdf which is in Wikimedia, commons, macroeconomics.