Sumner has repeated his claim that saving and investment are always equal as a matter of definition. Glasner has taken him to task. As always, I disagree with both of them.
Sumner is correct, but makes the same error as Keynes in giving these identities much significance.
I think Glasner is pretty much in error about the identities, but is correct that the equilibrium conditions are all that matter.
In my teaching, I have long emphasized what I was told is the "basic identify of macroeconomics." This identity is income equals output.
The reason that it is true, and true by definition is that profit is both defined to be a part of income and also as the value of output minus the other sorts of incomes--wages, interest and rents. Wages, interest, and rents usually involve some flow of funds from the firms, though they can just be an accrued cost. And the value of output usually represents a flow of funds to firms, but output that is unsold or else sold with no funds collected still counts.
Anyway, with profit being output minus other sorts of income, then by the definition of addition and subtraction, output must equal profit plus other sorts of income. Since profit plus other sorts of income is income (in total,) then income equals output.
That output equals expenditure is also an identity. That is because all output is counted as having been purchased by someone. And while most output is sold and purchased by some buyer, that part of output that is not purchased by anyone counts as inventory investment. The firm that produced it and did not sell it is counted as having purchased it.
Now, with expenditure equal to output due to inventory investment, and output equal to income because of the definition of profit, then by a matter of the definition, income equals expenditure.
The big fudge factor here is the profit on inventory investment. If firms produce something with the intention that they will sell it to someone else, and they don't, the payments they would have received as profit if they had sold it is counted as part of profit and so income. What kind of income is that? It is hardly something you can spend.
The equilibrium condition that Glasner emphasizes is that firms will not produce output to obtain these pseudo-profits, and so will adjust output to sales plus desired inventory investment. In other words, firms will adjust production to avoid unplanned inventory investment.
I am embarrassed to admit that it was just over the last few years after reading Nick Rowe it became obvious to me that much of this is irrelevant for the service sector--not a small consideration. The actual output of the services necessarily equals the expenditures on services. And so expenditures on services must then always equal income from services (including profit or loss.)
As I have pointed out before, this is equivalent to pointing out that purchases and sales for some good are equal. Spending by buyers matches receipts to sellers.
But, of course, in microeconomics, we are concerned with quantity supplied equaling quantity demanded, which involves planned purchases and sales--an equilibrium condition.
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.
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.
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.
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. What causes firms to choose to spend less on capital goods? It isn't that the definitions make them do it. Real firms have to choose not to order up capital goods. Now, if they didn't cut back their capital spending, then perhaps nominal income wouldn't have decreased as much after all.
Consider the expectation that nominal income will fall. Households respond by cutting consumption now, but just a little because of consumption smoothing. Firms cut planned investment a lot. But it is because the reduction in expected sales causes them to want to cut investment a lot, and it is that actual decision by firms that causes current nominal income to fall more than in proportion to the decrease in consumption. It isn't that there is a given decrease in nominal income and because consumption falls less than in proportion to the decrease in nominal income, investment must fall more than in proportion to the decrease in nominal income. The decrease in velocity (or increase in money demand) or even the decrease in the quantity of money due to the expectation of lower future nominal income depends on the decisions of the firms and households.