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. Here’s the statement I found objectionable.
Wren-Lewis seems to be . . . making a simple logical error (which is common among Keynesians.) He equates “spending” with “consumption.” But the part of income not “spent” is saved, which means it’s spent on investment projects. Remember that S=I, indeed saving is defined as the resources put into investment projects. So the tax on consumers will reduce their ability to save and invest.
I’m not going to quote any further from that discussion. If you’re interested here are links to the posts that I wrote (here, here, here, here, here, and this one in which I made an argument so obviously false that, in my embarrassment, I felt like giving up blogging, and this one in which I managed to undo, at least partially, the damage of the self-inflicted wound). But, probably out of exhaustion, that discussion came to an inconclusive end, and Scott and I went on with our lives with no hard feelings.
Well, in a recent post, Scott has again invoked the savings-equals-investment identity, so I am going to have to lodge another protest, even though I thought that, aside from his unfortunate reference to the savings-investment identity, his post made a lot of sense. So I am going to raise the issue one more time – we have had three years to get over our last discussion – hoping that I can now convince Scott to stop using accounting identities to make causal statements.
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.
There is a lot of ground to cover in these few lines. First of all, there are actually three relevant variables — income, output, and expenditure – not just two. Second aggregate income is not really the same thing as consumption and savings. Aggregate income is constituted by the aggregate earnings of all factors of production. However, an accounting identity assures us that all factor incomes accruing to factors of production, which are all ultimately owned by the households providing services to business firms, must be disposed of either by being spent on consumption or by being saved. Aggregate expenditure is different from aggregate income; expenditure is constituted not by the earnings of households, but by their spending on consumption and by the spending of businesses on investment, the purchase of durable equipment not physically embodied in output sold to households or other businesses. 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.
So what Scott should have said is that because NGDI and NGDP are equal in equilibrium, any model that explains one will, ipso facto, explain the other, because the equality between the two is the condition for finding a solution to the model. It therefore follows that savings and investment are absolutely not the same thing. Savings is the portion of household earnings from providing factor services that is not spent on consumption. Investment is what business firms spend on plant and equipment. The two magnitudes are obviously not the same, and they do not have to be equal. However, equality between savings and investment is, like the equality between income and expenditure, a condition for macroeconomic equilibrium. In an economy not in equilibrium, savings does not equal investment. But the inequality between savings and investment induces adjustments that, in a stable macroeconomic system, move the economy toward equilibrium. Back to Scott:
Nonetheless, I think if we focus on NGDI we are more likely to be able to think clearly about macro issues. Consider the recent comment left by Doug:
Regarding Investment, changes in private investment are the single biggest dynamic in the business cycle. While I may be 1/4 the size of C in terms of the contribution to spending, it is 6x more volatile. The economy doesn’t slip into recession because of a fluctuation in Consumption. Changes in Investment drive AD.
This is probably how most people look at things, but in my view it’s highly misleading. Monetary policy drives AD, and AD drives investment. This is easier to explain if we think in terms of NGDI, not NGDP. Tight money reduces NGDI. That means the sum of nominal consumption and nominal saving must fall, by the amount that NGDI declines. What about real income? If wages are sticky, then as NGDI declines, hours worked will fall, and real income will decline.
So far we have no reason to assume that C or S will fall at a different rate than NGDI. But if real income falls for temporary reasons (the business cycle), then the public will typically smooth consumption. Thus if NGDP falls by 4%, consumption might fall by 2% while saving might fall by something like 10%. This is a prediction of the permanent income hypothesis. And of course if saving falls much more sharply than gross income, investment will also decline sharply, because savings is exactly equal to investment.
First, I observe that consumption smoothing and the permanent-income hypothesis are irrelevant to the discussion, because Scott does not explain where any of his hypothetical numbers come from or how they are related. Based on commenter Doug’s suggestion that savings is ¼ the size of consumption, one could surmise that a 4% reduction in NGDP and a 2% reduction in consumption imply a marginal propensity to consumer of 0.4. Suppose that consumption did not change at all (consumption smoothing to the max), then savings, bearing the entire burden of adjustment, would fall through the floor. What would that imply for the new equilibrium of NGDI? In the standard Keynesian model, a zero marginal propensity to consume would imply a smaller effect on NGDP from a given shock than you get with an MPC of 0.4.
It seems to me that Scott is simply positing numbers and performing calculations independently of any model, and then tells us that the numbers have to to be what he says they are because of an accounting identity. That does not seem like an assertion not an argument, or, maybe like reasoning from a price change. Scott is trying to make an inference about how the world operates from an accounting identity between two magnitudes. The problem is that the two magnitudes are variables in an economic model, and their values are determined by the interaction of all the variables in the model. Just because you can solve the model mathematically by using the equality of two variables as an equilibrium condition does not entitle you to posit a change in one and then conclude that the other must change by the same amount. You have to show how the numbers you have posited are derived from the model.
If two variables are really identical, rather than just being equal in equilibrium, then they are literally the same thing, and you can’t draw any inference about the real world from the fact that they are equal, there being no possible state of the world in which they are not equal. It is only because savings and investment are not the same thing, and because in some states of the world they are not equal, that we can make any empirical statement about what the world is like when savings and investment are equal. Back to Scott:
This is where Keynesian economics has caused endless confusion. Keynesians don’t deny that (ex post) less saving leads to less investment, but they think this claim is misleading, because (they claim) an attempt by the public to save less will boost NGDP, and this will lead to more investment (and more realized saving.) In their model when the public attempts to save less (ex ante), it may well end up saving more (ex post.)
I agree that Keynesian economics has caused a lot of confusion about savings and investment, largely because Keynes, who, as a philosopher and a mathematician, should have known better, tied himself into knots by insisting that savings and investment are identical, while at the same time saying that their equality was brought about, not by variations in the rate of interest, but by variations in income. Hawtrey, Robertson, and Haberler, among others, pointed out the confusion, but Keynes never seemed to grasp the point. Textbook treatments of national-income accounting and the simple Keynesian cross still don’t seem to have figured this out. But despite his disdain for Keynesian economics, Scott still has to figure it out, too. The best place to start is Richard Lipsey’s classic article “The Foundations of the Theory of National Income: An Analysis of Some Fundamental Errors” (a gated link is available here).
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. The accelerator was later added to the basic Keynesian model Hicks and others in order to generate cyclical fluctuations in income and employment, but non-Keynesians like Ralph Hawtrey had discussed the accelerator model long before Keynes wrote the General Theory. Scott then contradicts himself in the next sentence by saying that Keynesians believe that by attempting to save less, the public may wind up saving more. Again this result relies on the assumption of an accelerator-type investment function, which is a non-Keynesian assumption. In the basic Keynesian model investment is determined by entrepreneurial expectations. An increase (decrease) in thrift will be self-defeating, because in the new equilibrium income will have fallen (risen) sufficiently to reduce (increase) savings back to the fixed amount of investment entrepreneurs planned to undertake, entrepreneurial expectations being held fixed over the relevant time period.
I more or less agree with the rest of Scott’s post, but Scott seems to have the same knee-jerk negative reaction to Keynes and Keynesians that I have to Friedman and Friedmanians. Maybe it’s time for both of us to lighten up a bit. Anyway in honor of Scott’s recent appoint to the Ralph Hawtrey Chair of Monetary Policy at the Mercatus Center at George Mason University, I will just close with this quotation from Ralph Hawtrey’s review of the General Theory (chapter 7 of Hawtrey’s Capital and Employment) about Keynes’s treatment of savings and investment as identically equal.
[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.