Friday, January 16, 2009

More about Stimulus and Eugene Fama

Continuing from my previous post to address subsequent arguments...

Eugene Fama acknowledges a point that Brad DeLong made about inventories (that much or all of the reduced investment from a fiscal stimulus is unintended inventory investment, which is technically counted as investment but which is not useful). Professor Fama argues that the amount of unintended inventory investment is not very large.

But again I take issue with both the original Fama argument and the DeLong counterargument. First, consider the latter. The Keynesian model does not depend on inventories. Economists often teach the model to undergraduates without mentioning inventories. And yet in the Keynesian model (in the simple version, or when there is a liquidity trap), private investment does not get displaced by the increased federal deficit. Rather private savings increases just enough to finance the increased deficit.

For example, suppose there is $100 billion tax cut, and suppose the marginal propensity to consume is 0.8. The people who receive the cut save $20 billion. The people in the first round of multiplier effects get $80 billion in extra income and save $16 billion of that. And so on. As I hinted in my previous post, if you calculate the infinite sum (or estimate it by simulation, if you don't like calculus), it comes to exactly $100 billion. It's no accident that the additional savings exactly compensates for the government's additional borrowing.

The Keyensian model is a reasonable special case in which the compensation is exact. More generally, I think it would be unreasonable to expect private savings not to rise at all in response to an increased deficit, and indeed, in the case where there is a liquidity trap, I think the exact compensation in the Keynesian model is a very good approximation to what would actually happen.

Per Professor Fama:
I want to restate my argument in simple terms.
  1. Bailouts and stimulus plans must be financed.

  2. If the financing takes the form of additional government debt, the added debt displaces other uses of the funds.

  3. Thus, stimulus plans only enhance incomes when they move resources from less productive to more productive uses.
Are any of these statements incorrect?
As to the first point, it depends on what you mean by "financed." Certainly the government needs to obtain cash, but that's a rather trivial matter. The Fed can create any cash the government needs, and as I argue elsewhere, such money creation isn't even necessary when the interest rate is zero, because T-bills have become essentially equivalent to money. In the purely monetary sense of the word "finance," the Treasury can effectively finance the stimulus by printing its own money.

But I don't think the argument is about financing in the strictly monetary sense. The savings-investment equation, which is presented as central to the argument, says that
in any given year private investment must equal the sum of private savings, corporate savings (retained earnings), and government savings (the government surplus, which is more likely negative, that is, a deficit)...
The issue is whether the government has reduced its savings in the sense of having reduced its net assets. The answer depends on whether you believe in Ricardian equivalence (as an underlying fact about government borrowing, not necessarily as a description of household behavior). If you do, then the government is using its future power of taxation to create a new asset called "deferred revenue," which it can set off against its new liability, leaving its net assets unchanged. It's like when someone borrows money to buy stock on margin: they haven't reduced their savings, they've merely added an offsetting asset and liability to their balance sheet. In that case, government savings (or rather dissavings) is unaffected by the stimulus. If you don't believe in Ricardian Equivalence, then yes, the deficit does need to be financed, but...

As to the second point, it depends on what you mean by "displaces." If you mean there is displacement ceteris paribus for the changes in the total amount of funds available, then yes, it does displace other uses of funds. But my point is that it is unreasonable to assume that the total amount of funds available will be constant. Rather, it is almost certain to rise significantly, as the government's debt is itself a vehicle for net private savings (in contrast, for example, to personal debt, which is savings for one private party and dissavings for another). In the absence of Ricardian Equivalence, new wealth has been created, so there is more to save. To avoid saving more, people would have to increase their consumption dramatically.

Thus, as to the third point, no:   unless people behave in accordance with Ricardian Equivalence, the stimulus almost certainly also mobilizes idle resources, by increasing total income (i.e. adding to total wealth), thus allowing private saving to rise even as consumption also rises. Aside from Ricardian Equivalence, and excluding the very special and unlikely case where private savings do not rise, the only way the stimulus would fail to mobilize resources is if those resources were not really idle in the first place (in which case the stimulus would only cause inflation).

UPDATE: More from Brad DeLong, and the story is starting to sound a little bit more like one I recognize:
...increases in government spending lead to unexpected declines in inventories and unexpected declines in inventories lead to firms to expand production, which leads to increases in income and saving.
The initial inventory disinvestment (in response to demand created by the stimulus) is only a minor part of the story. And inventories only matter at all because they happen to be the way firms get products to market. My logic would work even in a world without inventories, where firms could instantaneously change production in response to demand. In real terms, the new demand would result immediately in more production, which would raise real incomes and lead to more real saving out of those incomes.

That's the "real" story, but I understand Professor Fama to be telling a financial story rather than a "real" one. He uses words like "funds" that have meaning only in a financial world. The nominal national income accounts are compiled in financial terms -- based on accounting statements and the like -- so the national income identity must hold in financial terms, and I take that to be the basis of Professor Fama's argument.

Therefore I state my counterargument in financial terms: financially speaking, the increase in income occurs as soon as money changes hands. The most straightforward case is a tax rebate. As soon as people receive the money, it is income, whether or not anything new has been produced, and whether or not any change in inventories has occurred. (Certainly the people who receive the rebate think it is already income, as do their accountants, as do the people who compile the income side of national accounts.) They have a choice whether to save or spend that income. Any income they spend will go to someone else, who will have the same choice, and so on until it all gets saved. Technically, some of what I call saving will take the form of inventory disinvestment, but that's a minor point. It would work the same way if all production were done on the spot.

UPDATE2: Leigh Caldwell's comment makes me realize that I have exaggerated the importance of the government's creation of new wealth, because my same logic applies when the source of the increased consumption is a change in consumer behavior. The general principle is that every act of consumption by one entity (household or government) is an act of saving (or inventory reduction) by someone else.

When I take money out of savings to purchase something from a company, the company records part of the purchase as a profit and part as a reduction in inventory. The profit immediately becomes part of retained earnings and thus corporate savings. If the firm hires another worker in order to replenish its inventories, the cost of replenishing those inventories becomes the worker's income. Any part of that income that the worker chooses to spend becomes part of someone else's income (or someone else's inventory reduction), and so on until there is an overall increase in savings just large enough to offset exactly the original reduction in my savings. (I'm assuming all inventories are eventually replenished. Otherwise part of my purchase becomes not savings but a reduction in unproductive inventory investment, but the funds available for productive investment are unchanged.)

Ultimately, the only way to change the quantity of savings is by investment. For example, suppose a company decides to hire a programmer to develop a major piece of custom software that it will use in its business. The programmer's pay becomes part of his or her savings (until it is spent and becomes part of someone else's savings), but there is no reduction in retained earnings (savings) on the part of the company, because the company records the software as a capital asset. Thus the company's decision to make an investment has resulted in an increase in total savings. The same process works in reverse, if the company decides to lay off a programmer that would have been developing software. In the more general case, investment typically involves purchases from other businesses, and then the same logic in the paragraph above applies, except that purchaser does not reduce its savings, since it books the investment as a capital asset.



Leigh Caldwell said...

I think if you want to count the government's ability to raise future tax revenues as an asset, you also need to count a liability on those who the taxes will be raised from. On this basis, there isn't really a net increase in wealth. However that's a minor quibble.

I think you are inadvertently giving too much credence to Professor Fama's original argument by glossing over the logical flaw in it.

His new summary, which you quote, is a better argument, and is the basis of the Keynesian proposal: bring idle resources into use.

I believe Brad DeLong has it right: the debate has arisen because Fama's original article was flawed. It was based on the classical model in which all markets immediately clear, but posited that "there are idle resources" which cannot happen in that model.

The debate should be about whether and how those resources can be brought into use. All the points about debt and savings are, to a first approximation, a wash (acknowledging that there can be second order effects on incentives).

JKH said...

I think I agree with just about everything you’ve said. Allow me to play it back this way:

I liked Montagu Norman’s “weekend model” as excerpted by Delong ( It’s a reasonably close differential approximation to the instantaneous calculus logic that is required to understand all this, I think.

In a way you’ve implied that type of model here; e.g., when you say, “Perhaps, with today’s technology, you could spend it within a few seconds, but the instant after you receive the funds, your savings necessarily increase.”

This sort of thinking is very important stuff. It really should be a sort of prototype analysis.

In a very simple model, the first order change from a government stimulus would be an increase in GDP by the amount of the stimulus and an increase in saving by the same amount. New income generated by the stimulus must be saved because prior expenditure and investment is already accounted for in prior income. Then the investment multiplier kicks as people start to spend their new income, expanding GDP and incomes as second and higher order effects.

In linking the real economy interpretation to the financial one, I think it’s important to recognize Ricardian equivalence as balance sheet “transaction” but not an income statement one. If one “believes” in it, it means that today’s government borrowing must be offset by a “write-down” of household net worth by the amount of the Ricardian equivalence. The corresponding new income created is then added back at the same time. But the ultimate resolution of the postulated (now reserved) Ricardian equivalence will depend on the ultimate resolution of the Keynesian multiplier effects over future income and future income periods. Cumulative income effects over future periods will eventually converge or not converge to (i.e. fall short of or exceed) the balance sheet allowance.

Ricardian equivalence is a tax asset for the government and a tax liability for the private sector.

So whether or not you believe in Ricardian equivalence is irrelevant in terms of describing the dynamics of current and future income. It is only relevant to how you describe household wealth. In other words, the creation of new income as you describe it is independent from the creation of new wealth, which depends on the Ricardian equivalence debate. And the Ricardian equivalence debate is best framed by accounting for its probability in the form of a reserve against it in the accounting of household wealth (and in the accounting of government “wealth”, if we could ever get to that point).

You say, “My logic would work even in a world without inventories, where firms could instantaneously change production in response to demand.”

That seems logical and correct and right to me. I think the basic Keynesian model is best described in simple terms that way. The inventory adjustment is a real world first derivative adjustment to that model.

In connection with the inventory wrinkle, I wrote on Delong’s post:

“Inventories are the partial derivative of investment on the output side. New demand from any source is capable of converting a surplus inventory/investment state to a deficient inventory/investment state, given other demand and its effect on remaining inventory. An increase in aggregate employment, production, output, incomes, consumption, investment, and saving is then required to return inventory/investment to a balanced state as a proportion of the resulting total economy. The identity of saving and investment holds at any instant of the process, and does not prevent the absolute size of saving and investment from fluctuating as a function of its proportion of the total economy at the same instant.”

Nick Rowe said...

I think the problem is that everyone is forgetting what happens to the rate of interest and the excess supply of money.

Very short version: the excess demand for loans causes the rate of interest to rise, which creates an excess supply of money, which people lend to the government.

Slightly longer version here:

JKH said...


I think the company records the entire purchase as a reduction in inventory. Purchase proceeds are used to pay off funding reflecting the cost of goods sold, while leaving cash profits in the bank as the offset to retained earnings.

Neither is cash in the bank an ‘investment’ nor is retained earnings ‘savings’ in national accounts terms. Both investment and savings have declined at the point of sale, by the amount of the sale.

The subsequent rebuilding of inventory and income is separate from the previous conversion of investment to consumption. The multiplier effect starts from the level of inventory investment remaining after the sale and is then determined by the new activity that follows.

Nick Rowe said...

Andy: let me try again. Suppose, just for the sake of argument, that both the demand and the supply of money were perfectly interest-inelastic. So you get a vertical LM curve, so fiscal policy wouldn't work, so Fama would be right. The excess demand for loans would create a rise in the rate of interest, but wouldn't create an excess supply of money, and so wouldn't create an increased demand for goods. You need to talk about the rate of interest and excess supply of money to explain to Fama why he's wrong.

brad said...

I think inventories *have* to be in there. Without signals provided by changing prices, how do firms know they want to expand production unless they find themselves doing unexpected inventory disinvestment?

At least, that's the way I always understood it...

Andy Harless said...

If inventories have to be in there, then the whole thing only works in an industrial economy. Imagine a country where all the manufactured goods are imported. Do inventories still have to be in there?

I think the logic needs to be able to work for such an economy (especially since it's not such a distant approximation to the US today), but you can't have inventories of lectures, inventories of backrubs, inventories of concerts, inventories of advice. (Technically, you could have inventories of software, inventories of DVD's, etc., but those are only at the trivial retail level: if stores are running out of Windows XP, that's not necessarily a signal that you need to develop Vista.)

So how do professors, massage therapists, musicians, consultants, software developers, etc., know when they want to expand production? I guess when they start making more sales, but there is no disinvestment involved.

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