Archive for January, 2012

Krugman on Mistaken Identities

Last week I wrote a series of posts (starting with this and ending with this) that were mainly motivated by a single objective: to show how taking the accounting identity between savings and investment seriously can get someone, even a very fine economist, into serious trouble. That, I suggested, is what happened to Scott Sumner when, in a post about whether a temporary increase in government spending and taxes would increase GDP, he relied on the accounting identity between savings and investment to conclude that a reduction in savings necessarily leads to a reduction in investment. Trying to trace Scott’s mistake to misuse of an accounting identity led me a little further than I anticipated into the substance of the argument about how a temporary increase in government spending and taxes affects GDP, an argument that I am still not quite satisfied with, but which – you can relax — I am not going to discuss in this post. My aim in this post is merely to respond to one of Scott’s rejoinders to me, which is that he was just relying on a proposition – the identity of savings and investment – that is taught in just about every macro textbook, including textbooks by Paul Krugman and Greg Mankiw, two of the current heavyweights of the profession. If so, Scott observed, my argument is not really with him, but with the entire profession.

No doubt about it, Scott has a point, though I think that most textbooks and most economists have an intuitive understanding that the accounting identity is basically a fudge, and therefore, unlike Scott, generally do not rely on it for any substantive conclusions. The way that most textbooks try to handle the identity is to say that the identity really just refers to realized (ex post) saving and investment which must be equal, while planned (ex ante) investment and planned (ex ante) saving may not be equal, with the difference between planned investment and planned saving corresponding to unplanned investment (accumulation) of inventories. Equilibrium is determined by the equality of planned investment and planned saving, and any disequilibrium (corresponding to a divergence between planned saving and planned investment) is reflected in unplanned inventory accumulation (either positive or negative) which ensures that the identity between realized investment and realized saving is always satisfied.  The usual fudge distinguishing between planned and realized investment and saving and postulating that unplanned inventory investment is what accounts for any difference between planned investment and saving is itself problematic, but it at least puts one on notice that there is a difference between an equilibrium condition and an accounting identity, while nevertheless erroneously suggesting that the accounting identity has some economic significance.

Not entirely coincidentally, Scott having got started on this topic by responding to a post by Paul Krugman, Krugman himself weighed in on the subject of accounting identities last week, enthusiastically citing a post by Noah Smith warning about the misuse of accounting identities in arguments about economics. Now the truth is that there is not too much in Krugman’s post that I disagree with, but there are certain verbal slips or misstatements that betray the confusion between accounting identities and equilibrium conditions that I am trying to get people to recognize and to stay away from. While avoiding any substantive error, Krugman perpetuates the confusion, thus contributing unwittingly to the very problem that motivated his post. Thus, his confusion is not just annoying to compulsive grammarians like me; it is also unnecessary and easily avoidable, and creates the potential for more serious mistakes by the unwary. So there is really no excuse for continuing to pay lip service to the supposed identity between savings and investment, regardless of how deeply entrenched it has become as the result of many decades of unthinking, rote repetition on the part of textbook writers.

Here’s Krugman:

Via Mark Thoma, Noah Smith has a terrific piece on how to argue with economists. All the points are good, but I’d like to focus on Principle 4, “Argument by accounting identity almost never works.”

What he’s referring to, I assume, is arguments like “since savings equals investment, fiscal stimulus can’t affect overall spending”, or “since the current account balance is equal to the difference between domestic saving and domestic investment, exchange rates can’t affect trade”. The first argument is, more or less, Say’s Law and/or the Treasury view. The second argument is what John Williamson called the doctrine of immaculate transfer.

This is pretty straightforward, though I don’t care for the examples that Krugman gives, displaying a conventional misunderstanding of Say’s Law. But Say’s Law is a whole topic unto itself. Nor can the Treasury view be dismissed as nothing more than the misapplication of an accounting identity. So I’m just going to ignore those two specific examples for purposes of this discussion. Back to Krugman.

Why are such arguments so misleading? Noah doesn’t fully explain, so let me put in a further word. As I see it, economic explanations pretty much always have to involve micromotives and macrobehavior (the title of a book by Tom Schelling). That is, when we tell economic stories, they normally involve describing how the actions of individuals, driven by individual motives (and maybe, though not necessarily, by rational self-interest), add up to interesting behavior at the aggregate level.

Again, nothing to argue with there, though the verb “add up” has just faintest whiff of an identity insinuating itself into the discussion.

And the key point is that individuals in general [as opposed to those strange creatures called economists who do care about “aggregate accounting identities?] neither know nor care about aggregate accounting identities.

Ok, now we are starting to have a problem. Individuals in general neither know nor care about aggregate accounting identities. Does that mean that those strange creatures called economist should know or care about aggregate accounting identities? I have yet to hear any cogent reason why they should.

Take the doctrine of immaculate transfer: if you want to claim that a rise in savings translates directly into a fall in the trade deficit, without any depreciation of the currency, you have to tell me how that rise in savings induces domestic consumers to buy fewer foreign goods, or foreign consumers to buy more domestic goods. Don’t tell me about how the identity must hold, tell me about the mechanism that induces the individual decisions that make it hold.

Here is where Krugman, after skating on the edge, finally slips up and begins to talk nonsense — very subtle nonsense, but nonsense nonetheless. What does it mean to say that an identity must hold? It means that, by the very meaning of the terms that one is using, the identity of which one is speaking must be true. It is inconceivable that an identity would not hold. If the difference between investment and savings (in an open economy) is defined to be identitically equal to the trade deficit, then talking about a mechanism that induces individual decisions to make it hold makes as much sense as saying that there must be a mechanism that induces individual decisions to make 2 + 2 equal 4. If, by the very meaning of the terms that I am using, the difference between investment and savings must equal the trade deficit (which, to repeat, is what it means to say that there is an identity between those magnitudes) there is no conceivable set of circumstances in which the two magnitudes would not be equal. If, in the very nature of things, two magnitudes could never possibly be different, it is nonsense to say that there is a mechanism of any kind (much less one describable in terms of the decisions of individual human beings) that operates to bring it about that the equality actually holds.

And once you do that, you realize that something else has to be happening — a slump in the economy, a depreciation of the real exchange rate, it depends on the circumstances, but it can’t be immaculate, with nothing moving to enforce the identity.

No, no! A thousand times no! If we are really talking about an identity, nothing has to be happening to enforce the identity. Identities don’t have to be enforced. Something that could not conceivably be otherwise requires nothing to prevent the inconceivable from happening.

When it comes to confusions about the macro implications of S=I, again the question is how the identity gets reflected in individual motives — is it via the interest rate, via changes in GDP, or what?

There are no macro implications of an identity; an identity has no empirical implications of any kind — period, full stop. If S necessarily equals I, because they have been defined in such a way that they could not possibly be unequal, then there is no conceivable state of the world in which they are unequal. Obviously, if S and I are equal in every conceivable state of the world, the necessary identity between them cannot rule out any conceivable state of the world. That means that the identity between S and I has no empirical implications. It says nothing about what can or cannot be observed in the real world at either the micro or the macro level.

Accounting identities are important; in fact, they’re the law. But they should inform your stories about how people behave, not act as a substitute for behavioral analysis.

I don’t know what law Krugman is referring to, but usually laws of nature tell us that some conceivable observations are not possible. Accounting identities don’t tell us anything of the sort. They are merely express certain conventional meanings that we are assigning to specific terms that we are using. How an accounting identity that could not be inconsistent with any conceivable state of the world can inform anything is a mystery, but I heartily agree that an accounting identity cannot be “a substitute for behavioral analysis.”

I have been rather (perhaps overly) harsh in my criticism on Krugman, but not to show that I am smarter than he is, which I certainly am not, but to show how easily habitual ways of speaking about macro lead to (easily rectifiable) nonsense statements. The problem is not any real misunderstanding on his part. Indeed, I would be surprised if, should he ever read this, he did not immediately realize that he had been expressing himself sloppily. The point is that macroeconomists have gotten into a lot of bad habits in describing their models and in failing to distinguish properly between accounting identities, which are theoretically unimportant, and equilibrium conditions, which are essential. Everything that Krugman said would have made sense if he had properly distinguished between accounting identities and equilibrium conditions rather than mix them up as he did, and as textbooks have been doing for three generations.

Savings and investment are equal in equilibrium, because that equality is a necessary and sufficient condition for the existence of an equilibrium. If so, being out of equilibrium means that savings and investment are not equal. So if we think that a real economy is ever out of equilibrium, one way to test for the existence of disequilibrium would be to see if actual savings and actual investment are unequal, notwithstanding the presumed accounting identity between savings and investment. That accounting identity is a product of the special definitions assigned to savings and investment by national income accounting practices, not by the meaning that our theory of national income assigns to those terms.

PS I will once again mention (having done so in previous posts on accounting identities) that all the essential points I am making in this post are derived from the really outstanding and unfortunately not very widely known paper by Richard G. Lipsey, “The Foundations of the Theory of National Income” originally published in Essays in Honour of Lord Robbins and reprinted in Macroeconomic Theory and Policy:  Selected Essays of Richard G. Lipsey.

How Ronald Reagan (Not to Mention Republicans, Conservatives and the Wall Street Journal Editorial Board) Learned to Stop Worrying and Love Moderate Inflation

In my previous post, I pointed out that inflation (measured by both the GDP price deflator and the Personal Consumption Price Index) in the fourth quarter has fallen back to a level well below the Fed’s 2% target.  Indeed, it is running at nearly the lowest rate since the end of World War II. Later, when reading this post by Noah Smith commenting on this post by John Taylor’s (also see Taylor’s op-ed in the Wall Street Journal), it occurred to me that, viewed from the perspective of the current rhetoric about sound money and proposals to eliminate the dual mandate of the Fed and impose on the Fed a single unambiguous mandate of maintaining price stability, it is hard to understand why some people are so harshly critical of Mr. Obama’s record as President. If price stability is really the alpha and omega of monetary policy, then, based on his success in keeping inflation low, shouldn’t Mr. Obama be rated the most economically successful President in living memory?

If, despite President Obama’s stellar record in suppressing inflation – either directly or through his re-appointment of Ben Bernanke as Fed Chairman — is not enough to mollify the critics who loudly assert that the only macroeconomic objective of the Federal Reserve Board should be to ensure price stability, doesn’t that suggest that they actually care about more than price stability and that calls for the Fed to stop paying attention to anything but the rate of inflation are perhaps less than 100% sincere?  After all, inflation is lower now than it was during the administration of Ronald Reagan, and aside from his reputation as the quintessential Conservative, Reagan is also viewed as the slayer of inflation and the very paragon on a sound money man.  So I thought that it might be useful to go back and see what the Reagan administration itself had to say about inflation while it was in office.

So herewith I provide a few excerpts from the  Annual Reports of the Council of Economic Advisers published in the Economic Report of the President during the Reagan Presidency.

Economic Report of the President 1984

The tendency toward a slight increase in inflation over the year was also registered by the producer price index. Over the 6 months ending June, the index for total finished goods fell at annual rate of 0.9 percent,but over the second half of the year this index rose at 2.0 percent annual rate. Even so, inflation by this measure was lower than that in the recession phase of the cycle. The GNP implicit price deflator, the broadest measure of inflation, rose by 4.0 percent over the four quarters of the year. (p. 190)

The gradual reduction in inflation assumed by the Administration does not depend on a policy assumption that such a result will be “forced” by deliberate actions to choke off economic growth whenever there is any sign of a rise in inflation. Rather, the decline in inflation is the anticipated outcome of the assumed steady and predictable monetary and fiscal policies. As with real growth, it is expected that inflation may sometimes be higher and sometimes lower than the Administration assumption, but that the trend will be downward as indicated. (p. 199)

Economic Report of the President 1985

Although it is common for inflation to fall somewhat during the early stages of business cycle recoveries, few observers anticipated that the inflation rate would remain so low during a recovery as rapid as that experience in 1983-84. The inflation rate rose slightly in the second half of 1983 and early 1984, but there was no apparent tendency for the rate to rise further. Indeed, over the course of 1984 the inflation rate declined somewhat. However, inflation is still higher than desireable, and it worth noting that the services component of the CPI in 1984 showed some signs of slightly rising inflation. (p. 44)

The inflation outlook for 1985 is good. With moderate expansion in the money aggregates and continuing real growth, the inflation rate, as measured by the GNP deflator, is expected to average 4.3 percent over the four quarters of 1985. (p. 62)

Economic Report of the President 1986

After being lower than expected in 1985, the inflation rate, as measure by the GNP deflator, is expected to rise somewhat in 1986. Rapid monetary growth throughout 1985 as well as the depreciation of the dollar are expected to place upward pressure on prices. The projected rise in near-term inflation, however, is expected to be temporary, provided that a policy of gradual money-growth reduction is pursued. (p. 23)

The unsatisfactory economic performance associated with the rise of inflation and the adjustment problems that arise during disinflation provide a clear lesson: reacceleration of inflation must prevented. The surest way to avoid the costs of both inflation and disinflation is to avoid the policies that lead to an acceleration of inflation. Moreover, the experience of the past 3 years has indicated that substantial economic growth can occur without rekindling inflation. (p. 70)

Economic Report of the President 1987

More than 4 years of economic expansion, with the inflation rate remaining near or below 4 percent and interest rates declining to their lowest levels in 9 years, have laid te foundation for sustainable real growth with moderate inflation. (p. 19)

The inflation rate is 1987 is forecast to return to the 3.5 to 4 percent range of recent years, before the decline in oil prices temporarily depressed the inflation rate in 1986. Specifically the GNP deflator is forecast to rise at a 3.6 percent annual rate during 1987, after a 2.2 percent rate of increase during 1986. (p. 58)

Economic Report of the President 1988

Higher oil prices and higher import prices increased the 1987 inflation rate (as measured by the CPI) above the very low rate recorded in 1986. Higher import prices also are expected to contribute to consumer price inflation in 1988. However, after a year of slow growth of monetary aggregates, and in view of the expected slowing of real economic growth, acceleration of inflation is not seen as a likely danger in 1988. On a fourth-quarter to fourth-quarter basis, the CPI is forecast to rise 4.3 percent in 1988, a small decline from the rise in 1987. The GNP deflator, which is not affected directly by import prices, is forecast to rise 3.9 percent in 1988. (pp. 48-49)

Economic Report of the President 1989

An important legacy of this Administration is the refocusing of economic policy. The Administration deemphasized short-run stabilization policies; worked to provide a stable policy environment with market-based incentives for productive behavior, including low inflation; and attempted to extricate private markets from burdensome regulations. The strength and durability of the current expansion bear testimony to the soundness of these policies. In December 1988, the current economic expansion entered its seventh year, making it the longest peacetime expansion and the third longest on record. Most impressively, the inflation rate has not risen during this expansion, but has remained in the neighborhood of 3 to 4 percent. (pp. 258-59)

So it seems that President Reagan and his economic advisers thought that they were doing well to keep inflation at 4 percent a year.  Sure, they would have liked to get the inflation rate down a  bit, but they weren’t prepared to risk even a slowdown in the rate of decrease in unemployment to reduce inflation, much less tolerate any increase in the unemployment rate.  Promised reductions in the rate of inflation below the steady 3.5-4% rate that prevailed for the most part after the recovery started in 1983 just kept getting deferred further and further into the future.  Is that a record that John Taylor would like the next President of the United States to emulate?

Inflation? What Inflation?

Today’s announcement of the prelminary estimate of GDP for the fourth quarter of 2011 showed a modest improvement over the anemic growth rates earlier in the year, confirming the general impression that things have stopped getting worse. But we are barely at the long-run trend rate of growth, which means that there is still no recovery, in the sense of actually making up the ground lost relative to the long-run trend line since the Little Depression started.

The other striking result of the GDP report is that NGDP growth actually fell in the fourth quarter to a 3.2% annual rate, implying that inflation as measured by the GDP price deflator was only at a 0.4% annual rate, a sharp decline from the 2.6-2.7% rates of the previous three quarters. The decline reflects a possible tightening of monetary policy after QE2 was allowed to expire (though as long as the Fed is paying 0.25% interest on reserves, it is difficult to assess the stance of monetary policy) as well as the passing of the supply-side disturbances of last winter that fueled a rise in energy and commodity prices. So we now seem to be back at our new trend inflation rate, a rate clearly well under the 2% target that the FOMC has nominally adopted.

Despite the continuing cries about currency debasement and the danger of hyperinflation from all the usual suspects, current rates of inflation remain at historically  low levels.  The first of the two accompanying charts tracks the GDP price deflator since 1983. The deflator is clearly well below the rates that have prevailed since 1983 when the recovery to the 1981-82 recession started under the sainted Ronald Reagan of blessed memory.  The divergence between inflation in the Reagan era and the Obama era is striking.  Inflation under the radical Barack Obama is well below inflation under that quintessential conservative, Ronald Reagan.  Go figure!

The companion chart tracks the Personal Consumption Price index over the same period. The PCE index is similar to the CPI, and shows a similar (but even sharper) decline in the fourth quarter compared to the higher rates earlier in the year, owing to the importance of food and energy prices in the PCE index.  Again the contrast between inflation under Reagan and under Obama is clear.

In his press conference on Wednesday, Bernanke signaled, to the apparent dismay of the Wall Street Journal editorial board, that he will push for a monetary policy that adjusts as needed to keep the inflation rate from falling below 2% and might even tolerate some overshooting while unemployment remains unusually high. That signal apparently caused an immediate increase in inflation expectations as measured by the TIPS spread. The increase in inflation expecations was accompanied by a further decline in real interest rates, now -1% on 5-year TIPS and -0.16% on 10-year TIPS. With real interest rates that low, perhaps we will see a further increase in investment and a further increase in household purchases of consumer durables.  Perhaps some small reason for optimism amid all the reasons to be depressed.

Let’s Try Again

The point is to keep trying until you get it right.  I am sorry to say that I got it wrong last time, so I’m taking another shot at it.

Let’s consider, as does Simon Wren-Lewis a two-period model. The first period is in underemployment equilibrium. Let’s say that consumption in period 1 is given by the equation

C0 = 100 + bY0,

where b represents the marginal propensity to consume out of income.

Let’s say that investment is a fixed amount:

I0 = 100.

The expenditure (aggregate demand) equation is thus

E0 = 200 + bY0.

The equilibrium is determined by applying the equilibrium condition E0 = Y0, which gives us

Y0 = 200/(1-b).

Now the case that I posited in my previous post involved b = 0, reflecting income smoothing. This is tricky, because we have to make an assumption about what households expect their income to be in the next period, which can be assumed to be long relative to the initial period, though for simplicity I’m going to let the two periods be equal in length.  If households expect income in the next period to reflect full employment, presumably they would try to increase their consumption now, spending more and increasing equilibrium income now, so there is an inherent inconsistency in the model which needs to be resolved, but I am not going to worry about that either. Let’s just take the model at face value.

In this equilibrium, note that consumption, C0, is 100, investment, I0, is 100, and saving, S0, is also 100.

What happens if the government immediately tries to intervene to raise income by increasing government spending, G0, from 0 to 100, and imposes taxes, T0, of 100 to finance its spending?  The increased spending is only for this period and the taxation is only for this period, not the next one; in period 1, government spending and taxation go back to zero. What this does is to cause the consumption function to be revised as households choose a uniform level of consumption to be maintained for both periods, reflecting the liability to pay taxes this period, but no obligation to pay taxes next period.

Expecting income next period of 200, households would have chosen to consume 100 this period and 100 next period. But with a tax liability of 100 this period, households will choose, instead of consuming zero this period and 100 next period, to consume 50 this period and 50 next period. They have to borrow 50 this period to be able to pay their tax liability in order to have 50 left over for consumption. Next period, they will have to repay the loan of 50, and will have only 50 left over for consumption (income remaining at 200 with consumption equal to 50 and investment equal to 50, the loan repayment of 50 corresponding, it seems to me, to exports to shipped to foreigners). So the new consumption equation is

C’0 = 50 + bY0, where b is again equal to 0.

Now adding government spending and taxes, we have G = 100 and T = 100, so our new expenditure equation becomes

E’0 = 250 + b(Y’0 – 100).

But since b = 0, this reduces to

E’0 = 250 = Y’0.

We still have I0 = S0 = 100. Since b = MPC = 0, (1-b) = MPS = 1. The increase in income from 200 to 250 is just enough to generate another 50 in savings to offset the 50 in borrowing required to keep consumption level at 50 in period 0 and period 1.

The increase in government spending and taxes of 100 in period 0 raises the period-0 equilibrium (as compared with the case with no government spending and taxes) is 50, so the multiplier is .5.

Of course, this is not a full-equilibrium solution.  A full equilibrium should have Y1 also equal to 250 instead of 200, which means that consumption could have been increased by 25 in both periods, but I haven’t worked that solution out yet.

The reason why in this post I arrive at a result different from the result in my previous post is that I made a simple flunk-the-quiz mistake in the previous post, reducing the expenditure curve by 100 to reflect the reduction in disposable income from taxes as if it were a permanent reduction in disposable income rather than a one-period reduction in disposable income. So instead of assuming the MPC was 0 as I wanted to do, I was assuming, for purposes of the effect of taxes on consumption, an MPC of 1.  Yikes!  My assertion that everything depended on a positive MPC was entirely wrong.  In a simple Keynesian model, you get a balanced-budget multiplier of 1 provided that the MPC is less than 1.  That was a pretty bad blunder on my part, and I apologize. Scott, himself, seemed to perceive that something was amiss in a comment on the previous post, so I hope that we are now converging toward a solution.

Again my apologies for hastily posting my previous post without checking my work more carefully.  I had better get some rest now.

It All Depends on the MPC

UPDATE (01/25/12):  This post is erroneous and none of its conclusions should be relied upon.

OK, so it has come down to this.  I just asserted that the way to translate Lucas and Cochrane into the Keynesian model is to set the mpc equal to zero.  In that case, any increase in government spending that is offset by taxes causes no net increase in income, because as, Lucas puts it, the increase in government spending is exactly offset by a decrease in consumption of an equal amount thanks to the reduction in after-tax income.  This exercise is predicated on the assumption that the equal increase in government spending and taxes is permanent.  But in the exercise proposed by Wren-Lewis, the increase in government spending is temporary and the increase in taxes is also temporary.  How does the transitory nature of the increase in government spending and taxes alter the analysis under a Lucasian version of the Keynesian model?

Wren-Lewis claimed that you get a stimulative effect.  The increase in government spending is concentrated in the present, but the reduction in spending is spread out over the future, leaving a net positive effect in the current period.

Thanks to Scott Sumner’s comment on my previous post (which I too confidently pronounced definitive), I now see where Wren-Lewis and the rest of us went wrong.  The stimulative effect of the government spending is depends on the existence of a simple multiplier greater than 1 (i.e., an mpc greater than 0) [This is in error, a stimulative effect is present for any value of the MPC less than 1 for which a unique equilibrium exists in the simple Keynesian model.].  So to say that government spending must be stimulative, even if offset by taxation, begs the question whether government spending generates any increase in income beyond the amount of initial spending.  If you assume fully rational maximizing on the part of households (Ricardian equivalence), their mpc is equal to 0 (though that may perhaps be subject to some quibble, in which case there would still be room for argument on the effect of tax-financed government spending).  [The balanced budget multiplier is 1 in the simple Keynesian model even if the MPC equals 0.]

But if you are willing to grant for the sake of argument that the mpc is equal to 0, then it does seem that even a temporary increase in government spending would imply no net increase in income because of the absence of multiplier effects.  The increase in government spending would be offset by an equal decrease in consumption spending caused either by 1) increased taxes today or 2) by increased saving today in the expectation of future tax payments.  (I am now a bit troubled that this doesn’t seem to accord with Nick Rowe’s analysis, but I will  have to live with that until he weighs in again on the subject.)  [I should have realized that I was confused at this point and started over.]

Note that I didn’t need to say anything about accounting identities to get to this result.  (Gotta find that silver lining somewhere.)  But Scott can still feel good about having convinced me that his basic intuition was right.  The should teach us all to remember the old maxim, “Don’t Mess with Scott.”

PS At this stage, I am fully prepared to be proven wrong yet again, so I will be reading your comments very carefully to find the next surprise lying in store for me.

Time to Move On – But Not Before I Explain (Definitively) What it all Means

Update:  Continue reading, but then go to my next post to find out how it all turns out in the end.

Signs of fatigue are clearly evident and multiplying rapidly, so we had all better figure out and start executing our exit strategies from this convoluted, and at times acrimonious, debate about consumption smoothing. Things got started (two whole weeks ago!) when Simon Wren-Lewis picked on Robert Lucas for the following statement:

But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash.  It has no first-starter effect.  There’s no reason to expect any stimulation.  And, in some sense, there’s nothing to apply a multiplier to.  (Laughs.)  You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge.

and on John Cochrane for this statement:

Before we spend a trillion dollars or so, it’s important to understand how it’s supposed to work.  Spending supported by taxes pretty obviously won’t work:  If the government taxes A by $1 and gives the money to B, B can spend $1 more. But A spends $1 less and we are not collectively any better off.

Wren-Lewis made the following accusation:

Imagine a Nobel Prize winner in physics, who in public debate makes elementary errors that would embarrass a good undergraduate. Now imagine other academic colleagues, from one of the best faculties in the world, making the same errors. It could not happen. However that is exactly what has happened in macro over the last few years.

Paul Krugman followed up with a blast of his own at both Cochrane and Lucas, and John Cochrane weighed in, defending himself and Lucas.  The battles among the principals were accompanied by various interventions on either (or neither) side by Brad DeLong, Scott Sumner, Nick Rowe, Karl Smith (to name just a few) and by responses and rejoinders by Cochrane, Wren-Lewis and Krugman. I got involved mainly because I was upset that my friend Scott Sumner seemed to be making arguments invoking accounting identities in ways that I thought were illegitimate and even nonsensical. Scott, though apparently intervening on the side of Lucas and Cochrane, denied that he was supporting their substantive position, a denial that I, though apparently intervening on the side of Wren-Lewis and Krugman, also made.

I am not going to repeat my previous arguments against Scott, which mostly involved denials that any useful implication can be inferred from an accounting identity. I will merely reiterate that I hate – despise — all accounting identities, and deny that they can ever have any substantive implications about anything, serving only one function, namely, to force us to obey the laws of arithmetic. OK, I got that out of my system, and now I feel well enough to go on.

The key passage that we have all been arguing was this one from Wren-Lewis’s original post:

Both make the same simple error. If you spend X at time t to build a bridge, aggregate demand increases by X at time t. If you raise taxes by X at time t, consumers will smooth this effect over time, so their spending at time t will fall by much less than X. Put the two together and aggregate demand rises.

But surely very clever people cannot make simple errors of this kind? Perhaps there is some way to re-interpret such statements so that they make sense. They would make sense, for example, if the extra government spending was permanent. The only trouble is that both statements were made about a temporary fiscal stimulus package.

My next step is a bit tricky because I am going to have to refer to Scott’s criticism of Wren-Lewis, which, I must admit, I still do not fully understand. But the gist of at least part of what Scott was trying to say — and he, as well as Karl Smith, has repeated it in responding to me several times — is that Wren-Lewis was trying to force Lucas and Cochrane to accept the validity of the Keynesian model, when they simply don’t accept the model. My basic response to that has been that you can’t have a discussion about the effects of a policy unless you have some (at least implicit) model from which you are deriving your conclusions. It is not enough to invoke an accounting identity from which no conclusions (as Scott agrees) can be deduced. My first attempt to specify some model from which we could deduce the position adopted by Lucas and Cochrane was not too successful. I suggested that what they had in mind was some sort of crowding-out effect, the increase in government spending and taxes causing private investment to fall. I then combined this effect with a consumption-smoothing effect to produce a small short-term increase in Y as a result of building the bridge. This was unsatisfactory, because it was ad hoc, and because, as commenter John Hall pointed out, the change in consumption ought to (and could) have been derived rather than just assumed as I had done.

But I realized when responding to Scott’s comment on my previous post, that there is a simple way to reconcile what Lucas and Cochrane are saying with the basic Keynesian model, which, after all, is just a tool of analysis compatible with a variety of substantive assertions about the real world. So it is not correct to say that it is an unfair imposition on Lucas and Cochrane to require their position to be expressed in terms of a Keynesian model that they obviously reject. The Keynesian model is pretty flexible, and, by appropriate assumptions, you can get almost any substantive implication you want. So how does one interpret Lucas and Cochrane? Simple. They believe that households are rational maximizers basin their consumption decisions on their expected future income stream and expected future tax liabilities. They therefore engage in consumption smoothing, so that current consumption is fixed and independent of variations in current income, such variations being capitalized into their expected future income streams. Thus, the MPC out of current income in such a model is 0.

In terms of the Keynesian cross, you have an aggregate expenditure line that is horizontal (reflecting a 0 MPC). The multiplier with respect to a change in autonomous expenditure is one. However, since all government spending must be financed eventually by taxes, Ricardian equivalence implies that the increase in G is offset by an equal reduction in C, reflecting the effect on consumption of expected future taxes. That is precisely what Lucas and Cochrane were saying in the quotations above. Wren-Lewis, in his criticism, accepted that position. His point was that if the increase in government spending is temporary, the increase in government spending in the current period will rise by more than the fall in consumption this period due to the effect of expected future taxes (or borrowing this period to pay part of the current tax bill). This is not necessarily the end of the story (though, with a bit of luck, perhaps it will be), but this is the framework within which the argument must be carried out. It has nothing to do with accounting identities.

PS By the way Nick Rowe apparently had this all figured out almost two weeks ago. He could have saved us all this agony. But the truth is we loved every minute of it.

Advice to Scott: Avoid Accounting Identities at ALL Costs

It must have been a good feeling when Scott Sumner saw Karl Smith’s blog post last Thursday announcing that he had proved that Scott was right in asserting that Simon Wren-Lewis had committed a logical blunder in his demonstration that Robert Lucas and John Cochrane made a logical blunder in denying, on the basis of Ricardian equivalence, that government spending to build a bridge would be stimulative. I don’t begrudge Scott such innocent pleasures, and I feel slightly guilty for depriving him of that good feeling, but, you know the old saying: a blogger’s gotta do what a blogger’s gotta do. For any new readers who haven’t been following this twisted tale of claim and counterclaim, charge and countercharge, response and rejoinder, see my three previous posts (here, here, and here, and the far from comprehensive array of links in them to other posts on the topic).

My main problem with Scott’s argument against Wren-Lewis was that, at a crucial stage in his argument, he relied on the national income accounts identity that savings equals investment. Now in the General Theory, Keynes himself also asserted that savings and investment were identically equal and made a rather strange argument that the identity between savings and investment had a deep economic significance because there had to be an economic mechanism operating to ensure the ultimate satisfaction of the identity. That was a nonsense statement by Keynes, as pointed out by Robertson, Haberler, Hawtrey, Lutz and others, because if two magnitudes are identically equal, there is no possible state of the world in which the two magnitudes would not be equal, so there obviously is no mechanism required (or possible) to ensure equality between the magnitudes. The equality is simply a consequence of how we have defined the terms we are using, not a statement about what can or cannot happen in the world. The nonsense statement by Keynes did not invalidate his theory, it merely meant that Keynes was confused about how to interpret his theory.

I cannot resist observing that this is just one example of many showing that the notion that the original intent of the Framers of the Constitution has any special authority in Constitutional interpretation and adjudication is totally wrong, based on the misconception that the original inventor, discoverer, or articulator of a concept has any power to control its meaning and interpretation. Keynes, let us posit, invented the income-expenditure theory. But his understanding of the savings-equals-investment equilibrium condition of the theory was obviously wrong and defective. The Framers of the Constitution may have invented or may have first articulated any number of concepts mentioned in the Constitution, e.g., the prohibition against cruel and unusual punishment, due process of law, the right to bear arms, equal protection. That they invented or articulated those terms first does not give the Framers ownership over the meaning of those terms in the sense that their understanding of the meaning of those terms cannot establish an immutable understanding of what the terms mean any more than Keynes could impose the notion that savings is identically equal to investment simply because he provided the first articulation of a model that hinged on the equality of savings and investment. Sorry for that digression, but I just couldn’t help myself.

Now back to Scott. Based on the presumed identity between savings and investment, Scott asserted that the reduction in savings by which households would seek to smooth their consumption in response to a temporary increase in taxes would necessarily imply a reduction in spending on capital goods (i.e., a reduction in investment). But savings and investment are not identical; their equality is a condition of equilibrium. If savings fall, there has to be an economic mechanism (perhaps, but not necessarily, the one posited by the Keynesian model) that restores equality between saving and investment. The equality cannot be established by invoking an identity between savings and investment that is purely conventional and is the result of a special definition that ensures the equality of savings and investment in every conceivable state of the world, a definition that drains the identity of any and all empirical content.

Here’s what Karl Smith had to say on the subject on his blog:

Scott says

In a perfect world I’d lay out a concise logical proof that Simon Wren-Lewis and Paul Krugman are wrong.  And number each point.  They’d respond saying which of my points were wrong, and why.  Then I’d reply. . . .

Perhaps I can help.

Wren-Lewis said:

DY = DC + DS + DT = DC + DS + DG Λ DG > 0 Λ  -DC <  DT  ==> DY > 0

Karl’s notation is a bit cryptic. This is how I understand it:

DY = change in Y (income)

DC = change in C (consumption)

DS = change in S (saving)

DT= change in T (taxes)

DG = change in G (government spending)

The first equation says that a change in income can be decomposed into a change in consumption plus a change in savings plus a change in tax payments. This is derived from the definition of income in the income-expenditure model, namely that income is disposed of either by spending it on consumption, paying taxes or saving it. There is nothing else (in the model) that one can do with his income.

The next equation simply makes the substitution of G for T, which in the example under consideration were assumed to change by equal amounts.

The symbol “Λ” means something like “and furthermore,” so that we are supposed to assume that DG > 0, i.e., that government spending has increased. Then we are given another assumption, -DC < DT, which means that, because of consumption smoothing, the temporary increase in taxes is not financed entirely by a reduction in consumption, but partly by a reduction in consumption and partly by a reduction in savings, so that the reduction in consumption is less than the increase in taxes. This is Karl’s rendition of Simon Wren-Lewis’s argument that a temporary increase in taxes to finance the construction of a bridge would imply an increase in Y because G will increase by more than C falls. Karl continues:

Which is false.

Proof by example:

Let DG = DT = 2, DC =  -1, and DS = –1

Here Karl is saying let us assume that G and T both increase by 2. That part is fine. The problem is what comes next. He assumes that to finance the increase in taxes, consumption goes down by 1 and savings goes down by 1. Why is that a problem? Because he is reasoning in terms of an accounting identity rather than in terms of an economic model. Wren-Lewis was making an argument in terms of the implications of the income-expenditure model which consists of (yes!) definitions, causal or empirical functions (consumption, investment, etc.) and an equilibrium condition. The change in income cannot be derived from a simple definition, it is derived from the solution of the model. The model has a solution. You can solve for Y by taking the initial conditions and the empirical functions and applying the equilibrium condition. You can also express the equilibrium value of Y in a single equation as a reduced form in terms of all the parameters and initial conditions. If you want to solve for DY in terms of a change in one of the other initial conditions, like G and T or consumption function, you have to do so in terms of the reduced-form equation for Y, not in terms of the definition of Y. Doing that leads to the nonsense result that, I am sorry to say, Karl arrives at below.

Then both inequalities are satisfied and by the first equation.

DY = –1 –1 + 2 = 0

Which is what we were required to show.

It’s a nonsense result, because his solution does not correspond to the equilibrium condition of the model, which is either savings equals investment or expenditure equals income. In Karl’s nonsense result, savings is not equal to investment (because investment has not changed while savings has fallen by 1) and expenditure is not equal to income (because DC + DG + DI > DC + DS + DT). This is just the ABCs of comparative-statics analysis.

Now in a subsequent post, Karl seems to have retracted his “proof,” admitting:

S = –1 is not allowed [because investment has not changed].

Karl actually has interesting things to say about how to think about the effects of an increase in government spending and taxes in terms of a neo-classical analysis which is worth reading and thinking about. But the point is that to make any statement about the consequences of a change in the initial conditions or parameters of a model, one must reason in terms of the equilibrium solution of the model, not in terms of the definitions within the model, and certainly not in accounting identities that are completely separate from the model.

Finally, just one comment about Lucas and Cochrane. As Karl points out in his more recent post, Lucas and Cochrane offered reasons for rejecting the stimulative effect of building a bridge that were themselves couched in the very terms of the Keynesian income-expenditure model that they were criticizing. Thus, Lucas offered as his explanation for why building the bridge would have no stimulative effect that the increase in spending associated with building the bridge would be offset by a reduction in consumption associated with the taxes needed to finance the bridge as if that were an obvious internal contradiction within the model. Karl suggests a better response that Lucas and Cochrane might have given, but their response was simply an attempt to show that there was some gap in the logic of the model. That is why they invited such a brutal counter-attack from the Keynesians.

PS Have a look as well at Brad DeLong who has a new post quoting Paul Krugman quoting Noah Smith on the dangers of accounting identities, and also quoting moi.

PPS  Just to be clear, as Scott notes in a comment below, Noah did not mention Scott in his post.

About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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