Gauti Eggertsson has an important ("preliminary and incomplete") working paper. It has been discussed by Mark Thoma and Justin Wolfers. The main argument is that tax cuts could cause expected deflation, which would raise real interest rates if nominal rates are stuck at zero, and this would reduce aggregate demand and output. Tax cuts are therefore bad policy under current circumstances.

This is a really important conclusion, and we need to check if it is right. I think it is wrong for cuts in sales taxes (like GST in Canada or VAT in Europe). I am not sure if it is right for other taxes. Eggertson's result is sensitive to his assumption about firm's price-setting. It also depends on his assumption that the central bank targets inflation rather than the price level.

The main lesson I draw from his paper is that it is more important than ever to switch to a price level target, to prevent the possibility of these adverse effects.

Eggertson's model makes the standard New Keynesian assumption of Calvo price-setting. Under the Calvo assumption, the price level cannot "jump", but the inflation rate can. There is price level inertia, but not inflation inertia. Empirically, there seems to be both price level and inflation inertia, except that changes in sales taxes seem to cause the price level to jump.

New Classical macroeconomic models used to assume perfectly flexible prices. A change in aggregate demand or supply, or in expectations, could cause the price level to jump instantly to a new equilibrium. Stock market prices seem to jump like this, but the CPI does not. It seems to be sticky, or inertial. The CPI does adjust, but adjusts slowly. The biggest advance of New Keynesian macroeconomic models is that they built in sticky prices.

Nearly all New Keynesian models use the Calvo model of price adjustment. In the Calvo model, a random (1/n) fraction of the firms are allowed to change prices each period, so on average each price is fixed for n periods. This assumption means the average price level cannot jump instantly to the new equilibrium. But the rate of inflation can still jump.

An alternative is the Taylor model of price adjustment. In the Taylor model, it is not random. Each firm holds its price fixed for exactly n periods, and a fraction (1/n) changes price each period.

*Calvo inflation = (1/n)(New Price - average price)*

*Taylor inflation = (1/n)(New price - oldest price) *

The price level under Calvo is like a speedboat. It cannot jump to a new position in the ocean, but it can change direction instantly. The price level under Taylor is halfway between a speedboat and a supertanker. A supertanker can only change direction slowly.

The price level in the real world is more like a supertanker. It can't instantly jump up or down, and it can't even change direction instantly. Both the price level and the rate of inflation have inertia. Once inflation gets rolling, it wants to keep on rolling, and can only be stopped quickly at a cost. That was a lesson of the 1980's.

Why do New Keynesian macroeconomists assume Calvo when Taylor seems to fit the facts better? Because it is relatively easy to do the Calvo maths, and almost impossible to do the Taylor maths.

But there is one case where the price level does seem to jump: changes in sales taxes. Canadians have seen this happen. If (say) 60% of goods in the CPI have GST, then a very simple forecasting model says that a 1% cut in GST will cause an immediate 0.6% drop in the CPI relative to your previous forecast. It's an embarrassingly crude accountant's model of the price level, which totally ignores any equilibrium effects, rests on an appalling fallacy of composition, and should make any self-respecting macroeconomist cringe; but it works well in the short run.

Both Calvo and Taylor models seem to be wrong for changes in sales taxes. When the GST is cut by 1%, not just a fraction (1/n), but *all* firms cut their prices to consumers by 1%. It's the before-tax prices which are sticky, not the prices to consumers.

If there is a cut in taxes in Eggertsson's model, the price level does not jump, but the inflation rate immediately declines. Consumers have rational expectations, which they revise instantly, and so expected inflation immediately declines too. The nominal rate of interest is temporarily stuck at zero, so the real interest rate rises. This causes demand to fall, as consumers postpone consumption. So tax cuts make things worse.

But if Canadian experience is any guide, this is not what will happen for a cut in sales taxes. A 1% cut in sales taxes (assume on all goods) will cause an immediate 1% drop in the price level, and not a slow decline in prices. So I do not believe Eggertsson's results work for a cut in sales taxes.

And a temporary cut in sales taxes is very different. If there is substantial inertia in pre-tax inflation, as there seems to be, then a temporary cut in sales taxes will cause consumer prices to jump down instantly, then subsequently jump up when the tax is restored. So inflation will increase, and be expected to increase, so real interest rates fall, and demand increases.

I can't figure out how other taxes would affect inflation, if we replaced the Calvo assumption and assumed inflation inertia. But I do know that there would not be the discontinuous downward jump in inflation that a Calvo model would predict. Inflation inertia would prevent it. If tax cuts did cause inflation to eventually fall, that effect would build slowly over time. The question is whether the effect of tax cuts on disposable income and spending would kick in more quickly and strongly than the effects of tax cuts on inflation and real interest rates.

But whatever the result. if Eggertsson's central bank switched from targeting inflation to targeting the price level, his model economy would escape the liquidity trap more easily, and tax cuts would be less likely to have these contractionary effects. A price level target would mean that expectations of the future price level, after escaping the liquidity trap, would be pinned down independently of current fiscal policy. Neither tax cuts nor anything else could cause expected inflation to go down and stay down.

"Higher real interest rates are contractionary."

I must not be Neo-Keynsian because I thought the higher expected future yield occurs because the economy is expected to be more productive in the future.

Let me check with George Seglin on this.

Posted by: MattYoung | February 11, 2009 at 06:17 PM

We're both right Matt.

An increase (shift) in demand (curve) (because of expected higher future productivity for example) will cause an increase in the equilibrium real interest rate. (That's what you are thinking)

An increase in the real interest rate will cause a movement along a given demand curve, reducing quantity demanded. (That's what I was meaning).

Posted by: Nick Rowe | February 11, 2009 at 06:27 PM

I am not fully clear on the entire explanation given but would an income tax cut cause the same result? Cut income taxes, increase consumption and with nominal interest rates at zero, real interest rates increase causing a corresponding decrease in inflation?

Posted by: Mark | February 11, 2009 at 09:37 PM

Mark: It's the other way round. A cut in income taxes increases aggregate supply, and makes firms want lower prices, so they start cutting prices, so we get deflation, and expected deflation, which causes increased real interest rates (with nominal rates stuck at zero), which causes decreased consumption. This effect is bigger (in the model) than the standard effect, which goes: cut income taxes, increase disposable income, increase consumption.

Posted by: Nick Rowe | February 11, 2009 at 10:03 PM

Nick:

1) This is a stimulating post, the more so because of your discussion about how a sales-tax reduction will affect inflationary-expectations immediately.

2) In his paper, though, Eggertsson suggests that sales tax-cuts will likely --- "under certain assumptions" --- have the same impact as tax-cuts on labor (employees) will: they would shift downward and outward the supply curve, AS (FE: Firm Euler Equation in his paper), and so lead firms to cut prices and cause or reinforce deflation and deflationary-expectations.

From pp 2-3 (buggy paragraphing for readability)"

"Taxes in the standard New Keynesian model studied here are labor taxes.

Under certainThe result does therefore not establish that all tax cuts are contractionary at zero interest rates. My conjecture is that only those tax cuts that have a strong positive effect on aggregate spending will be successful in battling a recession at zero interest rates (e.g. tax credits aimed at increasing investment spending), while those aimed at supply incentives may be counterproductive.assumptions about the pricing behavior of firms, they can also be interpreted as sales taxes.

"At a loose and "intuitive" level policy should not be aimed at increasing the supply of goods – when there problem is that there are not enough buyers for the goods already produced."

....

3) Note though. Eggertsson only specifies what these assumptions might be at the bottom of p. 3, and only in passing. To wit:

" ... Aggregate supply is given by the FE equation (from "Firm Euler Equation")

πt = κ ˆ Yt + βEtπt+1 + κψˆτ t − κψσ−1 ˆGt

where the coefficients κ, ψ > 0 and 0 < β < 1.5

"

This equation is derived under the assumption that firm adjust their prices at stochastic intervals as in Calvo (1983). The tax rate ˆτ t is a labor tax rate. It can also be interpreted as a sales tax, under the assumption that the price that firms set at staggered intervals include the tax."(my italics and paragraphing, with footnotes removed)........

4) So you're right when you note the standard use of a Calvo price-adjustment assumption in Eggertsson's modeling . . . in line with fairly standard New Keynesian approaches. And, from the little I know about efforts to do the math for Taylor price-adjustments, you're likely to be right on that score too.

Interestingly, though, Eggertsson himself adds in the next paragraph that

"Monetary policy follows a Taylor rule:

it = max(0, ret + φππt + φyˆ Yt) "

....

Here I have a query: Not being an economist --- rather a political scientist who also has a Ph.D. in economics (and so not very familiar with the relevant literature) --- I would be grateful if you'd clarify Eggertsson's assumptions and your take on how Taylor pricing is "almost impossible to do" mathematically.

Specifically, if the Fed or your Canadian Central Bank can't do the math for Taylor pricing, how could they follow a Taylor rule? (The question, please note, isn't rhetorical or tricky. It reflects genuine curiosity on my part.)

......

5) Enter then your main claim in your own argument.

Forget the complexities of either Calvo or Taylor pricing on the behavior of firms on the AS (FE) side. You say that Canadian empirical evidence --- or at least the evidence captured by a simple forecasting model in the past and hence relevant for the present --- conflicts with the Eggertsson argument. And especially, you add later, if the cut in sales-taxes is permanent, not temporary.

For under any assumptions and apparently past price-trends in Canada, if rational behavior is assumed, then firms will --- faced with the prospect of a future increase in the sales-tax back to its pre-existing level --- will immediately cut prices. Presumably, then, consumer expectations about deflation and holding back consumption in the presece of falling prices will still hold . . . exactly as Eggertsson argues.

.......

6) Enter my own two-cents' worth here.

Your analysis, Nick, mainly focuses on the AS (FE) side of Eggertsson's argument. And up to a point that's sound . . . leaving aside the complexity of his assumptions and follow-up logical spinning-out of them in his model. Specifically, the cut in labor-taxes will reduce the costs of firms production. The AS curve then shifts downward and outward, which reflects a price drop and hence causes or accelerates the rate of deflation.

....

What is missing here, it seems, is more stress by you on the AD (CE) curve . . . at any rate as Eggertsson's argument progresses.

Its behavior under a nominal zero interest-rate bound turns out to be totally paradoxical --- and perverse. On the one hand, thanks to the tax-cut on their wages, workers think they now have a real-wage increase. On the other hand, the

realinterest rate increases in the presence of deflation . . . either caused by or reinforced by firms' cutting prices in response to the lower costs of doing business and in response to a fall in sales during a recession.The result?

The combined effects of 1) rising deflationary expectations on the part of consumers faced with a fall over multi-periods of a recession in the price level --- plus 2) of the greater costs of buying durable goods like cars and houses and big appliances (thanks to the rise in real interest-rates --- lead to a fully perverse shift in the AD (CE) curve. In particular, instead of sloping downward and outward in a normal AD way, it inverts and shifts upward and outward.

It shifts upward and outward because only a rise in expected inflation --- or a halt and reversal of deflation --- will cause consumers to buy more. And presumably the same applies to business-investment on the AD side. Amid deflation, the costs of their getting loans from banks or other sources of capital-credit have risen too . . . under the pressure of a higher real-interest rate.

.....

7) That brings us back to the zero-bound nominal interest-rate problem that is part of the wider economic environment in which this paradoxical inversion and upward-sloping AD curve materializes: a combination of deflationary prices, deflationary-expectations, and a higher real-interest rate amid multi-period recession.

For its this zero-bound nominal interest-rate problem that prevents the monetary authority --- the Fed or your Central Bank --- from reversing the rise in real interest-rates and affecting price-level movements: bluntly put, it can't continue to follow just a Taylor-rule targeting interest rates for nominal short-term rates. There is no way to lower those rates below zero.

That, to remind everyone, is the situation in which Japanese policymakers found themselves by the late 1990s and into this decade.

.....

8) Here, though --- pp. 13-17 --- Eggertsson then notes that there is a hypothetical solution. The Fed could switch to QE (quantitative easing or an increase in the money supply directly) and commit itself publicly to engendering inflation for so many years until a particular rate of inflation is reached.

Here Eggertsson notes the theoretical problem: a commitment to forcing the price-level upward to only such-and-such a rate --- and then stopping the rate cold --- is very difficult for a responsible central bank like the Fed or Japan's earlier on to make credible. It has to make the commitment credible if inflationary-expectations are to occur, but either the public would fear that the bank couldn't just stop inflation that way or --- alternatively --- would, as inflation rises in an upward-spiral amid growing inflationary expectations in the business and labor-markets, have to become irresponsible. And that isn't easy to do.

....

9) Oddly --- a word to underscore here --- Eggertsson nonetheless believes that such a credible inflation-commitment could be made somehow. And he endorses as well the Fed or Central Banks to deal with the zero-bound nominal interest-rates by buying --- as the Fed has started to do --- all sorts of long-term financial assets: foreign exchange, housing mortgages, stock-market equities, and so on . . . pp. 15-16.

And then, too, he notes somewhat oddly --- though in line with the logic of his modeled assumptions (the key one being a nominal zero-bound interest rate) --- that it would even be desirable not just NOT to cut payroll taxes on labor, but to RAISE them. That rise, after all, would increase the costs of doing business for firms and shift the AS (FE) curve upward and inward and hence force businesses to raise prices.

...

Note in passing that this paradoxical effect --- to raise payroll taxes in a serious ongoing recession --- is also in line with an earlier paper by Eggertsson that appeared last year: Eggertsson, Gauti, (2008b), "Was the New Deal Contractionary?", NYFed, mimeo. In it, Eggertsson defended the otherwise heavily criticized cartelizing policies of the New Deal after 1933 --- along with its destruction of agricultural output and support for unionization and a rise in real wages --- as a way to reverse deflationary expectations and stimulate both a rise in consumption and business investment amid a fall in the real interest-rate as prices rose.

.....

10) Note one other point Eggertson raises. Namely, he clarifies at the end of his argument (pp. 16-17) that his model and analysis do not look at the "Direct Impact" of tax-cuts on the AD curve through "spending".

Instead, his tax cuts have an "in effect through the incentive it creates for employment and thus 'shifts aggregate supply,' thus lowering real wages and stimulating firms to hire more workers."

.....

More specifically, he observes that:

* ---"One can envision various environment in which tax cuts stimulate spending, such as old fashion Keynesian models, or models where people have limited access to financial markets. In those models there will be positive spending effect of tax cuts, even payroll tax cuts like the ones in the standard New Keynesian model. For this reason I am bit hesitant to draw the lesson from this paper that it would be ideal to raise payroll taxes to stimulate the US economy today, although this clearly is a direct implication of the analysis."

He further notes that:

* --- "it is also worth raising another channel through tax cuts can stimulate the economy. Tax cuts would tend to increase budget deficits and thus increase government debt. That gives the government a higher incentive to inflate the economy. As we have just seen in section higher inflation expectations have a strong positive impact on demand at zero interest rates. Eggertsson (2006) model[s] this channel explicitly.

"In his model taxes have no effect on labor supply, but instead generate tax collection costs as in Barro (1978). In that environment tax cuts are expansionary because they increase debt and through that inflation expectations."

......

11) In his last paragraph, Eggertsson summarizes his policy-oriented views. There are, he ways, "are two general lessons":

[i] The problem facing the US today is unique (for others too presumably, save Japan): In a zero-bound nominal interest-rate environment, our problems of offsetting the growing recession are strictly

Demand-oriented. We should avoid, he says, any New Classical stress on increasing aggregate supply or AS. For tax-cuts other than those directly targeting business-investment will have the paradoxical effects set out in his paper. They will shift down the costs to firms of hiring more workers and reducing prices, which will cause or accelerate deflation and force the inversion of the normal AD curve to slope upward and outward as long as deflationary expectations exist.[ii.) We should ignore the work of Barro, Lucas, Sargant and others in the New Classical study of US GDP data and recessions where government spending and tax cuts were used for countercyclical effects. And so . . .

"... Policymakers today should view with great deal of scepticisms any empirical evidence on the effect of tax cuts or government spending based on post war US data. The number of these studies is high, and they are frequently cited in the current debate. The model presented here, which has by now become a workhorse model in macroeconomics, predicts

that the effect of tax cuts and government spending is fundamentally different at zero nominal interest rates than under normal circumstances."

......

Michael Gordon, AKA, the buggy professor

PS. For all its length, this post in reply to Nick's illuminating analysis and counter to Eggertsson's views --- at least as far as Canadian experience might go (which Eggertsson had ignored if the effects of tax cuts work directly on spending in aggregate demand, and not indirectly as in his piece) --- will, I trust, help summarize adequately the provocative and paradoxical argument that Eggertsson has unfolded with his New Keynesian model amid unprecedented zero-bound nominal interest-rates.

Posted by: gordongordomr | February 14, 2009 at 12:54 PM

Michael:

Thanks for your very detailed and thoughtful comment. This will take me some thought, and I have other things on right now.

Just one response for now: There is the Taylor rule for how central banks do or should set interest rates; and there is the Taylor theory of how firms adjust prices. Same Taylor, but totally different theories about different subjects. So the Taylor rule does not follow from Taylor pricing (or, if it does, nobody has figured out that it does).

This is not an easy paper to get one's head around. I'm really glad to see you try.

Will return later.

Posted by: Nick Rowe | February 14, 2009 at 02:40 PM

Michael: Returning to this difficult paper. A couple of comments on your comment:

Background: The simplest 2nd year textbook macro model has 3 equations: IS; LM (and IS and LM together create an AD curve); AS curve. Eggertsson's model, like all Neo-Wicksellian models, also has 3 equations: IS; Taylor rule (or some monetary policy rule), which replaces the LM; a Phillips curve (which in Eggertsson's case comes from the Calvo pricing model), which replaces the AS.

0. You have clearly read this paper very thoroughly.

1. Your point 10 is one I had missed seeing. Well spotted!

2. Your point 6. There's a point here you may or may not understand. Just in case you don't understand it, I'm going to lay it out explicitly. There's: the price level; and the rate of change of the price level (inflation).

We normally draw an AD sloping down in {price level, output} space. That (normally) makes sense in a model in which the nominal money supply is exogenous. A fall in the price level increases M/P, which cause a fall in the rate of interest, (and possibly a rise in real wealth), and so increases demand. But in this model the money supply is endogenous. And if the nominal interest rate is fixed at 0%, the interest rate cannot fall when M/P rises anyway. And there are no wealth effects on AD. So the AD curve is vertical in {P,Y} space. That is not surprising. It is a standard feature of Neo-Wicksellian models, where the central bank sets the rate of interest, so M is endogenous (and doesn't even appear as a variable in the model).

On the other hand, if we take the nominal interest rate as exogenous (at 0%), then a rise in expected inflation causes the real interest rate to fall, and AD to rise. Since expected = actual inflation in this model, this means the AD curve is upward-sloping in {inflation-output} space.

All that is absolutely standard. Indeed, his whole AD side is very standard. Qualitatively, it's exactly the same AD function you get from an ISLM, if you assumed the central bank sets the rate of interest (horizontal LM) rather than the nominal money supply (upward-sloping LM).

Except, as you note (and as I had foolishly missed) taxes don't appear in the AD function!

3. (Your 4) "Here I have a query: Not being an economist --- rather a political scientist who also has a Ph.D. in economics (and so not very familiar with the relevant literature) --- I would be grateful if you'd clarify Eggertsson's assumptions and your take on how Taylor pricing is "almost impossible to do" mathematically.

Specifically, if the Fed or your Canadian Central Bank can't do the math for Taylor pricing, how could they follow a Taylor rule? (The question, please note, isn't rhetorical or tricky. It reflects genuine curiosity on my part.)"

The Bank of Canada's main model is TOTEM. In the Technical Report describing the TOTEM model, they explain how they tried to introduce the Taylor model of firm pricing. But they couldn't, even with the computer doing the math for them. So they did a sort of second best technique, to try to get Taylor-like pricing.

What makes Taylor so hard, is that is that when, each period, a proportion 1/n of firms change prices, the inflation rate = (1/n)( new price - old price). But that old price depends on the expectations firms held n periods ago, of everything that would happen between t-n and t. So it's incredibly messy. And the Phillips curve equation, which specifies the rate of inflation, is therefore incredibly messy. But in Calvo pricing, where firms change prices at random, the inflation rate = (1/n) (new price - average price), which is very simple. The firms changing their prices this period are just a random sample of all firms, so their average price is just the average price of all firms.

This is just a major fudge in all New Keynesian models. They know it of course, and sometimes build in ad hoc inflation inertia, by throwing lagged inflation into the Phillips curve, so it fits the empirics better, even though theoretically it's a fudge.

But Eggerston's Calvo pricing Phillips curve assumes, even when there's a change in sales taxes at time t, that only a fraction (1/n) of all firms will change their post-tax prices; the rest will absorb the tax themselves. We KNOW that's false, just by looking. The true proportion is closer to 100%.

The Taylor rule for setting interest rates may or may not be an optimal monetary policy. It is used as a crude "rule of thumb" to describe monetary policy. It's simple, seems to describe policy fairly well, and is probably not too far from optimal.

That's all for now. Please respond, if I have missed something I ought to cover. I generally agree with your later points.

Posted by: Nick Rowe | February 14, 2009 at 10:04 PM

And, to answer your question on Economist's View: no, I don't think any of those commenters had even clicked on the link to Eggertsson's paper. (And I feel guilty about not having read it as carefully as you have done!).

BTW, the theoretical reason that taxes don't appear in the AD equation in Eggertsson's model is this: it's derived from an Euler equation for a household with an infinite horizon problem with perfect borrowing and lending. So Ricardian Equivalence would apply, and so tax cuts would not affect AD. (I should have seen this right away, but missed it. Damn!)

Posted by: Nick Rowe | February 14, 2009 at 10:35 PM