In recent weeks, there seems to have been a resurgence in the discussion of the relative effectiveness of counter-cyclical fiscal policy. This discussion is clouded by the fact that there are some whose political ideology seems to get in the way of reasonable discussion of evidence (and who believe that only those who disagree with them are biased!). In this post I would like to make the following points: (1) there is no such thing as “the” fiscal multiplier, (2) empirical and theoretical estimates are highly sensitive to assumptions about monetary policy — assumptions that seem to be violated by the behavior of central banks, and (3) New Keynesian models are flawed models for estimating a fiscal multiplier (especially in the context of log-linearized equations).

The most fundamental point surrounding the discussion of the fiscal multiplier is that there is, in fact, no such thing as “the” fiscal multiplier. Put differently, the fiscal multiplier is not a structural parameter that can be identified through careful theoretical or empirical work. To the extent that it is possible for a fiscal multiplier to exist, such a multiplier is likely to be dependent on a number of other factors such as the monetary regime and the composition of spending, to name two.

This point is important as it pertains to interpretations of empirical work designed to measure the magnitude of response of a change in fiscal policy. For example, in order to empirically estimate the magnitude of the effect of fiscal policy on output, one needs to find some sort of exogenous change in government purchases to avoid problems of endogeneity in estimation. To avoid the problem of endogeneity, many researchers have used military purchases since military build-ups in the face of war can be considered exogenous (i.e. the government isn’t building tanks to increase GDP, but to fight a war). These types of studies provide estimates of a multiplier effect of military purchases on real output. However, it is important to note that these estimates do not necessarily provide an estimate of a fiscal multiplier that corresponds with all forms of government spending. The composition of spending matters.

This point is particularly important when we consider the differences between the these estimates and the likely effects of the American Recovery and Reinvestment Act (ARRA), or as it is commonly referred as “the stimulus package.” The ARRA is not made up of a significant chunk of military spending. In fact, a significant portion of the ARRA consists of transfer payments. Even in the Keynesian income-expenditure model that is unfortunately still taught to undergraduates to understand macroeconomics, transfer payments have no effect on GDP. Thus, the multiplier effect of these provisions is zero. It follows that it would be incorrect to take an estimate of a fiscal multiplier from studies that use military spending as an explanatory variable and apply that multiplier to the total amount of spending. In addition, there is no obvious reason to apply this multiplier to the non-transfer payment fraction of the ARRA as it is not obvious that the marginal impact on real output from building a road, a bridge, or a school or buying a new fleet of government vehicles is equal to the marginal impact of military spending.

Even if we ignore the issue of the composition of spending on estimates of the multiplier, it is necessary to consider the effects of fiscal policy in light of monetary policy. If monetary policy responds actively to changes in economic conditions, then a purportedly effective fiscal policy will cause monetary policy to be more contractionary that it would have been otherwise. Put differently, monetary policy will offset, either in whole or in part, the effects of fiscal policy.

Recent theoretical and empirical work seems to appreciate this point, but argues that at the zero lower bound on nominal interest rates, monetary policy is ineffective and therefore fiscal policy can be effective. But how valid is this assumption? Central bankers certainly don’t believe that monetary policy is ineffective at the zero lower bound. If so, there would be no debate about quantitative easing because none would have taken place. In addition, this assumption requires that monetary policy work solely through the nominal interest rate (or the expected time path of the nominal interest rate). However, if this is the case, then monetary policy is always relatively ineffective because interest rates do not have strong marginal effects on variables like investment. Empirical work on monetary policy over the last 20 years seems to refute that ineffectiveness proposition. In fact, Ben Bernanke’s work on the credit channel is motivated by the very fact that the federal funds rate seems insufficient to understand transmission of monetary policy. Once we dispense with this notion of the ineffectiveness of monetary policy at the zero lower bound, we realize that empirical studies that estimate a fiscal multiplier by holding monetary policy constant are really estimating a strict upper bound.

These empirical estimates, however, have been informed by the predominant framework for monetary policy and business cycle analysis, the New Keynesian model. In the NK model, monetary policy works solely through changes in the interest rate. As a result, at the zero lower bound, fiscal policy can be effective — quite effective in some cases. Nonetheless, there are reasons to doubt these estimates of the fiscal multiplier. First, if monetary policy works through alternative transmission mechanisms, then the assumption that we can hold monetary policy constant is flawed. Second, even if we believe that the zero lower bound is a legitimate constraint on policy there is reason to believe that the estimated marginal effect of fiscal policy in the NK model is flawed.

The most compelling reason to doubt the multipliers that come from NK models, even imposing the constraint of the zero lower bound, is that these estimates are driven by the particular way in which these models are solved. For example, Gauti Eggertsson (and others) have pointed out that in the NK model at the zero lower bound, there is something called the paradox of toil. Intuitively, the paradox of toil refers to the characteristic in which the labor supply actually declines following a decrease in taxes. A paradox indeed! (Upon hearing this a commenter who shall remain nameless at a recent conference at the St. Louis Fed found it interesting that presumably it would be possible to increase government spending and fund the increase through higher taxes on labor income all while generating a multiplier effect.) This characteristic is part of a broader conceptualization of the world at the zero lower bound. In short, things look profoundly different than when the interest rate is positive.

But is the world really that different at the zero lower bound? The answer turns out to be no. As Tony Braun and his co-authors have shown, the funny business that goes on at the zero lower bound (i.e. the conclusions that run counter to the conventional wisdom in the discipline) is a figment of the way in which NK models are solved. In particular, the standard way to solve models in the literature is to take a set of non-linear equations that summarize equilibrium and log-linearize around the steady state. One can then generate theoretical impulse response functions from the log-linearized solution to the model. The impact multiplier from the change in government spending in the NK model is therefore a theoretical estimate of the fiscal multiplier. However, it turns out that when the models are solved through non-linear methods the counter-intuitive results disappear and the theoretical estimates of the multiplier are substantially lower — again, even imposing the zero lower bound as a constraint.

The general takeaway from all of this is that there is reason to be skeptical about the discussions and the purported precision of estimates of the fiscal multiplier — whether theoretical or empirical. (And that is to say nothing about the political constraints that go into devising the composition and allocation of spending!) However, what I have written does NOT necessarily imply that there is no role for fiscal policy during a recession. If some form of infrastructure investment by the government passes the cost-benefit test, I think that it is certainly reasonable to move such projects closer to the present because even in the absence of a multiplier effect these projects provide something of value to society. If there is an additional effect on output, then all the better.

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As someone who does empirical research in this area, and teaches undergraduates, I have one quibble: in the Keynesian income-expenditure model, taxes are usually defined to be taxes *net* of transfer payments. So the calculated multiplier on transfer payments would not be zero, it would be equal to the tax multiplier (mpc/1-mpc). I’m not arguing this is the “right” or “best” way to deal with transfers, but it is in there.

Also, although I agree that the Fed could offset fiscal policy, the question is would it do so in the middle of a recession? Scott Sumner in particular seems to assume that this would always be the case so that there’s no point to fiscal policy. I don’t agree. Of course, if fiscal policy didn’t have an inflationary effect, then maybe there’s no reason for the fed to intervene anyway.

There’s still a lot of work that needs to be done in this area but you’ve done a good job highlighting the issues.

Good article, most welcome. The problem with economics is that while in the very long run you may get some steady state solution, in the short run, which is what most people are concerned with, you have transient, nonlinear effects that may cancel out the long run. Hence something as seemingly undeniable as “Dutch Disease”, “Balassa–Samuelson hypothesis” and “Kuznets curve” are disputed, see their Wikipedia entries. An argument perhaps for letting things be (‘liaise-fair’).

I’m a layman, but my impression was like Steve: increasing transfers or taking in less taxes leads to deficits, which is stimulative. However, John Taylor recently argued that the A.R.R.A just lead to people saving the money or (particularly in the case of state governments) borrowing less. On the third hand, if the problem is a “balance sheet recession” we may not see immediate improvement even if household deleveraging from stimulus is moving them closer to where they will feel comfortable increasing their consumption.

Steve,

Thanks for your thoughtful comment. Yes, you are correct that the multiplier is not zero. What I should have said is that the multiplier effect is non-existent (i.e. the multiplier is less than one).

Regarding your second point, I don’t think that the Fed would purposely seek to counteract fiscal policy and I don’t think that is what Scott is saying either. I hope to do a post on this soon because I think this is a point that need substantial elaboration.

Wonks,

See my response to Steve above. I wrote that the multiplier effect of transfers is zero, not that the multiplier is zero. This is careless language and I apologize.

John Taylor’s point about the ARRA is noteworthy because when we consider the effects of fiscal policy, we also need to consider the effects on expectations. The income-expenditure model is not the correct framework to think about these questions.

Finally, it is hard to isolate what some call a “balance sheet recession” from the Fed’s failure to prevent the collapse in nominal income. Nominal GDP declined for the first time in the post-war era. I think that this is significant. It also suggests that monetary policy would be substantially more effective than fiscal policy.

Agree that cutting the deficit is needed; like to see SS retirement age raised to 68, and 65 for all federal employees, whether in uniform, overalls or tie and coat. And cut the annual trillion dollars in Defense, Homeland Security and VA outlays in half. Or more.

That said, there is the reality that the Fed has wiped out $2 trillion in federal debt recently. And is now on course to wipe out $1 trillion annually. (If the Fed buys MBS, if has to sell someday, or hold to maturity, resulting in reduction in federal debt as they transfer proceeds to Treasury)

QE can’t last?

Maybe. Japan went to zero bound, tried QE 2001-6, and suffered no inflation, quite the opposite. Still deflation.

If we get trapped in zero bound—I think likely, given Fed timidity and the Japan model—then QE moves beyond default, and become a conventional policy.

This suggests the Fed should be moved into the Treasury. It will be generating trillions in revenues for the US government. A Treasury function.

Globally, we see sovereign yields heading towards zero.

The next task for the economics profession is not wringing your hands over inflation, but what to do when the economy has slipped on the ice, and is in zero bound.That might be globally soon, thanks to central banker fixations on inflation.

Deficit spending does not work, see Japan. Certainly not if passive tightening is the rule.

And at zero bound, a central ban passively tightens, unless it conducts serious and sustained QE programs.

The stairway to heaven is the the joy of monetizing debt with only positive effects.

I know this is sacrilege, blasphemy to many.

But explain Japan, Explain the USA since the Fed started QE. We are seeing the lowest reading on the Cleveland Fed Index of Inflationary Expectations ever. After $2 trillion in QE.

The Fed should be targeting 2 percent inflation–as a floor.

So should the ECB and Japan. See the chart on sovereign yields. The world is headed to zero bound while central banker pompously pettifog about inflation.

And so far, no one has decided a real world lift-off from the zero bound.

That is where the danger lies.