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.