How Big Is the Multiplier?

by James Hanley

This guest post is in response to a discussion with Clawback on the multiplier effect of government spending for fiscal stimulus. I argued there was no consensus about whether that multiplier was positive or not, and Clawback argued that there is solid evidence about what the multiplier is, and that the lack of consensus was due only to politics. In starting a response to him based on looking at the literature, I realized it would be too long for a comment, so I have asked Erik to allow me a guest post.

The purpose is not to poke at Clawback, but simply to emphasize the lack of consensus among economists about what multiplier ought to be used as the basis for public policy. The unpleasant fact is that if we are wrong about the multiplier, our policies very likely will be wrong–and that’s true no matter in which direction we are wrong. And if in fact we don’t have any real certainty about what the multiplier is, we can never have certainty about the wisdom of our chosen policies–and that’s true not matter which anti-recessionary economic policy we choose. The purpose here is absolutely not to argue for either a specific multiplier or a specific policy. Also, I apologize up-front if this post is tough slogging. I just don’t know how to translate some of this arcane cant into plain English.

First, a short primer on the multiplier. When you spend a dollar that dollar becomes someone else’s to spend, and when they spend it it becomes someone else’s to spend. How much increased spending this causes is the multiplier. (Mathematically, the formula is Multiplier = 1/Marginal-Propensity-Save, meaning that the more likely people are to save, rather than spend, the smaller the multiplier.) Simply put, a multiplier of 1.0 means that my $1 in spending has caused total national output to rise by $1. A multiplier of 1.5 would mean that it caused total national output to rise by $1.50. And a multiplier of 0.5 would mean that it caused total national output to fall by 50 cents. Obviously, then, we want any fiscal policy–whether spending increases or tax cuts–to have a multiplier of greater than 1.0 or it will actually have a negative effect on the economy. And obviously the higher above 1.0 that it is, the more stimulus effect it will have.

So what is the multiplier for government fiscal policy? Ah, there’s the rub. Our best and brightest aren’t exactly in agreement. Peter Tulip, a senior economics researcher for the Reserve Bank of Australia, says,

Estimation of fiscal multipliers is controversial, and subject to substantial uncertainty.

Why so hard? That mathematical formula looked pretty simple, right? Well, Harold Uhligh says it is simple, but I’m not sure everyone here agrees with his definition of simple.

I contribute to answering that question by calculating fiscal multipliers in a baseline neoclassical growth model with endogenous labor supply and fiscal policy, allowing for government spending transfers, government debt and distortionary taxes on labor and capital income. The policy experiments are conducted holding transfers, consumption taxes and capital income taxes fixed, i.e. changes in taxation require
changes in the distortionary labor tax. The model is simple and fairly standard. [emphasis mine–JH]

So what estimates are there for the multiplier? Let’s start with the Obama administration’s report on the stimulus package, by Romer and Bernstein, which uses a multiplier for government spending of 1.5, which the authors say is the average of the estimated multipliers “from a leading private forecasting firm and the Federal Reserve’s FRB/US model.” Despite using only two numbers for their multipliers (one from from an unnamed source, grrrrr) they say, “The two sets of multipliers are similar and are broadly in line with other estimates.” Of course this is a political document, so there’s some reason for skepticism about how they chose their numbers, but I’m just going to state my discomfort here, and lacking anything resembling actual evidence, not accuse them of cooking the numbers.

But just how reliable is the FRB/US model? FRB researcher Robert Tetlow has analyzed the,

46 vintages of the [FRB/US] model the Federal Reserve Board staff has used to carry out forecasts and policy analysis from 1996 to 2007,

and found that

“model uncertainty is a substantial problem. Changes to the FRB/US model over the period of study were frequent and often important in their implications…the answers to questions a policy maker might ask di¤er depending on the vintage of
the model.”

Granted, Tetlow did not look specifically at the fiscal spending multiplier, but he did look at multipliers for four other variables, and there’s good reason to suspect that his conclusion travels.

Additionally, Romer and Bernstein acknowledge in that paper that

Our estimates of economic relationships and rules of thumb are derived from historical experience and so will not apply exactly
in any given episode.

In short, their multiplier is a guesstimate, folks. An educated and model-based guesstimate by top-notch economists, but yet not a solid reliable fact.

Greg Mankiw, referencing Valerie Ramey suggests a multiplier that’s slightly lower.

The best evidence comes from a recent study by Valerie A. Ramey, an economist at the University of California, San Diego. Based on the United States’ historical record, Professor Ramey estimates that each dollar of government spending increases the G.D.P. by only 1.4 dollars.”

That’s still positive, but in Mankiw’s words, “not very large.” (Of course Mankiw was/is an economic adviser to Bush/Romney, but before liberals squawk in anger and conservatives squeak in glee, note that Mankiw closes the reprint of this January, 2009 column at his own blog by saying, “given the condition the economy is in right now, I think we ought to be more worried about doing too little than about doing too much.”)

What other estimates are out there? Susan Woodward and Bob Hall suggest that it the multiplier is simply 1.0. At that rate, economic output increases exactly at the rate of government spending, neither boosting the economy nor dragging it down.

Robert Barro is considerably more dismal in his estimate. Focusing on wartime spending because in general “it is not easy to separate movements in government purchases from overall business” he finds the historical evidence–note, not theoretical, but historical–suggests a multiplier of 0.8, a rate that would mean government spending actually harms the economy. There’s room for criticism of Barro’s approach. Yglesias points out that WWII was an anomaly that actually required forced saving–e.g., government forced lack of demand, in contrast to Keynes’ assumption of a consumer-driven fall in demand. He concludes,

The question is whether you got a decent multiplier out of the first 5-10 percent of GDP you spend on stimulus. It shouldn’t surprise us if it turns out that defense spending eventually got somewhat higher than would be economically optimal in the middle of the largest war in history.

Krugman says WWII wass irrelevant because there was full employment. But there are problems with their critique. First, Krugman himself has used WWII as an example of how stimulus works, so as Tyler Cowen notes, “a fundamental decision has to be made on whether to run away from the WWII evidence or not.” Second, Krugman’s “full employment” argument assumes the increased spending of WWII began at a point of full employment, which of course is false–the actual unemployment rate for 1941 was 9.9% (slightly higher than any year in the recent/current crisis). Third, Yglesias and Krugman focus their criticism on WWII–which I think is in itself fair (and I think Krugman’s own use of WWII is wrong as well), but Barro also used WWI, the Korean War, and the Vietnam War in estimating 0.8 (although he gives greater emphasis to WWII), which Yglesias and Krugman ignore.

That doesn’t mean Barro’s right and Yglesias/Krugman are wrong–In fact I share Yglesias’ precise qualms about using WWII–but it does means that Barro’s estimation cannot simply be rejected out of hand.

Let’s return now to Uhlig, who has a fairly nuanced conclusion distinguishing between short-term and long-term multipliers. Analyzing a stimulus plan “similar to the one employed in the American Recovery and Reinvestment Act,” he finds that;

initially, net present value fiscal multipliers for government spending may exceed [1.0] for several years and possibly substantially so. But these fiscal multipliers may be highly misleading, as eventually 5.8 dollars of output are lost for each dollar spent on government stimulus, according to this model.

In other words, the short run multiplier might be pretty darn good, but the end result is a dramatically negative long run multiplier. Uhligh concludes that,

[T]he “price” of the output loss later on may be well worth “suffering” in order to “gain” the initial boost in output. But a discussion of fiscal stimulus without pointing out this price, i.e., the eventual and prolonged growth slowdown in output, appears incomplete.

Exactly. Neither the short run multiplier nor the long run multiplier standing alone provides sufficient guidance for policy. We have to decide whether the short run effects or the long run effects are more important, and reasonable people can disagree.

Further uncertainty about the exact multiplier is introduced in an National Bureau of Economic Research (NBER) working paper by Ilzetski, Mendoza and Végh, who study 44 countries and reach the following conclusions.

(i) the output effect of an increase in government consumption is larger in industrial than in developing countries, (ii) the fiscal multiplier is relatively large in economies operating under predetermined exchange rates but is zero in economies operating under flexible exchange rates; (iii) fiscal multipliers in open economies are smaller than in closed economies; (iv) fiscal multipliers in high-debt countries are negative.

OK, the U.S. is industrialized, so that’s a plus. We have flexible exchange rates, so that’s a minus. We have an open economy, so that’s a minus. As to high debt, I can’t access the whole paper right now, so I’m not sure how they classify the U.S., and I can see arguments either way on that. Still, that’s not entirely encouraging for the prospects for fiscal stimulus in the U.S.

Further disagreement in the profession about the multiplier is emphasized in a 2009 paper for the IMF, bySilimbergo, Symansky, and Schindler, who write;

The size of the fiscal multiplier is country-, time-, and circumstance-specific. In the March 2009 IMF staff note prepared for the G-20 Ministerial Meeting, a range of multipliers was used.6 The low set of multipliers included 0.3 on revenue, 0.5 on capital spending, and 0.3 on other spending. The high set of multipliers included 0.6 on revenue,1.8 on capital spending, and 1 for other spending…

Answering the question of how multipliers are calculated and whether they are reliable, the authors conclude that;

The profession disagrees on the reliability of the multipliers, partly because of methodological differences, and partly because the range of estimates, even for similar methodologies, is often quite large…

All methodologies have shortcomings and caveats. Any estimate of a multiplier should have in mind the assumptions under which it is valid.

I’ll conclude by returning to Valerie Ramey, who actually says a little bit more beyond her estimate that the multiplier is 1.4. In a paper prepared for a Journal of Economic Literature forum on the multiplier, she concludes;

We now have many more estimates of fiscal multipliers than we did in Fall 2008 and early 2009, when policy-makers were trying to decide whether to use fiscal policy to try to stimulate the economy. Many of the studies are so recent, however, that the profession needs more time to interpret results and to check their robustness before coming to any firm conclusions. At this point, it seems that the bulk of estimates imply that the aggregate multiplier for a temporary rise in government purchases not accompanied by an increase in current distortionary taxes is probably between 0.8 and 1.5.

Let’s parse that out just a bit.

First, “we now have so many more estimates of fiscal multipliers.” Not an estimate, but many different estimates.

Second, “Many…are so recent…that the profession needs more time to interpret the results and check their robustness before coming to any firm conclusions.” This is a 2011 paper, folks, just about a year-and-a-half old; the profession is still interpreting and checking.

Third, “the bulk of the estimates [are] probably between 0.8 and 1.5.” That is, the bulk of the estimates are between a negative effect and a positive effect of government spending. In other words, the bulk of the estimates are that government spending as fiscal policy could boost the economy or could further harm it.

That’s not the worst of it, though. Ramey also pointedly notes that,

most estimates lie in the range of 0.5 to 2 [and] [r]easonable people can argue…that the data do not reject [either] 0.5 or 2.

In other words, a reasonable person could argue that the data are not solid enough to reject the idea that fiscal policy via spending increases could either be much better or much worse than is normally believed.

That’s cold comfort for anyone who’s a policy wonk, for anyone who wants to base their economic policy preferences on data rather than on faith. And that applies both to advocates and critics of stimulus.