Cost-Benefit Calculus and Stimulus Spending

I’ve been thinking a bit about stimulus spending recently.  In part this is because Emi Nakamura and Jon Steinsson just recently published a paper on the multiplier in the American Economic Review but it also came up as I was skimming through Paul Krugman’s lecture slides for his Great Recession class.

The logic behind economic stimulus spending is pretty straightforward.  If you are in a recession caused by low demand, the government can step in as a surrogate spender to restore demand and hopefully get the economy out of trouble.  Here is Rachel Maddow describing how she understands stimulus spending during the crisis. Her description is actually pretty good.  The only thing she leaves out is much mention of the multiplier: the ratio between the final change in overall spending to the initial change in government spending. If the government spends money, the workers it employs spend some of their new income on other businesses, and so on …  In theory, this chain of spending can imply a multiplier greater than 1.  If stimulus is to be effective, it helps to have a multiplier as big as possible.

There is actually a fairly clear picture of how big multipliers are. The Nakamura and Steinsson paper is part of a family of papers that look use cross-sectional variation to quantify the effect of stimulus. They compare regions that get additional government spending to regions that don’t and ask whether the spending encourages economic activity.  (Other papers that focus on cross-sectional variation include Shoag (2011), Wilson (2012) and Hausmann 2013).  In the cross-sectional studies, the estimated multipliers seem to be quite large (roughly between 1.5 and 2.5).

A different set of studies focuses on aggregate variation in government spending. The aggregate studies have a much more sobering message. For the most part, the aggregate studies suggest that the government spending multiplier is less than 1 (typical estimates are between 0.5 and 0.8). With a multiplier less than 1, private spending contracts in response to increased government spending. (See Ramey and Zubairy 2013, Ramey, Owyang and Zubairy 2013, Hall 2009, Ramey and Shapiro 1998, and Barro and Redlick 2011). It’s perhaps not surprising that the aggregate studies find smaller multipliers. Large aggregate changes in spending entail some crowding out which the idiosyncratic spending in the cross-sectional studies won’t. The aggregate changes also come with price tags – if the Federal Government is going to spend more then U.S. tax payers are eventually on the hook for the cash. This isn’t true for a cross-sectional experiment. If Pensacola gets a new Naval contract then the money is coming from the rest of the country (and only partially from the people who live in Florida).  If we reserve stimulus spending for periods of economic slack (or liquidity traps / ZLB events), then, in theory, the multipliers will be somewhat bigger. The IS/LM model predicts that fiscal policy will have its greatest effects if the economy is in a liquidity trap. This intuition carries over to fully articulated DSGE models (see Christiano, Eichenbaum and Rebello 2011).  The empirical evidence is not as clear on this point. There is a study by Auerbach and Gorodnichenko (2012) which seems to find evidence in support of this idea.

Even if the multiplier is substantially above 1, it is not obvious that stimulus spending is a good idea. The reason is that we are not trying to maximize output and employment – we are trying to maximize overall social well-being. At a basic level, the idea behind stimulus spending is that the government will spend money on stuff that it wouldn’t have purchased if we weren’t in a recession. The classic caricature of stimulus spending is the idea of paying a worker to dig a hole and then paying another worker to fill the hole in. This type of stimulus spending will increase employment and GDP but it won’t really enhance social welfare. True, we might get the beneficial effects of the stimulus but we could achieve that by simply giving the workers the money without requiring that they dig the holes. If we simply give out the money, GDP increases by less but social well-being goes up by more since the work effort and time wasn’t required.


Even though the Keynesian hole-digging example is silly, the same argument can be applied to any type of government spending. If a project doesn’t meet the basic cost / benefit test, then it shouldn’t be funded, regardless of the need for stimulus.  Of course, one form of fiscal stimulus used in the ARRA was providing funds to state governments so they could maintain services that they would normally provide. This is perfectly sound policy because it is allowing the government to continue to fund projects that (presumably) do pass the cost / benefit calculation. If the social value of a government project exceeds its social cost then we should continue to fund the project whether we are in a recession or not. If the social value falls short of the social cost then, even if the economy is in “dire need” of stimulus we should not fund it. If we really need stimulus but there are no socially viable projects in the queue then the government should use tax cuts. Tax cuts can be adopted quickly and aggressively and, unlike spending initiatives, apply to virtually all Americans.

There are other “legitimate” reasons for the government to expand spending during a recession. The most obvious is that many things are relatively cheap in recessions. Reductions in manufacturing and construction employment may lower the cost for government projects. But again, this decision can be made on a simple cost / benefit basis. If prices fall because of a recession and this makes some projects socially viable as a result, then it’s perfectly correct for the government to fund those projects.

If it makes people feel better we could re-label tax cuts as spending. I could pay people $200 to look around for better paying jobs. This would be counted as $200 of job searching services purchased by the government but in reality, the money would be essentially the same as a tax cut. In the clip above, Rachel Maddow jokingly says that it might be better to simply put money in envelopes and hand them out to low-income families. If the choice is to either hand out money in envelopes or give out the same amount of money to have people perform work that doesn’t meet the cost benefit calculation, then Rachel is right. The envelopes would be better.

UPDATE: Rudi Bachmann points me to a paper by Eric Sims and Jonathan Wolff.  An excerpt :

(M)ovements in the welfare multiplier are quantitatively much larger than for the output multiplier. The output multiplier is high in bad states of the world resulting from negative \supply” shocks and low when bad states result from \demand” shocks. The welfare multiplier displays the opposite pattern { it tends to be high in demand-driven recessions and low in supply-driven downturns. In an historical simulation based on estimation of the model parameters, the output multiplier is found to be countercyclical and strongly negatively correlated with the welfare multiplier.

UPDATE No. 2: In the comments JADHazell points me to this “sketch” by Paul Krugman. This also seems related. My initial reaction is that Krugman is saying that the marginal social cost of government spending drops sharply if the economy enters the liquidity trap (i.e., the ZLB). This means that the cost/benefit calculation points to an opportunity for the government to load up on goods and services during such periods. It does not say that further expansion is justified in the name of fiscal stimulus. That is, I suspect that a version of Krugman’s model in which the marginal benefit of government spending to consumers were zero (say due to satiation) would justify stimulus spending even if the economy were below full employment.

UPDATE No. 3: In the comments thread at MarginalRevolution, Tom West says that “(i)It sounds like the author is advocating that certain benefits be excluded from (the cost/benefit) analysis.” This is exactly what I am saying.  If the direct social benefit of a bridge is $100, then all the government needs to consider is whether the cost of building the bridge is greater or less than $100. If you then tell me that, because we are in a recession, there are additional stimulus benefits from the project (e.g., the workers who build the bridge take their new wage income and buy goods and services from other businesses further stimulating demand, increasing employment, and so on.), the government should exclude these additional benefits from its calculation.


34 thoughts on “Cost-Benefit Calculus and Stimulus Spending

  1. It always goes without saying that there are lots of government projects that don’t pass the cost/benefit analysis, but these projects are rarely described. What would they be?

    Stay in the real world, please. What are some examples that actually passed Congress and became law?

    • I’m not sure I can say definitively which projects do or do not pass the cost/benefit test. This requires a detailed assessment of each project. The point is that spending should always be guided by the simple cost/benefit test and not by the “need” for fiscal stimulus. If a project passes the test then it should be funded regardless of the state of the economy. If it doesn’t then it should not be funded regardless of the state of the economy.

    • Thanks for the link. I’m updating the post based on your comment. Looking over the paper it seems like his point is that the cost/benefit calculation moves in a “favorable” direction in a liquidity trap. I think this is correct and I would think that it is probably correct even if the economy is simply depressed but not necessarily in the trap. Let me think about it a bit …

  2. The multiplier for tax cuts is not the same as for fiscal stimulus, it includes the marginal propensity to save. Fiscal stimulus will get spent, but with a tax cut you risk a lot disappearing into savings. Furthermore the main point of a fiscal stimulus is not the immediate cost/benefit of what it gets spent on (though obviously the more benefit the better), but to spend a downward demand spiral from destroying more of the productive capability of the economy and hopefully reinflate it towards natural production again. In other words the cost/benefit analysis of a fiscal stimulus program needs at a minimum to include the benefit of the economic activity that would disappear unless it was undertaken.

  3. Pingback: Chris House on stimulus spending

  4. “At a basic level, the idea behind stimulus spending is that the government will spend money on stuff that it wouldn’t have purchased if we weren’t in a recession.”

    I dispute that. Optimally, government times larger capital investment projects, such as investment in new infrastructure, for those times when it crowds out the least private investment. Therefore, when the economy is booming, the private sector recapitalizes; when the economy slumps, the government keeps employment and GDP up by using the opportunity to build the railways, highways, facilities, schools, libraries, etc, it wanted to build anyway.

    You could argue about the trade-offs of the hole-digging caricature you mentioned above, but keep in mind what Keynes himself wrote:

    “If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coalmines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez-faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.”

    He was deliberately making an in extremis argument about the moral and economic costs of inactivity and involuntary unemployment; he wasn’t suggesting that stimulus projects ought to be otherwise-purposeless make-work.

    • I think we are essentially in agreement. Your point about timing of capital investment projects is quite right though this is what I meant in the post about making a purchase during a recession because it is advantageous from typical cost benefit calculations.

      For example, suppose that there is a government initiative which would entail a public benefit of $100 but at a cost of $200. The government doesn’t fund the project. Then the economy goes into recession and the cost of the project falls to only $150. The government *still* shouldn’t fund the project even though we are below full employment. It should fund it only if its cost falls below $100. In that case, it will take the opportunity that the recession provides and build the railway, school, whatever.

      • The public benefit will increase rather rapidly from $100 if there is a Keynesian multiplier because involuntary unemployment effectively grinds away the value in workers (if you are unemployed for more than a few months you start to become “unemployable”, likely a market failure that must be corrected). In a recession, it’s like gremlins come out and start smashing idle machinery … except it’s not machinery, it’s people.

  5. NK models that show optimal fiscal expansion at the ZLB start by assuming that the spending is on public goods AND that initial levels of public goods spending are optimal. Thus, the fiscal expansion is on public goods that are only marginally inefficient. The fiscal expansion then has some role in solving some market failure. For example, the govt spending induces expected inflation that reduces the real interest rate toward the natural rate. Or, I guess, in Eggertson and Krugman, relaxes some binding borrowing constraint.

    I guess, in general, fiscal policy would only have a multiplier greater than 1 if: A) supply elasticities were such that there was little crowding out; and B) some market failure was solved inducing an actual increase in production of private goods. Even so, it is still probably true that completely wasteful (rather than marginally wasteful) government spending would probably still have negative welfare effects.

  6. A lot of ARRA funds went to states, which were in the throes of drastic spending cuts. A lot of those cuts were aimed at salaries to public employees. It seems to me public education I a worthwhile activity that passes the cost benefit test, and that a bad business cycle draw during childhood is a poor reason to derail a generation’s long term public investment in human capital. States don’t have their own currency and cannot (or at least were not prepared to) act as a spender of last resort.

    • I definitely agree — cuts to state spending were clearly a problem during the recession and the ARRA helped a lot on this dimension. I think some of the tax provisions in ARRA were also pretty good too.

      The green energy stuff on the other hand …

  7. Just a tangential note: I do not think using taxes for stimulus is appropriate, at least for the United States. The reality of U.S. politics is that there is a very high probability that any temporary countercyclical tax cut will become permanent.

    • This is not a tangential comment — one of the big drawbacks of all policies (spending and taxation) is that temporary policies end up living on far after their “need.” A good example is the 10 percent lower tax bracket introduced by George W. Bush in 2001 which is still in effect even though it was originally scheduled to sunset in 2011.

      • In this respect wouldn’t you say that ARRA was exceptional in that it ended (atleast the spending features) precisely when the original law had intended it to?

    • There are plenty of examples of independent institutions around the world. For example, the CBO in the States. no reason why they couldn’t do the CBA.

    • No, there is a difference between describing what should be done and what will be done. One is the optimal strategy, which Chris is describing. The other is the political equilibrium, which is what actually happens when politicians get involved.

  8. Your facts are wrong:
    “If we simply give out the money, GDP increases by less but social well-being goes up by more since the work effort and time wasn’t required.”
    People feel better about themselves when given money for labor; rather then given money for free.
    For proof – see my cousin Sam – he felt better getting paid for labor, then getting welfare.
    PS – my fact is not conclusive – but the conclusion can be proven, or dis-proven.

  9. If the social value falls short of the social cost then, even if the economy is in “dire need” of stimulus we should not fund it. If we really need stimulus but there are no socially viable projects in the queue then the government should use tax cuts. Tax cuts can be adopted quickly and aggressively and, unlike spending initiatives, apply to virtually all Americans.

    This is utterly wrong as tax cuts can be saved whereas spending increases definitely do increase demand.
    You make the common mistake (well, at least for mainstream macroeconomists who just do blow-up micro and are ignorant of the fallacy of composition) of mixing microeconomic cost/benefit investment analysis with macroeconomic fiscal policy. The latter is simply the only conventional tool available to stimulate demand when we are in a liquidity trap. Even the most hardcore deficit spending advocates are closet monetarists, we just want massive fiscal policy in once in a lifetime balance sheet recessions like the Great Depression or the Great Reessions, otherwise we are Friedmanites/Woodfordians.

    About the digging holes example, has anybody who actually read his Keynes? He was actually debunking, time-traveler style, your claim about “useful” social spending:

    “When involuntary unemployment exists, the marginal disutility of labour is necessarily less than the utility of the marginal product. Indeed it may be much less. For a man who has been long unemployed some measure of labour, instead of involving disutility, may have a positive utility. If this is accepted, the above reasoning shows how “wasteful” loan expenditure[8] may nevertheless enrich the community on balance. Pyramid-building, earthquakes, even wars may serve to increase wealth, if the education of our statesmen on the principles of the classical economics stands in the way of anything better.

    It is curious how common sense, wriggling for an escape from absurd conclusions, has been apt to reach a preference for wholly “wasteful” forms of loan expenditure rather than for partly wasteful forms, which, because they are not wholly wasteful, tend to be judged on strict “business” principles. For example, unemployment relief financed by loans is more readily accepted than the financing of improvements at a charge below the current rate of interest; whilst the form of digging holes in the ground known as gold-mining, which not only adds nothing whatever to the real wealth of the world but involves the disutility of labour, is the most acceptable of all solutions.

    If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coalmines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez-faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.

    The analogy between this expedient and the goldmines of the real world is complete. At periods when gold is available at suitable depths experience shows that the real wealth of the world increases rapidly; and when but little of it is so available, our wealth suffers stagnation or decline. Thus gold-mines are of the greatest value and importance to civilisation. just as wars have been the only form of large-scale loan expenditure which statesmen have thought justifiable, so gold-mining is the only pretext for digging holes in the ground which has recommended itself to bankers as sound finance; and each of these activities has played its part in progress-failing something better. To mention a detail, the tendency in slumps for the price of gold to rise in terms of labour and materials aids eventual recovery, because it increases the depth at which gold-digging pays and lowers the minimum grade of ore which is payable.” – General Theory, Chapter 10

    • I hate to be blunt but it is beyond me how a MACROeconomist can seriously evaluate fiscal policy in a recession based on a narrow cost/benefit analysis and totally ignore the MACRObenefit of increased output and employment (I hope I do not have to add the caveat that this only applies when multipliers are high like right now and not in an ordinary recessions).
      Of course it is important to think about the explicit financing costs and the implicit costs via disincentive effects of taxation when evaluating public spending programs (from an academic point of view, we all know that this does not happen in the real world). But this is micro and not MACRO.

      This post is involuntarily paradigmatic, it shows what has gone wrong in the last 30 years.

    • You aren’t calculating the impact of the spending correctly. True “demand” will go up typically more if the government spends but welfare will increase more only if the government spending meets the cost-benefit test. The typical undergraduate demand calculation goes like this. Let m denote the marginal propensity to consume. For every 1$ of government spending, aggregate demand increases by

      1 + m + m^2 + m^3 + … = 1/(1-m)

      while for every 1$ of tax cuts, demand increases by

      m + m^2 + m^3 + … = m/(1-m)

      The former exceeds the latter since we typically assume that m < 1.
      However, the correct calculation requires looking at the change in welfare. Let's assume that the social net welfare from the government project is WG. This will be positive as long as the project passes the cost-benefit test but it also could be negative (e.g., digging holes, breaking windows, building pyramids, etc.). For private spending, typically each purchase entails some consumer and producer welfare (otherwise the transaction won't occur) – let's assume that each purchase has associated with it a welfare gain of 'w' per dollar. That is, if 1$ is spent, total aggregate welfare typically goes up by w$. Let's now re-do the calculation: The change in welfare from government spending is

      WG + mw + w*m^2 + w*m^3 + … = WG + w*(m/(1-m)).

      For the tax cut its

      mw + w*m^2 + w*m^3 + … = w*(m/(1-m)).

      The two differ only by the term WG which is positive if and only if the project passes the cost benefit test.

      • First of all, I like your idea of transforming the output multiplier into a welfare multiplier and your result is neat.

        But there are endogenity issues, m is not a fixed parameter in basic IS-LM but the marginal propensity to consume which depends upon income. In strict IS-LM it would nonetheless not change the result.
        But if we stop being model-slaves and think about how the MPC is influenced in the real world it becomes clear that in a situation in which consumers are faced with uncertainty concerning future employment and in which all economic agents, households, firms and banks, have to deleverage most of a tax cut will be saved and not spent.

        I would totally agree with you if this were a normal recessions (we would not have this discussion then as monetary policy should do the demand stabilisation job in normal recessions) but we are not in Kansas anymore but in a balance sheet recession so we cannot ignore debt and how it influences spending behaviour.

        So in the rare once-in-a-lifetime recessions in which fiscal policy has to enter the stage it should be via massive deficit SPENDing and not via tax cuts that ease deleveraging but do not directly increase demand significantly enough.

  10. Furthermore I think that this discussion is fairly academic. Nobody disagrees that governments should spent resources on socially benefical stuff and that deficit spending should not come in the form of useless projects. Hell, not even the most hardcore deficit spending advocate thinks that it is a great thing that Greece continues to buy German submarines while its welfare state is crushed!

    The composition of government spending always matters. But when economists mix this structural long-run issue with the short-run necessity of demand management via fiscal policy there are, at least between the lines, discounting the need for the latter. Not to mention that they are involuntarily playing into the hands of the economic ignoramuses who confuse short-run with long run issues, i.e. the temporary increase of the size of the state during a recession with the long-run size of the government.

    • I think the idea that the government should spend with abandon comes up quite often in recessions. Summers’s famous quote is that the recession “can only be resolved with more confidence, more borrowing and lending, and more spending.” It would be nice if the government understood that the spending part needs to meet the cost-benefit calculation above.

      • But that’s not what you said before. Before, you said that spending can always meet a minimal cost-benefit threshold. The public can be counted on to decide how to spend a helicopter drop. If the government wants to decide how to spend the money, they need to show that their decision is better than the public’s decision. You implied it wasn’t a question about whether or not spending was needed; it was a question about who should decide what to spend on.

  11. It would be nice if mainstream macroeconomists understood that balance sheet recessions are not ordinary recessions.

    As much as I argue for massive deficit spending worldwide right now I would argue against it in an ordinary recessions. And when natural resource price shocks will come along in this century I will vigorously argue against using demand management at all.

    You on the other hand just ignore the central differences among these three types of recessions.

    The social usefulness of public spending is a long-run issue and if you were really serious about it you would talk about ALREADY EXISTING socially useless government spending and about the MARGINAL government program which doesn’t come anyway as the entire Western World is engaged in austerity.
    Last and least I wanna add that the evaluation of the benefits of public programs are inherently political (or in econspeak, the social benefit of a public spending program depends upon the preferences of the electorate). Right-wingers think e.g. that a strong military is useful whereas left-wingers think that a strong welfare state is useful. You can play the preference aggregation game but you can never ever talk about objective benefits of a public program. We can try to estimate the costs though but then again the literature on disincentive effects of taxation is hardly unambiguous either.

  12. Pingback: Paul Krugman’s View of Aggregate Demand and Aggregate Supply | Orderstatistic

  13. Why doesn’t the multiplier count as a benefit? Surely its size is dependent on the condition of the economy. Hence in good times government might delay investment, but bring it forward in bad times (due to the impact of the multiplier in the cost/benefit calculation).

  14. Pingback: More Thoughts on the Welfare Consequences of Stimulus Spending | Orderstatistic

  15. Pingback: for good measure | Noah Smith, Chris House and mistakes we teach MBA students to avoid

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