Unpacking the Multiplier: Making Sense of Recent Assessments of Fiscal Stimulus Policy

We will shed some light on meaning of empirical estimates of the multiplier an their proper use. On the general level, we will undertake a critique of the multiplier, explaining the role that various assumptions play in the three leading methodologies for calculating multiplier values. We find that two types of assumptions are crucial: “counterfactual assumptions” that specify the baseline against which the impact of the stimulus is judged and “behavioral assumptions” about the decision-making processes of economic agents. On the specific level, we apply what we learn from the critique to a sample of recent work claiming that certain aspects of the 2009 American Recovery and Reinvestment Act’s (ARRA) stimulus were ineffective—in particular, work by Stanford’s John Cogan and John Taylor claiming that ARRA funds funneled through state governments had no effect because states saved rather than spent the funds. We argue that the conclusions of these studies are highly sensitive to counterfactual and behavioral assumptions that are in some cases questionable and in others clearly implausible. We conclude with some general thoughts on the proper use and interpretation of the multiplier in assessing fiscal stimulus programs.

governm ent spending m ultiplier is a nebulous and contingent concept.
It is nebulous in the sense that there are many possible values for the m ultiplier for any single case o f stim ulus depending, for exam ple, "on the type o f governm ent spending, its persistence, and how it is financed" (Ramey 2011, 673).The m ultiplier is contingent in the sense that its m ean in g depends upon the ostensible goals o f the stim ulus policy and the counterfactual path again st which its perform ance is assessed.We cannot answ er the question "does this value o f the m ulti plier m ean that the stim ulus was a success?"without reference to the questions "what was it supposed to accom plish?" and "relative to w hat are we assessin g its success?" In light o f this, it is little w onder that recent m ultiplier-based assessm en ts o f the w isdom o f fiscal stim ulus have been all over the m ap-ranging from the highly pessim istic (the 0.64 m ultiplier o f Cogan et al. [2011]) to the highly optim istic (Gordon and Krenn's 2011 value o f 1.8).1 Each o f these individual assessm ents was calculated on a partic u lar set o f assum ptions, u sin g a particular m ethodology, at various levels o f aggregation, exam ining a particular tim e frame.Under such circum stances, it would be m uch m ore surprising if there had been general agreem ent on "th e" m ultiplier's value.Various m ultipliers are m easuring different relationships between stim ulus and output, and if we want to understand ju st w hat each is actually m easuring, how the various concepts are related to each other, and what their significance is for fiscal stim ulus policy, we will need to exhum e the assum ptions upon which they are built and exam ine the role o f these assum ptions in their proper interpretation.
In what follows, we shed some light on the meaning o f empirical estim ates o f the m ultiplier and their proper use.On the general level, we will undertake a critique o f the multiplier, explaining the role that vari ous assum ptions play in the three leading m ethodologies for calculat ing multiplier values.We find that two types o f assumptions are crucial: "counterfactual assum ptions" that specify the baseline against which the im pact o f the stimulus is judged and "behavioral assum ptions" about the decision-making processes o f economic agents.On the specific level, we apply what we learn from the critique to a sample o f recent work claim ing that certain aspects o f the 2009 American Recovery and Reinvestment Act's (ARRA) stimulus were ineffective-in particular, work by Stanford's John Cogan and John Taylor claim ing that ARRA funds funneled through state governments had no effect because states saved rather than spent the funds.We argue that the conclusions o f these studies are highly sensi tive to counterfactual and behavioral assum ptions that are in some cases questionable and in others clearly implausible.We conclude with some general thoughts on the proper use and interpretation o f the multiplier in assessing fiscal stimulus programs.

THE MULTIPLIER IN THEORY
The concept o f the m ultiplier as we know it originated with Richard Kahn, a student o f Keynes.In a p am ph let coauthored w ith D. H.
Henderson to support the Liberal election cam paign in 1929, Keynes had argued th at ripple effects from governm ent spending w ould enhance the im pact o f the origin al outlay on the economy, and he assigned Kahn the task o f developing a m odel to quantify these ripple effects.The basic idea is that a new purchase calls forth not only an im m ediate addition to production but also an im m ediate increase in incom e for the producer, and therefore a subsequent increase in his purchases.These purchases in turn represen t new incom e for som e other producers, and new spending on their part.In principle the chain continues indefinitely.
The question Kahn set out to answ er was how much additional spending and income could be expected from an initial expenditure o f one pound.Kahn's insight was that though the num ber o f rounds m ight be infinite, each round o f spending w ould be sm aller because som e o f the incom e would "leak " into saving and im ports, not to m ention taxes.So from £1 o f governm ent spending, the workers, contractors, and other direct recipients o f incom e m ight spend only h a lf a pound on consum ption, creating only 50 pence o f additional income.If in turn the recipients o f this 50p also spend only half, the next round o f spend ing will produce only 25p o f new output and income.
In this analysis the crucial determ inant o f the size o f ripple effects is the proportion o f new incom e that individuals spend-in Keynes's vocabulary, their "m arginal propensity to consum e."That is, the increase in GDP that occurs from each extra dollar o f governm ent spending (over and above the direct effect o f that dollar on GDP) is posi tively proportional to and solely dependent on the Marginal Propensity to Consume (see Appendix A).
The w orld is obviously a m ore com plicated place th an the stripped-down expository m odel o f the General Theory, and the m ulti plier will require four qualifications.First, there is a conceptual differ ence between the m ultiplier as it is applied in present-day m odels and Keynes's original exposition.In Keynes's sim ple m odel, the original expenditure-his exam ple used a change in private investm ent rather than in governm ent spending-stim ulates the economy until eventually A second qualification is that the m ultiplier form ula im plicitly assum es an exact equivalence between expenditure and the creation o f new goods and services in response.2This is likely to be the case if there is considerable slack in the economy but m uch less likely if the econom y is already near to fully utilizing the available resources.In the second case, crowding out m ay prevent the original stim ulus spend ing from generating output and incom e on a dollar for dollar b asis.3Neoclassical and New Keynesian m odels often reflect this by including a negative relationship betw een the interest rate and investm ent.In these m odels, stim ulus financed through borrow ing will drive inter est rates up, effectively crow ding the private sector out o f the credit m arkets.Alternatively, if private dem and is not sufficiently curbed by rising interest rates, the pressure on resources will be reflected in higher prices.In both cases, output would rise by a factor o f less than the original m ultiplier (see A ppendix B).
A third qualification introduces two reasons other than crowd ing out to explain why the num erator o f the m ultiplier m ight be less than 1, resultin g in sm aller m ultipliers.Unlike crowding out, these reasons cannot be assum ed to affect the initial and subsequent rounds o f spending sym m etrically.In Keynes's expository m odels, the origi nal spending goes to purchases o f goods and services that go into capi tal form ation-plant, equipm ent, railroads, and houses, for instance.
The corresponding elem ent o f fiscal stim ulus policies would be direct purchases by the federal governm ent o f newly produced goods and services, but fiscal stim ulus often involves using funds in ways other than such direct purchases.Most o f the $800 billion dollar stim ulus in the 2009 Am erican Recovery and Reinvestment Act, as John Cogan and John Taylor (2012, 89-91) rem ind us, actually took the form o f transfers and tax breaks to individuals and businesses, as well as grants to states to supplem ent the already m assive grants-in-aid that have been part o f our fiscal system for the past generation.This would not m atter to the calculation o f the m ultiplier if the beneficiaries o f federal largesse were them selves to spend all the stim ulus m oney they receive or, in the case o f tax breaks, all the m oney they do not have to pay to the IRS.If this were the case, the num erator o f the m ultiplier form ula would continue to be determ ined by the degree to which expenditure sim ply crowds out other production.But suppose the direct beneficiaries take a more conservative approach to spending.If none o f the original stim ulus is spent, the m ultiplier would be zero.
Both these extrem es bend the original logic o f the m ultiplier, according to which the fraction o f income spent is neither 0 nor 1. Indeed, the textbook m ultiplier for taxes and transfers conventionally assum es that, at least as a first approxim ation, the direct beneficiaries spend a fraction equal to the average for the economy, namely, the m arginal propensity to consume.This m eans that the first-round im pact o f each This list o f qualifications shows there is great variability in the m ultiplier, which, in turn, w ould seem to counsel a nuanced use o f m ultipliers w hen assessin g the prospects o f fiscal stimulus.If a particu lar stim ulus program is targeted tow ard low-income individuals at a tim e when the econom y is in recession, or is directed at large corpo rations in m ore prosperous tim es, we would want to know w hat the m ultiplier is for these particular situations.An im agined generic value o f "the m ultiplier" that covers all situations at all tim es m ay be a legiti m ate sim plification for introductory textbooks, but is not, or at least ought not to be, the stu ff o f policymaking.This point is well understood by practitioners.In evaluating the Obama stim ulus, the Congressional Budget Office (CBO), for exam ple, used a variety o f multipliers, and indeed a range o f values rather than a single point estim ate for each.The ranges varied from 0 to 0.4 for certain corporate tax breaks and 0.1 to 0.6 for tax cuts for high-income people to 0.3 to 1.5 for tax cuts for middle-income folks and 0.4 to 2.1 for transfer paym ents like food stam ps and unem ploym ent com pensation.
For paym ents to states to supplem ent education and Medicaid budgets the CBO m ultiplier ranged from 0.4 to 2.1 (Congressional Budget Office 2012, 6-7, table 2).
The different ranges o f m ultiplier estimates for different elements o f the stim ulus raises an obvious question: If the point w as to add dem and to a w eakening private sector and thereby m aintain prereces sion levels o f employment and output, why would stimulus money take the form o f tax breaks directed to corporations and high-income indi viduals?A m uch greater bang for the buck was available from tax cuts for middle-income people and transfers to the poor and unemployed, not to m ention transfers to the states.The answer is that tax breaks for the rich and tax breaks for corporations were never intended to stimulate.
One reading suggests that perhaps as m uch as one-quarter o f the total stim ulus went toward paying the political price o f the stimulus, rather than toward the stimulus itself (Marglin and Spiegler 2013a).Tax breaks for the wealthy represent the price o f getting a Congress dominated by special interests to act.On another, m ore generous reading, these tax breaks were not intended to stim ulate spending directly but rather to help private agents get their balance sheets in order after the excesses o f the Bush years."Stimulus," or at least a substantial part of it, was, like the Toxic Asset Relief Program (TARP), really about swapping high-quality federal government debt for the tarnished (if not absolutely toxic) debt o f private individuals and businesses, as well as state and local govern m ents.A case can be m ade that these agents would not be in a position to spend until their own financial houses were in order.This m ight qualify as indirect stim ulus under an elastic definition o f the term, but not as stim ulus is conventionally defined.
Notw ithstanding the obvious advantages o f allow ing the m ulti plier to have m ore than one value, recent argum ents against the effi Unpacking the M ultiplier 825 cacy o f the stim ulus treat the m ultiplier as singular, claim ing that the fraction o f new spending that displaces existing production is always at or near one, or the fraction o f tax reductions spent by beneficiaries is always at or near zero.Robert Barro (2009), for exam ple, focuses on crowding out.If the fraction o f new spending that displaces existing production is at one,4 the m ultiplier is reduced to zero, regardless o f the value o f the other param eters.John Cochrane (2009) agrees with Barro and also argues that the fraction o f tax reductions spent by bene ficiaries is zero on the grounds that any rational agent who receives a tax cut, transfer, or gran t will take into account the debt the federal governm ent incurs to finance the stim ulus.5If she does her arithmetic, she will, according to the "Ricardian Equivalence" theory developed by Barro in the 1970s and 1980s (Barro 1989),6 put the stim ulus m oney into a bank account to repay her share o f the new taxes that will be required to pay o ff the debt.O f course, the rational agents who do not benefit from the stim ulus will still recalculate their spending to take account o f their future tax obligations.The result is a tie: according to the theory, any new spending by stim ulus recipients w ill be ju st canceled out by spending reductions elsewhere in the economy.
The very general prescriptions o f these argum ents regarding the w isdom o f fiscal stim ulus, however, are unw arranted.An argum ent that crowding out will absorb the m ultiplier is surely relevant to stim ulus program s launched in tim es o f high-capacity utilization but not otherwise.High-capacity utilization was the reality in the World War II-era-the tim e period covered in Barro (2009)-but has little bearing on the Great Recession.By mid-2009, when the ARRA stim ulus kicked in, the unem ploym ent rate had clim bed to alm ost 10 percent.There was, accordingly, plenty o f spare capacity and an abundance o f avail able labor: crowding out w as hardly an issue.7 The argum ent that the fraction o f tax reductions spent by bene ficiaries is zero due to Ricardian Equivalence is questionable even on the individual level, let alone as a general behavioral assum ption for all economic actors.How m any o f us could actually do the calculations im plied in Ricardian equivalence?Moreover, if debt-financed stim ulus succeeds in fostering econom ic growth (or at least preventing it from falling as m uch as it would have in the absence o f stimulus), then tax revenues would rise without a future lum p-sum tax or rise in the tax rate.It is telling that Barro (2009) him self, the architect o f Ricardian Equivalence, did not see fit to em phasize this line o f thought in attack ing the stimulus.
Another argum ent why the m ultiplier is zero is harder to dismiss.
Joh n Taylor, along with John Cogan (Taylor 2011a;Cogan and Taylor 2012), argue that the fraction o f tax reductions spent by beneficiaries is zero because beneficiaries o f tax rebates and transfers, recogniz ing the tem porary nature o f federal largesse, did not treat it as they w ould a regular source o f incom e but rather as a one-time addition to their assets, to be doled out in little bits over the long-term future.

Significantly, Cogan and Taylor attribute this caution not to Ricardian
Equivalence but rather to "rational expenditure sm oothing." The b asic idea is very fam iliar to econom ists: in an optim al spending plan, a rational agent w ill insulate spending from fluctua a generation later, that gran ts end up fortifying state balance sheets (Gramlich 1978;1979).Before G ram lich, the terrain o f how governm ent spending is determ ined had been left m ainly to students o f politics.As early as the 1960s, Aaron W ildavsky argued the position that would later inform Gram lich's work: last year's expenditures are the prim ary determ inant o f this year's expenditures.An im portant difference betw een Wildavsky and G ram lich, Taylor, and other econom ists who invoke expen di ture sm oothing is th at W ildavsky claim ed no ration al b asis-on the contrary-for the workings o f the budgetary process (Wildavsky 1964;Davis, Dempster, and W ildavsky 1966, 529-547;1974,419-452), nor did he apply his argum ents to the operation o f state and local government.
His focus was instead on the process that determ ined agency budgets within the federal governm ent, an altogether different environm ent from the states and cities. (For starters, no balanced budget constraints operate at the federal level.) For the pu rp o ses o f this paper, however, the qu estion is not m erely w hether exp en d itu re sm ooth in g is a p lau sib le behavioral assum ption.The pertin ent questions for us are w hether and to what extent the initial recipients o f fiscal stim ulus actually engage in ratio nal expenditure sm oothing, w hether in stitutions (such as state and local governm ents) behave the sam e or differently in this regard, and how we would em pirically distinguish a rational expenditure sm ooth in g m otive from oth er m ech an ism s th at m igh t gen erate sim ilar behavior.
As with crowding out and Ricardian Equivalence, there are at least prim a facie reasons to be skeptical about rational expenditure sm ooth ing as a general assum ption.First, m any agents are sim ply unable to engage in expenditure sm oothing-they have little or no savings and equally little access to credit m arkets.This is the focus o f the literature on w hat are called "liquidity constrained households." Second, in our view the econ om ist's notion o f "rationality" in "ration al con sum ption sm o oth in g" m ak es unten able dem ands on decision m akers with respect both to their intertem poral utility func tions and their intertem poral budget constraints.Most people simply do not know enough about their future needs and w ants, m uch less about their future incomes, for the fram ew ork o f the standard theory o f consum er choice to make sense.8Instead, people fall back on habit, rules o f thum b, and other perhaps less elegant but more realistic ways o f coping than what the econom ist's ideas o f optim al planning dictate (Marglin 2008, 119-122).Moreover, real world rationality m ay suggest a higher prem iu m on solidarity and sh arin g than the econ om ist's paradigm o f individual choice allows.A poor person em bedded in a com m unity m ay feel that sharing a tax rebate with her less fortunate neighbors, particularly the neighbor faced w ith eviction if the rent goes unpaid or a blackout i f paying the electricity bill is put off, is a higher priority than replenishing her own bank account.She knows that som eday it will be her turn to rely on the com m unity (Stack 1975, quoted in Marglin 2008, 23).

THE MULTIPLIER IN USE: ESTIM ATIO N, SIM ULATIO N, AND ASSUMPTIONS
Theory, however, can only take us so far.Ideally, we would like to be able to adjudicate disagreem ents over the appropriate m easure and use o f the m ultiplier em pirically by appealing to the data.Unfortunately, there are significant challenges to doing so.The greatest o f these is the task o f isolating the effect o f the stim ulus from other contem po One problem w ith th is approach w as that, because all o f the variables were sim ultaneously m utually determ ining, it w as difficult to draw causal stories from the results.The solution to this was to add " structure" to the VAR by im posing restrictions on how the residuals o f each o f the variables (unexpected m ovem ents in them) related to each other.This allowed econom ists to specify which o f the variables w as to be interpreted as the first m over and which were responding.
The resulting estim ates o f the coefficients on the lagged variables allow econom ists to construct "im pulse response functions" (IRFs) that trace the change in a given variable over tim e in response to an initial shock ("im pulse") to another variable.When the im pulse is a shock to govern m ent spending, the IRF o f GDP can be used to construct an estim ate o f the multiplier.argues, we should not understand DSGE m odels as tools for assessin g the likely im pact o f a particular policy on the actual economy but rather as "storytelling devices" about w hat would be true o f the econom ic data if it had been generated by the kind o f behavior depicted in the model.
To the extent that the particular situation we are concerned with under standing strays in im portant ways from the DSGE m odel's depiction of the economy, the m odel will be inherently inappropriate as a guide to policy.For these reasons, Sim s concludes that "m aking forecasts, policy projections, and (especially) welfare evaluations o f policies with these m odels as if their behavioral interpretation were exactly correct is a m istake" (Sims 2007,153).But this is precisely w hat one im plicitly does when interpreting a DSGE-based m ultiplier estim ate as reflective o f the actual multiplier.

It is im portant to be clear about precisely what kind o f m istake
th is is-since it is a seriou s problem and one that is d istressin gly com m on am ong recent critiques o f fiscal stim ulus.Essentially, the m istake lies in treating on e's identifying assum ptions as though they were hypotheses to be tested by the m odel.For exam ple, in a DSGE m odel that im pu tes ration al con sum ption sm oothin g b ehavior to econom ic agents, we should not interpret param eter estim ates that seem to indicate that consum ption sm oothing is exhibited in the data as evidence that rational consum ption sm oothing is a general feature o f economic agents.Rather, the proper interpretation o f such a result is that to the extent that rational consum ption sm oothing is a general feature o f economic agents and that all agents engage in it uniformly, then the particular param eter values we have estim ated m easure that effect.W hat the DSGE m odel is doing is calibrating the extent o f rational consum ption sm oothing, assum ing that it takes the assum ed form.The assum ption itself is not, and cannot be, tested by the process used to estim ate the m odel because that process depends on the assum ption.10This general point is ju st as true for SVAR (and o f any estim ation tech nique for that matter) as it is for DSGE, but is particularly im portant in the latter case because DSGE's identifying assum ptions include so many restrictions on the structure o f economic behavior.If we were to inter pret the m ere fact o f being able to estim ate param eter values for these m odels as evidence o f the accuracy o f the structure they posit for the economy, we would be taking m uch m ore on board than is warranted.11W ith respect to fiscal stim ulus policy, one particularly im por tant restriction o f DSGE m odels is that they depict the behavior o f a "representative agen t" and so do not allow for the consideration of differential effects o f a policy targeted to different groups with differ ent behavior and circum stances.For exam ple, while the assum ption o f rational expenditure sm oothing behavior may be broadly applicable, DSGE m odels obscure the im portance o f the fact that the ability to fore stall spending from windfalls or to borrow in lean tim es differs am ong those at different points in the income scale.For the reasons discussed above, it would be wrong to interpret a DSGE m odel that fits the data well as an inherent refutation o f this, but such interpretations are not uncom m on.Cogan et al. (2009, 3-4, 15), for exam ple, m ake precisely

REMEDIES
Crucially, effectively investigating the assum ptions underlying m ulti plier estim ates will require evidence from outside o f the m odel itself.
In this section, we will present an exam ple o f two such strategies we em ployed in two recents papers (Marglin andSpiegler 2013a, 2013b) in vestigating the assum ption that recipients o f fiscal stim ulus save rather than spend it.13Our particular focus is recent w ork by John Taylor and John Cogan claim ing that the portion o f the ARRA stim u lus that went to state and local governm ents-accounting for roughly $250 billion o f the total $800 billion program -was ineffective because states had engaged in the sam e kind o f rational expenditure sm ooth ing that economic theory ascribes to individuals (Taylor 2011a;2011b;Cogan and Taylor 2011;2012).14Specifically, they claim that the states saved rather than spent the stim ulus funds, and that in the absence o f the stim ulus states would have m aintained their previous levels o f expenditures by borrowing and/or drawing down savings.
Their evidence for this w as drawn from a tim e-series analysis o f state governm ent data from 1969 to 2010 that separately regressed (1) current purchases o f goods and services against lagged purchases, federal receipts w ithout the ARRA stim ulus, and the ARRA stim u lus itself; and (2) transfer paym ents against lagged transfers, federal receipts w ithout the ARRA, and the ARRA stim ulus itself.In both equa tions, they found that the lagged variables explained m ost o f the varia tion over tim e in state governm ent spending, and that the coefficients on revenues were correspondingly low.The killer result w as that the coefficients on the ARRA stim ulus indicated that the im pact o f ARRA m oney on overall spending was, statistically, nil.They interpret these results as dem onstrating that states engage in rational consum ption sm oothing because they tend to hold expenditures steady (thus giving the significantly positive coefficients on the lagged variables), and adjust to current windfalls or shortfalls by adjusting net borrow ing and lending.Stim ulus channeled through the states, then, has no positive im pact on the economy because the states do not use it to increase net spending.
We challenged these findings on many grounds.First, we found reason to be skeptical that the high t-values on the coefficients in the Cogan-Taylor regressions and the high R2's were convincing evidence for their chosen specification.It is a cliché that correlation does not prove causality, but in the specific case o f Cogan and Taylor's u se o f lagged dependent variables, the reliance on correlation is m ore m islead ing than usual.Suppose that in fact-a m essenger o f God told us so-it is the other variables (that is, revenues in the Cogan-Taylor equations) that are driving expenditures.Nonetheless, lagged dependent variables will still show up with high t-values and bias the estim ates o f the true drivers o f expenditures downward, provided that in the correct speci fication (the one that God's m essenger vouched for) the independent variables (revenues) and the error term are b oth serially correlated (Achen 2001).This does not disprove Cogan and Taylor's interpretation o f the data, but it does suggest that their econom etric evidence should not be taken as support for their claims.Observe that m appears both in the num erator and the denomi nator if, as we assum e, crowding out is assum ed to affect every round o f spending equally.

AP P EN D IX C
The 7. For a contrary view, see Conley and Dupor (2011).8.Most people, not everybody: the late Jam es Duesenberry once quipped that the life-cycle hypothesis is exactly the theory one would expect from a middle-aged college professor, thus dem onstrating that some people's quips are as profound as other people's theories.9.The m atrix would have i rows and j columns, where i is the num ber of dependent variables a n d j the num ber o f lags included.10.This is true not only for em pirical m odels but also for theoretical m odels.For elaboration o f this point with reference to the history and present o f economics, see Spiegler (2012).For an analysis o f the m isch ief caused by this issue in recent literature in institutional economics, see Spiegler and Milberg (2009).15.W ilson issues a caveat to his findings that supports our general argum ent in this paper: "It should be em phasized that the stimulus effects estim ated in this paper correspond to the effects o f one partic ular stim ulus program enacted in a unique economic environment" (Wilson 2011, 31).
16.There are a few notable exceptions.For exam ple, Henderson (1938) and Meade and Andrews' (1938)  19.This sentim ent was expressed to us by state budget officers whose current adm inistration is Republican-in particular, those from Ohio, Wyoming, and Kansas-or whose state was under a Republican ad m in istratio n du rin g the years in q u estio n -in particular, Minnesota.
people's saving (what they don't spend on consumption) ju st balances the original investment.For expositional simplicity, Keynes focused on the chain o f consum ption expenditures, but what really m atters for the m ultiplier is the fraction o f newly created income that goes to purchase dom estically produced goods and services.This enlarges the scope o f the m ultiplier since the expenditure chain includes investm ent and governm ent spending.So w hat we are calling the "m arginal propensity to consum e" actually represents the "m arginal propensity to spend on anything reflected in GDP." dollar o f tax cuts (or transfer increases) will not be one dollar, but one dollar multiplied by the m arginal propensity to consume: the numerator is less than one with or without crowding out (see Appendix C).Crowding out apart, the logic o f the generic tax m ultiplier works only i f the spending o f direct beneficiaries o f the stim ulus m irrors the average spending pattern in the economy, which brings us to the fourth qualification.Although we can justify using an economy-wide average for the second, third, and subsequent rounds o f spending-since there is no way o f tracing out the expenditure o f each incom e recipient in the chain-we can surely do better in m easuring the im pact on the spend ing o f the direct beneficiaries (that is, in the first round).The direct beneficiaries are responding to specific tax cuts, transfers, and grants, and we norm ally have inform ation not only about the specifics o f tax cuts but about the characteristics o f the beneficiaries, including their particular circum stances and constraints.This inform ation allows us to m ultiply our m ultiplier by the fraction o f tax reductions (transfers and grants) spent by beneficiaries (see Appendix D).We can think o f the fraction o f tax reductions spent by beneficiaries as a valve control ling the flow o f the initial stim ulus into the economy.If the fraction is zero then the valve is shut and none o f the tax reductions are spent by beneficiaries.The spending never m akes it into the economy, so the m ultiplier has nothing to multiply.
tions in incom e by laying aside, investing, or lending surplus (in times o f plenty) and borrowing (in tim es o f dearth).This is the kernel o f the theory o f househ old spending developed independently by Milton Friedm an (1957) with the perm anent incom e hypothesis, and by Franco Modigliani (Modigliani and Brum berg 1954; Ando and Modigliani 1963) with the life-cycle hypothesis.These theories becam e a central pillar of the counterrevolution against Keynesian economics.Despite an array o f refinem ents to Friedman and M odigliani's original form ulations, the essence o f the theory rem ains the expenditure sm oothing that rational agents engage in when income fluctuates.The rational expenditure sm oothing assum ption plays a dual role in argum ents against fiscal stim ulus, as it pertains both to potentially observable behavior and to unobservable (counterfactual) behavior.In principle, it should be possible to ascertain w hat proportion o f the stim ulus funds is actually spent by recipients.But rational expendi ture sm oothing also im plies the counterfactual assum ption that in the absence o f stim ulus, individuals would have m aintained their prereces Unpacking the M ultiplier 827 sion expenditures by borrow ing and dipping into savings.Both o f these facets o f the assum ption are im portant in the Cogan and Taylor argu m ent against stim ulus: not only do individuals spend little o f what they receive, but the proper baseline against which to com pare this sm all or zero change is stable spending rather than a drop in spending.A relatively novel featu re o f Cogan and Taylor's argu m en t is the idea th at the sam e logic th at applies to households also applies to state an d lo cal go vern m en ts.C ogan and Taylor note Edw ard G ram lich's pioneering w ork on the effects o f federal grants on state budgets.Gram lich is skeptical o f the efficacy o f trying to stim ulate the econom y through gran ts to states, arguing as Cogan and Taylor do, Unpacking the M ultiplier 8 2 9 raneous m acroeconom ic activity-a standard difficulty o f econom etric analyses but one that is m ade particularly acute in the case o f estim at ing the m ultiplier due to the relative dearth o f adequate data.Not only are fiscal stim ulus program s relatively rare, they are also nonuniform.This turns a relatively sm all num ber o f historical stim ulus program s into a collection o f even sm aller pools o f different types o f program s deployed under different circum stances.Concretely, this m eans that when we are prospectively assessing the w isdom o f a particular stim u lus program , we cannot draw on a large sam ple o f sim ilar past episodes as a guide to its likely impact.The response o f econom ists to this state o f affairs has been to use estim ation and sim ulation techniques that lean heavily on theoretical structure and various kinds o f assum ptions to draw sharp inferences about the m ultiplier, the lack o f data notw ithstanding.These tech niques have yielded a wealth o f estim ates o f the m ultiplier, especially during the recent upsurge in interest in fiscal stim ulus engendered by the global recession.In a recent review o f the literature, Ramey (2011) reports estim ates from 18 such studies.In m an y cases, however, the sh arp n ess o f the in feren ce is purchased at the expense o f flexibility and applicability.The estim ates are useful only in situations in which the underlying assum ptions that generated the estim ates hold.Worse, as Taylor em phasizes (2011a, 687), the failure to explicitly acknow ledge these assum ption s as assu m p tions often leads to a circularity o f logic in argum ents em ploying the m ultiplier estim ates to assess fiscal policy: the m ultipliers are justified in part on the b asis o f the correctness o f the underlying assum ptions and the faith in the underlying assum ptions is attributed to the m ulti plier estim ates.In the rem ainder o f this section, we will illustrate the im portance o f these issues by reviewing three leading techniques o f m ultiplier estim ation and highlighting the im portance o f identifying assum ptions in applying the estim ates to fiscal policy assessm ent.Although there is significant variation in m ultiplier estim ation techniques, it is u seful to separate them into three broad categories according to the identification strategies they use to isolate the effect o f fiscal stim ulus: (1) the sophisticated statistical technique o f Vector A utoregression (VAR); (2) the construction o f behavioral m odels o f the m icro foundations o f m acroeconom ic activity (Dynamic Stochastic General Equilibrium, or DSGE, models); and (3) detailed sim ulation o f the econom y via Large-Scale M acroeconomic (LSM) models.The use o f VAR in m acroeconom ic m odeling was first suggested by Christopher Sim s (1980) as a way o f im proving on existing m acroecono m etric m odels that estim ated aggregate m acroeconom ic dynam ics by com bining m any separately estim ated partial equilibrium models.This approach was inadequate, according to Sim s, because the individual restrictions and assum ptions used in the separate m odels were often ad hoc and did not aggregate well into valid restrictions and assum ptions for the general m odel.That is, the m odels were som ew hat awkward patchworks rather than seam less wholes.VAR m ethods were m eant to unify the analysis by sim ultaneously regressing a vector o f all o f the variables o f interest (such as governm ent spending, tax revenues, and GDP) against a m atrix o f lagged values o f those variables.9The prom ise o f VAR techniques was that they would capture the com plex struc ture o f interactions between and am ong the variables o f interest-both contem poraneously and through tim e-to give a statistically robust picture o f their join t evolution.
Unpacking the M ultiplier 831The prim ary advantage o f these structured VAR (SVAR) models is that they have proved superior to alternative m acroeconom etric tech niques in fitting the data.They are now in regular and widespread use in m acroeconom ics, including in estim ation o f m ultipliers, and are often used as benchm arks against which to assess the accuracy o f non-VAR m odels(Smets and W outers 2007, 595-6).The strengths o f SVAR are, however, a double-edged sword.The statistical and com putational com plexity o f the technique necessitates certain sim plifications th at dim inish their effectiveness as guides to fiscal policy.Two factors in particular are significant.The first is the parsim ony required w ith respect to the num ber and level o f aggrega tion o f the dependent variables.Each new variable that is added to an SVAR entails a large num ber o f new estim ation tasks, a num ber that grow s with the n um ber o f lags included.As such, SVARs typically include only a few variables.Blanchard and Perotti's (2002) sem inal paper, for exam ple, includes only governm ent spending, tax revenues, and GDP.Because o f this parsimony, SVARs can provide little guidance to policym akers in the com plex and im portant issue o f fiscal stimulus design-for exam ple, how the stim ulus should be targeted, and what channels it should be targeted through.The second lim iting factor is what Jonathan Parker (2011) has referred to as the "linearity" o f SVAR models.They are linear in the sense that the calculated im pact o f a fiscal shock on GDP "by assumption . . . is constrained to be the sam e independent o f the state o f the business cycle" (Parker 2011, 709, em phasis in original).That is, SVARs do not take into account the fluctuation of the business cycle.This assum ption o f linearity m akes SVAR estim ates o f the m ultiplier particularly inap propriate for prospective assessm ent o f fiscal stim ulus during a reces sion.It biases the estim ate in two ways.First, it would not be able to capture any difference between the im pact o f government spending on GDP in a recession versus an expansion.To the extent that the m ulti plier would be greater in the form er state (due, for exam ple, to m ore slack in the economy or binding liquidity constraints) the SVAR estimate would be biased downward.Second, by treating recession and expansion symmetrically, the estim ate im plicitly assum es that the proper base line for evaluating the im pact o f government spending on GDP is some m easure o f the average performance o f the economy over the course of the business cycle.If, on the other hand, we expect that counterfactually (that is, absent increased government spending) economic performance would be significantly worse in a recession than in a boom, then a given increase in GDP due to government spending would actually represent a higher impact in a recessionary period versus a prosperous one.Recognition o f these potential biases has recently led to attem pts to construct SVARs that control for variations in the state o f the econ omy.Auerbach and G orodnichenko (2012), for exam ple, explicitly in corporate the possibility o f sw itch ing betw een recession ary and expansionary regim es into their SVAR and estim ate significantly higher governm ent spending m ultipliers in the recessionary regime.But such innovations do not address the first criticism, the general insensitivity o f SVARs to differential im pacts o f stim ulus am ong different popula tions o f stim ulus recipients.For this, we need estim ation m ethods that m odel the spending behavior(s) o f heterogeneous populations.It is to two such m ethods that we now turn.Dynamic Stochastic G eneral Equilibrium m odels are detailed structural m odels built on m icro foundations o f m acroeconom ic activ ity.A typical DSGE m odel consists o f a system o f equations depicting dem and and supply relations and the lower level relations that inform dem and and supply-for exam ple, price-and wage-setting relations, a consum ption function, an arbitrage condition for the value o f capi tal, and a m onetary policy reaction function, inter alia (Sm ets and W outers 2007).The functional form s o f the relations are determ ined by economic theory.In m ost DSGE m odels, the theoretical base is "New Keynesian," which is essentially neoclassical theory augm ented with various adjustm en t frictions (for exam ple, sticky w ages and prices).The agents in these m odels are forward-looking, incorporating expecta tions into their current decision-making.This is usually reflected by the assum ption that they engage in som e level o f expenditure sm oothing along the lines o f the perm anent incom e or life cycle hypotheses.Unpacking the M ultiplier 833In contrast to SVAR, the high degree o f structure im posed in DSGE m odels facilitates detailed economic interpretation o f the result ing param eter estim ates.For this reason, DSGE models are widely used by both academ ic and policy-oriented m acroeconom ists.But as with SVAR, the strength o f DSGE is also a weakness when it com es to apply ing its m ultiplier estim ates.The intricate structure im posed on the data leads to estim ates o f the param eters on the assumption that the economy actually is structured in the manner specified in the model.This assum ption is not tested by the m odel b u t is rather a putative fact necessary for interpreting the results.Consequently, as Christopher Sim s(2007,153) this claim in pointing to the good data-fitting perform ance o f an influ ential DSGE m odel (Smets and W outers 2007) as evidence that credit and inform ational constraints on consum ers do not play a significant role in the perform ance o f fiscal stimulus.The ability o f DSGE m odels to relax the many restrictions im posed by th eir identifying assu m ptio n s is lim ited by their com putational complexity.Typically, param eter estim ates are only possible for linear ized versions o f the full m odel, and this m eans that all o f the problem s o f linearity noted by Parker (2011) with respect to SVAR models apply Unpacking the M ultiplier 835 to DSGE as well.The study o f optim al fiscal policy in a linearized DSGE, he w rites, "is based on the answ er to the question 'can the govern m ent raise model-based utility by conditioning governm ent spending linearly on the state o f the econom y given that its effects are always the sam e?' and not 'can the governm ent raise output or consum ption m ore by increasing governm ent spending in a recession than a boom and so should it?"'(Parker 2011, 708) The typical represen tation o f m onetary policy in DSGE m odels (a sim ple reaction function called a "Taylor Rule" ), for exam ple, cannot contem plate fundam ental shifts in m onetary policy regim es.They therefore obscure the im portance o f constraints on m onetary policy in severe recessions-for exam ple, the constraint that n om inal interest rates cannot go lower than zero (the "zero interest lower bou n d"), which can be a binding constraint for central banks especially during long or deep recessions.Several recent studies have su ggested that m ultiplier estim ates are signifi cantly higher in such cases (Krugman 1998; Christiano, Eichenbaum andR ebelo 2011).Large-Scale M acroeconomic m odels are sim ilar to DSGE m odels but, as the nam e suggests, are m uch larger in scale.A typical LSM m odel com prises anywhere from hundreds to thousands o f equations and accounting identities.The US Federal Reserve system 's FRB/US model, which is used to analyze and forecast domestic m acroeconom ic activ ity, consists o f roughly 300 behavioral equations and accounting identi ties.It is part o f the larger FRB/Global model, which com prises roughly 2,000 equations and identities.The aim o f such m odels is essentially to replicate the economy in as m uch detail as possible, subject to relevance and to com puting constraints.Because o f their extrem ely high com pu tational and m aintenance dem ands, LSMs are generally created and run only by organizations that can dedicate large economic research staffs to the task-for exam ple, central banks and private m acroeconom ic research firm s such as M oody's Analytics, M acroeconom ic Advisers, and IHF Global Insight.The high level o f detail in LSM m odels uniquely equips them to sim ulate, evaluate, and forecast the effects o f (am ong other things) fiscal policies in a highly disaggregated manner.In this sense, they are ideal vehicles for estim ating m ore nuanced m ultipliers than are possi ble with SVAR or DSGE m odels and for using these nuanced m ultiplier estim ates to provide guidance regarding the w isdom o f fiscal stim ulus or austerity policies.This capacity has been used in several recent stud ies o f the potential im pact o f the Am erican Recovery and Reinvestment Act stim ulus.Blinder and Zandi (2010) use the Moody's Analytics LSM m odel to sim ulate the effects o f the ARRA stim ulus on the economy, as well as the effects o f several alternative scenarios to form the base line for their assessm ent o f the im pact o f ARRA.This exercise generates specific m ultiplier estim ates for a range o f different tax cuts and spend in g increases.The m u ltipliers are higher for stim ulative program s aim ed at those lower on the incom e scale-for exam ple, 1.24 for a payroll tax holiday versus 0.37 for m aking dividend and capital gains tax cuts perm anent.Romer and Bernstein (2009) use a disaggregated set o f historical m ultipliers generated by the FRB/US m odel and that o f a private firm to estim ate the im pact o f ARRA by straightforwardly apply ing the historical m ultipliers to the appropriate parts o f the stim ulus program .On this basis, they estim ate a governm ent spending m ulti plier that would reach 1.57 by the eighth quarter o f the program .Despite the gain in nuance, however, LSM models do not entirely escape the problem s associated w ith DSGE models.The fact that LSM m odels break economic activity down into such sm all pieces does m ean that they are not dependent upon the kind o f strict, sw eeping assum p tions o f DSGE m odels since the m ore expressions one uses to represent a given aspect o f the economy, the less one needs to assum e hom ogene ity.All the sam e, som e identifying assum ptions will always be neces sary and, to the extent that these are significantly inaccurate, so will be the m ultiplier estim ates.Indeed, this is one way o f interpreting the breakdown o f the first generation o f LSM models during the 1970s and the subsequent "Lucas Critique" (Lucas 1976)12.The foregoing discussion highlights the central im portance o f scrutinizing the assum ptions underlying estim ates o f the m ultiplier w hen using these estim ates to assess the w isdom o f fiscal stim ulus Unpacking the M ultiplier 837 policy.The im portant questions for econom ists and policym akers in such cases m ust be specific questions-about the likely im pact o f vari ous possible stim ulus designs on the particular populations at which they are targeted in the specific economic circum stances in which the policy will be implem ented.D eterm ination o f the usefulness o f m ulti plier estim ates, then, m ust include investigation o f the plausibility o f their underlying assum ptions within these specific circumstances.
The problem s with the Cogan-Taylor analysis were not m erely econom etric.A closer look at the structure o f interpretation in the Cogan-Taylor analysis provides a good illustration o f the dependence o f m ultiplier estim ates on untested assum ptions that we discussed above.In order for the zero coefficient on ARRA expenditures in the Cogan-Taylor regressions to be taken as evidence o f the failure o f the ARRA, it m ust be the case that states would have and could have engaged in expenditure sm oothing-that is, borrow ing to m aintain prerecession expenditure patterns.This corresponds to a counterfactual assum ption o f steady spending in the absence o f stimulus.The entire weight o f their Unpacking the M ultiplier 8 3 9 interpretation rests on this assum ption.If, on the contrary, we assum e that the recession had pushed states into an expenditure cutting regime, then the zero coefficient would indicate that the ARRA had indeed been effective in supporting otherw ise unsupportable levels o f spending.Evaluating the plausibility o f this crucial assum ption requires learn ing som ething about states' likely actions.Cogan and Taylor, however,   rest  the plausibility o f the counterfactual assum ption on a behavioral assum ption with regard to expenditure sm oothing.They support this assum ption by appealing to the results o f their analysis: the positive coefficient on the lagged variables is evidence th at states engage in consum ption smoothing.But this logic is circular.If the proper coun terfactual assum ption is expenditure cutting, then Cogan and Taylor's coefficient estim ates actually refute the assum ption o f expenditure sm oothing.To evaluate their results we need a way to break out o f this circularity and exam ine the assum ptions directly.We did so in two ways.First, we looked behind the aggregate num bers by com paring the individual states' spending responses to the ARRA stim ulus.This removed the counterfactual assum ption that the proper baseline against which to com pare actual post-ARRA spending is steady spending at pre-ARRA levels.Our cross-sectional analysis sought to determ ine, instead, the im pact o f an extra dollar o f ARRA funds on a state's spending relative to other states, controlling for the level o f financial solvency o f the state.Our results show ed that the m arginal dollar o f ARRA funds was associated with an additional $0.66 in spend ing and $0.34 in decreases in borrowing (again, controlling for financial solvency).This com ports w ith other recent cross-state studies o f the effects o f ARRA.Chodorow-Reich et al. (2012), for exam ple, estim ate that ARRA M edicaid assistance to states produced 38 job-years per $1 m illion.W ilson (2011) estim ates that ARRA created or saved roughly 2 m illion nonfarm jobs in its first year, and 3.4 m illion by 2011.15Thesecross-state studies cast som e doubt on the counterfactual assu m p tio n underlying Cogan and Taylor's in terp retation o f their results, but they do so in a relatively indirect way: by dem onstrating that an alternative specification that drops that counterfactual assum p tion produces different results.A m ore direct approach would be to m ake the assum ption itself the subject o f the study, as recommended byParker (2011).In two recent papers, for exam ple, Parker and his coauthors exam in ed the ration al con sum ption sm oothin g assum p tion directly by studying the effects o f tax rebates issued during the 2001 and 2008 recessions on con sum ption , allow ing for variation in response alon g incom e level and different types o f consum ption(Johnson, Parker, and Souleles 2006;Parker et al. 2011).They found that the effect w as larger than would be expected under the assum ption o f rational expectations behavior and that it w as larger for low-income and low-asset households.But m icroeconom etric studies are not the only way to glean infor m ation about the plausibility o f behavioral assum ptions and perhaps not even the best way.Despite their considerable advantages, econo metric analyses will always be lim ited in their ability to reveal the true nature o f the su b jects' lived experience-m ost notably by the need to convert th at experience into data am enable to econom etric analy sis and by the restricting effects o f identifying assum ptions.Another valuable source o f inform ation, and one that suffers less from these drawbacks, is direct acquaintance with the on-the-ground realities o f econom ic agents.O f course, direct appeal to agents has traditionally been m ore w ithin the province o f an th ropology th an econom ics.E conom ists generally resist askin g agents for inform ation abou t why they do w hat they do or w hat they w ould have done if the circum stances had been different.16Often, there is good reason for th is reluctance: there are too m any agents, it is hard to get a representative sam ple, and agents m ay have tro u ble recon stru ctin g the circu m stan ces o f th eir deci sions w ell enough to answer, especially w hen the questions involve a counterfactual.W ith respect to the qu estion o f w hether state governm ents engaged in rational expenditure sm oothing during the Great Recession, however, none o f these reasons apply.There are only 50 states, and state budget officers are a highly professional group o f m en and women.A Unpacking the M ultiplier 841 priori, then, it seem ed sensible to ask these officers w hat they would have done had there been no ARRA funds to offset lost revenues and increased dem ands for expenditure that were the twin results o f the Great Recession.We devised a relatively open set o f interview/survey questions to pose to the 50 state budget officers, with the goal o f ascertaining the extent to which they engage in expenditure sm oothing in general and the extent to which, in the particular case o f the period during which ARRA funds were adm inistered, they would have been able to m ain tain their expenditure at the observed levels in the absence o f ARRA funding.17The results o f the interview s/surveys indicated that while the behavioral assum ption o f an expenditure sm oothing motive was valid in som e respects, the counterfactual assum ption that states would have been able to spend at the observed levels in the absence o f ARRA was invalid.18W ith the exception o f the few states th at had significant reve nues from fo ssil fuels, the respondents were virtually unanim ous in stating that significant expenditure cuts and revenue increases would have been necessary in the absence o f ARRA.M ichigan's State Office o f the Budget, for exam ple, reported that "had no ARRA funding come to M ichigan, general fund reductions o f approxim ately 18% would have been required each fiscal year and would have been in addition to m easures taken to close a $1.4 billion budget gap for fiscal 2009, and $1.8 billion in general fund reductions enacted for fiscal 2010."Moreover, m any o f the respondents com m ented that it was likely that the balance o f the adjustm ent to lower revenues would likely have been weighted heavily toward spending cuts rather than tax or fee increases due to political considerations.These responses cast serious doubt on Cogan and Taylor's interpretation o f relatively flat spending data in the wake o f the ARRA stim ulus as an indication that it was ineffective.If significant cuts in expenditure w as the proper counterfactual, as our interviews/surveys suggest, then the correct interpretation o f the data is precisely the opposite: that ARRA had the positive effect o f avoiding a significant decline in spending.The sentim ent th at low er operatin g expen ditures w ould have been necessary w ithout ARRA w as n ot sensitive to political partyit was voiced equally by those states w ith Dem ocratic or Republican governors.There w as, however, som e difference along political lines with respect to the attitude tow ard the m aintenance o f spending that w as enabled by ARRA.Several officials from Republican states told us that w hile their states w ould likely have enacted m ore spending cuts in the absence o f ARRA, this w ould have been a positive rather than a negative for econom ic health .19We heard this com m ent both with respect to spending in general, and specifically with respect to M edicaid and education-two areas w here ARRA m oney cam e w ith m aintenance o f effort ("MOE") provisions.In general, the them e o f these com m ents was that ARRA allow ed the state governm ent to put o ff dealing with budgetary problem s, som e o f which were structural and would still have to be dealt w ith once the ARRA funds dried up.Many o f the budget officials com m ented that they were wary o f creat in g a "fiscal cliff" by u sin g ARRA m oney to continue to fund program s at levels th at w ould likely be u n su stain ab le post-ARRA.However, d espite th ese differen ces in p o litical attitu d es tow ard the stim u lus, the verdict w ith respect to the Cogan and Taylor counterfactual assum ption was uniform ly negative.Of course, some o f the doubt cast on Cogan and Taylor's counterfactual assum ption com es sim ply from form al legal and institutional facts about state governm ent budgeting.Constitutional and statutory provisions prevent all 50 state governm ents from borrow ing to fund operating budget deficits.As such, one m ight argue that it would have been possible to ju dge the plausibility o f Cogan and Taylor's counterfactual assum ption sim ply by determ ining whether the savings states had built up prior to 2009 would have been sufficient to fill their oper ating shortfalls in the absence o f ARRA.In fact, we perform ed this veiy calculation using public data and found the so-called rainy-day funds w oefully inadequate to w ith stand the shock o f the Great Recession (Marglin and Spiegler 2013a, 2013b).But direct interaction was needed to determ ine whether the actual practice o f state budgeting included Unpacking the M ultiplier 8 4 3 strategies for creatively circum venting the limits o f rainy-day funds in tim es o f crisis.We learned (1) that som e such strategies are available to budget officers, (2) th at there is significant variation across states in their nature and usage, and (3) that even taking such strategies into consideration, it still would not have been possible for the vast m ajority o f the responding states to have avoided significant expenditure cuts in the absence o f ARRA.Our study o f state budget officers' experience with the ARRA stim ulus highlights the im portance not only o f assessin g the assum p tions underlying m u ltiplier calculations, but also o f m atchin g the choice o f investigative m ethods to the level and type o f inform ation n ecessary to perform such an assessm en t.M icroeconom etric and partial-equilibrium m acroeconom etric studies can elicit som e types o f in form ation abou t beh avioral responses to stim ulus paym ents, but they are constrained to do so by im posin g structure on ag en ts' experience to m ake it am enable to econom etric analysis.This is the well-known "looking under the lam ppost" problem o f economic m eth odology (because it is capable only o f analyzing problem s and inform a tion o f a certain form, econom ists are constrained to ignore problem s and inform ation that are not o f this form).Direct appeal to agents using qualitative m ethods can help us to shed light on the dark areas beyond the bailiwick o f our form al m ethods.By exploring the m eaning o f the agen ts' circum stances and behavior from their own perspective, we allow for the possibility that relevant types o f inform ation and concep tions o f the problem m ight be other than we had initially imagined.In light o f the high stakes involved in evaluating the possibilities o f fiscal stim ulus, and the heavy dependence o f current m ultiplier estim ation techniques on untested assum ptions, these advantages o f qualitative, interpretive techniques seem to u s to outweigh their logistical costs.CONCLUSION Empirical estim ates o f the m ultiplier are imperfect tools for assessin g the w isdom o f fiscal stim ulus policy.To solve the enorm ous identifi cation problem o f isolatin g the im pact o f governm ent spending in a dynamic economy, restrictive assum ptions m ust be m ade that severely lim it the applicability o f the resu ltin g estim ate.The leading identifi cation techniques in the recent literature produce estim ates that are either im plausibly general-for exam ple, they posit a single m ultiplier that is insensitive to variation in econom ic conditions or the com posi tion o f the economic agents receiving the stim ulus-or that are im plau sibly specific-they, for instance, are generated by highly structured m odels that can only produce estim ates o f w hat the m ultiplier would be if their assum ptions about econom ic behavior and dynam ics were correct.In the case o f DSGE models, the estim ates actually suffer from both o f these problems.A ssessm ent o f the w isdom o f fiscal stim ulus policy, if it is to be done responsibly, requires paying attention to the actual (or poten tial) design features o f the policy and the actual characteristics o f the economy into which the stim ulus is being introduced.If we are to use m ultipliers as part o f our assessm en t toolkit, then it w ould be m ost desirable to prospectively design studies to estim ate specific m ultipli ers for specific fiscal stim ulus episodes-that is, studies that reflect the characteristics and conditions relevant to the particular fiscal stim ulus we w ant to assess.If we are to use historical estim ates o f the m ulti plier responsibly, we m ust at the very least subject their identifying assum ptions to rigorous scrutiny before claim ing that the estim ates are relevant to the particular fiscal stim ulus program we aim to assess.Our study o f recent work by John Taylor and John Cogan reveals the dangers o f not doing so.Taylor and Cogan's conclusion that one o f the m ost substantial elem ents o f the ARRA stim ulus had been a fail ure was fundam entally dependent on untested assum ptions that were at b est questionable and at w orst clearly im plausible.N onetheless, Cogan and Taylor claim ed th at both the finding and the underlying assum ptions had been vindicated by the data, and their claim was given the im plicit im prim atur o f the discipline by its publication in one o f the econom ics profession 's elite jou rn als (Taylor 2011a).The stakes surrounding the policy debate over fiscal stim ulus are too high to allow such porous standards for assessin g multiplier-based arguments.Unpacking the Multiplier 8 4 5 AP P EN D IX B We can reflect crow ding out in the m ultiplier form ula by adjusting the m ultiplicand.If CO represents the fraction o f new spending which displaces existing production and m = 1 -CO, the initial spending o f $1 now generates only $m o f new output.A ssum ing subsequent rounds of spending are subject to the sam e degree o f crowding out, the second round generates $mx(mx MPC), the third round $m x (m x MPC) x (m x MFC), and so on.The m ultiplier sum becom es + m M P C * +...) and the m ultiplier, instead o f being 1/(1 -MPC), is Spending Multiplier with Crowding Out = m /1 -mMPC) m ultiplier sum becomes Generic Tax M ultiplier = $MPC (1 + MPC + MPC 2 + MPC 3 + -) = MPC/ (1 -MPC) Here we are assum in g no crowding out, so that the fraction o f incom e spent on purchases o f goods and services actually leads to an equal increase in new production.Observe that governm ent spending exactly offset by taxes leads to a m ultiplier o f 1.The form ula is Generic Spending Multiplier -Generic Tax Multiplier = 1 MPC I-M PC 1 -M PC = l -t Unpacking the M ultiplier 8 4 7 This is the so-called balanced-budget multiplier.W ith crowding out, the tax m ultiplier becom es Generic Tax Multiplier with Crowding Out = mMPC / (1 -mMPC) A P P EN D IX D Taking this qualification into account, we have the tax m ultiplier as Specific Tax Multiplier with Crowding Out = mv / (1 -mMPC) where v = fraction o f tax reductions (transfers, grants) spent by benefi ciaries.The param eter v is an additional adjustm en t to the m ultipli cand that we can think o f as a valve controlling the flow o f the initial stim ulus into the economy.If v = 0, then the valve is shut.The spending never m akes it into the economy, and so the m ultiplier has nothing to multiply.government spending m ultiplier m easures the marginal impact o f a dollar o f extra governm ent spending on GDP.A value below 1 indicates an im pact on GDP less than the initial dollar spent and, therefore, a negative effect o f government spending to values o f GDP. 2. AY/AG = 1 / ( 1 -MPC).3. "Crowding out" refers to the process by which investment spending by one sector o f the economy (in this case, the government) reduces opportunities for other sectors (in this case, private investment).4. Refer to Appendix B. m = 1 -CO, w hen CO = 1, m = 0, Spending Multiplier with Crowding Out = m / (1 -mMPC) = 0. 5. Refer to Appendix C, v = 0. 6.J. Bradford DeLong and Lawrence Summers (2012) argue that deficit spending m ay be self-financing because a higher level o f economic activity may forestall a decline in potential GDP associated with the existence o f underutilized capacity.
11.One could object that it is not sim ply estim ating param eter values that should give us confidence in the identifying assum ptions but rather estim ating parameters values that give the m odel a close fit to the data.But we can never be certain what the param eter estimates and data fit are telling us about the identifying assum ptions because o f the interdependence o f the two.12.The Lucas Critique asserts that the effects o f a change in economic policy cannot be predicted by observing historical data.13.That is, that v = 0. 14.The site www.recovery.govputs the cumulative total o f ARRA.expen ditures at $804 billion, as o f February 2013.The $250 billion figure for funds flowing to state governments is our own calculation (Marglin and Spiegler 2013a), based on data from the Bureau o f Economic Analysis and www.recovery.gov.It includes supplem ental Medicaid assistance and funds going to local governments.
use o f interviews with businessm en to explore the im pact o f the interest rate in the determ ination o f Unpacking the M ultiplier 8 4 9 investment; and Blinder et al. (1998) and Bewley's (1999) discussions with relevant econom ic actors to explore the reasons behind the stickiness o f prices and wages, respectively.17.We sent the questions alon g with a cover letter explaining our research to all o f the state budget officers via email, offering them the options o f answering the questions in writing or through a telephone interview.In one case (Massachusetts) our interview was conducted in person.18.Of the 50 state budget directors we contacted, we received written responses from had phone interviews w ith 29.Obviously, our aim was to collect inform ation from all o f the states, and we m ade efforts over a five-month period to collect a comprehensive set o f responses.Despite these efforts, however, we received no response from 21 states.Nonetheless, we feel that our group o f respondents is large and com prehensive enough and sim ilar enough to the nonresponse set in many im portant demographic aspects to give us som e confidence that the responses are not tainted with selection bias.The responding states accounted for 64 percent o f US GDP, 61 percent o f the population, 64 percent o f total state government expenditures, and had an average GDP per capita o f $47,603 versus the national figure o f $45,457 (Marglin and Spiegler 2013b; all figures from 2009).