Fiscal reaction rules are necessary in both real and model economies to specifyhow fiscal policy would change after an economic shock to prevent the ratio of
∗ Tel.: +1-816-881-2349; fax:+1-816-881-2199.E-mail address: [email protected] (R. Johnson).1 The author is an economist at the Federal Reserve Bank of Kansas City. This paper was largely
written while the author was working in the Fiscal Policies Division of the European Central Bank.
640 R. Johnson / Journal of Policy Modeling 25 (2003) 639–653
government debt to GDP from exploding. Many fiscal reaction rules would preventthe debt-to-GDP ratio from exploding, so policymakers and modellers face thequestion of which rule to choose. Policymakers’ choice of fiscal reaction rule willaffect the time-path of taxes and thus economic efficiency and the distribution ofwealth across generations. Modellers’ choice of fiscal reaction rule will affect theperformance of their models and thus any advice based on them. Central banks’and forecasters’ simulation models contain a wide variety of fiscal reaction rules,showing there is little agreement on what these rules should be.
This paper uses the IMF’s MULTIMOD simulation model to compare the con-sequences of two fiscal reaction rules for consumers’ utility. MULTIMOD’s fiscalreaction rule, itself typical of central bank models’ fiscal rules, makes tax ratesreact to the deviation last period of the government debt-to-GDP ratio from a tar-get. This type of reaction makes the path of aggregate consumption rather volatile.By contrast,Barro’s (1979)rule of keeping the tax rate constant at the level thatstabilizes the debt-to-GDP ratio in the long run generates smoother paths of aggre-gate consumption, which would be preferable to a representative indefinitely-livedconsumer.
This result has two implications. First, since they assume arbitrary and subopti-mal fiscal policy, many of the large-scale models in use at central banks and otherpolicy institutions may generate misleading forecasts. Second, fiscal reaction rulesbased on simple targets for debt or deficit ratios can impose unnecessary costs onconsumers. This criticism applies also to the E.U.’s Stability and Growth Pact andthe often-proposed balanced-budget amendment to the U.S. constitution, whichare also simple limits for the deficit or debt-to-GDP ratio. While such simple lim-its may help enhance the credibility of governments’ promise to repay their debtswithout monetization, their costs should also be recognized.
This paper adds to the optimal fiscal policy literature by comparing fiscal rulesoutside the specific settings amenable to theoretical analysis.Barro (1979)showedthat in a particular reduced-form deterministic model, a constant tax rate is optimal.The intuition of this result is that constant taxes allow the burden of temporarilyhigh spending, such as on a war, to be spread over the entire future. While aconstant tax rate is not optimal in all environments, this paper shows that theintuition behind it carries over into the MULTIMOD model. This paper also addsto papers byMitchell, Sault, and Wallis (2000)andChurch, Sault, Sgherri, andWallis (2001)comparing debt and deficit-targeting rules in simulation models byshowing how such rules compare to the qualitatively different constant-tax-raterule.
This paper proceeds as follows.Section 2explains the need for fiscal reac-tion rules.Section 3reviews previous literature on fiscal reaction rules.Section 4describes fiscal rules in several working macroeconomic models, and comparestheir properties to those of the constant-tax-rate rule.Section 5compares eco-nomic outcomes given a government spending shock under the constant-tax ruleand MULTIMOD’s fiscal reaction rule.Section 6concludes that simple debt ordeficit-targeting rules impose real economic costs. Restrictions on fiscal policy
R. Johnson / Journal of Policy Modeling 25 (2003) 639–653 641
intended to increase the credibility of government’s commitments to repay theirdebts should therefore be designed to minimize these costs.
2. The need for a fiscal reaction rule
This section discusses whether fiscal reaction rules are necessary parts of theeconomy in two settings. In a closed-market Ramsey model, a fiscal reaction ruleis not necessary, but might be desirable to prevent fiscal policy from affecting theprice level. In a long-run macroeconomic simulation model, a fiscal reaction ruleis typically necessary to ensure that fiscal policy is on a sustainable path by theend of the simulation horizon.
Analysis of the government’s budget constraint explains the role of fiscalreaction rules. I now briefly summarizeDaniel’s (2001)clear analysis of thegovernment’s budget constraint in a closed-economy Ramsey model.2 This flowconstraint in real terms is
bt + mt = rt(bt + mt) + gt − �t − itmt, (1)
whereb is the real stock of government bonds,r and i are the real and nomi-nal interest rate, respectively,m is the real money stock,g is government spend-ing, and� is tax revenues. Both bonds and money can be thought of as instru-ments through which the government borrows from consumers. IntegratingEq. (1)gives
Since this integral is the net present value of the government’s borrowing fromconsumers, the government’s intertemporal budget constraint holds if
limT→∞
(bT + mT )�T =∫ ∞
t=0(gt − �t − itmt)�t dt + b0 + m0 = 0. (2)
Since consumers do not wish to lend to the government without being repaid inpresent value, market equilibrium requires that constraintEq. (2)holds. Thus, arule for the behaviour of fiscal policy is not required to close the model; changesin the price levelP will ensure that (2) holds for any fiscal policy. This is the“fiscal theory of the price level,” stating that for a given path of future surpluses,additional government spending today will increase the price level.
Policymakers may desire that a monetary authority have control over the pricelevel. To achieve this, the fiscal authority would need to commit to a fiscal re-
2 Daniel (2001)gives full details of the model.
642 R. Johnson / Journal of Policy Modeling 25 (2003) 639–653
action rule changing taxes or spending in response to any shock such that thenon-monetary elements of (2) sum to zero in present value for allP, or such that
limT→∞
(bT )�T =∫ ∞
t=0(gt − �t)�t dt + b0 = 0, ∀P. (3)
Given such a fiscal reaction rule,Eq. (2) implies that issuance of money willdetermine the price levelP. Thus, a fiscal reaction rule, or limits for governmentdebt or deficits as in the E.U.’s Stability and Growth Pact, would allow the monetaryauthority to control prices.
Simulation models of a macroeconomy must also include the flow intertemporalbudget constraint (1). If taxes, spending and the supply of money are fixed, andthe economy is subject to a shock, growth of real debt at the rater may lead togovernment debt reaching, say, 500% of GDP by the end of a 100-year simulationhorizon. Such an outcome would imply that a large adjustment to taxes, spending,prices or all three must occur beyond the horizon’s end. Macroeconomic modellerstypically prefer their simulations to end with the economy at or near a sustainablefiscal position. Thus, asLaxton, Isard, Faruqee, Prasad, and Turtelboom (1998)state, a fiscal reaction rule is necessary “to preclude unrealistic model solutions inwhich the stock of government debt grows without bound relative to GNP.”3
3. Literature review
This section discusses literature on optimal fiscal policy rules, and literatureon fiscal reaction rules in numerical simulation models. The latter literature hasdrawn little from the former, however, typically seeking only to stabilise debtwithout seeking to do in an optimal manner.
Literature on optimal fiscal policy has studied whether optimal labour taxes areconstant in a deterministic model, and how tax rates would optimally respond toshocks.Barro (1979)showed that in a deterministic reduced-form model, the opti-mal tax rate is constant, and went on to claim that the optimal tax rate in a stochasticmodel would be a random walk. More recent work has amended both conclusions.Zhu (1992)finds that in a fully-specified Ramsey model optimal labour tax ratesare constant for some preferences but not others.Chari and Kehoe (1999)showthat in a stochastic model without capital, optimal labour tax rates do not follow arandom walk but rather follow the stochastic properties of shocks to governmentconsumption. However, the work of both Zhu, Chari, and Kehoe reflects Barro’sintuition that optimal tax policy would seek to minimize the volatility of tax ratesover time. Thus, I interpret Barro’s constant-future tax not as being optimal in awide class of models but as providing an interesting comparison with fiscal rulesprescribed in law and in existing macroeconomic models.
3 Laxton et al. (1998, p. 10).
R. Johnson / Journal of Policy Modeling 25 (2003) 639–653 643
Literature on fiscal reaction rules has three themes. The first, as inColetti,Hunt, Rose, and Tetlow (1996)andLaxton et al. (1998)is that simulation modelsrequire fiscal reaction rules. The second theme is the description of the rules used incurrent models and demonstrations that they do indeed prevent the debt ratio fromexploding. The third theme, as inMitchell et al. (2000)andChurch et al. (2001),is that the performance of economic models and presumably thus also of realeconomies depends heavily on the fiscal reaction rule chosen. One might interpretthis result as suggesting that fiscal reaction rules should be chosen in some optimalway. However, the design of fiscal rules in existing simulation models draws littlefrom the optimal tax literature, with modellers typically emphasizing only thattheir rule stabilizes debt, not that it does so in any optimal way. Existing fiscalreaction rules are also typically arbitrary, and have some unfortunate features, asthe next section describes.
4. Fiscal reaction rules in macroeconomic simulation models
This section describes three fiscal reaction rules representative of those in ex-isting simulation models. It then describes their properties and compares theseproperties to those of the constant-future-tax rule.
Descriptions of fiscal rules in current macroeconomic simulation models reveala wide variety of functional forms. The Mark III version of MULTIMOD adjuststhe tax rate� at times to ensure the debt-to-GDP ratio returns to an exogenoustarget value, according to
�t = � + �
i=t+2∑
i=t−2
�i + �
(Bt−1
Yt−1−
(B
Y
)∗) , (4)
whereB is nominal government debt,Y is the nominal GNP, and (B/Y)∗ is the targetratio. However, the Federal Reserve’s FRB/US4 model uses the different rule forthe tax rate:
�trendt = �trend
t−1 + �
((B
Y
)t−1
−(
B
Y
)∗
t−1
)+ �
((B
Y
)t−2
−(
B
Y
)∗
t−2
),
(5)
and the Federal Reserve’s FRB/Global model5 uses the different, if related rule
�t = k + m
((B
Y
)t−1
−(
B
Y
)∗) ∣∣∣∣(
B
Y
)t−1
−(
B
Y
)∗∣∣∣∣ . (6)
4 Brayton and Tinsley (1996)describe the FRB/US model but do not give equations. These areavailable upon request from David Reifschneider of the Federal Reserve Board.
5 See the description inLevin, Rogers, and Tryon (1997).
644 R. Johnson / Journal of Policy Modeling 25 (2003) 639–653
The variety of different fiscal rules in current macroeconomic models suggests thatall these rules are somewhat arbitrary.
Inspection of existing fiscal rules shows two properties likely to induce sub-optimal fiscal policy. First, rules (5) and (6) make current tax rates a function ofpresent and past debt, but not of future spending. Therefore, they are backwardrather than forward-looking. This will induce suboptimal responses to temporaryshocks if governments know how long such shocks will persist. Most macroe-conomic simulation models assume consumers foresee future variables, so it isplausible to think governments would also have some information about them.Although rule (4) sets taxes in a somewhat forward-looking way, so that taxes risebefore any increase in government spending, in practice it performs very simi-larly to the backward-looking rules (5) and (6). Second, rules (4)–(6) all constrainthe debt-to-GDP ratio to return to a target level, which is exogenous both to thehistory of shocks hitting the economy and to parameters of the economy such asits growth rate. Stability of the debt ratio at any level would prevent debt fromexploding, however, so the requirement that the debt ratio return to a target valueis unnecessary.
By contrast, the sustainable level of the tax rate under the constant-future-taxrule is a function of the future path of government spending, which I assume thepresent government knows, and all other aspects of the economy, such as its trendgrowth path. The sustainable level of the tax rate determines the level at which theratio of government debt to GDP will stabilise in the long run. Like the tax rate,this debt ratio will also be endogenous to the history of shocks hitting the economyand to all other aspects of the economy.
The qualitatively different response to spending shocks of debt-targeting rulessuch as (4)–(6) is relevant to two current debates over fiscal rules. The first is theconcern that the Stability and Growth Pact and the proposed U.S. balanced budgetamendment tend to prevent governments from running temporary deficits in orderto fight wars or respond to natural disasters. The constant-tax-rate rule ensuresfiscal sustainability while permitting temporary deficits for such emergencies. Asis shown below, temporary deficits tend to allow a smoother and thus preferablepath of consumption.
A second debate over the Stability and Growth Pact concerns whether its rulesare appropriate for a varied collection of economies. This is a concern in particularof the ten new member countries of the E.U. These countries are likely to experiencefaster GDP growth than the rest of the E.U. for some period, and could thereforesustain higher government deficit-to-GDP while keeping the ratio of debt-to-GDPstable. These countries may also wish to run large deficits in the short run soas to invest in infrastructure. Since the constant-tax-rate rule makes the tax rate afunction of the economy’s future growth path, it permits government deficits duringa developmental period if these are consistent with a sustainable fiscal policy. Bycontrast, simple debt or deficit-targeting rules such as (4)–(6) and the Stability andGrowth Pact tend to prohibit large government deficits. For this reasonBuiter andGrafe (2002)argue that the constant-tax-rate rule is superior to the Stability and
R. Johnson / Journal of Policy Modeling 25 (2003) 639–653 645
Growth Pact. An interesting extension to the current paper would be to comparethe implications of the constant-tax-rate rule with those of the Stability and GrowthPact for a variety of different economies.
5. Simulation of the constant-tax rule and a simple debt-targeting rule
This section describes the IMF’s MULTIMOD model, and briefly discusseshow I implement the constant-tax-rate rule in it. It then compares the response ofa model economy to a shock to government spending under the constant-tax-raterule and MULTIMOD’s existing fiscal rule. While this single comparison doesnot test which rule is preferable in general, it shows the qualitative differencebetween these rules, and why the constant-tax-rate rule may in general inducehigher consumer utility.
MULTIMOD is a multi-country macroeconomic model used to study the trans-mission of shocks across the world economy and the consequences of differentfiscal and monetary policies. Due to various simplifications its tax rates do notcreate all the efficiency losses studied by public finance economists. It containsa tax on capital income, which affects the long-run capital stock, and a tax onhousehold income. An important feature of the model is that private consumptiondepends heavily on current disposable income, so changes in the tax rate on house-hold income affect private consumption and GDP in a Keynesian manner. Laboursupply is exogenous and thus not affected by taxes. MULTIMOD’s fiscal reactionrule,Eq. (4), adjusts the basic tax rate, or the share of tax revenues in GNP, to keepthe ratio of government debt to GNP at its target level. Movements in the basic taxrate also change the tax rates on capital and labour.
Implementing a constant tax rate in MULTIMOD requires searching numer-ically for a constant tax rate� and a steady-state debt ratio (B/Y)∗ which areconsistent with each other given the assumed path of economic shocks. In fact, noconstant tax rate can make the debt ratio entirely stable by the end of the model’shorizon in 2150. Thus, to implement a constant tax rate I find a tax rate and long-rundebt ratio that are very nearly consistent and use MULTIMOD’s existing fiscal rulein the later part of each simulation to ensure the tax rate adjusts to stabilize thedebt ratio at this level. The resulting path of the tax rate is thus constant but for aslight wobble late in each simulation, which makes a negligible difference to eachsimulation’s economic content.6
I compare the constant-tax rule with MULTIMOD’s existing rule given theshock that, in 2010, government consumption is reduced permanently by 1% ofGDP. I model this shock as being a surprise in 2010 but not afterwards by startingthe simulations in 2010. The simulated economy reaches a steady state in 2150.Fig. 1 shows the constant tax rate which is a sustainable response to this shock
6 The working paper version of this paper, available atwww.kc.frb.org/Publicat/Reswkpap/rwp01.htm, gives a longer description of how I implement a constant tax rate in MULTIMOD.
Fig. 1. Tax rate under MULTIMOD and constant-tax rules, government spending decreased by 1% of GDP permanently and unexpectedly in 2010.
R. Johnson / Journal of Policy Modeling 25 (2003) 639–653 647
and the tax rate path given by MULTIMOD’s existing rule. The constant-tax ratepath falls heavily in 2010 when the spending shock becomes known. This path isthen constant but for a small wobble in 2040, which results from my adjustment toensure that the debt ratio is entirely stable by 2150. MULTIMOD’s fiscal rule (4)does not reduce the tax rate as fast as the constant-tax rule in 2010 or 2011. The taxrate then overshoots the level of the constant tax rate before stabilizing at a similarlevel. This overshooting is not surprising, since the debt ratio would explode werethe tax rate always above or always below the level of the sustainable constant taxrate.
Fig. 2compares GDP under the constant-tax-rate rule and MULTIMOD’s fiscalrule. The units of they-axis are percentage-point differences from the baseline path.The decline in government consumption starting in 2010 reduces demand and thusoutput that year. This effect is offset by reductions in the tax rate, however. Becausethe fall in the constant tax rate is larger in 2010, the decline in GDP in this year issmaller under this rule than under MULTIMOD’s fiscal rule. The path of GDP isalso smoother thereafter under the constant-tax-rate rule, since the MULTIMODrule produces more fluctuations in the tax rate.
Since labour supply is exogenous in MULTIMOD, I calculate private utility asa function of aggregate consumption at each date.Fig. 3shows the time-paths ofprivate consumption under the constant-tax-rate rule and MULTIMOD’s rule. Theconstant-tax-rate rule’s large cut in taxes in 2010 induces a large increase in con-sumption that year. Thereafter consumption grows fairly smoothly, though againwith a small wobble after 2040. Under MULTIMOD’s fiscal rule, consumptionreflects the sluggish adjustment of the tax rate by rising more slowly in 2010–2012,and then fluctuating around the consumption path under the constant-tax rule. Iconstruct “aggregate utility” from these two consumption paths from 2010 to 30107
using the utility function:
U =S=N∑S=1
c1−�s
1 − �(1 + �)−s, (7)
where� reflects a consumer’s willingness to substitute consumption over time and� is the private rate at which future flows of utility are discounted back to thepresent. Ideally I would compare utility from consumption until infinity; lackingan expression for (7) asN → ∞ I cannot do this, but the net present value of differ-ences after 3010 is probably small.Table 1shows the calculated percentage-pointincrease in “aggregate utility” from consumption under the constant-tax rule com-pared to that under MULTIMOD’s rule, for values of� from 1 to 4 and valuesof � from 0.03 to 0.09. The utility increases are all positive, so for a wide rangeof parameter values the consumption path induced by the constant-tax-rate rule ispreferable in this aggregative sense. The utility differences are small, because the
7 The MULTIMOD simulations run to 2149, from which date I extend the consumption seriesforward at their trend growth rates of 2.2007% per year.
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.Johnson/Journal
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-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
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2039
2041
2043
2045
2047
2049
Year
Per
cen
tag
e-P
oin
t C
han
ge
fro
m B
asel
ine
MULTIMOD
Constant Tax Rate
Fig. 2. GDP.
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/Journalof
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odeling25
(2003)639–653
649
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
2001
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2029
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2047
2049
Year
Co
nsu
mp
tio
n, P
erce
nta
ge-
Po
int
Ch
ang
e fr
om
Bas
elin
e
MULTIMOD
Constant Tax Rate
Fig. 3. Private consumption.
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25(2003)
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0.32
0.325
0.33
0.335
0.34
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
2021
Go
vern
men
t D
ebt/
GN
P
2023
2025
2027
2029
2031
2033
2035
2037
2039
2041
2043
2045
2047
2049
Year
MULTIMOD
Constant Tax Rate
Fig. 4. Government debt/GNP.
R. Johnson / Journal of Policy Modeling 25 (2003) 639–653 651
Table 1Percentage-point increase in aggregate utility of consumption path, constant-tax-rate rule over MUL-TIMOD rule
Note. Aggregate utility is constructed from aggregate private consumption from 2010 to 3010,using the iso-elastic utility function,Eq. (7) in the text. Private consumption is simulated until 2149and assumed to grow at the trend rate of 2.2007% per year thereafter.
different rules induce very similar consumption in the long run, but increase withhigher� and� as both make the differences in consumption in 2010–2012 moreimportant.
The evolution of the debt–GNP ratio is qualitatively different under the twofiscal rules, asFig. 4 shows. MULTIMOD’s fiscal rule returns this ratio fairlyswiftly to its baseline value. The constant-tax-rate rule instead allows the debtratio to asymptote towards a new level. Due to my method of implementing theconstant tax rate, the debt-to-GNP ratio does not asymptote completely smoothlyto its new level, instead following a slight shoulder onto its new long-run ratio in2040 as the tax rate is adjusted slightly. In general, the constant-tax-rate rule couldresult in a higher or lower long-run debt ratio than the target of MULTIMOD’sfiscal rule.
In summary, under the given shock to government spending, MULTIMOD’sfiscal rule induces a tax-rate-path that is more volatile than that under the policy ofmaking a one-time adjustment to an otherwise constant tax rate. Using the metricof the utility generated by an iso-elastic utility function, the constant-tax-rate rulegenerates a preferable path of aggregate consumption. Although I have shownthe case of only one economic shock,Figs. 1–4show qualitatively how the factthat MULTIMOD’s fiscal rule is largely backward-looking and forces the ratio ofgovernment debt-to-GNP to return to its starting value induces more volatility inthe tax rate and thus in consumption than the constant-tax-rate rule.8
6. Conclusion
This paper has shown that, while most current macroeconomic simulation mod-els contain arbitrary fiscal reaction rules, it is possible to implement a constant
8 The working paper version of this paper, available atwww.kc.frb.org/Publicat/Reswkpap/rwp01.htm, shows simulated responses to other shocks. In all cases the constant-tax-rate rule inducedsmoother and hence more desirable consumption paths.
652 R. Johnson / Journal of Policy Modeling 25 (2003) 639–653
future tax rate in those models. Although a constant future tax rate is not optimalin all models, the simulations shown here suggest that the lower degree of con-sumption volatility it induces may often make it preferable to the type of fiscal rulecurrent models include. Macroeconomic modellers should thus be concerned thattheir forecasts may be influenced by the assumption of arbitrary and suboptimalfiscal rules.
The finding that the constant-tax-rate rule may be preferable to simple debt-targeting fiscal rules also suggests two weaknesses of the E.U.’s Stability andGrowth Pact. This Pact was intended to construct limits on fiscal policy whichwere simple enough for their enforcement to be credible. However, as shown here,simple fiscal limits are likely to be inferior to the constant-tax-rate rule becausethey do not allow taxes to be set as a function of the properties of each differentshock and because they do not allow fiscal policy to be tailored to the parametersof different economies. Since adherence to simple fiscal targets generally involveseconomic costs, limits on fiscal policy should presumably be designed to minimizethese costs. One method of doing so would be to re-write the Stability and GrowthPact so that it would not restrict the fiscal policies of countries whose debt-to-GDPratios fell below a threshold such as 40%. The Pact could then concentrate oncountries whose fiscal policies appear unsustainable without micro-managing thefiscal policy of countries with little debt.
Acknowledgments
The author would like to thank the IMF’s Douglas Laxton, Peter Isard, HamidFaruqee, Eswar Prasad, and Bart Turtelboom for making their MULTIMOD MarkIII model available atwww.imf.org/external/np/res/mmod/mark3/index.htm, and,along with David Altig and V.V. Chari, for their comments on this paper. Theviews expressed herein are solely those of the author and do not reflect those ofthe Federal Reserve Bank of Kansas City or the Federal Reserve System.
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Levin, A. T., Rogers, J. H., & Tryon, R. W. (1997, August).A guide to FRB/Global. Boardof Governors of the Federal Reserve System, International Finance Discussion paper 588,www.bog.frb.fed.us/pubs/ifdp/1997/588/default.htm.
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