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Inflation and Taxation with Optimizing Governments

James M. Poterba; Julio J. Rotemberg

Journal of Money, Credit and Banking , Vol. 22, No. 1. (Feb., 1990), pp. 1-18.

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J A M E S M . PO T E R B AJ U L I O J . R O T E M B E R G

Inflation and Taxation withOptimizing Governments

G O V E R N M E N T C A N SATISFY ITS UDGET C O N S T R A I N T

either by printing money or by levying taxes. Each method of finance has effi-ciency costs. High er inflation r ates ma y adversely affect the economy s tran sac-tion m echanism an d lead to inefficiencies in contracting . Higher tax es may d is-tort labor supply, saving, and investment decisions. Numerous authors haveexamined the op timal inflation rate in the presence of ta x finance , describing thebehavior of governments concerned only with minimizing the deadweightburd en of raising a given revenue.] Whe ther these prescriptions are consistentwith actual gov ernm ent behavior is an unresolved an d relatively unstudied issue.Mank iw (1987) repo rts a striking positive correlatio n between tax b urde ns an dinflation rates in the postwar United States, a findin g consistent with the predic-tions of these optim izing governm ent m odels.

This paper extends previous work on the interac tion between taxes and infla-tion. W e present new emp irical evidence o n the correlation between inflation an dta x ra tes in a sample ofOE D countries , and conclude th at optimizing modelswith time-invariant tastes cannot explain the observed correlations in m ost cou n-

Th e auth ors ar e grateful to B arry Perlstein for research assistance, to G regory M ankiw, LawrenceSu mm ers, members of the NBER Tax ation G roup , the editor, three referees, and especially D avidRo me r, for helpful comm ents. This research was supported by the National Science Fou nda tion an dthe Alfred P. S loan F oundatio n. A data app endix for this project has beendeposited with the IC PS Rin Ann Arbor, Michigan.

IPrevious studies include Phelps (1973), Calvo (1978), Dra zen (1979), He lp m an an d S ad ka (1979),Kimbrough (1986), Lucas (1986), and Romer (1987).

J A M E S is professo r of econom ics Massachusetts Institute of Tech nology.. POTERBAJU LI O. ROTEMBERGs professor of applied economics M I T Scho ol of Managem ent.



3A M E S M . P O T E R B A A N D JU L .1 0J R O T E M B E R G :

first consider the case where commitment is possible, then examine how the ab-sence of commitment affects the results.

The government s objective is to minimize the expected total cost of raisingrevenue, given by

where is a discount factor, 0 equals the ratio of taxes to incom e a tax rate)inperiod t , and is the price level. We assume that k is a monotone increasingfunction while h , the tax distortion, is increasing and convex.

The increasing and concave function v( )gives the benefits from deflation sothat the costs of inflation are -v( . This function is not just intended to capturethe distortionary effects of inflation on the demand for money, as in Drazen(1979), Phelps (1973), Kimbrough (1986), and Lucas (1986). Instead, it reflectsthe many possible consequences of inflation enumerated by Fischer and Modig-liani (1978).4 In particular, the government might be concerned with the distribu-tional consequences of inflation as well as with the difficulties inflation intro-duces in a world with pervasive nominal contracts.

The government s budget constraint is described by the evolution of real gov-ernment debt, b , :

where m , ,g , , and y denote real money balances, real government spending, andreal income, respectively. The nominal interest rate is t We treat governmentspending as exogenous, but allow real income to depend on the tax rate. Realmoney balances and the nominal interest rate at t depend on anticipated inflationbetween t and t+ 1.5

The Com mitme nt CaseSuppose the government chooses a tax schedule which specifies payments as a

function only of past actions. Absent reputational effects, such a government willregard all taxes as nondistortionary. While there are distortions from anticipa-tion of these taxes, they do not influence the government s ex post actions. Arather different situation arises when the government chooses taxes which spec-ify payments as functions of current or future decisions. Such a government s

choice of tax instruments may be guided by considerations of excess burden. At

4Because we consider relatively many effects of inflation, there is no presu mption, as in the m orenarrow m odels of Kimbrough 1986) or Faig 1987), that the optimal tax rate on moneyis given by



M O N E Y, C R E D I T, A N D B A N K I N G

least in the U nited State s, we routinely take governm ent com m itm ent regardingtax rates for gran ted. Incom e ta x schedules are often legislated several years inadvance. This commitment is in part the result of t ime lags in the legislative

process.M one tary policy differs from fiscal policy in several im porta nt ways. Fir st , theFederal Reserve ca n react quickly to changed circumstances: t ime lags are sho rt-er. Second, the Fed announces its intentions about future policy only in verybroad te rms. There i s no cou nterpar t to the publica tion of fu ture tax tables.Verifying breaches of comm itment by the central ban k is therefore muc h mo redifficult tha n identifying similar breaches by the ta x aut hority . These considera-t ions d o not imply tha t comm itment by the m onetary authori t ies is impossible .Repu tat ional forces might be stron g enough to ensure that the money supply

a lways remains on the ag r ted-upo n pa th . W hether centra l banks can comm it tofuture actions is therefore all emprical matte r.

Optim al policies with com mitm ent ca n be modeled by al lowing the govern-me nt , which m aximizes 1 ) subject to 2 )a t t ime t , to pick a contingency plan forta x rates an d, by choosing future mon ey supplies, fo r prices att+ 1. This plan,which allows taxes a nd inflation to depend o n the realizations of allt+ variablesincludingg, , , andy,,, is chosen before hou seholds cho ose their m oney holdings.Thus , real money d em and an d interest rates are determined after the governmentchooses the next period s taxes an d inflat ion. Th e governme nt choosing taxesan d inflation for period t+l takes a s given the end -of-period stock of governmen tliabilities, 6 , m , . Th e stock of l iabili ties is the only state variable for the go v-ernment s prob lem , the sole cha nne l throu gh which policy choices in periodtaffect future values of m oney d em and , prices, an d o utp ut . Th e division of thesel iabil it ies between money an d bond s, however, depends on the government s de-cisions in period t .

Holding c onsta nt the end-of-period stoc k of l iabili ties6 , m , ,altering infla-tion between pe riods t and t+ an d taxes in period t+ only affects interest ratesand real money d em and in periodt an d ou tput in period t 1 .6 These shifts leavethe path of government revenue unchanged, so at the opt im um they ca nnot affectthe government s welfare. Forma lly, equat ion 2 ) implies that the differentialchange in the tax rate O that raises enough revenue to offset a change in

P I /P olding con stan t the level of gov ernm ent l iabili t ies at the e nd of periodt+l is



A M E S M . P O T F R B A A N D J U L I O J . R O T EM B E R G :

where we have assumed that real returns, R = (l+i,)P,/P,+, are constant. Inour notation, g is the elasticity of income with respect to taxes and is theelasticity of money demand with respect to the nominal interest rate. A govern-

ment minimizing social losses in I ) subject to this revenue constraint will choosetax rates and inflation rates satisfying the first-order condition:

where 4 = (-v ) -I, 4 < 0. This expression equates the excess burden per unitrevenue for each revenue source.

Equation (4) implies that positive shocks to government spending that raisetaxes and their associated excess burden should be accompanied by increases ininflation that raise the marginal excess burden from seigniorage. It also statesthat inflation between and t+l should be an increasing function of m,/y,+, .When this ratio is large, the revenue from a given inflation rate is high since, withcommitment, revenue from inflation is obtained at t+l as people replenish themoney that has been depleted by inflation. When more money is carried over,these replenishments are larger and the relative cost of inflation is lower.

The No Commitment CaseWhen commitment about inflation is impossible, the government in period t

can only choose the tax rate and the price level at t. The government recognizesthat it can cause unexpected inflation at t. Of course, if there were no exogenousuncertainty, the government s problem at t would be known at t-1 so therewould be no unexpected inflation in equilibrium. The equilibrium inflation rateis just that rate at which the government will not choose to induce any unex-pected inflation. Inflation will only be finite without commitment if it is none-theless costly so that the function \) ) does not become degenerate.

Some might argue that the costs of inflation are much lower for a governmentthat cannot precommit. One of the costs of expected inflation, the increase intransaction costs due to economizing on money holdings at t- 1 is immaterial forsuch governments since the government that picks the price level at t cannot al terthe choice of money holdings at t-1. Many other costs nevertheless remain evenwhen inflation is unanticipated. For example, the government may be averse toredistributing wealth between debtors and creditors. Reestablishing the originaldistribution of wealth may require the use of distortionary taxes and subsidies.

Alternatively, even unanticipated inflation may distort subsequent behavior byhouseholds and firms in ways the government finds undesirable. For example,workers may press for premature renegotiation of their contracts, firms mayincur additional costs of changing prices, and individuals may be forced to en-



6 M ONEY. C R F D I T, N D B N K I N G

gage in additional financial transactions to restore their liquidity. Indeed, insofaras the costs of inflation are due to its deleterious effects on nominal contracts,unexpected inflation may be more costly than anticipated inflation because it has

not been reflected in contracts.In the absence of commitment, the only state variable when taxes and the pricelevel at t are chosen is the total beginning of period level of liabilities,Q b,-,(l+i,-,) + m,-, The government a t t then chooses both the tax rateand nominal money balances at t . These choices determine interest rates and theprice level.

At the policy optimum without commitment, the government must be indif-ferent to small perturbations in the policy mix which leave h, , next period's he

ginning of period stock of government liabilities, unchanged. Feasible perturba-

tions thus satisfy

This expression differs from the trade-off in the commitment case because itexcludes the response of money demand and nominal interest rates to expectedinflation. Maximizing 1) subject to 5) gives a first-order condition for the no-commitment case:

Inflation is a positive function of both taxes and total government liabilities as ashare of G N P. As in the commitment case, when high deadweight burdens arebeing imposed with the tax instrument, higher inflation taxes will also be ap-propriate. The positive effect of outstanding liabilities obtains because govern-ments with large nominal obligations will find inflation more attractive than

those with less heavy debt burdens, since inflation erodes the value of theseobligations.*The inflationary erosion of government liabilities is totally anticipated, at least

in models without stochastic disturbances. It is nevertheless possible for govern-ments to accumulate stocks of such obligations, provided they are willing to paysufficiently high nominal yields. It is even possible for inflaton t o raise no rev-enue: the revenue raised ex post from reducing the value of bonds and moneymay be more than offset ex ante by increases in nominal interest rates and reduc-tions in the demand for real money balances.

f the government has access to a tax levied solely on the income from government bonds, then it isagain the level of money and not the stock of nominal liabilities outstanding that affects the inflation



7A M E S M . P O T ER B A A N D J U I I J . R O T E M B E R G

2. T H E E M P I R I C A L R E L AT I O N S H I P B E TW E E N I N F LAT I O N A N D TA X E S

Th is section evalutes the m ode l of the p revious section by exam ining the rela-tionship between taxes and inflation in several nations and over several timeperiod^.^ We first consider the empirical counterpart of equation( 4 ) ,which is

valid with commitment. 'o M ankiw(1987)estimates an equa tion similar to this onpostwar U .S. da ta. We also estimate the empirical co unte rpar t of (6), the first-order condition that holds without com mitment.

T o estimate the first-order cond ition implied by governm ent optimization, wemust specify functional form s forh ( ) and v ), the deadweight losses du e totaxation and inflation respectively. We assume constant elasticity functionsso tha t o ur objective function is a generalization of theCES welfare function:

h ( 8 , ) K , 8; a nd v ( P , _ , P, ) K , ( P, - , P, ) for K , , K ? , a nd p positiveconstants. This implies that( 4 )can be written as

where y , a l p a nd y , 1l p Th is specification relaxes M ankiw's(1987)as-sump tion th at the ratio ofm , - , to y is constan t.

If the functio nsh ) a n d v )w ere literally time-inv ariant an d correctly speci-f ied, equation (7) would hold w ithout e rror. Th is literal version of o ur m odel is

easy to reject. We a re n ot, how ever, interested in testing the pro position th at thetheory can explain the exact relationship between taxes and inflation, but inexploring w hether the theory ca n explain a sub stantial fraction of the movem entsin these series. We therefore test the prediction th at high er taxes tend t o be asso-ciated w ith higher inflation by simply add ing an er ro r term ,,, to ( 7 )and estimat-ing the resulting equation for several countries.

O ur estimation employs ann ual d ata fo r five countries: the United States, Brit-ain, Fran ce, Germany. and Ja pa n. O ur analysis is confined to taxes levied by thecentral governm ent, since this is the level of gov ernmen t choo sing mo neta ry pol-icy. Price indices, measured using consu me r prices in each country , are annu alaverage values. The stocks of mon ey an d de bt are measured as midyear values oryearly averages. Since both inflation and the tax rate are highly persistent,ordinary-least-squares estimation of( 7 )would recover the trends in the two se-ries. We therefore add a time trend to( 7 ) and estimate the resulting equationallowing fo r residual au toco rrelatio n, o r we difference(7) and estimate the result-ing specification by ord inary least square s.

We begin by analyzing the time series evidence for the United States, using twomeasures of the tax rate8,. The first is the ratio of federal governm ent ta x receipts

9U nder ou r assumptio n that the Fisher hypothesis holds, the empirical results do not depend onwhe ther inflation o r the nom inal interest rate is used as the depend ent variable. Ma nkiw(1987)found



8 : M O N E Y, C R E D I T, A N D B A N K I N G

to G N P, each measured as flows during the calendar year. If the governm entchooses its mix of tax instruments optimally, then the ratio of taxes to G X P is asumm ary statistic for the degree of ta x distortion. This is a crude taxr te an d it is

available for a long time period. The second m easure of the ta x burd en is theweighted average marginal tax rate on labor income computed by Barro andSah asak ul 1986 ). Their tax m easure, including both federal income an d SocialSecu rity tax es, is available for the 1916- 1985 period. D at a lim itations restrictedour sample period to begin in 1890, even when we useT/ NP for our taxmeasure. 2

The results of estimating equa tion 7 for a variety of different sample periodsare shown in Table 1 The ta x rate is positively correlated with the inflation ratefor all the sam ple periods, but the strength of this correlation is strongest fo r the

post-W orld W ar I1 period. Fo r the entire 189 1986 period, a ten-percentage-point increase in the share of taxes in G N P predicts a one-half of one-percentage-point increase in the inflation rate. The ta x rate an d tren d, however, explain lessth an 6 percent of the variation in inflation rates. The estimates in the AR 1) withtren d a nd th e differenced equ atio ns ar e similar, with slightly larger effects of thetax rate o n inflation in the latte r equation s. For the period since 1919 but exclud-ing Wo rld W ar 11, the coefficient estimates a re close to th ose fo r the full sample,althou gh now the null hypothesis of no ta x effect on inflation can not be rejectedat s tan da rd levels.

Th is conclusion is reversed wh en the sample is restricted t o the postw ar perio d.A 10 percent of G K P increase in taxes now raises the inflation rate by appro xi-mately 3.4 percen t, and th e imp act coefficient is estimated mu ch m ore preciselythan fo r the longer sample periods. When the B arro-Sahasakul m arginal tax rateseries is used in place of the tax- to- G N P ratio , the estimated inflation effect of ata x increase is smalle r. A ten-percentage-point rise in the m arginal ta x rate raisesthe inflation rate by just under two percentage po ints.

The coefficient on lo g m ,-,/ y, ) in the full sample equa tions in Table isnegative, although th e null hypothesis that i t is zero ca nnot be rejected a t stan-da rd confidence levels. Since the coefficient on this variable is P the negativeestima te is inconsistent w ith the theory underlying equ atio n 7). Th e negativeparam eter est imates are apparently du e to the prewar sample since the est imatesfo r the post-W orld W ar I1 period suggest a positive effect of the mo ney-to-income ratio on the inflation rate. The same coefficient pattern, negative inlonger samples and positive for the postw ar period , emerges in both the AR 1)and the differenced esimates.13

12The Consumer Price Index fo r the United States is reported in Historical Statistics of the UnitedStates and was updated using the Economic Report of the President. The money stock is the stock ofhigh-powered money, reported in Fr ie d~ na n nd Schwartz (1982, Table 4.8). The interest rate is thenominal call money rate , again as reported in Friedman and Schwart l with updates by the authors.Government debt is measured as the publicly held stock of government debt on July I of each year, asreported in Federal Reserve Board Banking and Monetary Statistics



1 : M O N E Y. C R E D I T, A N D B A N K IN G

Institution al changes during the postwar period, notably the shift from fixedto flexible exchan ge rates in 1973, could affect the stability of the coefficientslinking taxes to inflation rates. We test this possibility by allowing the coeffi-

cients in (7) to differ before a nd after 1973. Th e hypothesis of con sta nt coeffi-cients is not rejected in an y of the equ atio ns estimated over long sample periods,eith er 1891-1985 o r 1919-1985.14 For the postw ar period, howeve r, the AR (1)equa tions fail the test of subsample stability while the differenced eq uation s d ono t. We e xam ine the source of this failure by constrainingy and y to be con-sta nt, while allowing the intercept an d trend coefficients to differ before a nd after1973. Th e null hypothesis of consta ncy f or this subset of coefficients is no t re-jected ; the ~ 2 ( 2 )tatistics ar e 1.96 when the ta x rate variable is G N P an d 3.66with the Barro-Sahasakul marginal tax rate series (the .05 critical value for a

~ 2 ( 2 )andom variable is 5.99).O ur findings for the United States s trengthen Mankiw s (1987) conclusions

based on the po stwa r period. To eva luate the robustness of the positive relation-ship between inflation and ta x rates, however, we now consider da ta from fo uraddit ional countries . Fo r France, Germany, and Ja pa n, we draw data from theInternat ional Monetary Fun dInternational Financial Statistics for the postwarperiod to construct tax -to-G NP ratios and inflation rates.15 Mo re extensive dat aare available for B ritain. F or the period 1872-1985, we construc ted a tax-to-G N P rat io us ing data f romBritish Historical Statistics an d various issues of theAnnua l Abstract of Statistics. The annual price index was measured using theRetail Price Inde x (post-1948) an d theStatist price index.I6

Ta ble 2 reports estimates of (7) for these fou r countries . The positive associa-tion between inflation and taxes th at a ppea rs in U.S. data does n ot generalize.The Fre nc h and British da ta show a statistically significant an dnegative relation-ship between ta x levels an d the inflation rate. In G erm any the relation is againnegative althoug h the sta nda rd error of the estima ted coefficient is too large toreject the null hypothesis of no ta x effect. Only the Jap an ese da ta confirm th e

verify th at ou r results are not d ue to ou r inclusion of log (m,-]/ J we also est imated a modifiedversion of (7) excluding this variable. The estimated coefficients on the tax rate variable declineslightly, and the sta nda rd errors increase. Th e overall conclusions abo ut the links between tax ratesand inflation are not affected by this change in specification.

I4The likelihood ratio test statistic for the constant-coefficient hypothesis when(7) is estimate d inlevels w ith an AR(1) correc tion is 4.2 6f or th e 1891- 1985 sam ple, and 5.92 for the 1919-40, 1946-85samp le. Both tests have fou r degrees freedom (the constan t and time trend coefficient are alsoallowed to vary). The .05 level of the (4) distrib ution is 9.50.

IsData on an nua l averages of consum er prlce indexes, as well a s reserve money, govern ment de btoutstan ding, gross domestic prod uct , and call money interest rates, were draw n from the IFS. Insome cases these series were spliced toge ther using values from several different I F S publications anddome stic statistical sources. Th e tax receipts of the central govern ment a re reported in theU N Na-tional A ccounts.

I6Interest rates and the stock of high-powered m oney are draw n from Friedm an and Schw artz(1982, Table 4.9). Th e stock of governme nt debt is dra wn fr omBritish Hzstorical Statistics updated

i th A l Ab t t f St t i t i I li it i f d t f th ld t d d i th



Level Specilicat ~on D~ff eren ce pecificattonSample Constant Tax Rate M Y Trend R Constant ax Rate M Y R

Fra n c e . 3 3 2 - .68 .252 ,013 .805 .647 .Ol l -.589 .302 .5981948- 1985 (.250) . 123) (.076) (.003) (.095) (.008) . 129) (.075)Ge rma n v ,175 -.041 .088 ,0014 ,595 ,121 .0014 -.084 ,076 ,077

1955-1984U .K .1872- 1984U.K.1947- 1984

Estimates correspond t o equatlon ( 7 ) in the text. Standard errors are shown ~n parentheses. Equat~ons re estimated usmg 0I.S country by country with no cross equalton conrtratnt s or allowance forcontemporaneous residual correlat~on .



12 : MONEY. CRE DIT, AND BANKING

U.S. finding of a positive relationship between inflation and taxes. A 10 percentof GNP increase in the tax burden is estimated to increase the inflation rate by 3.1percent in the AR(1) specification, and by 4.7 percent in the differenced model.

The estimated effects of the money-to-income ratio are positive in each equationin Table 2, in contrast to the often negative coefficients for the United States.

We repeated our analysis of subsample stability for the equations reported inTable 2. Constancy of y and y , is not rejected for the United Kingdom, Ger-many, o r Japan. In France, however, there is evidence of parameter instability.In equation (7) with all coefficients free to change in 1974, the pre-1974 estimateof y is -.56 (. lo), with an estimated change for the period after 1974 of .79 (.63).Most of the evidence against parameter constancy arises from the change in thecoefficient on the money-to-income ratio, however. The pre-1974 estimate is .53

(.08), while the change is -.5 . 13).The first four rows of Table 2 report country-by-country estimates of equation

(4). These estimates ignore the information about inflation rates in one countrythat may be contained in the coincident experience of other nations. To remedythis problem, we also estimated the equations for the postwar period in all coun-tries using the seemingly unrelated regression technique. The resulting estimatesare shown in Table 3, and are quite similar to the country-by-country findings inTable 2. The last row of Table 3 reports estimates which constrain y and y, to beconstant across countries. The levels equation yields a small and statisticallyinsignificant coefficient linking tax rates and inflation rates. In the differencedspecification, even though three of the five countries show negative coefficientswhen estimated alone, the constrained estimate of is . l l (.03). In both specifi-cations, however, the hypothesis of constant ( y ,, y,) across countries is clearlyrejected.18 We therefore focus primarily on the unconstrained results, which yielda negative correlation between inflation and tax rates in three of the fivecountries.

Our failure to find a positive association between t ax rates and inflation mightbe due to an incorrect specification. We have assumed that governments caneither precommit or that they can tax outstanding government debt without re-sorting to inflation. If these assumptions are incorrect, the first-order conditionlinking taxes and inflation rates is equation (6) which includes the government'soutstanding interest-bearing debt. Under the same parametric assumptions usedto derive (7) from (4), the version of (6) that we estimate is

As in the United States data se t, excluding log(m,, i ~ oes not affect the broad charac ter of thefindings. Franc e and Britain continue to show stat ist~callyignificant negative coefficients on the taxvariable. F or Ja pa n, the tax variable has an even stronger positive association with inflation when weexclude the money-to-income ratio . Finally, the coefficient o n the tax share for Ge rmany moves fromnegative in the equat ion wi th l n ( m , ,1y, ) to pos itive withou t this variable, bu t the coefficient is never



13A M E S M P O T E R B A A N D J l l L l O J . R O T E M B E R G

Since the earlier results suggest that differencing and autoregressive correctionswith time trends yield similar results, we present only the latter.

Table 4 reports estimates of 8) for all five countries in our sample. The inclu-sion of the broad government liabilities variable does not substantively alter ourestimates of the association between taxes and inflation. In particular, the coeffi-cient on the tax rate remains negative and statistically significant for Britain andFrance, positive and significant for Japan and the United States, and statisticallyinsignificant for Germany. The broad liability measure is less correlated with

inflation than In m,-,/ y , , . The point estimates for the total liability variable arenegative that is, incorrectly signed) for Germany and Japan, whereas the money-to-GNP ratio had the sign predicted by the foregoing theory.

The superiority of models including only the ratio of money to GNP, relativeto models with total government liabilities as a share of GNP, can be demon-strated by estimating regression equations which include oth variables. This isequivalent to the nonnested hypothesis test of the null hypothesis that one vari-able affects the inflation rate against the alternative that the other variable affectsit. For the United States, Germany, and Japan, including both variables yields anegative coefficient on the liability variable but a positive and usually statisticallysignificant coefficient on the money variable. For France both variables havepositive and statistically insignificant coefficients, while for Britain both are posi-tive and statistically significant, but the coefficient on money is roughly threetimes as large as that on the broader liability measure. Overall, the results aremore supportive of a specification including the ratio of lagged money to GNPthan the total level of government liabilities.I9

A referee argued that inflation and the tax-to-GNP ratio are affected by manycommon factors, and that a more appropriate test of the theory would focus onthe variation in each due to changes in government outlays. We performed suchtests, estimating 7) by instrumental variables IV) with 7 GNPtreated as endog-enous and using the ratio of government consumption to GNP as an instru-ment. See Table 5.) For the United States, the IV results are similar to the OLSfindings, but for the other nations, changes erratically and the standard errorsrise substantially, making it impossible to draw any firm conclusions. The nullhypothesis that 0 is not rejected by the IV results for any nation except theUnited States.

9According o he standard theory o foptima l tax atio n, tax rate changes should not be predictableusing any lagged info rm atio n such as past inflation rates. A n earlier version o f his paper explored thelinks betweenchanges in tax rates and the level o f inflation yielding substantial evidence that infla



INTERNATIONAL ON INFLATION S U R RESULTSVIDENCE A N D TAX RATES:

Sample Constant Tax Rateeve1 Speclflca tlon

MI Trend AWL) ConstantD~fference pec~f~cat~on

Ta x Rate MI

France -.506 , 5 7 5 .22 ,00781948- 1985Germany

(.349),095

. 109). 0 7 3

(.067).097

(.OO 18),0014

1954-1984Japan1955-1984U.S.

. 147)2.106(.360).312

(.086).544. 162),172

(.032),181

(.074).074

(.0008)p.0113(.0029).0029

1948- 1985 . 130)U.K. ,0251948- 1984 . 104)Constrained

Estimates correspond to equatlon 7) ~n the text. Standard er rors are chown n parentheses. Equat~ ons re estimated by reern~ngly nrelated regresslo ,. values for the systems allow~ ng reehe l~kel~hoodparameters for l and ~neachequat~on re489 6 n the levels system, 486.25 Indlfferencec The Ilkellhood valuerfo rthec onstr a~ned yste ms.allowingfree I nterceptsand I the first system) tlmetrend andautocorrelation coeff~clents. re 463.63 and 454 I8 recpect~vely



T BLE 5

INFLATIONA N D TA X RATES:I N S T R U M E N T L VARIABLES ESTIMATES

Sample Conctant la x RateLevel Specll~cat~on

M Trend ConstantD~lierence pecliication

Tax Rate M I Y

Fran ce1950 1985

German y1954 1984

J a p a n1957 1983

U K1947 1985U.S.1946 1 985

Estimates correcpond toeq uat~o n 7) the text The tax rate 15 treated asendogenousand t h e e q u a t ~ o n s a r e e s t ~ m a t e d uslngthelogarlthm oltheratlooigovernment consumptiontoy ~nstrumentalvar~ablesGD P as the inctrument for log T, CNI ). Standard errors are shown ~n parentheses



J A M E S M . P O T E RB A A N D J U L I O J . R O T E M B E R G 7

policy preferences of given political actors, o r models of mu ltiparty gove rnm entwith intertem poral variation in the identity of political actors, could explain o urfindings. Alesina a nd Sachs (1988) provide some su ppo rt for the view th at differ-

ent political parties in the U nited States have different mac roecon om ic prefer-ences, and Hibbs (1982) documents intertemporal variation in the inflation-unem ploym ent preferences of the U .S. electorate. If governments th at ar e willingto tolera te infla tion also like expansiona ry policies in general, then to tal revenueswill decline in periods of high inflation, reinforcing the negative inflation-taxcorrelation.21

The view that negative inflation-tax correla tions are due to un stable govern-ment tastes is mildly s uppo rted by the fact that countries with m ore stable gov-ernments a nd less diverse political parties, such as postwar J ap an and the U nited

States, exhibit positive tax-inflation correlations . Countries w ith more politicalinstability, such a s Britain a nd Fran ce, tend to exhibit negative correlations.Roubini and Sachs (1988) present intriguing evidence on other links betweenpolitical structure and the nature of fiscal policy. Further work could usefullyexplore how political institutions o r othe r aspec ts of social stru ctu re ar e relatedto the inflation-tax correlation.

L I TE R AT U R E C I T E D

Alesina, Alb erto, an d Jeffrey Sachs. Political Parties and the Business Cycle in theUnited States, 1948-1984. Journal of M on ey Credit and Banking 20 (February1988), 63-82.

Alesina, Alberto, and G uido Tabellini. Rules and Discretion w ith Nonco ordinatedMonetary and Fiscal Policy. Economic Inquiry 25 (1987), 619-30.

Barro, Robert J . On the Determination of Public Debt.Journal of Political Economy87 (Octo ber 1979), 940-71.

Interest Rate Smoothing. National Bureau of Econo mic Research W orkingPap er 258 1, M ay 1988, Cam bridg e, M ass.

Barro, Rob ert J. , and David G ordon . A Positive Theory of Mon etary Policy in a NaturalRate M odel. Journal of Political Economy 91 (A ug ust 1983), 589-610.

Barro, Robert J. , and Ch aipat Sahasakul. Average M arginal Tax R ates from SocialSecurity and the Individual Income Tax. Journal of Business 59 (October 1986),555-66.

Bohn, Henning. Why D o We Have Nom inal Government Debt?Journal of M onetaryEconomics 21 (January 1988), 127-40.

2lThe possibility that mone tary policy is set based on stabilization objectives, rather than dead-weight loss minim ization, cann ot explain ou r findings. Trad ition al Keynesian policy would call f o rcoincident reductions in tax burdens and increases in the money stock. The observed correlationbetween taxes and inflation is nevertheless likely to remain positive since stabilization policy re-spond s to shocks. When exogenous factors cause a business slowdown, both inflat ion and the shareof taxes in G N P are likely to decline If the government responds with a m onetary expansion accom



18 . M O N E Y. C R E D I T, A N D B A N K I N G

Calvo, Guillermo. On the Tim e Consistency of Op tima l Policy in a M one tary Econ-omy. conometrics 46 (N ov em ber 1978), 141 1-28.

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Faig, Miguel. Characterization of the Optimal Tax o n Money When It Functions as aMedium of Exchance. Journal of Monetary Economics 22 (1987), 137-48.

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Fr iedman, Mi l ton , and A nna J . Schwar tz .Mo netary Trends in the U nited States and theUnited Kingd on?: Their Relation to Income Prices and Interest Rates 1867-1975.Chicago: University of Chicago Press, 1982.

Helpman, E lhanan, and Efraim Sad ka. Optimal Financing of the Government's Budget:Taxes, Bonds, or M oney? American Economic Review69 (March 1979), 1952-60.

Hibbs, Douglas. On the Deman d for Economic Outcomes: Macroeconomic Perfor-mance and Mass Political Sup po rt in the U.S., Great Britain, and Germany.Journalof Politics 44 (1982), 426-6 1.

Kim brough , Kent P . The Optim um Quantity of Money R ule in Public Finance.Journalof Monetary Economics 18 (No vem ber 1986), 277-84.

Lucas, Rob ert E., Jr . Principles of Fiscal an d Mo netary Policy.Journalof MonetaryEconomics 17 (Jan ua ry 1986), 17-34.

Mankiw, N. Grego ry. The O ptim al Collection of Seigniorage: Theory and Evidence.

Journal of Monetary Economics 20 (Septem ber 1987), 327-42.Phelps, Edm und S. Inflation in the Theory of Public Finance.Swedish Journa lof Eco-

nomics 75 (M arc h 1973), 67-82.Rogoff, Ken neth. Repu tational Con straints on Mon etary Policy Carnegie-Rochester

Conference Series on Public Policy 26 (1987), 141-82.Rogo ff, Kenn eth, an d An ne Sib ert. Macroeco nom ic Policy Cycles.Review of Eco-

nom ic Studies 55 (1988), 1-16.Rom er, David. Why Sh ould Gov ernmen ts Issue Bonds. Princeton University, mimeo,

1987.Rotem berg, Julio J. Constituencies with Finite Lives an d the Valuation of Governmen t

Bonds. Ma ssach usetts Institute of Tech nolo gy, mimeo, 1987.Ro ub ini, Nouriel, and Jeffrey Sachs. Political an d Econom ic Determinan ts of Budget

Deficits in Industrial Demo cracies. National Bureau of Economic Research WorkingPap er 2682, August 1988, Cam bridge, M ass.

Sahasak ul, Ch aipa t. The U .S. Evidence on Optim al Tax ation over Time.Journal ofMonetary Economics 18 (N ov em ber 1986), 25 1-75.



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Inflation and Taxation with Optimizing GovernmentsJames M. Poterba; Julio J. Rotemberg Journal of Money, Credit and Banking , Vol. 22, No. 1. (Feb., 1990), pp. 1-18.Stable URL:http://links.jstor.org/sici?sici=0022-2879%28199002%2922%3A1%3C1%3AIATWOG%3E2.0.CO%3B2-C

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[Footnotes]

1 On the Time Consistency of Optimal Policy in a Monetary EconomyGuillermo A. Calvo Econometrica , Vol. 46, No. 6. (Nov., 1978), pp. 1411-1428.

Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197811%2946%3A6%3C1411%3AOTTCOO%3E2.0.CO%3B2-K

1 Optimal Financing of the Government's Budget: Taxes, Bonds, or Money?Elhanan Helpman; Efraim SadkaThe American Economic Review , Vol. 69, No. 1. (Mar., 1979), pp. 152-160.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197903%2969%3A1%3C152%3AOFOTGB%3E2.0.CO%3B2-W

7 A Positive Theory of Monetary Policy in a Natural Rate ModelRobert J. Barro; David B. GordonThe Journal of Political Economy , Vol. 91, No. 4. (Aug., 1983), pp. 589-610.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28198308%2991%3A4%3C589%3AAPTOMP%3E2.0.CO%3B2-I

20 Elections and Macroeconomic Policy CyclesKenneth Rogoff; Anne SibertThe Review of Economic Studies , Vol. 55, No. 1. (Jan., 1988), pp. 1-16.Stable URL:http://links.jstor.org/sici?sici=0034-6527%28198801%2955%3A1%3C1%3AEAMPC%3E2.0.CO%3B2-E

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Literature Cited

Political Parties and the Business Cycle in the United States, 1948-1984Alberto Alesina; Jeffrey Sachs Journal of Money, Credit and Banking , Vol. 20, No. 1. (Feb., 1988), pp. 63-82.Stable URL:

http://links.jstor.org/sici?sici=0022-2879%28198802%2920%3A1%3C63%3APPATBC%3E2.0.CO%3B2-D

On the Determination of the Public DebtRobert J. BarroThe Journal of Political Economy , Vol. 87, No. 5, Part 1. (Oct., 1979), pp. 940-971.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28197910%2987%3A5%3C940%3AOTDOTP%3E2.0.CO%3B2-K

A Positive Theory of Monetary Policy in a Natural Rate ModelRobert J. Barro; David B. Gordon

The Journal of Political Economy , Vol. 91, No. 4. (Aug., 1983), pp. 589-610.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28198308%2991%3A4%3C589%3AAPTOMP%3E2.0.CO%3B2-I

Average Marginal Tax Rates from Social Security and the Individual Income TaxRobert J. Barro; Chaipat SahasakulThe Journal of Business , Vol. 59, No. 4, Part 1. (Oct., 1986), pp. 555-566.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28198610%2959%3A4%3C555%3AAMTRFS%3E2.0.CO%3B2-A

On the Time Consistency of Optimal Policy in a Monetary EconomyGuillermo A. Calvo Econometrica , Vol. 46, No. 6. (Nov., 1978), pp. 1411-1428.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197811%2946%3A6%3C1411%3AOTTCOO%3E2.0.CO%3B2-K



NOTE: The reference numbering from the original has been maintained in this citation list.

http://links.jstor.org/sici?sici=0022-2879%28198802%2920%3A1%3C63%3APPATBC%3E2.0.CO%3B2-D&origin=JSTOR-pdf

http://links.jstor.org/sici?sici=0022-3808%28197910%2987%3A5%3C940%3AOTDOTP%3E2.0.CO%3B2-K&origin=JSTOR-pdf


http://links.jstor.org/sici?sici=0021-9398%28198610%2959%3A4%3C555%3AAMTRFS%3E2.0.CO%3B2-A&origin=JSTOR-pdf



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http://links.jstor.org/sici?sici=0022-2879%28198802%2920%3A1%3C63%3APPATBC%3E2.0.CO%3B2-D&origin=JSTOR-pdf



Optimal Financing of the Government's Budget: Taxes, Bonds, or Money?Elhanan Helpman; Efraim SadkaThe American Economic Review , Vol. 69, No. 1. (Mar., 1979), pp. 152-160.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197903%2969%3A1%3C152%3AOFOTGB%3E2.0.CO%3B2-W

On the Demand for Economic Outcomes: Macroeconomic Performance and Mass Political

Support in the United States, Great Britain, and GermanyDouglas A. Hibbs, Jr.; R. Douglas Rivers; Nicholas VasilatosThe Journal of Politics , Vol. 44, No. 2. (May, 1982), pp. 426-462.Stable URL:http://links.jstor.org/sici?sici=0022-3816%28198205%2944%3A2%3C426%3AOTDFEO%3E2.0.CO%3B2-J

Elections and Macroeconomic Policy CyclesKenneth Rogoff; Anne SibertThe Review of Economic Studies , Vol. 55, No. 1. (Jan., 1988), pp. 1-16.Stable URL:http://links.jstor.org/sici?sici=0034-6527%28198801%2955%3A1%3C1%3AEAMPC%3E2.0.CO%3B2-E




http://links.jstor.org/sici?sici=0022-3816%28198205%2944%3A2%3C426%3AOTDFEO%3E2.0.CO%3B2-J&origin=JSTOR-pdf



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the relationship between inflation and taxes

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