Ricardian equivalence with uninformed consumers?

European Journal of Political EconomyŽ .Vol. 15 1999 747–758

Ricardian equivalence with uninformedconsumers?

Michael Reiter )

Department of Economics and Business, UniÕersitat Pompeu Fabra, Ramon Trias Fargas 25-27,E-08005 Barcelona, Spain

Received 1 February 1997; received in revised form 1 July 1998; accepted 1 November 1998

Abstract

Empirical studies have shown that the majority of people are poorly informed about thesize of government debts and deficits. This paper investigates whether it is neverthelesspossible for households to mimic Ricardian behavior on the basis of those variables thatthey actually observe. In a simple two-period model, it is shown that imperfect informationabout government debt can lead to departures from Ricardian equivalence even if thehouseholds’ estimates of debt are unbiased. The paper discusses why households facedifficulties in obtaining relevant information about government debt. q 1999 Published byElsevier Science B.V. All rights reserved.

JEL classification: H31; H62

Keywords: Ricardian equivalence; Government deficits; Bounded rationality

1. Introduction

The literature on Ricardian equivalence indicates that the required assumptionsare much too stringent to be expected to be literally true. Deviations fromRicardian equivalence can arise because of financial market imperfections, such asliquidity constraints, because of finite lives together with a too weak bequest

Ž .motive, and other reasons cf. Seater, 1993, Section 2 . Plausible estimates of the

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0176-2680r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0176-2680 99 00033-6

( )M. ReiterrEuropean Journal of Political Economy 15 1999 747–758748

size of these deviations, however, suggest that Ricardian equivalence may well bea good approximation to reality. The issue has been subjected to extensive

Žempirical testing, with very mixed results. Four contributions Barro, 1989;.Bernheim, 1989; Eisner, 1989; Gramlich, 1989 from a symposium on government

debt demonstrate very well the conflicting points of view. Two reviews of theŽ .literature Bernheim, 1987; Seater, 1993 come to radically different conclusions.

Ž .On top of that, Cardia 1997 shows in the framework of general equilibriummodels that the most widely used empirical tests can lead to conflicting results, nomatter whether Ricardian equivalence is true or not.

It seems a reasonable conjecture that the lack of belief of many economists inthe Ricardian equivalence hypothesis may not come from an impartial reading ofthe econometric evidence, but from a priori skepticism about its plausibility. 1

Ricardian equivalence may be thought to require a degree of consumer rationalitythat is hard to believe. This view is not often expressed in academic publications,in particular not in refereed journals. In a more popular book by a prominenteconomist, however, we find a very clear and explicit statement of this view:

. . . Barro’s theory requires that ordinary households be extremely well in-formed and rational about the future tax implications of current governmentspending — to a degree that seems quite unlikely. What fraction of theAmerican public knows anything of substance about the federal budget? Thenotion that ordinary Americans can readily form reasonable estimates of thebudget’s implications for their tax rates over the rest of their lives strains

Ž .credulity. Krugman, 1994, p. 95

There is now some evidence in the literature that consumers are actually veryŽ .badly informed about public debt. Mayer 1995 cites a Gallup poll that has

examined whether American households know the size of the budget deficit, andalso whether they know what ‘‘budget deficit’’ means. The result is that about50% can tick the right answer about the meaning of the deficit, while most of theothers confuse the budget deficit with the trade deficit. When confronted with thechoice between different levels of government debt, most respondents choose amuch too high number.

A larger scale study with Dutch consumers was undertaken by Allers et al.Ž .1996 . They conducted a newspaper survey, eliciting more than 15,000 responses.

1 Ž . Ž .This view is held by Mayer 1995 p. 38 :

It is therefore not necessarily wrong for economists to be skeptical about the econometric evidencesupporting Ricardian equivalence because they think Ricardian equivalence is inconsistent withcommon sense. What is more questionable, and has done much harm, is the failure to articulate thisobjection.

( )M. ReiterrEuropean Journal of Political Economy 15 1999 747–758 749

Ž .Their main results are that 27% 39% of the respondents gave an approximatelyŽ .right answer about the size of the central government debt deficit , where

‘‘approximately right’’ roughly means correct "30%. Only 12% of the respon-dents indicate that they base saving decisions on their expected future taxes. Thisis despite the fact that the questionnaire explained the relevant issues. Thedistribution of all answers varies with age, education and other variables, but isindependent of whether the respondents have children or not. The authors arguethat selection bias leads to overestimation of the number of correct answers.According to both studies, the deviations of respondents’ estimates from the truevalues are not unsystematic, but strongly biased. In the Gallup poll, the debt

Ž .estimates were strongly upward biased, while in Allers et al. 1996 , mean andmedian of the debt estimates as well as the median of the deficit estimate werebelow the true values, while the mean of the estimated deficit was above the truevalue. The authors note that the design of the questionnaire effectively restrictedpossible answers to a certain range of values, which shapes the answers of thoserespondents who have no relevant idea about the correct numbers. 2

Mainstream economists may consider the fact that people are rather ignorantabout public debt as irrelevant for the validity of the Ricardian equivalencehypothesis. It is now almost universally accepted that economic theory assumeseconomic agents to behave ‘‘as if’’ rational, which is possible even if they are notable to solve the relevant problems in mathematical form. Proponents of thisargument often refer to Friedman’s famous example of expert billiard playersŽ .Friedman, 1953 , who behave as if they knew the laws of physics, which theyprobably do not.

To assess the relevance of the ‘‘as if’’ argument in the present context, it isimportant to distinguish two aspects: what the argument shows is that people are

Ž . Ž .able at least in some instances to perform the approximately optimal action,given their information set, despite the fact that they are not literally able to solvean optimization problem in mathematical form. The explanation for this is thepossibility to learn by trial and error, combined with the selective pressure fromcompetitive markets. What the argument does not show, however, is that peoplecan consistently find the right action even if they do not have all the relevantinformation. On the contrary, most of the recent developments in microeconomicsexplore the consequences of imperfect, usually asymmetric, information. Refer-ence to ‘‘as if’’ rationality does therefore not automatically prove that publicignorance about deficits can be neglected. On the other hand, we cannot be

2 A problem with both studies is that they asked for the size of debt in absolute Õalues, rather thanas percentage of GDP. Everyday experience suggests that most people are unable to handle very largenumbers; probably, most cannot even write down a number such as two trillion. So, it seems mostunlikely that they can obtain information about their own future tax burden from aggregate figures.However, if they know that debt is about 80% of annual GDP, for example, they can start with anestimate of their debt of 80% of their annual income. Future studies should take this into account.


satisfied with the assumption that households have no information on public debt:contrary to standard models of imperfect information, where some relevantinformation is impossible or very costly to obtain, it seems rather easy to obtaininformation about public debt: relevant figures are published in newspapers,reported in TV news, enter political discussions, etc. To stress this distinction, I

Ž .will use the term ‘‘uninformed’’ for consumers and their behavior who do notuse information that is easily available.

Since theory tells us that fiscal policy is relevant for the consumers’ savingsdecisions, the seeming ignorance about public debt leaves us with essentially two

Ž .interpretations: either people are able to come to approximately optimal deci-sions based on the variables they know, such as taxes, transfers, etc., and withoutexplicit knowledge about public debt, or they display at least some degree ofirrationality. The paper makes a step towards exploring which of these alternativesis true, and to what extent we can expect Ricardian equivalence to hold under suchcircumstances.

The plan of the paper is as follows: Section 2 contains the main analysis.Section 2.1 investigates whether Ricardian equivalence may hold in the aggregateeven if only a subset of consumers follows Ricardian predictions. Section 2.2studies the implications of imperfect information for Ricardian equivalence in theframework of a simple model. Some reasons why it is difficult for households toobtain sufficient information about government debt are discussed in Section 2.3.Section 3 further interprets the results.

2. Is imperfect information compatible with Ricardian equivalence?

2.1. Do all consumers haÕe to be Ricardian?

The empirical studies cited above seem to make clear that a fraction of thepopulation is badly informed about government debt. One might discard therelevance of this fact by arguing that perhaps not all consumers need to be wellinformed about government debt in order for Ricardian equivalence to hold. Manypredictions of economic theory require only a certain fraction of agents to followthe predictions of the theory. For example, not all traders need to be rational to

Ž .make financial markets efficient. Russell and Thaler 1985 investigate in a moreabstract setup the proportion of rational agents necessary to obtain a ‘‘rational’’

Ž .market outcome cf. Conlisk, 1996 for more examples .The situation is different with the Ricardian equivalence proposition. Consider

the simplest case of a small open economy with perfect capital mobility. Theinterest rate is exogenous, and the saving decisions of different households areunrelated. Consequently, if some households in the economy behave in a Ricar-

Ždian way and others behave in a Keynesian way for lack of information, or.whatever reason , the deviation from Ricardian equivalence is proportional to the


fraction of Keynesian consumers. The picture is slightly more complicated in aclosed economy, but under standard assumptions it appears that Ricardian equiva-lence holds exactly in the aggregate only if either all consumers behave in aRicardian way, or if deviations from Ricardian behavior are unbiased so that theycancel in the aggregate.

2.2. A simple model of the effects of imperfect information

In this section, I will develop a framework in which we can investigate how theRicardian equivalence proposition for aggregate data is affected by imperfectinformation about public debt.

To keep the analysis as simple as possible, let us consider a two-periodŽlife-cycle model with linear decision rules and certainty equivalence which can be

.rationalized by a linear-quadratic decision problem . In period t, ts1, 2, house-hold i earns exogenous labor income Y , receives a random net transfer T fromt i t i

the government, and buys a consumption good C . The interest rate is exogenoust i

and both the interest rate and the rate of time preference are normalized to zero.The household budget constraint is then

Y qT yC q Y qT yC s0.Ž .1 i 1 i 1 i 2 i 2 i 2 i

Under the standard life-cycle model with rational expectations, consumptionbehavior is described by

1w xC s Y qT qE T , 1Ž .Ž .1 i i 1 i V 2 ii2

where Y denotes expected lifetime labor income Y qE Y , and the expecta-i 1 i V 2 ii

tions are taken conditional on V , the information set of household i at the timei

when first period consumption is chosen. We assume that households decide onconsumption only after observing transfers, so that V contains at least Y andi 1 i

T .1 i

To close the model, we have to specify government behavior. In the firstŽ .period, the government provides normally distributed random transfers with

expectation zero and identical variance across individuals. Transfers may becorrelated across households. The parameter g denotes the correlation of individ-ual transfers with total transfers and is the same for all households. The govern-ment does not consume any resources. At the end of period 1, the economy hasaccumulated public debt DsÝ T . For simplicity, we assume that second periodi 1 i

transfers are nonrandom: every household receives the same transfer, so that thegovernment budget constraint Ý T qÝ T s0 is met. Government behavior isi 1 i i 2 i

summarized by the following equations:

T ;N 0,s 2Ž .1 i T

1 1T sy Dsy T Corr T , T sg .Ý Ý2 i 1 i 1 i 1 iž /n n i i


This completes the description of the model. Since we assume rational expecta-tions, Ricardian equivalence holds in this model if V contains D, i.e., if publici

debt is perfectly observed by all households. In that case, there is no uncertaintyleft in the second period.

We now assume that, for whatever reason, households do not have perfectinformation about aggregate debt when they choose first period consumption, butwe maintain the assumption of rational expectations. In that case, household iforms an estimate of debt, Dest, based on its information set V . The informationi i

set includes its own first period transfer, T , but not the transfers received by1 i

other households. In addition, the household observes debt, but imperfectly: theobservation of debt, Dobs, is contaminated by a form of ‘‘measurement error’’. Toi

adopt the mildest form of imperfect information, I assume that Dobs is an unbiasedi

estimate of D:

obs 2 <D sDqe , e ;N 0,s , E e D s0. 2Ž .Ž .i i i e i

Under these assumptions, Dest, the household’s optimal estimate of D, is given byiŽ .cf. Appendix A

s 2 1yg 2 ng 2s 2Ž .D eest obsD s D q T , 3Ž .i i 1 i2 2 2 2 2 2s 1yg qs s 1yg qsŽ . Ž .D e D e

where s 2 is the variance of government debt, which is equal to n2g 2s 2. Since theD TŽ . est Ž . Ž .expected value of T is y1rn D , inserting Eq. 3 into Eq. 4 and summing2 i i

over households gives aggregate consumption as

2 2 2 21 s 1yg 1 s 1ygŽ . Ž .D eC s Y y e q D .Ý Ý1 i i i2 2 2 2 2 2ž /2 ns 1yg qs s 1yg qsŽ . Ž .D e D ei i

4Ž .

Ž . Ž .We can interpret formulas 3 and 4 by considering some limiting cases with2 2 Ž .respect to the parameters g and s . Obviously, if s s0 and therefore e s0 ,e e i

est obs Ž .we have D sD sD and aggregate consumption is Ý C s 1r2 Ý Y , whichi i i 1 i i i

means that Ricardian equivalence holds. More interesting are the following cases.

Case 1: gs0. This is the limiting case when transfers are uncorrelated acrosshouseholds and the number of households goes to infinity. Own taxes are then

Ž . Ž .uninformative about aggregate debt, and formulas 3 and 4 reduce to

s 2Dest obsD s D 5Ž .i i2 2s qsD e

2 21 s 1 sD eC s Y y e q D . 6Ž .Ý Ý1 i i i2 2 2 2ž /2 ns qs s qsD e D ei i


We see that Ricardian equivalence breaks down: government debt has an effecton aggregate consumption, since it cannot be perfectly measured by households.The effect arises because the households have to solve a signal extraction problem

Ž .very similar to that in the Lucas 1975 island parable. And analogously, underrational expectations, it is only random fluctuations, not systematic fluctuations infiscal policy, that give rise to non-Ricardian effects.

Case 2: gs1. Then own taxes are perfectly informative about aggregate debt,Ž .formula 3 reduces to

Dest snT 7Ž .i 1 i

Ž .and aggregate consumption is given by Ý C s 1r2 Ý Y . We are back ati 1 i i i

Ricardian equivalence. Here, transfers are perfectly correlated, people know thatthere is no redistribution involved, and they perfectly know their future tax burden.

Case 3: s 2 s`. Here, the households have to rely on their own transfers toe

estimate public debt, and the best estimate is

Dest sng 2T . 8Ž .i 1 i

Aggregate consumption is then

12C s Y q 1yg D 9Ž .Ž .Ý Ý1 i i2i i

and we see that, the smaller the correlation between individual and aggregatetransfers, the stronger the deviation from Ricardian equivalence.

We can summarize the results as follows: Ricardian equivalence only holds ifŽ 2households have perfect information about government debt, either directly s se

.0 or indirectly through variables that are perfectly correlated with governmentŽ .debt Case 2, gs1 . With imperfect information, Ricardian equivalence breaks

down.This raises the obvious questions of how large s 2 and g are in reality. On g ,e

the correlation between individual and aggregate net transfers, I have no directevidence. The fact that some households only receive transfers, others only paytaxes, with different rates for different types of taxes, suggests that g is not closeto one. This, however, remains a topic for future research. In order to interpretestimates of g obtained from time series or panel data, one would also need tohave a more elaborate dynamic model. 3

3 A multiperiod generalization of the model raises some difficult issues. Assuming perfect Bayesianupdating on part of the households, observation of debt in consecutive periods can reduce theuncertainty about true government debt. By how much uncertainty is reduced depends mainly on theserial correlation of observation errors. Since the paper argues that observation errors are systematic,serial correlation can be high and the gain in accuracy over time might not be very great.


Let us turn now to s 2, the measurement error of government debt. Thee

discussion so far has been purely formal, and we have not yet said why people donot perfectly observe government debt. Two interpretations have to be distin-guished. The first is that e can be considered as a genuine measurement error. Ini

Section 2.3, I will argue that this is a relevant point and that even people who tryto be well-informed face serious difficulties in forming satisfactory estimates ofgovernment debt. It therefore seems worth noting that imperfectly measuredgovernment debt in conjunction with rational expectations leads to a departurefrom Ricardian equivalence.

However, the empirical studies cited in the introduction document that afraction of the households is badly informed about government debt to a degreethat can hardly be explained by objective difficulties. A second possible interpreta-tion of the model is therefore that it describes uninformed behavior in the senseexplained in the introduction. In this interpretation, Dest stands for the individualestimate of D, however, good or bad the guess may be. One might reject thisinterpretation of the model because it is inconsistent in the following sense: whilethere is obviously some form of bounded rationality involved if households do notuse information that is publicly available, we have modeled them as havingrational expectations about the economy, and making optimal Bayesian estimates.This objection is certainly valid, and the above model can hardly be defended as apositive theory of the behavior of uninformed or boundedly rational agents. Themodel is nevertheless very relevant for our purpose, since it shows that imperfectinformation leads to a deviation from Ricardian equivalence eÕen if people behaveperfectly rationally otherwise. We may expect uninformed consumers to displaymore deviations from perfect rationality, but there is no reason to assume that theadditional irrationality should offset the lack of information so as to restoreRicardian equivalence. 4

The relevance of the above results can perhaps be best illustrated by con-Ž .fronting it with the natural view cf., for example, Alesina and Perotti, 1994 that

not all households are perfectly informed about government debt, but that devia-tions in their estimates are unsystematic. The analysis of this section has estab-lished that Ricardian equivalence cannot be expected to hold in the aggregate ifpeople have flawed information about public debt, eÕen if their estimates of publicdebt are unbiased. Biased estimates, as manifested in the empirical studiesmentioned in the introduction, obviously strengthen the case against Ricardianequivalence.

4 If one assumes that people take their flawed estimate of government debt at face value, behavingas if it was a perfect estimate, unbiasedness of debt estimates and linear decision rules obviously leadto Ricardian equivalence in the aggregate. This set of behavioral assumptions appears to be veryspecial, however.


2.3. Information on goÕernment debt

Even for households well educated in economic theory, it is not easy to obtainsatisfactory information on public debt. The problem begins with the fact that data

Ž .from different sources source country statistics, OECD, IMF sometimes differ bynonnegligible amounts, due to subtle differences in definitions. Further questionsconcern the decision of market vs. par values and the treatment of government

Ž .assets cf. Eisner, 1989 for the discussion of many more issues . To be wellinformed, a household would also have to obtain information about public pensionliabilities.

The situation is much more severe for somewhat less sophisticated households,who mainly rely on the information distributed by the media, because the publicdebate usually focuses on the ‘‘wrong’’ variables. With regard to debt, the mostimportant shortcoming is the concentration on gross rather than net public debt,where it seems clear that net debt is the more relevant series. Even the Maastrichtcriteria refer to gross public debt. Changes in gross and in net debt can differsubstantially for a long period of time, as shown in Fig. 1 for German data. Thedifference in the evolution of both series is mainly due to the sale of governmentfinancial assets. That net debt is not easy to measure seems not to be a sufficientexcuse for ignoring all changes in public asset holdings.

Most of the time, public debate is not about debt, but about deficits. This is thecase for the US, and was also true in Europe before the Maastricht controversy. Aserious shortcoming is the failure to recognize the inflationary devaluation ofpublic debt: the public debate in the mass media is based on nominal deficits,

Žwhich is misleading during times of high inflation such as the 1970s Eisner,.1989 .

Fig. 1. German government debt.


The above discussion suggests that media do not give accurate informationabout those fiscal policy data that economists consider relevant. To counter thiskind of argument, one might propose that published economic data are not theonly information households can use to react to fiscal policy. Consider as anexample the discussion about the national pay-as-you-go pension systems. Thepublic debate in many countries suggests that pension systems are being under-mined by adverse demographic effects, and that more individual saving efforts arenecessary. This may well induce people to save more, even if they are unaware ofany statistics on the pension system, or quantitative predictions about futurereceipts from the system. Mass media might provide qualitative information aboutfiscal policy, and the appropriate private reaction to it, in a form that is easier touse for households than aggregate debt data.

Is it possible to obtain Ricardian equivalence through qualitative information?This question is obviously difficult to answer unless the exact nature of thetransmitted information is specified. However, one should not be too optimisticabout the effectiveness of this kind of information, since it is limited by thefollowing dilemma: the information must be given to households in a form that isquite different from aggregate statistics; otherwise its advantage over standardpublic debt figures is unclear. On the other hand, the information must be providedin a very accurate form: if it contains a substantial ‘‘measurement error’’, weknow from Section 2.2 that Ricardian equivalence will be violated. The tworequirements seem hard to satisfy simultaneously.

This section has provided arguments why the informational requirements forRicardian equivalence are not likely to be satisfied. In addition, there is animportant conclusion for further research: if the question of information is takenseriously, empirical research should focus on variables which are widely discussedin debates in the media, rather than on variables that appear to be ideal from thepoint of view of economic theory.

3. Concluding question: why is there so little interest in exact data on debt?

Section 2 has shown that households, even if they have no direct informationon public debt, may mimic Ricardian behavior if they can indirectly obtain thenecessary information. Different channels through which households may obtainthis information have been considered, but we argued that it is rather unlikely thatthe information thus obtained allows households to follow the Ricardian predic-tions with any accuracy. This leaves open the question why people do not caremore about aggregate data on debts and deficits, given that this information can beobtained practically without cost.

What is perhaps even more surprising in this context is that there are no seriousefforts, neither by statistical agencies nor by private researchers, to provide and


Ž .distribute the most reliable and most relevant debt figures. Seater 1981 writesthat he has computed market values for outstanding government debt, because theofficial par value data are useless for testing Ricardian equivalence. If it is themarket values that are relevant for economic behavior, why does nobody bother tocompute them except for some researchers who try to test a theory? Data on netpublic debt are published by the OECD, but are not much used outside academia.Public interest in these figures seems to be small, and this is not easily reconcil-able with a theory that asserts the importance of these data for individual behavior.

These considerations lead us to suspect that the deviations from perfectlyRicardian behavior, caused by ignorance about public debt, only lead to smalllosses in the utility of households. The failure of households to care for aggregatedebt data may therefore be rationalized by the difficulty of using this information,

Ž .and the corresponding ‘‘deliberation costs’’ cf. Conlisk, 1996 . Support for thisidea is given by the envelope theorem, which states that first order variations inpolicy lead only to second order variations in utility, at the optimum. Moreover,

Ž .Cochrane 1989 shows that even large deviations from the permanent incomemodel give rise to only small losses in utility, if standard utility functions areassumed. In our specific application, one should also keep in mind that knowledgeabout government debt does not change the resources available for consumption. Itonly decreases the uncertainty about resources and helps allocate consumptionbetween periods in a way that reduces the variance of consumption and therebyincreases the utility of a risk averse consumer.

The considerations raised add some new potential reasons to be sceptical aboutthe Ricardian equivalence hypothesis. Despite extensive empirical research,economists’ beliefs about the relevance of this hypothesis continue to differwidely. Probably, this is partly due to different a priori views about its plausibility.Only a discussion of the mechanisms through which households might behave in aRicardian manner, despite their limited knowledge of fiscal policy measures, willbring economists closer to a consensus about the relevance of Ricardian equiva-lence.

Acknowledgements

I am grateful to Helmut Frisch, Jakob de Haan, seminar participants in Munichand Vienna and to three anonymous referees for helpful comments and discus-sions.

Appendix A. Optimal estimates of debt

Ž .This appendix derives Eq. 3 . If x and y are vectors of jointly normallydistributed, zero mean random variables, the expectation of y conditional on x is


given by

< y1w xE y x sS S x , 10Ž .y x x x

where S and S denote the respective variance and covariance matrices. Sincey x x x

the variance of D, s 2, is equal to n2g 2s 2, we obtainD T

obs 2 2 2 2 2E D D T s n g s ng s 11Ž .Ž . Ž .i i T T

obs n2g 2s 2 qs 2 ng 2s 2D T e TiVar s . 12Ž .2 2 2ž /T ž /ng s si T T

Ž . Ž . Ž . Ž .Applying formula 10 to formulas 11 and 12 gives formula 3 in the text.

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