## Abstract

We analyse the impact of public spending on tax evasion using a two-period model in which the government and taxpayers make their decisions in terms of level and quality of expenditures to set and taxes to pay. Results predict that tax evasion increases with government inefficiency.

## Introduction

Tax evasion is a serious problem for the economies of many countries. Among the potential determinants of tax evasion, the public finance literature has mainly paid attention to enforcement, the individual characteristics of taxpayers and the latter’s social interactions (for a review, see Pickhardt and Prinz, 2014). However, very little is currently known about the impact that the quality of public spending has on taxpayers’ behaviour.

We begin to fill this knowledge gap by presenting a two-period model where the government makes a decision about the tax rate and the level of public expenditure in each period (fiscal year). The government provides an essential public good if the expenditure level is set low, and it can decide whether to invest the extra expenditure to provide public services (high-quality spending) or to finance patronage or red-tape procedures, or both (low-quality spending). On the other side, taxpayers decide to evade taxes after observing the tax rate and the level of public expenditure but not the quality of public goods provided in the first period. In order to verify how taxpayers’ satisfaction affects the decision to evade taxes, we assume that taxpayers are motivated by the probability of being audited and possibly fined if rated by the fiscal authority as evaders, and by the return they get from public expenditure. The model predicts that taxpayers do not evade if they expect to be audited with a probability above a threshold level. Otherwise, the model shows that: (1) tax evasion increases if the extra expenditure is of low quality; and (2) citizens pay taxes if public expenditure is set high in the last period but the government provides only an essential level of public goods in the previous period. Moreover, we find that this last equilibrium is more likely to happen in low-income regions. Taken together, these results predict that tax evasion increases with the inefficiency of the government.

A large body of the experimental and theoretical literature, starting from the analyses carried out by Alligham and Sandmo (1972) and Friedland et al (1978), has found that increasing the audit probability or the penalty rate, or both, positively affects tax compliance. Nevertheless, there is agreement that these drivers of tax compliance only provide a partial, not an exhaustive, explanation of the tax-evasion phenomenon.

An alternative approach has focused on tax morale, intended as ‘any nonpecuniary motivations for tax compliance as well as factors that fall outside the standard, expected utility framework’ (Luttmer and Singhal, 2014: 150). In our model, the non-pecuniary motivation is the degree of satisfaction taxpayers receive from the provision of public goods. That is to say, our model is an application of the so-called ‘exchange equity’ theory: taxpayers comply if they feel that the utility gained from the consumption of public goods matches the amount of taxes paid to finance them; if this is not the case, taxpayers attempt to restore equity through tax evasion.

Exchange equity finds support on both theoretical and experimental grounds. Theoretically, Bordignon (1993) assumes that the taxpayer is able to understand what a fair trade between taxes and public expenditure is, evading only if the former exceeds the latter. Falkinger (1995) argues that evasion decreases with perceived equity if and only if the taxpayer’s risk aversion is an increasing function of equity. More recently, Pellizzari and Rizzi (2014) show that tax compliance depends on both the enforcement power of the government and citizens’ appreciation of public goods, where the latter is more important than the former. Experimentally, Torgler (2002) considers groups of citizens with different incomes whose surplus from public expenditure changes according to the group’s surplus multiplier. He finds that low-income taxpayers are more likely to undertake full tax evasion, but the effect of equity remains unclear. Alm and Malézieux (2021), by means of a meta-analysis based on more than 70 experimental studies, highlight that the investment of taxes in real-life public goods has a positive impact on tax compliance.

Likewise, the empirical literature agrees that taxpayers are more likely to evade if they feel that their money is not well spent (see, for example, Barone and Mocetti, 2011). Related to this point, Cowell and Gordon (1988) predict a positive relation between the tax rate (associated with public expenditure) and tax evasion when public goods are underprovided (for example, because the initial tax rate is low); however, a further increase in the tax rate once public goods are overprovided would lead to a downward change in tax evasion. Conversely, Russo (2013) shows a negative relationship between tax morale and dissatisfaction with public services.

Finally, D’Agostino et al (2021) analyse the impact of government size on tax evasion at the provincial level in Italy over the period 2001–15. They show by means of a Generalized Method of Moments (GMM) approach that current spending does not affect the propensity to evade taxes, whereas an increase in capital expenditure produces a benevolent impact on taxpayers’ behaviour. They also provide a theoretical model and find that tax evasion increases (decreases) in equilibrium if public goods of bad quality (of good quality and of general interest) are provided, whereas the result is ambiguous if good-quality expenditures of specific interest are supplied. Although there are some similarities in the structure and in the players’ strategy profiles, our model differs in many ways. First, unlike D’Agostino et al (2021), we incorporate auditing as one of the main drivers of taxpayers’ compliance decision. Second, taxpayers hold homogeneous tastes in our model, with no distinction between high-quality public expenditure of general and specific interest. Third, in the first period, we consider all taxpayers as optimistic (rather than assuming that some of them are also sceptical) about the policy implemented by the government. Fourth, the capability of observing the quality of public expenditure diverges: we suppose that only a fraction of taxpayers in the last period is informed about the quality of public spending, with no regard to their *a priori* beliefs. Instead, in D’Agostino et al’s (2021) model, taxpayers always observe the quality of the type of expenditure they prefer the most, and only a fraction of them observe the quality if the policy set by the government does not mirror their best choice. Lastly, we check whether the predictions of our model are heterogeneous among different geographic areas according to the level of income.

## Model

The game is played by two players, the local government (*G*) and a unit mass of taxpayers (*T*), for two periods (*t* = 1, 2), corresponding to two fiscal years. In Period 1, *G* sets the policy {*τ*, *e*, *q*}, where is the tax rate and is the level of public expenditure, where corresponds to the amount of public expenditure borne to provide an essential level of public goods, whereas includes an extra expenditure, whose nature depends on , that is, the quality of . If , then only essential public goods are provided, without any choice on quality; accordingly, we say that . If , then is relevant since *G* can decide either to enhance the quality of public goods, such as public transportation, lightening of streets and so on, or to finance patronage and red tape procedures. Hence, we state that the quality of this extra expenditure can be either high (*h*) or low (*l*).

When in Period 1, we assume that the choice about quality affects *G*’s policy in Period 2: if *G* has spent money on bureaucracy and patronage (that is, ), for example, new office-holders have been hired in Period 1, it cannot dismiss them in the following period to allocate resources to other purposes but can only change the tax rate. Conversely, if in Period 1, then *G* is free to change its amount (and therefore quality and, eventually, the tax rate) in Period 2. Therefore, a strategy for *G* is to set a policy {*τ*, *e*, *q*} in each period *t* = {1, 2}, where is unchanged if in *t* = 1.

We define as the cost for *G* to provide *e*. It should be noted that is a discrete variable, where . To simplify notation, we set , and , with min{} > 0 and max{} < . *G* also controls a fraction of individuals and applies a fine times the amount of evaded taxes. For the sake of simplicity, we consider the auditing system as random and costless for *G*.

As regards taxpayers *T*, we assume they hold homogeneous preferences on fiscal policies, , which is increasing in *q*. Since both *e* and *q* are discrete variables, all we need to know is that , and , with . To simplify notation, we set , and , where and *Y* is equal for every taxpayer. To simplify notation, we set *Y* = 1, we also use instead of .

We also posit that in Period 1, *T* can observe only and *e*, not *q*, and believe that *h*. If *G* has provided , at the end of Period 1, a proportion of *T* observes *q*; for example, it could be the effect of yardstick competition or the different tendency among taxpayers to experience quality due to their job or political attitudes. A proportion does not experience *q* and maintains its aprioristic beliefs. Conversely, if *G* has provided in Period 1, *T* cannot observe *q* because by assumption , . Hence, a strategy for *T* in each period is to pay or evade taxes given the observed policy. *T* know that they will be audited with probability , and if discovered by the fiscal authority to be tax evaders, they will be charged a fine , where .

*G*’s utility is given by , where

*α*is the percentage of aware taxpayers who evade in Period 2 and

*Y*is

*T*’s income. Each period,

*T*get if they decide to pay taxes and if they decide to evade. To emphasise the effect of public goods provision on the decision to evade taxes or not, we say that

*T*decide to pay taxes if min{0,}; this means that, regardless of the auditing efficiency,

*T*always pay taxes if they are satisfied by the policy (that is, ). The aforementioned condition also denotes that we exclude taxpayers who are

*a priori*honest or dishonest, so that they always pay or evade taxes without any consideration of the government’s policy. We characterise pure-strategy perfect Bayesian equilibria

^{1}and assume that social welfare satisfies the following:

meaning that providing is the most efficient policy, the second-best being and the third-best being .

## Results and predictions

Proposition 1: If , there exists a unique equilibrium in which G sets {} and all

Tpay taxes in both periods.

l-equilibrium: If , there exists a unique equilibrium in which

Gsets {} in both periods, all T pay taxes in Period 1 and only unawareTpay taxes in Period 2.

-equilibrium: If and , there exists a unique equilibrium in which

Gsets {} in Period 1 and {} in Period 2, and all T pay taxes.

h-equilibrium: If and there exists a unique equilibrium in whichGsetsh} in both periods and allTpay taxes.

For the proof, see the Appendix.

The simplicity of the model allows us to verify taxpayers’ reactions to different policies implemented in Period 1. It is useful to recall that we are interested in the behaviour of taxpayers who consider evading taxes as a reaction, in terms of disappointment, to the policy implemented by the government. What is of great interest is therefore the behaviour of taxpayers in Period 2 if , that is, if the decision of paying taxes exclusively depends on *T*’s satisfaction with *G*’s policy.

We find that a high proportion of aware taxpayers is necessary to exclude the less efficient outcome (that is, the *l-*equilibrium) but not sufficient to ensure the best outcome (that is, the *h-*equilibrium), which also requires a small enough . The intuition is the following: if is small enough, the *h-*equilibrium prevails over the -equilibrium because *G* would gain from all *T* (and not just from a proportion ) paying taxes in both periods; contrariwise, if is large, then offering high-quality public goods is very expensive and not profitable compared to the -equilibrium. These results follow from the assumption that *q* cannot be modified over time.

It should be noted that the -equilibrium exists because we have assumed , that is, compared to the essential level of public expenditure, having a high level may be either better or worse for taxpayers, depending on the (unknown) quality provided.^{2}

Theorem 1a: Tax evasion is positively affected by an increase in public expenditure when a large proportion of taxpayers feels disappointed about the quality of public goods provided.

Theorem 1b: Tax evasion decreases in accordance with an upward shift in public expenditure over time when the initial level of spending is low.

Theorem 1a comes from the joint analysis of the *l-*equilibrium and *h-*equilibrium. In the *l-*equilibrium, taxpayers may decide to evade taxes in Period 2 if they feel disappointed about how the government has spent their money in Period 1. This effect increases with λ. However, if *G* expects a low λ, it can be pushed to set the highest available level of public expenditure to finance patronage. The final result suggests an increase in the proportion of disappointed taxpayers, leading, in turn, to a high level of tax evasion. An opposite outcome is found in the *h-*equilibrium if λ in Period 2 is relatively high: financing patronage is not profitable, as the amount of revenues coming from the tax levy would be very low.

Theorem 1b follows from the -equilibrium: taxpayers prefer a high expenditure level, conditional on the good quality of public goods provided in equilibrium. If the proportion of aware taxpayers is large enough, revenues in Period 2 will decrease if *G* provides bad-quality public goods due to massive evasion: if *G* provides a low level of expenditure in Period 1, *T* cannot experience *q* (so that and are still willing to pay up to in Period 2 for high expenditure. As a result, public expenditure increases in Period 2 but quality may turn out to be bad because *G* will exploit *T*’s trust and unawareness.

*Y*. Now, we relax the last assumption and suppose that there are two governments (for example, two regional governments), and , which essentially differ in terms of average income gained by their taxpayers: and , with . It turns out that even assuming that taxpayers are homogeneous in their willingness to pay for a given level and quality of public expenditure (namely, , and are kept fixed), revenues coming from the tax levy will significantly differ; in formal terms, and so on:

Theorem 2: If enough taxpayers become aware of the quality of public expenditure and , then it is more likely that the government increases public expenditure from a low level to a high level in poor regions and keeps public expenditure at a high level over time in rich regions.

Theorem 2 comes directly from Proposition 1. If λ is large enough to exclude the *l-*equilibrium, we need different conditions on to choose between the -equilibrium and the *h-*equilibrium (see Table 1). It clearly turns out that the *h-*equilibrium (-equilibrium) is more likely to take place in ().

Governments with heterogeneous income levels

h-equilibrium | ||

-equilibrium |

## Concluding remarks

We have provided a simple two-period model explaining how the level and the quality of public spending affects taxpayers’ willingness to evade the payment of taxes. All in all, our results suggest that policymakers aiming to overcome tax evasion need to provide high-quality public goods: taxpayers are more willing to contribute if public expenditure is of high quality and when the quality of public goods provided increases over time; whereas if public expenditure of bad quality is set high, taxpayers are pushed to evade taxes.

In order to isolate the effect that the level/quality of public expenditure has on taxpayers’ decision to evade taxes, we assumed that the ex ante probability that a taxpayer evades, regardless of any consideration on public expenditure, is 0. It might also be interesting to relax this assumption to understand whether the decision to evade taxes affects the level and quality of spending set by the government ex ante.

## Notes

^{1}

According to Fudenberg and Tirole (1991), it is the set of strategies and beliefs such that at each stage of the game, strategies are optimal given the beliefs, and the beliefs are obtained from equilibrium strategies using Bayes’ rule. Since a proportion λ of taxpayers holds fixed and possibly false beliefs, the definition applies only to government and to (1 – λ) aware taxpayers.

^{2}

Reversing the inequality would mean that the -equilibrium would not exist because both players would prefer high rather than low public expenditure. In turn, this would diminish the impact of quality.

## Funding

No funding applies to this article.

## Acknowledgements

The authors thank the editor and the anonymous referees for helpful comments. The usual caveat applies.

## Conflict of interest

The authors declare that there is no conflict of interest.

## References

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*Experimental Economics*, 24(3): 699–750. doi: 10.1007/s10683-020-09679-3Barone, G. and Mocetti, S. (2011) Tax morale and public spending inefficiency,

*International Tax and Public Finance*, 18(6): 724–49. doi: 10.1007/s10797-011-9174-zBordignon, M. (1993) A fairness approach to income tax evasion,

*Journal of Public Economics*, 52(3): 345–62. doi: 10.1016/0047-2727(93)90039-VCowell, F.A. and Gordon, J.P.F. (1988) Unwillingness to pay. Tax evasion and public good provision,

*Journal of Public Economics*, 36(3): 305–21. doi: 10.1016/0047-2727(88)90013-8D’Agostino, E., De Benedetto, M.A. and Sobbrio, G. (2021) Tax evasion and government size: evidence from Italian provinces,

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*Journal of Economic Perspectives*, 28(4): 149–68. doi: 10.1257/jep.28.4.149Pellizzari, P. and Rizzi, D. (2014) Citizenship and power in an agent-based model of tax compliance with public expenditure,

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## Appendix: Proof of proposition 1

We prove the existence of all equilibria backwards, starting from players’ payoffs on the path and excluding any possible deviation.

**Proof**

Suppose . It is easy to show that aware *T* find it profitable to pay taxes in Period 2, even if disappointed by *G*’s policy, because the risk of being audited and fined is too high. As a result, *G* will set in both periods and all *T* will pay.

l-equilibrium: Assume thatGsets in both periods and allTpay taxes in Period 1 (only []Tin Period 2).

*G*cannot change

*q*and would get from keeping the same policy, where is the expected revenue coming from auditing (note that because all aware taxpayers evade). The only alternative for

*G*would be to reduce taxes to in order to push disappointed optimists (proportion ) to pay, getting . Such a deviation is not profitable for

*G*only if:

In Period 1, since *T* believe that *q = h*, if *e*_{H} is provided and *T* will be happy to pay up to , *G* maximises its payoff in Period 1, setting ; its total payoff is therefore equal to .

*T*would believe

*q = q*

_{H}and would pay up to if

*e = e*

_{H}.

*G*would get from such a deviation, which is not profitable if:

*T*would always pay taxes (including proportion

*λT*that become aware of

*q*in the former case) and

*G*would get and , respectively. Since , both deviations are not profitable if:

e_{L}-equilibrium: Suppose thatGsets in Period 1 and in Period 2, and all taxpayers,T, pay taxes in both periods.

In Period 2, *G* gets because *T* are not aware of *q* (given *q =* 0 in Period 1) and the Efficiency Condition proves that *G* cannot profitably deviate to either or

In Period 1, *G*’s total profit on the path equals . We now have to exclude profitable deviations, like setting or in both periods, or setting in Period 1 and in Period 2. In the latter case, all *T* would pay taxes in both periods and *G* would get , which is clearly unprofitable.

h-equilibrium: SupposeGsets in both periods, andTpay taxes in both periods.

In Period 2, *G* gets on the path and cannot profitably deviate to charging a lower tax rate. Since *q* is fixed across periods, there is no other feasible deviation.

*G*’s total payoff equals 2() on the path, and the Efficiency Condition implies that it cannot profitably deviate to setting in both periods. We now have to exclude a deviation to in Period 1 and in Period 2.

*G*would get , which is unprofitable iff:

*G*would get , which is unprofitable iff: