3.1 Tax Compliance: Theory and Evidence

As pointed out by Andreoni et al. (1998), the problem of tax evasion and noncompliance has been introduced in the economic literature just as an additional “risky asset” to the household's portfolio. The first theoretical representations of individual taxpayer's compliance date back to the 1970s: the most influential, and probably the most criticized, rational choice models have been developed by Allingham and Sandmo (1972) and Srinivasan (1973). As outlined in Chapter 1, these models portray the taxpayer's decision problem as an investment choice involving a sure and a risky lottery, and adopt the formalization of expected utility theory (von Neumann and Morgenstern, 1944). Taxpayers are supposed to choose the extent of income declaration that maximizes their expected utility, defined according to income level, individual risk propensity, audit probability, and monetary punishment, in case of evasion (or noncompliance) detection. These studies focus the effect of such parameters on evasion: for instance, a higher audit probability and/or a punishment proportional to the evaded tax reduces the expected value of evasion, and thus its attractiveness (Yitzhaki, 1974).

However, some issues on the aforementioned models have been raised, and their validity has been questioned, as the portfolio approach fails to address real-world complexity. Taxpayers are assumed to be able to determine the optimal proportion of tax to evade by making burdensome calculations, and having accurate information on the audit strategies adopted by the tax authority. Under these rather unrealistic conditions, such models predict that all taxpayers should evade if the audit probability and the fines most commonly used in reality were adopted. Furthermore, the label of “tax compliance” is generally adopted to refer to a wide variety of behaviors – such as evasion of value added tax,¹ income underreporting, or tax burden reduction – which, though exhibiting remarkably different idiosyncratic characteristics, are treated with no distinction. For a recent review see Muehlbacher and Kirchler (2016).

Graetz and Wilde (1985) suggest that taxpayers' decisions cannot be entirely explained by the level of enforcement, as tax compliance is not only a matter of rates and penalties. Furthermore, as it is not easy to obtain precise information on the actual audit procedure that the tax authority adopt to discover tax evasion, taxpayers may not know the actual risk of being audited, and need to rely on their own estimate of such a risk, in order to make a compliance decision. Such an uncertainty about the probability of getting caught is likely to influence taxpayers' behavior.

This is supported by empirical evidence documented in many countries, coming from different sources such as random audits, surveys, and laboratory and field experiments. Hence, many researchers, behavioral economists included, have tried to find models with a better fit for real taxpayers' behavior, and with a focus on potentially relevant psychosociological factors. This development process has often been built upon an experimental approach: just to list a few examples, the high degree of control and the greater parallelism with the natural world are among the main motivations leading researchers to turn to laboratory experiments, instead of relying only on theoretical analyses. In this sense, one can say that experiments on tax evasion are mainly motivated by economists' dissatisfaction with theoretical models: “Rather than question the experimental method, […] it is perhaps the theory which needs revision” (Baldry, 1987). In fact, experiments can provide a valuable support in studying people's behavior, especially when clandestine activities are involved: the extent of tax evasion as a result of a specific interaction between micro and macro factors cannot be directly measured in an entirely natural and uncontrolled setting. It is not easy to collect evidence on tax compliance, and, even if this was possible, the specific conditions determining tax decisions would not be easily kept under control. In contrast, a detailed investigation of individuals' behavior is allowed by the laboratory approach, which can be considered as the proper system to understand specific real-world phenomena.

To this purpose, many extensions based on experimental findings have been proposed in order to integrate theoretical models and make them closer to the intended domain of application: audits are costly for any audited person; the tax authority is distinct from the remainder of the government (Melumad and Mookherjee, 1989); tax collection is delegated (Sanchez and Sobel, 1993); moral and social dynamics, in terms of shame, moral rules, fairness to the tax code and its application (e.g., Erard and Feinstein, 1994; Spicer and Becker, 1980; Benjamini and Maital, 1985; Baldry, 1986; Gordon, 1989; Myles and Naylor, 1996; Torgler, 2002; Eisenhauer, 2006, 2008; Casal and Mittone, 2016), and evaluation of government expenditure and service provision (Cowell and Gordon, 1988) are included; the impact of the decision framework is tested. In this respect, Mittone (2002) finds that the introduction of an environmental structure closer to the one outside the laboratory fosters tax compliance thanks to the creation of social ties among participants. Finally, the investigation of taxpayers' views of the audit probability has shown the inadequacy of expected utility theory for tax evasion (e.g., Friedland, 1982; Spicer and Thomas, 1982; Alm et al., 1992b,c; Hessing et al., 1992; Sheffrin and Triest, 1992; Scholz and Pinney, 1995): people usually exhibit cognitive difficulties in estimating probability relationships and computing expected values (Einhorn and Hogarth, 1985; Casey and Scholz, 1991a,b), and the common uncertainty about the probability of being audited makes taxpayers' decisions more difficult than those made under the full information characterizing the laboratory environment. As traditional economic models rely on the unrealistic assumption that taxpayers have accurate information on auditing strategies, actual taxpayers' behavior cannot be predicted. Therefore, experiments with imprecise information appear to be more realistic.

A further step toward a greater realism in tax research is due to the introduction of bounded rationality (Simon, 1955, 1956). As suggested by Alm (1999), standard theoretical models, grounded on the simplifying assumptions of taxpayers' full rationality and homogeneity, should be revised. These models rely on the adoption of a unique representative agent and disregard the interaction among different types, while human behavior exhibits not only evident anomalies but also a remarkable heterogeneity (Alm et al., 1992c): for instance, some individuals may overweight the occurrence of fiscal audits, or comply because they value what they are financing. Furthermore, laboratory experiments help prove that human beings are not always able to perform complex computations and to choose the utility-maximizing action. They are not making an investment decision in isolation, but are affected by many different “emotional” factors and noneconomic considerations that make their decision process rather complex to model.

However, all these aspects, which have been defined and first investigated at the micro level, as allowed by laboratory experiments and tax theoretical models, may have unexpected consequences and give striking results at an aggregate level. For example, the vast majority of macro-empirical research reports a strong deterrent effect of tax audits on evasion. In contrast, Gemmell and Ratto (2012) empirically explore compliance response to fiscal audit at an individual level, and observe contrasting results, due to many factors, such as the opportunity to underreport and past audit experience. This implies that, in order to obtain relevant policy suggestions, neither of the two dimensions has to be disregarded. In this respect, as reviewed by Alm (2010), a growing number of researchers have adopted behavioral techniques, which rely on both human-based experimental economics and agent-based modeling, in order to address this micro–macro issue, and to gain new insights on taxpayers' behavior, which could not be observed otherwise. Micro-level experimental findings have widely shown that human agents are not rational, as assumed in theoretical models; on the contrary, they are guided by emotions, psychological and moral constraints, which might be mimicked in a computational simulation, as agents are calibrated according to human-based experimental evidence. In such a way, interesting and useful considerations can derive from agent-based modeling: on the one hand, it allows the implementation of a rather realistic system of individuals, with the intent of uncovering and testing specific cognitive aspects of taxpayers' decision process; on the other hand, the societal evolution, as due to an interaction among heterogeneous agents, can be studied from a macro perspective.

Hence, we point out that a synergic adoption of a human- and a computer-based approach gives the opportunity of gaining a deeper understanding of empirical phenomena or behavioral patterns, by scientifically studying a valid representation of these in the laboratory. Thanks to the combination of these two approaches, compliance decisions are studied both at an individual and at a collective level: the exploration of the overall behavior of the society requires taking into account social interactions among heterogeneous and boundedly rational human beings. Agent-based simulations might provide valuable support, since they can rely on realistic assumptions – that is, behavioral regularities previously observed in the laboratory – and allow the implementation of complex settings in which both micro and macro factors interact and affect agents' behavior, as it usually happens outside the walls of the experimental laboratory.

3.2 Research on Tax Compliance: A Methodological Analysis

According to the previously presented evolution of research on tax compliance, an apparent challenge between economic theoretical models and the experimental approach seems to emerge. On the one hand, experimenters claim that anomalies observed in the laboratory are an important proof of the failure of theory in describing and predicting taxpayers' behavior in an accurate way. On the other hand, however, theorists reply that their models are intended to address phenomena taking place in the real world and not in the artificial environment of the laboratory. Alm et al. (1992b) point out that “ […] experimental results can contribute significantly to policy debates, as long as some conditions are met: the payoffs, and the experimental setting must capture the essential properties of the naturally occurring setting that is the object of investigation. Laboratory methods may offer the only opportunity to investigate the behavioral responses to policy changes.”

In such a framework, the necessity of external validity of grounding experiments is evident: researchers claim that results are not always generalizable, that is, applicable to the real world, because the environment reproduced in the laboratory is too simplistic and does not take into account many relevant variables. For instance, Webley (1991) argues that “ [experimental] results may reflect a person's understanding of economics rather than the behavior that would be displayed in the real situation.” The experimental setting might be perceived as too artificial and far from the environment outside the laboratory, if it is not a perfect replica of the real world. The experimental system needs an external validity hypothesis, which maps laboratory elements onto elements of the phenomenon observed in the field. Only if this hypothesis holds, can researchers draw valuable inferences on individuals' decision process from the laboratory and move to the world outside (Guala, 2002).

The present chapter enters such a debate and explicitly focuses on the problem of external validity of tax experiments, adding to the small literature available on the topic. On the contrary, it disregards the internal validity issue, which has already received much attention in the experimental literature. Specifically, the novelty of this methodological review resides in the proposal of a synergic approach, involving both human-based observations and agent-based simulations as a valuable tool aimed at solving the problem of external validity of tax experiments.

In a very recent contribution, Muehlbacher and Kirchler (2016) address this methodological issue, providing an interesting review of both experimental and empirical research on tax compliance. The authors point out that little is known about the external validity of tax experiments and identify a number of criticisms: in addition to a rather general critique on artificiality, participants' self-selection, experimenter effect, social desirability, and social blaming, a more detailed methodological review on tax research is offered. For instance, as already well documented in previous studies, income-reporting decisions in a tax setting systematically differ from those in an abstract setting (Baldry, 1986; Alm et al., 1992c; Mittone, 2006; Choo and Fonseca, 2016); the introduction of a redistribution mechanism strongly affects taxpayers' decisions (Alm et al., 1992a,c; Mittone, 2006); students might not be representative because they have no experience in paying taxes (Webley, 1991). Furthermore, compliance depends on the way in which subjects' income is provided (Boylan and Sprinkle, 2001; Boylan, 2010; Durham et al., 2014). Finally, in reality, there is a temporal distance between compliance decisions and audits, which might have a significant effect on actual compliance decisions, and make experiments disregarding this issue less reliable (Kogler et al., 2016). Based on this, Muehlbacher and Kirchler (2016) suggest that experimental investigations in the laboratory should induce the same psychological mechanisms taxpayers adopt outside, and take into account possible interactions between treatment factors and setting characteristics. If such requirements are met, experimental findings can be applied also outside the laboratory, and thus provide useful insights for policy interventions.

According to Alm et al. (1995), “a government compliance strategy based only on detection and punishment may well be a reasonable starting point but not a good ending point. Instead, what is needed is a multifaceted approach (…) Put differently, explaining tax compliance requires recognizing the myriad factors that motivate individual behavior, factors that go much beyond the standard economics-of-crime approach to include theories of behavior suggested by psychologists, sociologists, and other social scientists. Until this effort is made, it seems unlikely that we will come much closer to unravelling the puzzle of tax compliance.” Following the same approach, Guala and Mittone (2005) get into this debate on the role and external validity of experiments, suggesting that experiments might help theoretical models to get closer to real-world phenomena, and thus answer specific questions about causal relationships.

From this viewpoint, Guala and Mittone (2005) claim that experiments serve as epistemic mediators between theoretical models and empirical economic phenomena. In fact, theory and experiments are not considered as two distinct entities: they both require initial hypotheses and inference; they are two useful and complementary structures to study and subsequently understand economic behavior. Figure 3.1 shows this relationship as presented by Guala and Mittone (2005): They identify a gap between theoretical models and the intended domain of application, and experimental systems occupy the middle ground between the two. Nevertheless, both experiments and targeted economic phenomena belong to the same “real world”: in fact, according to the authors, compared to theoretical models, experimental systems are closer to the target, since they actually allow the collection of observations of real people's behavior under specific conditions, although in an environment that has been artificially manipulated by the experimenter.

Figure 3.1 also refers to the way in which the gap – or better, the gap between theory and experiments, and the one between these and the target – can be closed. On the one hand, internal validity – in terms of testing different hypotheses in isolation by controlling for confounding variables and ruling out undesired effects – bridges the gap between theoretical models and experiments. On the other hand, external validity – in terms of laboratory identification of mechanisms that characterize also the targeted phenomena – is intended to bridge the gap between experimental systems and the specific domain of application. While the former has received much attention in the economic literature, little can be found on the analysis of external validity (Muehlbacher and Kirchler, 2016). The problem of internal validity can be “easily” solved by adopting a number of techniques allowing the identification of causal relationships. However, even a high degree of internal validity does not ensure that the external validity requirement is met. Experiments provide a higher degree of concreteness with respect to theoretical models, by including features that could be reasonable for externally valid inferences. However, they are still artificially isolated from the world outside the walls of the laboratory, in which a wide variety of micro and macro factors – tax audit plans, risk preference, reasoning biases, moral constraints, social norms, social comparison, interaction and imitation, fairness, trust, just to name a few – interact in determining actual taxpayers' behavior. Experiments try to implement these factors, yet under the constraint of balancing between internal and external validity: an excessively complicated experimental setting impairs the identification of clear causal effects, and makes experimental results harder to interpret (Cowell, 1991). Therefore, most laboratory experiments are not able to perfectly replicate the specific targeted phenomena, and feed back into the theoretical literature. Experiments can help at an intermediate stage, as they cannot bridge the gap between the target and the theoretical model: the highly controlled experimental setting is aimed to determine which theory better explains a certain pattern of data, but this explanation might not be valid outside the laboratory (Guala, 1998, 1999, 2003).

Nevertheless, as suggested by Guala and Mittone (2005), experiments might also be intended to discover new real and robust empirical phenomena, not necessarily explained by existing theories to be tested in the laboratory. These phenomena might include generic psychological effects, biases, and heuristics to be applied to specific empirical situations. In such a case, experiments do not need to perfectly reproduce the target but may contribute to the creation of a library of phenomena (Guala and Mittone, 2005): they simply discover new facts useful from a policy perspective.

In addition, Guala and Mittone (2005) propose interesting examples of robust biases involved in probabilistic reasoning and the effects of uncertainty that have been identified and extensively studied in the laboratory and in the field, also as strictly related to research on tax compliance. Both Sheffrin and Triest (1992) and Scholz and Pinney (1995) perform an econometric analysis of the influence of taxpayers' perceived probability of detection on compliance decisions. The former analysis finds that individuals who perceive a higher audit probability expect significantly less evasion in the population, and those not trusting others or the government engage in more evasion. Nevertheless, such an analysis solely relies on survey data, and therefore, as suggested by Andreoni et al. (1998), the results could be biased by the coherent image individuals tend to convey in surveys. In contrast, Scholz and Pinney (1995) also collect tax-return data, and their analysis is intended to investigate the extent of people's guilt and moral obligation, by testing the duty heuristic hypothesis: if taxpayers have no accurate information on the probability of detection, they can rely on heuristics to derive subjective estimates of the risk and to make their compliance choice. The authors observe a significant positive relationship between subjective probability and duty, which in fact leads to an overestimation of the risk of getting caught, and therefore to a higher degree of compliance. Such an effect is even strengthened by people's tax knowledge and previous contacts with the authority. This evidence is supported also by Hessing et al. (1992): although, according to Andreoni et al. (1998), their results seem to partially contradict those reported by Scholz and Pinney (1995), it emerges that the duty is fostered by mere contacts between taxpayers and the tax authority, while it is impaired by previous audits and fines. In fact, traditional enforcement activities built on coercive power seem to negatively affect taxpayers' sense of duty ( Kirchler et al., 2008); tax agencies prefer to adopt a horizontal monitoring approach, by treating taxpayers as customers to whom they can provide useful services.

Friedland (1982), Spicer and Thomas (1982), and Alm et al. (1992b) manipulate the quality and the accuracy of information on fines and probabilities in the laboratory: they observe that a higher degree of informational ambiguity enhances compliance. Nevertheless, as theoretically proved by Snow and Warren (2005), such an effect strictly depends on individual ambiguity aversion.

From a similar viewpoint, Bernasconi (1998) suggests that the portfolio approach needs to be integrated with subjects' probability weighting. The nonlinear weight function proposed according to rank dependent utility models (Quiggin, 1982), and prospect theory (Kahneman and Tversky, 1979) may describe the higher degree of compliance actually observed, compared to the theoretically predicted low level. In this respect, prospect theory provides new approaches to modeling tax evasion decisions (Schepanski and Shearer, 1995; Dhami and Al-Nowaihi, 2007; Ping and Tao, 2007; Trotin, 2010; Piolatto and Rablen, 2014; Piolatto and Trotin, 2016), by taking into account probability weighting and reference dependence (Copeland and Cuccia, 2002; Bernasconi and Zanardi, 2004; Watrin and Ullmann, 2008).

Also Erard and Feinstein (1994) underline the significant impact of probability weighting on taxpayers' decisions: in order to provide useful and reliable behavioral insights, fiscal models have to take into account the difference between actual audit probabilities and estimates. In support of the occurrence of this probability weighting process, Spicer and Hero (1985) build a repeated measurement setting and find that the extent of underreporting diminishes as the number of audits previously undergone increases. This evidence has been explained by the availability heuristic: people tend to rely on immediate examples they recall when evaluating a decision problem (Tversky and Kahneman, 1973). An alternative explanation is the target effect, according to which people assume that a fiscal investigation is likely to be followed by another one (Hashimzade et al., 2013).

In contrast, Mittone (1997) reports on an experiment investigating the difference between probability subjective estimation and weighting: taxpayers exhibit overestimation when simply asked to judge the probability of being audited, and underweighting when asked to actually make a decision. Specifically, according to their estimated probability, compliance is expected to ensure a higher expected value than evasion does; however, in the compliance decision, evasion is the predominant choice.

More detailed analyses of the dynamics underlying taxpayers' decisions in a repeated measurement framework, mimicking a “taxpayer's life span,” are provided by Mittone (2006) and Kastlunger et al. (2009). In contrast to Bayesian updating, such that audited taxpayers have higher estimates of audit probability than nonaudited taxpayers, and are more deterred from evasion, these authors observe that the occurrence of an audit seems to make taxpayers more prone to evade. This result is commonly referred to as the bomb crater effect: the probability of observing compliance decreases if a taxpayer has just undergone a fiscal audit. According to Guala and Mittone (2005), this phenomenon observed in the laboratory has to be tested under a variety of conditions in order to verify whether it exhibits robustness and external validity. As for the former property, Kastlunger et al. (2009) find similar results and report that the decrease in compliance after an audit is very rarely due to loss-repair tendencies: the decrease in compliance seems not to depend on whether the taxpayer is fined in the previous round or found to be compliant. As for the latter, it might not be easy to observe the bomb crater effect outside the laboratory: in many countries, variability in declarations increases the probability of being investigated. Nevertheless, such an effect might emerge under specific conditions. Studies about the impact of audits on subsequent compliance have shown that the decline in compliance after an audit can also be observed in real taxpaying situations (DeBacker et al., 2015), and not only with respect to income tax. Bergman and Nevarez (2006) analyze VAT data from individual tax return information in Argentina and Chile and identify the effect; however, the authors also argue that taxpayers who evade more tend to be less deterred by audits.

The so-called echo effect is another laboratory phenomenon Guala and Mittone (2005) deal with. Mittone (2006) studies the effect of different patterns of audits over time, and finds that frequent audits experienced early in “tax life” may lead to higher compliance at later stages. Guala and Mittone (2005) report that this phenomenon is robust to changes in the experimental setting, and suggest that this laboratory evidence is supported by a number of real life examples: for instance, fare evasion on Italian public transport is increased by the experience of infrequent controls. Therefore, it seems reasonable to assume that taxpayers evaluate or weight the audit probability according to their experience: repeated audits may lead to a decrease in evasion even in the long run because of chance misperception. Taxpayers learn that the likelihood of audits is higher than the objective probability when these are rather frequent in the beginning; therefore, they rely on this sample to form their probability evaluations and stick to a high compliance level even when the frequency of investigations diminishes.

In summary, our analysis starts recalling the approach by Guala and Mittone (2005) who identify the mediator role of economic experiments in the study of empirical phenomena. Experiments rely on hypotheses and allow the investigation of specific, framed and concrete settings: individuals' decisions are real, although in an artificial environment. We recognize the undeniable relevance of experimental systems in supporting theoretical models and providing better insights on empirical regularities, which otherwise could not be studied and understood so clearly outside the laboratory. For this reason, experiments call for internal validity, while an a priori external validity is not necessary: as previously pointed out, experimental investigations might contribute to the identification of robust economic and psychological phenomena that can be borrowed and applied to specific cases inside or outside the laboratory. At the same time, however, it is also true that, in order to increase their reliability, experimental findings might need to be further tested before valid inferences are drawn.

In this respect, we provide a novel contribution to the literature on experimental methodology in tax research, by extending the framework presented by Guala and Mittone (2005) and claiming that agent-based simulations offer valuable support. In fact, both theoretical economic models and related experiments are mainly defined in a microeconomic setting and they address empirical issues with a high degree of specificity. In addition to this, experiments cannot control for all cognitive drivers involved in the decision process of tax compliance, but only for those specifically targeted and isolated by the experimental design. In this framework, a computational approach to the study of tax evasion tests not only the robustness of experimental findings but also their external validity. On the one hand, agent-based simulations may provide valuable insights of cognitive nature, which an experimenter would not be able to get by simply observing the behavior of a limited sample of human subjects in the laboratory. Human-based experiments contribute to the library of phenomena; computer-based simulations aim at validating laboratory findings, and help understand complex cognitive processes involving psychological biases and heuristics. On the other hand, simulations allow the combination of micro- and macro-level factors actually interacting outside the laboratory and determining people's compliance.

3.3 From Human-Subject to Computational-Agent Experiments

From the previous analysis, it is evident that a pure theoretical approach may offer an “unrealistic [or better, incomplete] picture of human decision-making,” which is neither based on nor confirmed by empirical evidence (Selten, 2001). Therefore, it requires to be mediated by an experimental approach, in order to effectively target the empirical domain of interest. This implies the adoption of heterogeneous and less strict assumptions on individual behavior. Nevertheless, in spite of helping theoretical models target specific phenomena, some experiments might still lack external validity. On the one hand, decisions observed in the laboratory are real and the choice setting is specifically intended to address the issue of interest; on the other hand, human samples usually are rather small, and the setting might turn out to be too simple and prevent valid inferences to be transferred outside the laboratory. According to the materiality thesis by Guala (2002), experiments may not display a formal similarity to the complex framework of the target system, although being able to replicate almost the same causal processes taking place in the real world outside the laboratory. Therefore, relying on the assumption that human beings are basically the same inside and outside the laboratory, it is possible to identify a correspondence at a “material” level between the experimental and the target system, but not necessarily at a “formal” and “abstract” level, which might hinder the external validity of experiments.

In this framework, agent-based computational economics (ACE) may significantly contribute to the development of more realistic decision-making models; it helps bridge the gap between economic models and the intended domain of application. Similar to theoretical and experimental approaches, simulations require a formal definition of behavioral types. As a matter of fact, ACE is not intended to disregard theoretical considerations, as relationships describing human behavior need to be known in advance for the calibration of agents. Nevertheless, simulations can rely on behavioral assumptions (and experimental observations) so that different agent types are defined, the standard neoclassical economics idea of a homogeneous representative agent is overcome, and a realistic replication of the world is provided. In this sense, both the theoretical and the experimental analysis are enriched by the introduction and the robustness check of heterogeneous behavioral patterns, which might be designed according to previously collected empirical and experimental evidence.

Nevertheless, in contrast to laboratory experiments, according to the ontological analysis by Guala (2002), simulations rely on a process of abstraction: the external validity requirement might be hardly met at a material level, as the correspondence between the simulating and the target system is of a more “formal” kind. ACE agents are virtual entities endowed with specific attributes, purposes, and behaviors; they interact with a rather complex landscape – it consists of institutions, enforcement rules, social networks, and so on – which, in general, resembles the real world but cannot be replicated in human experiments; they receive an input and, based on this, select an action allowing them to reach their predefined goals, such as wealth, happiness, or honesty.

Nowadays, in the field of economic behavior, the spectrum of possible experimental methodologies is quite broad and ranges from 100% human-subject to 100% computational-agent experiments. These two extremes were first thought to be either in opposition or completely unrelated: until a few years ago, the majority of ACE researchers did not consider human-subject experiments as a valuable and real source of information and results in order to build and calibrate simulation models, as reviewed by Duffy (2006). Similarly, the great majority of experimentalists tend to exclusively rely on human-based tests or explorative investigations, without trying to increase the potential and the extent of their experimental results by means of computational simulations.

However, these two methodologies tend to converge: half way, different techniques, such as a mixture of human and computer agents interacting with each other, human-calibrated computer agents, and computer agents with real-world data streaming, are gaining relevance. Researchers admit that the laboratory with human subjects is a rather artificial context: time is compressed, subjects are asked to make unnatural repeated decisions so that lifetime span can be mimicked, and the landscape is fully controlled and manipulated by the experimenter. Experimental design factors, such as round numerosity, are strictly related to the specific aim of the investigation: even a few rounds are enough to study some simple learning processes, while a higher number of repetitions are necessary if more complex behavioral dynamics are investigated. Nevertheless, an excessive increase in the number of rounds can often harm the results' reliability, as participants get bored. Therefore, from this viewpoint, well-designed experiments allow researchers to carefully study and deeply understand simple dynamics and individual behaviors. In a complementary way, simulations permit to disregard the boredom issue and analyze more complex and dynamic behavioral processes over an extended period of time and among heterogeneous agents: in order to see the emergence and the evolution of behaviors over time and investigate cognitive processes, ACE researchers implement artificial agents that make decisions and react to consequences and signals. As this approach is based on heterogeneous and predominantly boundedly rational agents acting within a dynamic environment, it extends the idea of the representative agent that does not evolve, is fully rational, and is endowed with an unlimited computational power.

In doing this, simulation models may rely on data from human-subject experiments. The agent-based methodology can be used to understand results from human-based studies, since it allows the exploration of the decision process in a more complex economic environment, by replacing humans with agents. The potential of experimental results can be increased by means of these computational tests: it is possible to explore the psychological mechanisms giving rise to phenomena whose robustness and external validity can be checked. Simulations relate the micro-level (i.e., agent-level) behavior to macro-level (i.e., system-level) dynamics, represent multiple scales of analysis in a natural way, and investigate adaptation and learning. Agents are built on experimental evidence, and behave according to actually observed heuristics; in addition, the implementation of an interaction among different agents over time provides insights into macro evolution, which could not be investigated in a simpler human-based experiment. The “formal” similarity ensured by simulations is combined with the “material” one provided by laboratory experiments in a complementary way. The potential of both methodologies is exploited in order to meet the external validity requirement (Guala, 2002). Therefore, from this viewpoint, not only simulations contribute to the external validity hypothesis of experimental systems, but, in turn, experiments increase ACE studies' validity, which is considered as one of the key aspects to judge the performance of a computational model (Taber and Timpone, 1996). In fact, simulation results can be tested in the laboratory in order to better grasp human behavior in computational settings and observe whether and why computer and human behaviors differ. Collected data can feed the software model and contribute to ameliorate agent-based predictions of real-world economic behaviors, and ground them on a material basis, rather than a merely formal one.

Based on this synergic approach, agents' behavioral traits are no longer defined only according to simplifying theoretical assumptions but according to observations actually taken from the real world: behavioral regularities discovered in economics and psychology experiments (e.g., Andreoni et al., 1998; Mittone, 2002, 2006; Kirchler, 2007) can be used to calibrate and/or test simulation models, which, in turn, can help check and explain experimental results. Therefore, both approaches gain in external validity: the high number of degrees of freedom in agent-based models can be managed with human calibration, and human-based experiments, which are not always able to perfectly manipulate subjects' behavior and control their cognitive processes, can find a further confirmation in simulations.

In light of the above, the complementarity of simulations and laboratory experiment also emerges as a support to external validity: the “formal” similarity between simulations and real-world phenomena can be combined with the “material” similarity characterizing the relationship between the experimental and the target systems. On the one hand, the simulations' need for a relevant background knowledge can be met by means of an experiment-based calibration: evidence on human decision processes are collected in the laboratory and used to feed simulated agents, so that they can resemble real decision makers also at a more material level.² On the other hand, the mere materiality of laboratory experiments is enriched by simulations' formal correspondence to reality: people's behavior is first observed in a rather simple and artificial laboratory setting; then, it is further investigated and tested in a more realistic environment, in which human-calibrated agents interact. Therefore, it seems possible to conclude that none of the two methodologies has epistemic privilege over the other (Parke, 2014): “material” and “formal” correspondence should be used in a complementary manner, so that each methodology can take advantage from the other while addressing the common external validity issue.

A graphical analysis of this relationship between experiments and ACE models is provided in Figure 3.2: the framework adopted by Guala and Mittone (2005) is extended in order to include agent-based simulations as a support for experiments in studying empirical economic phenomena and bridging the external validity gap. The figure shows that ACE simulations rely on both macro and micro theoretical models: in fact, they allow the investigation of the evolution over time of network systems involving heterogeneous individuals, and this heterogeneity is built upon micro experimental evidence. In this sense, simulations also belong to the real world as experimental observations are used for agents' calibration, and complex and more complete settings can be implemented to the purpose of making experimental results more likely to be externally valid. Agent-based models rely on preference assumptions but they exhibit a high degree of complexity with respect to human-based experiments, as they mimic societies made of heterogeneous individuals. Not only can human-calibrated agents be endowed with diverse attributes, such as income level, risk propensity, compliance preferences, norm adherence, heuristics, biases, and so on, but various policy parameters and the effect of these on the interaction among agents can also be taken into account.³ This allows both the investigation of taxpayers' cognitive process and the combination of micro-level evidence and macro dynamics among heterogeneous agents in a unique decision setting resembling the economic environment of interest. The analysis of tax compliance dynamics in a pretty realistic, though complex, system may lead to discover new and efficient policy options (Garrido and Mittone, 2013; Pickhardt and Seibold, 2014), which could take into account the variety of reactions emerging in a population of heterogeneous taxpayers.

3.4 An Agent-Based Approach to Taxpayers' Behavior

With a closer focus on tax experiments, this section proposes two separate ACE approaches intended to pursue the aforementioned goal of filling the external validity gap: both of them are aimed at tackling the limitations of full rationality and behavioral homogeneity, which impair the external validity of theoretical and experimental claims.

Firstly, agent-based models may analyze the interaction among types and study the subsequent emerging macro dynamics; this is mainly based on the implementation of recurring behavioral styles in the population of taxpayers previously identified in laboratory experiments (Mittone and Patelli, 2000; Davis et al., 2003; Antunes et al., 2007; Hokamp and Pickhardt, 2010; Hokamp, 2014). Owing to their scope, these models are usually characterized by a modest degree of granularity: they try to tackle the unrealistic theoretical assumption of a lack of heterogeneity in taxpayers' behavior, yet without always addressing the bounded rationality issue. They are not intended to explore individuals' cognitive dynamics; therefore, behavioral types are specified as rather simple agents. This interest in the identification of groups of taxpayers dates back at least to the 1990s. Building on Cowell (1991), Hessing et al. (1992) identify three behavioral types according to willingness to comply, and underline the importance of behavioral heterogeneity to evaluate the extent of efficiency and effectiveness of different policy instruments: some auditing strategies might have the negative impact of crowding out honesty, and thus reducing individual willingness to comply; in contrast, an efficient strategy might fight tax evasion by sustaining honesty and compliance. In this respect, contrary to human-based experiments, agent-based simulations allow the implementation and manipulation of population heterogeneity in a highly controlled manner, so that this, and its interaction with other variables, can be treated and analyzed as a determinant of the efficacy of policies. In a synergic view, such simulation results can be subsequently tested on human subjects.

Secondly, simulations may also look into micro behavioral patterns that go beyond the macro type specification. Therefore, they are characterized by a higher granularity, since agents are more complex in their attributes. In fact, in this case, human behavior is first investigated at an individual level in the laboratory and then reproduced by means of artificial agents (Bloomquist, 2006; Garrido and Mittone, 2008; Méder et al., 2012): simulations help uncover and understand human cognitive processes and psychological drivers, which cannot be fully investigated in a purely human setting. Therefore, this kind of analysis is well suited to the implementation of boundedly rational decision makers, that are intended to mimic human subjects, and choose according to a restricted set of information.

The following sections provide an exemplification of the methodological validity of combining human- and agent-based techniques in the study of tax phenomena. To this purpose, the aforementioned distinction between mainly macro or micro computational analysis is adopted; in addition, some attempts of reconciling such a distinction are analyzed (e.g., Korobow et al., 2007; Garrido and Mittone, 2013; Mittone and Jesi, 2016). The analysis of these simulation examples is aimed at offering guidance in the implementation of the synergic approach, involving both human- and agent-based models, with the intent of filling the external validity gap of economic experiments. Providing an extensive review of research with human-calibrated models is, instead, beyond the scope of the present chapter.

3.4.1 The Macroeconomic Approach

Mittone and Patelli (2000) carry out a dynamic simulation in order to model a fiscal environment in which different types of taxpayers interact and, according to their degree of compliance, a public good is provided.⁴ The two authors investigate taxpayers' psychological and moral motives by using human-calibrated simulation models. The idea of studying specific taxpayers' behavioral traits is developed in the seminal work by Mittone (2002): he categorizes behavioral regularities and identifies classes of subjects reacting in a similar way to certain economic and moral factors.⁵

Mittone (2002) verifies whether subjects' behaviors can be captured and classified in homogeneous categories by performing a cluster analysis.⁶ He finds four main clusters:⁷ the great majority of subjects do not exhibit a stable behavior, in line with the intuition that previous experience affects taxpayers' decisions. Behavioral clusters are almost identical across experimental conditions. Results confirm the difficulty of modeling and explaining the actual dynamics of taxpayers' behavior by simply relying on the traditional expected utility approach: refinements based on empirical and experimental observations are necessary, in order to understand the interaction between behavioral heterogeneity and enforcement policies. As pointed out by Mittone (2002), contrary to rational predictions, participants seem not to be comfortable with repeated choices under risk, and alternate opposite choices, probably because the ongoing interaction with the environment leads them to weight probabilities, and not to stick with a predetermined pure strategy. However, he also reports that tax yield redistribution triggers honesty. This change in the composition of the population due to the institutional setting might have serious policy implications: these experimental results seem to suggest that the policy maker should implement fiscal plans designed according to the institutional setting, and subsequently exploit the composition of taxpayers' population to foster honesty imitation, as proposed by Hessing et al. (1992). To this purpose, a valid support is offered by ACE simulations, which test the efficiency and the efficacy of different enforcement strategies on a large population consisting of a realistic variety of human-calibrated types. This computational approach adds to the experimental one, since it manipulates the composition of the population, and thus controls for the macro effects deriving from the interaction among different behavioral types under given institutional and fiscal settings.

Building on this, Mittone and Patelli (2000) study the true nature of tax compliance, by focusing not only on the effect of tax authority enforcement but also on social interaction and moral concerns. They focus on the coexistence of three different behavioral styles that require agents' interaction in order to evolve, and adopt a computational approach that might contribute to the validity of experimental findings. The work by Mittone and Patelli (2000) can be considered as a good example of the synergic approach of ACE simulations and human-based experiments aimed at providing greater realism and concreteness for the subsequent application of results to specific policy targets. In fact, Mittone (2002) identifies in the laboratory some behavioral regularities; Mittone and Patelli (2000) not only test the robustness of laboratory findings but also study the macro evolution of a dynamic and heterogeneous population facing different enforcement systems. Behavioral types identified with the experimental micro approach are used to calibrate agents, whose behavior is analyzed from a macroeconomic viewpoint: type imitation and population evolution are the main scopes of this ACE investigation. These types include the honest taxpayer, the imitative taxpayer, and the perfect free-rider.⁸ Agents share a decision algorithm, led by utility maximization, while each type has a unique utility function that specifies its behavior.⁹ This allows the implementation of heterogeneous agents, and aims to extend microeconomic models toward the investigation of behavioral evolution and evasion activity in a population of interacting taxpayers, who have different preference structures.

In such a system, at regular intervals, a genetic algorithm can be activated in order to update the composition of the population, without modifying the overall number of agents. The two authors set an initial scenario, and observe how a given population composition evolves over time: taxpayers initially belong to one of the three categories, but then they can decide to switch to another type, according to the degree of success of their style in pursuing the goal of utility maximization.

This optimization strictly depends on tax-payment decision and the risk of being investigated. In fact, in each round, a fixed number of agents are audited according to either a uniform auditing (all agents have the same probability of being investigated) or a low-tail auditing strategy (agents who report the lowest amount of tax have a higher probability of being audited). This diversification is intended to investigate the effect that different auditing policies produce on taxpayers' behavior, also depending on the specific degree of population heterogeneity. Figure 3.3 shows the functioning of the simulated economy: it is evident that agents' decisions are determined by both social interaction and the enforcement activity of the tax authority.

In summary, Mittone and Patelli (2000) study the macro experimental interaction among behavioral types identified by means of a microeconomic approach; they test the efficacy of different audit strategies in fighting tax compliance when population heterogeneity is not the result of abstract assumptions but of real-world observations. Such a controlled exploration of the interaction of different population compositions with the environment would not be easily implementable in a purely human-based setting. This justifies the adoption of an agent-based approach, which allows the observation of macro behavioral dynamics, but needs human calibration for the implementation of realistic taxpayers.

Results show that a uniform auditing strategy is more effective than a low-tail one in fostering compliance; imitating the honest behavior is a winning strategy when low-tail auditing is implemented. Finally, genetic selection favors honesty, as frequently observed also inside and outside the laboratory when moral concerns on contribution are involved in the decision process. When taxpayers are aware that they will actually benefit from their fiscal contribution, they appear to be more prone to comply.

Hence, if combined with theoretical models and laboratory experiments, agent-based simulations can help understand and explain behavioral processes underlying tax payment decisions. The novelty of this study resides in the implementation of a simulation model investigating the relationship between enforcement activity and social interaction among different behavioral styles, which have emerged as regularities in previous human-based experiments. Taxpayers are heterogeneous and their behavior is described by utility functions; furthermore, they can switch to a different type according to the “satisfaction” they are able to derive from the behavior of their own category. Nevertheless, agents' decision-making process still relies on optimization, and depends only on the information they receive from the system. In this sense, they are myopic, since they are not designed to take into account either intertemporal or strategic expectation on the evolution of the environment. For this reason, a further development in this direction might include a distinction between naive and sophisticated agents, where the latter should be modeled in order to mimic agents capable of making efficient predictions about their future behavior and that of their mates.

3.4.3 Micro-Level Dynamics for Macro-Level Interactions among Behavioral Types

This section deals with ACE models that combine micro behavioral aspects and macro dynamics, with the intent of providing a better understanding of both experimental evidence and economic phenomena taking place outside the laboratory. Therefore, this kind of comprehensive analysis can be of great relevance for policy implications, by relying on the implementation of human-calibrated agents.

The first example is the work by Garrido and Mittone (2013), which analyzes how the efficiency and the efficacy of an enforcement strategy – defined in terms of audit frequency and targeting – can be considered as a function of the population composition. However, contrary to the macro analysis by Mittone and Patelli (2000), behavioral types are defined according to income distribution and specific traits that characterize individual cognitive process (Garrido and Mittone, 2008). Taxpayers are endowed with a decision function, and, in each round, they choose whether to evade. Honest taxpayers tend to comply in any case, irrespective of their current state; strategic evaders behave according to the bomb crater effect. Right after all taxpayers make their decisions, the policy maker applies an optimizing selection rule that targets a subset of agents to audit: on the one hand, collected tax increases revenues; on the other hand, audits are costly and not always successful.¹³

Garrido and Mittone (2013) conclude that the optimal audit scheme must take into account income distribution, the possibility of identifying behavioral patterns with micro foundations, and the specific fiscal history of individuals. Micro-level behavioral regularities emerging in laboratory experiments turn out to be fundamental in designing an auditing strategy: being aware of some cognitive biases can help predict people's behavior; agent-based simulations built on these biases are useful to plan a coherent and efficient fiscal policy. As income inequality increases, the optimal plan targets the richest taxpayers, and frequently repeats two consecutive audits as a strategy against the bomb crater effect. In contrast, as income distribution becomes more uniform, the optimal plan suggests spreading audits throughout the entire population. Every time an agent is investigated, his last four declarations are verified: if the tax authority audits each agent every four periods, also strategic evaders are caught.

Nevertheless, despite the relevant contribution of this study in understanding how the policy maker can address the issue of tax evasion when realistically dealing with a heterogeneous population, results are partially due both to the rationality assumption on the tax authority and to the main characteristics of taxpayers' choice function (no intensive decision is allowed, and no actual learning is implemented). This simplifying decision process might lead to partially misleading behaviors: in fact, in their laboratory experiment, authors allow for intensive decisions, and observe that rich individuals often prefer to evade a small amount of tax with the aim of reducing the probability of being targeted. In contrast, the simulation by Garrido and Mittone (2013) disregards this important aspect, and the optimal plan might target the richest taxpayers so that expected revenues of the tax authority are maximized.

The second example of a computational analysis combining the macro and the micro approach is the one by Mittone and Jesi (2016). By extending the agent-based analysis by Garrido and Mittone (2013) and Mittone and Patelli (2000), they build a complex adaptive system in which a variety of behavioral types coexist. However, contrary to Mittone and Patelli (2000), these types are based on the definition of simple heuristics, and not of utility functions to optimize. In addition, with the intent of overcoming the limitations of the model by Garrido and Mittone (2013), they also allow for intensive decisions, learning, different risk perceptions, and for probability weighting as a common feature of individuals' decision process. Specifically, Mittone and Jesi (2016) investigate the functioning and the evolution of a system where boundedly rational agents cope with a public good that might be consumed and created by the agents themselves. The authors build a self-reproducing economy as a setting for the study of the emergence of a responsible behavior in managing a renewable resource. They study the necessity of an exogenous mechanism of auditing in order to achieve a sustainable setup.

In every period, agents extract their private endowment from the good; then, they contribute by paying their tax due. These actions are carried out according to a limited set of heuristics (basically either imitative behaviors or habits) and to the employment type of the agent (employee vs self-employed):¹⁴ heuristics suggest the amount to take in order to perform a satisfying extraction, but the agent can try to extract more resources. In the beginning, each agent is randomly assigned a type and one of the five available heuristics; then, in order to keep the system dynamic, new agents are injected into the economy, and individuals can switch from one heuristic to another according to the achieved satisfaction level: the higher the level of sadness (i.e., the lower the degree of satisfaction), the higher the probability that an agent opts for switching to another heuristic. This sadness is mainly determined by the level of the extracted endowment, and the proportion of agents actually contributing to the public good. In addition, irrespective of the individual heuristic adopted, agents share the bomb crater effect as a common micro-founded psychological trait: as widely observed in human-based experiments, after an investigation occurs, the audited agent evades, underestimating the probability of a repeated audit. Such a characterization makes agents closer to human beings: they are not supposed to be rational, but rather emotional and biased in their decision process. For this reason, results can be of great interest and relevance for externally valid policy suggestions.

At the end of every period, the tax authority performs random audits and the good reproduces itself so that it cannot extinguish. Before the reproduction takes place, the good triggers a signal if the critical status in terms of quantity is reached. Agents react to this alarm according to their sensitivity level, that is, to their propensity to take risk and their adopted heuristic. See Figure 3.4 for a comprehensive representation of the overall system structure.

Thanks to the implementation of this complex framework with a micro-founded behavioral heterogeneity, Mittone and Jesi (2016) identify the extent of behavioral heterogeneity that is able to trigger a responsible behavior, and thus find interesting results from a normative point of view. In fact, as already suggested by Hessing et al. (1992), they claim that selfishness, and thus evasion, can be effectively counterbalanced if other behavioral types are more attractive for taxpayers. In their model, an efficient fiscal policy can tremendously decrease tax evasion not only by means of audit deterrence, but also by sustaining the advantage that a taxpayer can get adopting an honest behavior. From this perspective, an efficient policy should exploit behavioral heterogeneity and induce taxpayers to the imitation of honest agents by making compliance more attractive for both employees and self-employed workers.

Hence, also in this case, the validity of the synergic approach of human-based and agent-based experiments is undeniable: human evidence serves as a basis to build behavioral types, and simulations allow the manipulation of population heterogeneity as a treatment variable, with the intent of leveraging the full potential and overcoming the limits of human-based experiments. This results in a more complete and deeper analysis of tax payment decisions: useful policy suggestions can be derived, as it is possible to implement a rather realistic system in which different fiscal strategies are tested on a dynamic and heterogeneous population of interacting agents.

3.5 Conclusions

Since the appearance of the first theoretical models in the early 1970s, the study of tax compliance has moved a long way toward the development of new models, taking into account psychological regularities and anomalies of decision making. The increasing success of the application of behavioral economics has shown the importance of relying on empirical and experimental data in order to integrate theoretical analyses and overcome the traditional limit of the representative agent. In fact, recent evidence from laboratory experiments and surveys underlines the impact of noneconomic considerations in determining individuals' behavioral heterogeneity in real-world compliance, and the relevance of understanding taxpayers' behavior and the underlying cognitive process, in order to provide useful normative policies able to sustain compliance and deter evasion.

From our perspective, much interest and effort need to be devoted to the combination of experimental techniques and agent-based models, in order to investigate the interaction between taxpayers' cognitive process and the surrounding environment. This would not only contribute to the external validity of experimental findings by testing the robustness of human subjects' behavior in systems with an increased degree of complexity, but it would also allow the integration of a micro-level perspective with macro-level considerations: dynamics at an aggregate level can be studied starting from micro-level observations.

This chapter explains how simulations can increase external validity of tax experiments in two different ways. On the one hand, agent-based models consist in the implementation of a set of human-based behavioral types and extend experimental analyses by manipulating the composition of agents' population. This provides a greater adherence to the environment outside the laboratory and tests the effects of a variety of policies on a heterogeneous population. In fact, agent-based models may define different macro behavioral types interacting with diverse policy solutions adopted by the tax authority, and this heterogeneity can be based on the identification of micro-level behavioral dynamics emerging from psychology, economics laboratory experiments, and empirical studies. On the other hand, external validity of experiments can be increased by identifying the main cognitive drivers that explain phenomena observed in the laboratory. Human-based experiments contribute to the library of phenomena, by simply searching for facts and regularities, while agent-based simulations analyze and test these phenomena, so that they can be applied to specific cases to a normative purpose.

Overall, this kind of innovative approach adds to the ongoing discussion about the inclusion of behavioral realism into theoretical studies in the literature on tax evasion. Therefore, it supports a greater parallelism with the natural world, yet without denying the importance of model development: the synergic combination of theoretical analyzes and human-calibrated simulations may help shed new light on the issue of tax evasion, since it focuses on the specific problem of new policy implementations in a rigorous way and in a realistic environment, before actual application in the field.

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