6.2.1.1 Purpose

The TAXSIM model was originally created in 2007 as an exercise to understand the applicability of the method of agent-based simulation to the study of tax compliance and tax evasion. Since its first version, TAXSIM was extended significantly in a series of steps, but the general scope and focus of the model remains. The purpose of TAXSIM is to perform abstract, theoretical studies in the domain of tax evasion and shadow economy in the form of computational thought exercises. In particular, TAXSIM is capable of demonstrating complex, nontrivial potential consequences of changes in regulations or government policies (Szabó et al., 2008).

The model was designed for researchers interested in the theoretical questions of the economics of taxes. It can be used to perform what–if scenario analyses or to study the complex dependence between the model's behavioral or regulational parameters and the emerging system level tax compliance, as well as the potential consequences of different control strategies by tax authorities.

6.2.1.2 Entities, State Variables, Scales

The main concern of TAXSIM is the behavior of two kinds of agents: employees and employers. This is complemented by two agents: the (tax) authority and the government. (For our purposes, the tax authority is not the government. The former is responsible for enforcing the collection of taxes, while the latter represents the rest of the government and provides services to other agents.) The authority and government are singletons: there is only a single existing copy of them in the model. In contrast, there is a collection of both employees and employers.

There is a fifth separate component to the model: the demand function (over time) of the market in question. This is modeled as an external function (submodel), which, in the interest of simplicity, is implemented as a constant function. For further details see Section 6.2.4.3.

6.2.1.3 Process Overview and Scheduling

In TAXSIM, none of the agents have perfect information. Thus, the tax authority does not know about possible tax evasion until control audits are executed and even then there is uncertainty about discovering any potential wrongdoing. Similarly, employees and employers do not know about the behavior of other agents: they do not know the tax adherence of others (except for the cases of their own contracts with each other), about the authorities' audit strategy, frequency, or accuracy, or about the quality of governmental services. On the other hand, employees and employers share information in their respective social networks and make estimates based on these communications, in addition to their own experiences related to audits and governmental services.

The employees and employers use this collected knowledge and estimates during the negotiations of their new employment contracts. During this procedure, the agents' expectations depend on their respective satisfaction with the government and on the estimated costs and benefits of evasion. Previous interactions with the authority agent (audits) and information derived from the social network determine cost and benefit estimations.

6.2.2.1 Theoretical and Empirical Background

In the study of tax compliance and evasion (Cowell, 1985; Alm, 1988), as discussed in Chapter 1, there is a history of the utilitarian approach, as started by Allingham and Sandmo (1972), operating with an explicit utility function (Sandmo, 1981). Agent-based versions usually incorporate heterogeneity by using an ensemble of various such utilities (Mittone and Patelli, 2000; Davis et al., 2003). Interactions and a social network among the agents play an important role in other works (Balsa et al., 2006; Bloomquist, 2006; Korobow et al., 2007). The effect of social networks is also considered in Chapters 5, 7, and 8.

TAXSIM joins this volume of literature by considering tax evasion as an economic choice by agents, where the choice is finer grained than a simple binary or ternary choice (see Table 6.1 and Section 6.2.4.3) (Mittone and Patelli (2000), Davis et al. (2003)). In addition, in TAXSIM the utilitarian choice driven by competition among market players is colored by ethical preferences and by satisfaction with public services. Social networks also play an important role in sharing and disseminating information in TAXSIM. The design of the model is based on empirical observations (see Tóth and Semjén (2008)), but not on actual data.

The key theoretical component in TAXSIM is comprised of the respective decision-making processes of employees and employers during job negotiations. This is the point when agents try to balance their economic incentives (i.e., the difference between the amount of evaded taxes and the expected costs of discovery) and their individual beliefs (i.e., desired rate to pay, based on own and social neighbors' experiences with public services).

During this procedure the agents' expectations depend on their respective satisfaction with the government and on the estimated costs and benefits of evasion. Previous interactions with the authority agent (audits) and information derived from the social network determine cost and benefit estimations. It is assumed that all agents utilize some services provided by the government (e.g., a company wants to register a trademark, or a person wants to get a passport). These interactions (the experienced effectiveness, corruption, etc.) determine the contentment level of the agent.

From the perspective of the employer (who needs to make a job offer) the economic incentives are simple; the following function needs to be maximized:

6.1

where is the salary cost (constant during the simulation), is the offer made by the employer, and , , and are the audit probability, authority accuracy, and fine for unpaid taxes, respectively (all constants during the simulation), while is the percentage of taxes not paid according to the given offer:

The employer estimates the values of and . The following formula is equivalent to Eq. (6.1):

6.2

The latter formula implies that is indifferent if

.

It also implies that if the estimated costs of evasion () are greater than 1 noncompliance produces deficit, and that when it is below 1 tax evasion is profitable.

There is a very similar decision faced by employees, making illicit behavior profitable if the gains from avoided taxes exceed the expected costs of discovery and illness.

TAXSIM complements the above utility functions with another dimension of tax compliance. It is assumed that both employers and employees regularly use public services and that their level of satisfaction acts as a motivating force to comply. This component is valuable because it provides a kind of counter-balance to the economic incentives (purely pointing toward evasion, except for the potential costs incurred).

Employers will not make offers below their current level of desired tax rate, which depends on their satisfaction with public services. (The latter value is estimated from own experiences and from information via their social network.) Similarly, employees will not accept job offers with less tax content than they feel desirable. (They also develop this notion from their experiences with government services and through interactions in their social network.) There is a single exception: employees having been unemployed for long enough to deplete their reserves will accept any job offer to make a living.

6.2.2.2 Individual Decision-Making

The dynamics of the model are driven by the decisions made by employees and employers and by the controlling behavior of the tax authority. These decision-making algorithms are described in detail in Sections 6.2.1.3 and 6.2.2.3. Similarly, to many agent-based models, the agents of TAXSIM are bounded rational (Mansury and Gulyás, 2007).

In particular, on the part of the employees and employers the most important decision-making occurs during the negotiations of the terms (employment type, tax content) of a new contract. This is discussed in Section 6.2.1.3.

During negotiations agents try to balance their economic incentives (i.e., the difference between the amount of evaded taxes and the expected costs of discovery) with their individual beliefs (i.e., desired rate to pay, based on own and social neighbors' experiences with public services). The background of this fundamental topic was discussed in Sections 6.2.1 and 6.2.2.1.

On the part of employers, there is another important decision-making that ensures their budget balance. This relatively simple rule makes sure they fire their most costly employees if they earn less than expected (from their current sales) and that they hire new employees if they have the budget to grow. These rules are described in Section 6.2.1.3.

Social norms are not modeled explicitly, although both employees and employers maintain a desired tax rate, which bounds their behavior and which is partially dependent on observed behavior in their respective social networks. (Employers never offer jobs with “darker conditions” than this value.)

TAXSIM is a nonspatial model. Therefore, decisions do not have a spatial component either. They also lack the temporal dimension, except for the agents' adapting their internal decision-making parameters. On the other hand, several aspects of the agents' decision-making process are stochastic. These aspects are summarized in Section 6.2.2.9.

6.2.2.3 Learning

Müller et al. (2013) differentiates between adaptation and learning by stating that “decision rules are prone to adaptation, where the information used by the rules to generate a decision changes and prone to learning where the rules themselves change over time.” Given this definition, agents in TAXSIM do not learn. Employees and employers do adapt, however, by adjusting their desired tax rate (i.e., target employment type) and their estimations of relevant system-level properties based on their own experiences and on information gathered through their social network about, for example, the frequency and accuracy of audits by the tax authority or about the tax adherence of other employees and employers.

In the base version of the model, the tax authority implements a static audit strategy and thus neither learns nor adapts. In some of the extended versions of the model the tax authority implements an adaptive audit strategy, preferring to probe employers in the social neighborhood of employers who have previously been found evading.

Adaptation plays an important role in the behavior of both employees and employers and this is at the heart of their negotiations about the terms of new contracts as well (see Section 6.2.1.3). These will be detailed next.

6.2.2.4 Individual Sensing

In the traditional sense of the term, agents in TAXSIM do not sense their environment. However, they do collect information about

• the desired tax rate of others through the average value of neighbors in the agent's social network (employees, employers);
• the chance of discovery by the tax authority (employees, employers) through personal experiences and through the average of the neighbors' estimations in the agent's social network;
• the chance of audit by the tax authority (employer) through personal experiences;
• level of governmental services (employees and employers) through personal experiences;
• tax adherence of employees and employers (authority) through audits.

The government is a static, reactive agent. It does not collect information. It provides a static, stochastic response to queries by other agents (employees and employers).

None of the agents have perfect information. Thus, the tax authority does not know about possible tax evasion until control audits are executed and even then there is uncertainty about discovering any potential wrongdoing. Similarly, employees and employers do not know about the behavior of other agents: they do not know the tax adherence of others (except for the cases of their own contracts with each other), the authorities' audit strategy, frequency, or accuracy, or about the quality of governmental services. On the other hand, employees and employers share information in their respective social networks and make estimates based on these communications, in addition to their own experiences related to audits and governmental services.

Errors or noise are not modeled. All information collected in the above interactions is perfect (but often based on imperfect estimations of others) and free. The only exception is during the tax audits, when the authority discovers the true nature of every illicit contract only with a certain probability (governed by the audit accuracy parameter).

6.2.2.5 Individual Prediction

Agents in TAXSIM do not make predictions. Employees and employers base their tax-evading decisions on the expected value of fines, based on their individual estimations of the probability of discovery.

6.2.2.6 Interaction

Employees and employers both occasionally request services from the government. This is the only type of direct interaction between the government and agents of other types. During such interactions employees and employers contact the government directly. The tax authority regularly audits employers (and their employees). This is the single interaction that the tax authority participates in.

Both employees and employers have their respective (separate) social networks. The agents exchange information about their estimations and preferences through these contacts. In the social networks the agents interact only with their network neighbors. (The structure of the social networks used is discussed in Section 6.2.4.3.) Interaction in the social networks is implemented in a minimalistic way: average values of neighbors' relevant variables are passed directly to the updating agent.

Interaction between employees and employers takes place during salary payment via direct money transfer and during negotiations via posted job offers and feedbacks about them.

6.2.2.7 Collectives

There are two collectives in the model: one containing all the employees and another grouping all the employers.⁷

6.2.2.8 Heterogeneity

Employee and employer agents are initially homogeneous within their respective groups, except for their location in their respective social networks. Differences among the agents, that is, varying estimations, emerge due to different experiences during the simulation. An important part of the emerging agent heterogeneity is induced by interaction among the agents over their respective social networks (Dugundji and Gulyás, 2008).

6.2.2.9 Stochasticity

There are several sources of stochasticity in TAXSIM.

The social networks of employees and employers are generated using stochastic models of social networks (see Section 6.2.4.3). Apart from this, randomization plays no further role in the initialization of the model.

However, stochasticity is at the heart of the dynamics of TAXSIM. Agents of the same type always execute the same action (e.g., paying salaries, hiring, or exchanging information in their social networks) in a randomized order that is reshuffled before each time step so as to avoid artifacts and lock-step behavior.

Furthermore, each agent type has some random component in its activity set:

• Employees pick a random selection of job advertisements to evaluate when looking for a new job. Also, when employed, they look for a better job governed by a random variable. In addition, employees get sick and seek public medical services according to a random variable.
• Employers request services from the government according to a random variable. In addition, bankrupt employers are replaced with a certain probability (which avoids immediate replacement).
• The tax authority selects its audit targets randomly. (Stochastic elements are present even when using the adaptive audit strategy.) Moreover, illicit employment contracts are discovered stochastically (c.f., limited information or noise).
• The government services requests by employers and employees at random. More precisely, whether these services are satisfactory or not is determined by a random variable.

In addition to the agents' actions, the market submodel also has a random component. When fulfilling purchase orders, products are bought from the cheapest producer first, but ties are resolved randomly.

6.2.4.1 Initialization

TAXSIM is initialized by creating the agents and the social networks of the employers and employees, respectively. The initialization is driven by the parameters that are not directly anchored in empirical data. Initialization with a given set of parameters always yields the same initial configuration, except for the stochasticity in the generating models underlying the social networks. (This randomness, however, can be controlled for by the appropriate seed parameter to the pseudo-random generator used for network generation purposes.)

The agents' internal variables are initialized assuming no prior knowledge. That is, they expect no audits and, not having prior experience with the government either, their desired tax rate is zero.

6.2.4.2 Input Data

TAXSIM, in its current form, is not an empirically grounded, data-driven model. Thus, it does not use input from external sources.

6.2.4.3 Submodels

There are no real submodels in TAXSIM - at least, not in the sense of compact, self-containing complex models. However, there are four parts of TAXSIM that were designed to be independent, easy-to-change-and-replace components, even though their baseline implementations are relatively simple. We discuss these in this section.

The Employment Type

The employment type system is a model of the complexities of illicit employment practices. The shadow economy is a resourceful place when it comes to implementing laws creatively or coming up with new types of (illicit) compensations. (Tóth and Semjén, 2008) TAXSIM considers 23 combinations of 5 types of benefits (see Table 6.1). The employment-type system submodel is responsible for converting the discrete employment type (combination of compensations) into a scalar tax content.

In the baseline implementation a simple linear function is used; the tax content (percentage) for the th combination (row in the table) is given by

3

As discussed in Section 6.3.4, one of the extensions of TAXSIM includes the possibility of minimum wage policies. The impact of such policies on the tax system is that it forces a minimum tax content on every employment contract that has at least one legal component. Technically, this means a modification of Eq. (3) to guarantee a minimum value for all mixed and legal employment mixes.

Model Parameters

TAXSIM has a rich set of parameters, presented in Tables 6.2 and 6.3. Some of these are control variables, while others are technical parameters not varied during experiments. Some of the parameters are only applicable to some of the extensions of TAXSIM (see the descriptions).

Parameter	Description
Number of employees	The number of employees in the system
Number of employers	The number of employers in the system
Tax rate ()	The percentage of tax to be paid
Fine ()	The fee to be paid when hidden employment is discovered (Percentage of the tax not paid)
Audit probability () (also called audit frequency)	The likelihood for an employer to be audited. The expected number of audits per time step is: audit probability number of employers
Audit accuracy	The likelihood for any illicit contract to get discovered when the employer in question is audited
Chance of illness	The probability that an employee needs medical services (per time step)
Employer frequency of requesting government services	The probability that an employer requests services from the government (per time step)
Quality of government services to employees	The probability that the government provides satisfactory services when responding to employee requests
Quality of government services to employers	The probability that the government provides satisfactory services when responding to employer requests
Employee job search probability	The likelihood that an employee shops for a better job when employed
Employee network density	The probability of a link between any pair of employees (in case of Erds–Rényi networks). The probability of shortcuts (in Watts–Strogatz networks)
Employee network neighborhood size	The size of the abstract neighborhood in which all employees are connected to each other (in Watts–Strogatz networks). A value of 0 means that we work with Erds–Rényi networks
Employer network density	The probability of a link between any pair of employers (in case of Erds–Rényi networks). The probability of shortcuts (in Watts–Strogatz networks)
Employer network neighborhood size	The size of the abstract neighborhood in which all employers are connected to each other (in Watts–Strogatz networks). A value of 0 means that we work with Erds–Rényi networks
Number of employee and employer groups	The number of loosely coupled networks used in the special experiments with extremely large-scale systems (see Sections 6.2.2.6 and 6.2.4.3). The value of 0 (used throughout this chapter) means that this option is not activated

Parameter	Description
Minimum size of companies	The number of employees sought when employers are created
Maximum size of companies	The maximum number of employees allowed for any employer (A value larger than the number of employees means no upper limit)
Chance of new employer	Bankrupt employers are removed from the system. They are subsequently replaced by freshly initialized employer agents. However, this replacement occurs in a probabilistic fashion to “smoothen out” the change. This parameter gives the probability (per time step) that a new employer is created (if the current number of employers is less than the value of the number of employers parameter)
Salary cost	The nominal wage (for all contracts). A technical scaling parameter only
Medical costs	The amount to be paid for medical services (per time step)
Profit rate	The multiplier generating the selling price of producers (employers) (Larger than 1)
Market demand (#units bought)	The number of product units purchased (from the ensemble of employers) per time step
Market update frequency (time steps)	The number of time steps between two procurement events. The length of the procurement cycle
Social network update frequency (time steps)	The length of the information sharing cycle. The number of time steps between two occasions of agents updating their estimations based on information from their social network
Estimations update frequency (time steps)	The number of time steps between two occasions that the employers update their estimations of the audit probability
Preference updating delta	The number of rows (in the employment table, see Table 6.1) by which agents adjust their desired tax rate (d)
Ratio of adaptive audits	The ratio of adaptive audits (over random selections) in experiments with adaptive audit strategies
Minimum tax	The minimum tax (in percentage) to be paid after any employment mix that has a legal component, used in experiments with minimum wage policies. A value of means there is no minimum wage (and thus, no minimum tax)

6.3.1.1 Improving Government Services

We will assume a strong will on the part of policy makers to legalize the dark economy we have set up in TAXSIM. There are some obvious steps lending themselves to decision makers, including stepped up efforts to collect taxes: increased number of audits and improved efficiency of the discovery of noncompliant behavior. Given their obviousness, we will omit these from the following experiments. (We will revisit the issue in Section 6.3.2 when studying the effects of various TAXSIM parameters in detail.) Instead, we imagine a hard-working administration steadily improving the quality of its services. After the bootstrapping period, the quality of governmental services is upgraded by 7.5%, in every 500 time steps. As demonstrated in Figure 6.1 (a) the persistent improvement of governmental services leads to persistent legalization. However, improvement in compliance is not linear. Hidden contracts gradually become mixed and then, following further improvements of service quality, they eventually become legal. This also means that the marginal impact of increasing quality of service differs, especially, if measured only by change in legal or totally hidden employment ratio. (The latter shows decaying rate of improvement, while the former improves progressively.)

Figure 6.2(b) shows the taxes collected over time during the above experiment. The government is clearly rewarded for its efforts. This becomes especially clear when comparing the time series to the baseline scenario without service quality improvements (shown in Figure 6.2(a)). However, the catch is the nonlinearity that is also obvious. For the initial efforts, the return is moderate and slowly increasing. It is only after the third round of improvements (time step 1500) that steep increase in tax income is observable. Not surprisingly, this increase will eventually decay, with the income level getting saturated.

6.3.1.2 Entrance of Companies with Preferential Taxes

Improving governmental services is often desirable, but it might often be a rather costly and uncertain means to legalize an economy. Another desirable goal is to improve the tax and business culture of market players, for example, by attracting players from different, more established economies with higher general tax compliance. One way of achieving this is to offer lower, preferential tax rates, at last for a certain period, to large international companies in return for their establishing a local branch in the country. This was not an uncommon practice in Eastern Europe after the systems change (Sass, 2003; Semjén and Tóth, 2004; Tóth and Semjén, 2008; Bakos et al., 2008). Unquestionably, attracting foreign investment, creating new jobs, and modernizing market sectors are very valid goals and they can possibly be achieved by attractive tax cuts to multinational companies. Yet, the practice was often accompanied, at least at the level of rhetoric, with the hope that law-abiding foreign companies disseminate their best practices, including their tax practices and improve the standards of their employees and later, via spill-over, those of their competitors as well.⁸

In our computational experiment, three international companies enter the market after the bootstrapping period (at time step 500). Their preferential tax rate is 36% (as opposed to the normal 45%, corresponding to a 20% tax cut). On the other hand, these three employers are fully compliant, rule-abiding operations.⁹

TAXSIM does not offer means to assess the impact of tax-incentivized international enterprises on the general development of an economy. It can, however, help us theorize about the effect of said companies on system level tax compliance and government tax income. The appearance of the three compliant companies do generate a minor increase in governmental income (not shown here), but that is not significant. What is interesting, however, is how they influence the general compliance level of the system.

Surprisingly, the appearance of fully abiding companies increases the number of hidden contracts in comparison to the baseline scenario (see Figure 6.1). The number of legal contracts increases as the new companies gain market share and thus the overall level of illegal employment decreases - there is no question about that. However, mixed employment is almost swept out of the market, as artificial legalization splits the sector into the two extremes. Taking advantage of the lower taxes, the new multinational companies are able to offer competitive salaries: approximately the same as employers who evade most of the taxes. As a consequence, firms offering mixed type employment are driven bankrupt or are forced to make illegal contracts.

6.3.2.1 The Effect of Governmental Services

We now turn our attention toward the factor with the third largest effect in our factorial experiment: the level of governmental services. In Section 6.3.1.1, we introduced gradual improvements of governmental services when market equilibrium has been reached. In contrast, we now compare the emerging equilibrium outcomes of separate runs with various service quality levels.

In TAXSIM the government provides two types of services: one for employees and another for employers. In the interest of getting a full picture, we vary the quality of both of these services systematically. Figure 6.7 shows the percentage of legal, mixed, and hidden contracts, as well as the amount of taxes collected, as a function of the various levels of the two types of government services. The parameters controlling the quality of the different services are varied between their theoretical extremes (between 0 and 1). The horizontal and vertical axes represent services for employees and those for employers, respectively. The grayscale-coded percentage values shown are snapshots taken after 6000 time steps and averaged over 10 independent runs for each parameter combination. The rest of the parameters are fixed according to Tables 6.5 and 6.6 with audit probability at 25% and audit accuracy at 0.45.

As demonstrated in the figure, the quality of services for employers dominates the quality of those provided for employees. This is likely due to the heavy competition in the labor market: employees are forced to take advantage of any job opportunity and thus are less driven by their own compliance preferences during job negotiations.

It is also clear that the better the quality of services for employers, the more compliant the market sector becomes. In case of low quality of services employment contracts are mostly illegal. In the mid-quality range, contracts become mixed, while with high quality of services legal contracts tend to dominate the market. (Yet, with the given parameter settings totally legal markets are not very frequent.) The above general trends are modulated by the quality of services to employees. This becomes visible in the transitional regions, where better services for employees pay off by more legalized emergent economies.

The plot of tax incomes is much smoother, but it shows the same general trends.