László Gulyás, Tamás Máhr and István J. Tóth
Taxation is a crucial means to operate the complex machinery of society. Its web of complex patterns of interaction and transfers are not only based on law, but trust, social pressure, enforcement, and economic motivations contribute to its emerging delicate balance alike.
This chapter describes TAXSIM1, a generative approach to study tax evasion. TAXSIM is an agent-based model, concerned with the operations of a single market sector. The economic well-being of agents depends on the employment contracts they make among each other and on their tax content. In this model tax evasion is a technique to reduce costs (and to raise wages); therefore, tax evasion is a matter of degree rather than a simple binary or ternary choice (e.g., complier/evader, or complier/evader/sceptic) (see Chapter 11). TAXSIM was inspired by the Hungarian tax system, where the burden of the employee's personal income tax is split between employers and employees. Other taxes, such as corporate income tax and value-added tax are not considered.
In TAXSIM, agents have no perfect information; they estimate the various system-level parameters (such as the frequency and accuracy of audits). These estimations are based on the agents' individual experiences, as well as on experiences of others. Because of the latter, the social network of agents plays an important role in disseminating information.
The final core component of TAXSIM is the assumption that both employees and employers interact regularly with the government and take advantage of the public services offered. The quality of these services (e.g., observed efficiency or level of corruption encountered) determines the agents' underlying motivation to pay their dues. If the experiences with public services are bad, the agents become more prone to accepting the economic incentives of tax evasion (provided that they can rationally do so, given the expected costs derived from the estimated system-level variables).
Earlier works on TAXSIM discussed its basic capabilities (Szabó et al., 2008, 2009a–2010) and provided an overview of the various emergent responses it can provide (Szabó et al., 2009b; Gulyás et al., 2015). Moreover, Szabó et al. (2011) discussed explorations with various types of social networks Erds and Rényi (1959), Watts and Strogatz (1998), Barabási and Albert (1999). In Kurowski et al. (2009) computational experiments with realistic population sizes (–) were considered. (As a comparison, Hungary, the home of the authors, has about inhabitants.)
The main goal of this chapter is to provide a consolidated description of the TAXSIM model, providing a detailed specification according to the ODD+D protocol (Müller et al., 2013). In addition, the chapter also provides a demonstration of the main capabilities of the model. This is first done through two what–if scenarios: one studying the effect of extended efforts of the government to improve its services, and the other exploring the consequences of the entry of a few tax-preferred, tax-compliant multinational companies. Our results show that the increasing quality of public services helps make the market more tax compliant, but the effect size depends on the current state of the economy. On the other hand, the entry of tax-preferred firms increases the number of hidden contracts.
A detailed study of the model's rich parameter space is also provided, identifying the main driving factors and then systematically studying their effects. Our demonstration is completed by analyzing two “virtual policy experiments”: one studying the potential consequences of adopting a policy of minimum wages and the other exploring an audit strategy that selects audited companies from the social network of previously discovered evaders. We identify audit probability and audit frequency as the most important factors across the entire parameter space, with a phase transition between hidden and legal economy across both axes. However, for realistic combinations of these parameters, values of other parameters become important. Here the quality of government services stands out again, having a greater effect on employers than on employees.
The rest of the chapter is structured as follows. Section 6.2 provides a detailed, ODD+D compliant description of TAXSIM and its variants. This is followed by discussions of various computational results generated by TAXSIM. Section 6.4 concludes the chapter.
TAXSIM is a family of models that has been created between 2007 and 2015 (Szabó et al., 2008, 2009a,b, 2010, 2011; Kurowski et al., 2009; Gulyás et al., 2015)
This section provides a consolidated description, focusing on the base model and its properties, but briefly discussing the most important extensions separately as well.
Szabó et al. (2010, p. 17) introduces TAXSIM as follows:
The TAXSIM model is concerned with the operations of a single market sector, where there are four kinds of agents involved: employee, employer, (tax) authority, and government. The economic well-being of employees depend on their net wages, while that of the employers' is a function of the market demand and the level of gross wages they are forced to pay. The rate of tax evasion is an agreement between an employer and an employee that is made when the employee occupies a new job. As the agreed employment type [see Table 6.1] determines the income of the employee and the (producing) costs of the employer, both participating agents have a motivation to evade.
The government and the tax authority have service providing and regulatory roles, respectively.
In TAXSIM market demand is generated by a submodel and thus is exogenous to the four types of agents concerned. This market sector submodel is minimalistic. Companies (employers) producing the cheapest goods sell first. When demand is less than the total productivity, companies producing expensively will not be able to sell. Since the product is a perishable good, unsold items will be lost, causing financial losses to their producers. Employers (producers) and employees (workers) are assumed to be homogeneous in technological and productive ability: each employment contract between a pair of an employee and an employer agent produces exactly one unit of good in every production (procurement) cycle. The homogeneity also means that employers have the same production costs, produce the same quality of goods, and have the same profit rate. Thus, every employer offers the same gross wage to every employee. As a consequence, the level of income for the employees and the competitiveness of the employers are determined by their respective approach to taxes. Therefore, in TAXSIM, tax evasion is a technique to reduce costs (and to raise wages): the gains from taxes evaded are split equally between the employee and the employer involved. Importantly, this utilitarian approach means that the agents' decision about tax compliance or tax evasion is not a binary choice: it is a decision about the level of taxes to be paid.
TAXSIM considers five types of payments, those found empirically most common in Hungary – both legal and illegal ones (Tóth and Semjén, 2008). Among these, two are perfectly legal (but pay different levels of taxes), while three are considered as illegal practices. An employment type chosen by TAXSIM agents is a combination of these five payment types: reported wage, fringe benefits, ad hoc engagement agreement, unreported wage, and payment in kind.2 TAXSIM uses 23 combinations of these five types of payments (see Table 6.1; for more discussion see Section 6.2.4.3). Note that fringe benefits have no meaning without a reported wage, so all combinations that include the first without the other (eight items) are omitted. Furthermore, the employment types are grouped so that when there's no reported wage it is termed illegal (or hidden). On the other hand, we call combinations with only reported wage and/or fringe benefits legal. The remaining combinations belong to the group of mixed employments.
Table 6.1 The 23 employment types considered in TAXSIM
No. | Reported wage | Fringe benefits | Ad hoc engagement agreementa | Unreported wage | Payment in kind | Class |
1 | Legal | |||||
2 | Legal | |||||
3 | Mixed | |||||
4 | Mixed | |||||
5 | Mixed | |||||
6 | Mixed | |||||
7 | Mixed | |||||
8 | Mixed | |||||
9 | Mixed | |||||
10 | Mixed | |||||
11 | Mixed | |||||
12 | Mixed | |||||
13 | Mixed | |||||
14 | Mixed | |||||
15 | Mixed | |||||
16 | Mixed | |||||
17 | Hidden | |||||
18 | Hidden | |||||
19 | Hidden | |||||
20 | Hidden | |||||
21 | Hidden | |||||
22 | Hidden | |||||
23 | Hidden |
Illicit practices are marked with gray background.
a “Ad hoc engagement agreement” means permanent employment reported as ad hoc agreement.
Employers incurring financial losses (from unsold goods) need to increase their competitiveness by reducing their costs. They can achieve this only by renewing their pool of employment contracts to include employment types with lower tax content. A similar situation may be faced by the employees. If their contracts are deemed too costly by their current employer, they become unemployed. After a period of unemployment they gradually decrease their job expectations (i.e., the amount of taxes paid) and will eventually accept any job offer. (The employee's period of patience depends on its reserves that, in turn, depend on the length of the agent's previous employment.)
As discussed, lowering the amount of taxes paid increases the competitiveness of both employers and employees. However, it comes with the risk of being eventually discovered and with fines expected to be paid. The level of this risk and the amount of the fines depend on the efficiency of the tax authority.
The agents, however, have no perfect information. Thus employees and employers have to learn about the effectiveness and accuracy of the tax authority. They learn from their own previous experiences, but they also share and gather information via their respective social networks. Similarly, they also gather information about their neighbors' tax preferences. This is crucial for optimizing their competitiveness. The agents use their collected knowledge when they negotiate the terms of a new employment contract.
Employees live forever: there is no aging or any fluctuation in the population of the employees. The financial status of the employee has no effect on its work abilities, but it shortens the period it looks for a desirable job. Employers, on the other hand, may go bankrupt, in which case they are replaced with new market players.
In TAXSIM agents are assumed to regularly utilize some public services provided by the government (a company benefiting from transport infrastructure or a person registering its new car, etc.). Satisfaction with the level of these services (the experienced effectiveness or perceived corruption, etc.) motivates the agents to pay their taxes, providing a potential balance to their economic incentives to evade.
TAXSIM has a rich structure that enables it to produce very different market equilibria with a wide variety of employment type distributions. This will be demonstrated in Section 6.3.
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.
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.
The most important state variable links the agent to its current employer (no parallel employment is possible) or shows that the agent is unemployed. Employees store their current employment type (see Section 6.2.4.3) and salary (net and gross) as well.
Employees have a desired tax rate based on their satisfaction with the government. They also estimate the chance of their misbehavior getting discovered (chance of discovery) by the authorities. The estimation is partially based on the actual percentage experienced by the given agent. Thus, each of them keeps tabs on the total length of the time periods it was illegally employed and on the number of times it was discovered.
Employees also have a reserve that they fill up when employed and deplete when unemployed (in the current version both happen linearly and the reserve is bound from above by a parameter). When reserves are depleted, the employee will accept any job offer, independent of its own tax preferences.
Employees are also embedded in a social network. (About the different types of social networks used, see Section 6.2.4.3.) At every couple of time steps, employees exchange their current preferred tax rate and their estimation of the chance of getting discovered with their neighbors in the social network.
Employers maintain a list of their current employees and have a certain amount of financial resources (checking balance). They keep their books, administrating an update on their total salary cap (total salary cost), their budget per time step (budget per month, based on the checking balance and the value of the parameter governing the frequency of sales), the net salary and employment type of their last offered employment, as well as the average effective tax content of their employment contracts.
Employers also have a desired tax rate based on their satisfaction with the government and on their perception of the average tax compliance of others. They also estimate the chance of their misbehavior getting discovered (chance of discovery) during an audit and the likelihood of getting audited by authorities (chance of audit). These estimations are based on their actual experiences as well as on information from their social networks. (About the different types of social networks used, see Section 6.2.4.3.)
Similarly to employees, employers also regularly exchange information with their social network neighbors. At every couple of time steps, they share their current preferred tax rate and their current estimation of the chance of getting discovered.
There are also a number of technical variables maintained by employers that are used during the negotiations of new employment contracts. These keep track of the feedbacks received about the current job offer (the salary was too low, the employment type did not satisfy the employee, etc.)
The authority agent has no internal variables in the original TAXSIM model. Its behavior is driven entirely by three system-level parameters: audit probability, audit accuracy, and the fine (penalty, a percentage of the tax evaded) to be paid by evaders.
One of the extensions of TAXSIM implements a tax authority with an adaptive strategy. This strategy prefers to select the targets of audits from the social network of employers previously discovered with noncompliant behavior. In this extension the tax authority also maintains a list of previously discovered wrongdoers (employers).
The Government has a single role in TAXSIM: to provide services for both employees and employers. In the interest of simplicity, these are implemented as probabilistic draws of quality from two separate uniform distributions. The draws are controlled by two global parameters: quality of government services to employees and quality of government services to employers.
The model has no spatial component and thus it does not have a spatial scale either. (Some versions of the social networks for employees or employers do rely on an assumed geographical distance between the nodes; see Section 6.2.4.3. Yet, this assumed geographical distance is abstract without any grounding in any empirical scale.)
Since TAXSIM is intended for abstract thought experiments, its temporal scale is also abstract and arbitrary. Sometimes, it helps to think of time steps as months, but in most cases we simply talk about abstract units of time: time steps.
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.
In every time step, every employee is activated (in a randomized order) to perform the following activities:
With probability chance of illness, the agent gets sick. If sick, the agent receives public medical services3
When an agent is caught evading, it is forced to quit its current employment and updates its estimation of the chances of getting discovered. (See Section 6.2.2.3 for details.)
In every time step, every employer is activated (in a randomized order) to perform the following activities:
Employers maintain their budget (income) and the total salary costs of their enterprise. Given the frequency of market sales (a parameter), they calculate their salary budget per time step. If this budget has room for an additional employee at the cost of the last employee, the employer attempts to hire a new person. That is, if the employer has enough money and did not reach the maximum size allowed (parameter maximum size of companies), then the employer posts an advertisement on the job market.
When an employer is discovered to have illegal employment contracts,
The market is not a real agent, but we discuss the activities of the demand submodel here. Market demand (for the products of the employers) is a constant number of units (governed by the market demand parameter) purchased at regular intervals (according to the market update frequency parameter).
The market buys from the cheapest producer (employer) first. If it has more units on sale than the current demand, only the amount satisfying the demand will be sold. If the demand is larger than the inventory of the cheapest producer, then the remaining amount is bought from the second cheapest producer, and so on.
In TAXSIM employers and employees have to agree on the terms of employment. By assumption all employees possess the same skills and productivity, and all employers offer the same salary. Thus, the negotiation is concerned with the employment type only. The amount of taxes not paid is divided equally between the employee and the employer. This provides an economic incentive to both parties to hide (parts of) the contract. However, a deal must be reached that is compatible with the risk estimations and desired tax rates of both sides. This is done through the negotiation process that may span several time steps. This is detailed now.
Employees evaluate the selected open positions:
, where is the offer in question, is the net wage offered, while the expected fine and expected medical costs are calculated as follows, respectively:
, where
and .
Here , , and stand for the system level values of tax rate, medical costs, and fine, respectively. is the rate of tax to be paid according to the current offer and and are the agent's current estimates of the chances of discovery and of the chances of illness, respectively.
If the best evaluated offer is superior to the agent's current job (if it has any), the agent accepts the offer and takes the contract. Note that several agents may be evaluating the same offer. Thus, the (randomized) order of their actions is important. If their selected best offer is not available anymore, agents work with their second best option, and so on.
The employers update their offers. If the last offer was not accepted, the updates are based on the feedback received when candidates turned down the offer. See Section 6.2.2.3 for details.
If the majority of the rejecting candidates said that the offered employment type was not compliant enough for them, then the employer makes its offer more legal.
The basic behavior of the tax authority is rather simple. In every time step, it selects every employer for audit with a fixed probability (parameter audit probability, also called audit frequency).
For each audited company, the tax authority iterates through all employment contracts and discovers their true nature with probability audit accuracy (or accuracy for short). If the authority fails to observe the true type of the contract, it is always mistaken to think it is legal.
If the observed true type of the contract is illicit, the authority removes the contract in question (the employee gets fired) and fines the employee and the employer. The fine to be paid is the taxes not paid (in the given time step), multiplied by the fine parameter.
In Szabó et al. (2011) and Gulyás et al. (2015) an extension of TAXSIM was introduced that includes a simple adaptive strategy on the part of the tax authority. In this version, the expected number of audits per time step is still audit probability number of employers as in the base version. However, the targets of some of these audits are selected differently. With a certain probability (parameter ratio of adaptive audits), the targets are selected from the social network neighborhood of previous tax offenders. The remaining targets (or if there are not enough discovered offenders yet) are selected at random. The audits are carried out in the same way as in the base model.
The government is a passive agent. It does not initiate any actions; it only reacts to requests by employees or employers. Upon request, it draws the quality of the given service from one of the two separate uniform distributions. With probability quality of government services to employees and quality of government services to employers, respectively, the service is of satisfactory quality.
After initialization, the process flow of TAXSIM is uniform: agents perform the same activities in the same order as described above. (Agents in the same collective perform the same actions in a randomized order, reshuffled at the beginning of each time step.)
Audits happen after employers had a chance to hire new employees and before bankrupt employers are replaced by new entries. Market demand is satisfied after agents interact with the government. This is followed by the exchange of information over the social network.
This section details the theoretical considerations behind the TAXSIM model, as well as provides a detailed description of the agents' actions and behavior.
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:
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):
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.
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.
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.
When an employee gets sick and receives public medical services, it updates its desired tax rate (d) based on the experience (i.e., on the quality of services received):
where
if the agent is satisfied and otherwise.
At the same time, the employee also updates its estimation of the chance of getting sick:
, where stands for the chance of illness and if the agent was sick and 0 otherwise.
Adaptation also occurs, when an employee exchanges information with its social network neighbors (in every social network update frequency step). During the exchange, the agent adjusts its estimations:
updates the chance of getting discovered based on the average of the neighbors' estimation, and
, updates the desired tax rate, where stands for the average of the neighbors' (desired tax rate).
When an employee is caught evading, it updates its estimation of the chances () of getting discovered:
, where and stand for the number of times the agent had an illegal job and when it had been discovered, respectively.
During the negotiation process unsuccessful employers update their open positions. If the last offer was not accepted, the agents' updates are based on the feedback received when candidates turned down the offer:
If the last offer of the employer was accepted during negotiations, then the employer updates6
After obtaining services from the government employers update their desired tax rate (d) based on the experience:
, where
if the agent is satisfied and otherwise.
Adaptation also occurs when employers exchange information with their social network neighbors and adjust their estimations:
updates the chance of getting discovered based on the average of the neighbors' estimation, and
, updates the desired tax rate, where stands for the average of the neighbors' (desired tax rate).
When an employer is caught evading, it updates its estimation of audit accuracy (discovery):
, where is the ratio of discovered illegal contracts to the number of illegal contracts the agent actually had.
In the traditional sense of the term, agents in TAXSIM do not sense their environment. However, they do collect information about
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).
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.
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.
There are two collectives in the model: one containing all the employees and another grouping all the employers.7
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).
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:
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.
The following emergent model output is collected at the end of every time step of the simulation: employment rate (the total number of active employment relationships), number of legal, mixed, and hidden employment relationships, the taxes collected by the tax authority.
There are a number of interesting emergent behaviors generated by the model. One important observation is that changes in the composition of employment types (and thus in the taxes collected) are often nonlinear. This means that the actual response to parameter or policy changes may be very dependent on the actual state of the economy. In particular, sharp transitions occur in several parameters (e.g., audit frequency and accuracy), meaning that minor changes in parameter values result in drastically different outcomes in certain parameter ranges.
TAXSIM was originally implemented using Repast J (version 3.1). North et al. (2006) One version was re-implemented in the QosCosGrid framework (Kurowski et al., 2011) to increase scalability and to perform large-scale experiments (Kurowski et al., 2009). Later, the results were confirmed by a NetLogo implementation (Wilensky, 1999).
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.
TAXSIM, in its current form, is not an empirically grounded, data-driven model. Thus, it does not use input from external sources.
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 market sector is responsible for generating the demand for the products produced through the collaboration of employers and employees. It is also responsible for regularly balancing the economy. The exact algorithm for the purchases is dependent on the submodel.
In the baseline implementation, the market sector purchases a fixed amount of products (controlled by the market demand parameter) at every market update frequency time steps. The products are bought from the cheapest producers first, and then in increasing price order.
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
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.
Social networks in TAXSIM play the role of disseminating and sharing information among market players, providing the bases for the agents' estimations. There are two separate networks: one for the employees and one for the employers.
The baseline version of TAXSIM uses random networks (Erds–Rényi networks Erds and Rényi (1959)) for these components. The single parameter of these networks is density (or the uniform probability of any edge to be present in the network). In later versions, Watts–Strogatz type (small-world) networks (Watts and Strogatz, 1998) were also experimented with. Here, two parameters regulate the networks: the size of the neighborhood within which geographically close nodes are all connected and the probability of rewiring (or shortcuts), that is, the amount of probabilistic (long-range) connections laid upon the geography-driven regular structure.
Experiments showed that there is little difference between TAXSIM's emergent outcomes in case of Erds–Rényi or Watts–Strogatz networks, provided that the average path length is low. (This is the case for all connected Erds–Rényi networks and for most Watts–Strogatz networks.) However, regular, two-dimensional lattices violate this constraint, which exhibit more shadowy economies as information spread is slow and thus agents have lower chances to correct their estimations. (Szabó et al., 2011) Scale-free networks (see Barabási and Albert (1999)) were also experimented with, but were not included in the consolidated version, as having short average path lengths, they provided no significant contributions to the emergent results.
During a series of experiments with realistic population sizes (several millions of agents) a special network structure was implemented. (Kurowski et al., 2009) This structure classified employees and employers in groups (a form of submarkets), so that employers could only contract employees from the same group. Each group had its own social network for both employees and employers (Watt–Strogatz type of networks) for information sharing. In order to make information exchange among groups possible, group-level social networks were connected loosely in a ring.
Services by the government are regularly requested by both employees and employers. It is only the quality of these services that is of concern in TAXSIM. Therefore, governmental services are modeled as random variables, one for employers and another for employees. They yield satisfactory services with probability quality of government services to employers and quality of government services to employees, respectively.
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).
Table 6.2 Parameters of TAXSIM (part 1)
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 |
Table 6.3 Parameters of TAXSIM (part 2)
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) |
In this section, we first provide a snapshot of the kind of what–if experiments made possible by TAXSIM. These experiments were reported in detail in Szabó et al. (2009a–2010). This will be followed by an analysis of the rich parameter space of the model, exploring the sensitivities of model behavior as a function of the various parameters. In the end, we turn our attention toward two “virtual policy experiments”: one studying the potential consequences of adopting a policy of minimum wages and the other exploring an audit strategy that selects audited companies from the social network of previously discovered evaders.
TAXSIM is capable of modeling very different economic and compliance scenarios and a wide range of employment type distributions, covering the entire spectrum from a totally “hidden economy,” via various combinations of illegal and legal employments, to an entirely law-abiding market. Importantly, these are emerging properties of the system, not rules coded directly into the model that can be turned on by a control switch. This feature has both advantages and disadvantages. On one hand, the lack of direct control over system-level properties such as tax compliance reflects reality. On the other hand, the emergent nature of the qualitative class of the system (hidden economy, mostly compliant market players, etc.) means that one needs to have some experience with the model to be able to set parameters for experiments with particular types of economies. It also means that exact levels of the response variables (e.g., unemployment rate or tax compliance) cannot be directly set.
In the following experiments, TAXSIM was set up to model a market sector with high levels of noncompliance. With the parameter settings selected (see Table 6.4) the system reaches equilibrium after a transient period of about 300 time steps. While 300 months is a rather long time in real life, we consider this initial period as the bootstrapping needed to initialize the simulation. In the (dynamic) equilibrium, the level of unemployment is approximately 15%, while legal employment is at 5%, mixed employment is at around 10%, and illegal employment amounts to 70%. These levels will probably not fit most economies very well. Yet, they suit the kind of “thought experiments” we intend to carry out here. A more thorough analysis of the parameter spectrum and the corresponding model behaviors will be provided in Section 6.3.2.
Table 6.4 Parameters used in the scenario experiments
Parameter | Value | Parameter | Value |
Number of employees | 200 | Number of employers | 40 |
Tax rate | 45% | Fine | 150% |
Audit probability | 27.5% | Audit accuracy | 0.3 |
Quality of government services to employees | 0.1 | Quality of government services to employers | 0.33 |
Employer frequency of requesting government services | 0.1 | Chance of new employer | 0.1 |
Chance of illness | 0.2 | Medical costs | 10 |
Employee network density | 0.1 | Employee network neighborhood size | 0 |
Employer network density | 0.1 | Employer network neighborhood size | 0 |
Number of employee and employer groups | 0 | ||
Minimum size of companies | 1 | Maximum size of companies | 3000 |
Employee job search probability | 0.01 | Minimum tax | None |
Market demand (no. of units bought) | 170 | Market update frequency (time steps) | 6 |
Salary cost | 100 | Profit rate | 1.1 |
Social network update frequency (time steps) | 12 | Estimations update frequency (time steps) | 6 |
Ratio of adaptive audits | 0% | Preference updating delta | 1 |
Source: Reproduced from Szabó et al. (2009a–2010)
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.
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.
TAXSIM is a rich model with many parameters and a complex set of behaviors. It is impossible to assess its repertoire without systematically testing its responses to changes in its numerous parameters. A complete analysis is out of the scope of this chapter, but in the following we provide a brief overview of the main points. (More details can be found in Szabó et al. (2009b) and Gulyás et al. (2015).)
We first perform a two-level factorial analysis of the main input parameters (factors). That is, we select two values (low and high) for each factor and run the simulation (“take samples”) for all combinations of these parameter values: combinations for factors. (In fact, we run the simulation several times for each combination and average the outcomes for the same combinations.) The purpose of this experiment is to screen the parameter space and identify the factors (parameters) that have the highest effect on the response variables, that is, the ones that are worth focusing our analysis on. This is done by fitting a linear model to the results and sorting the coefficients of the factors and their interactions. While complex systems and thus computational simulations of complex social systems rarely exhibit linear behavior, the simple linear estimation (based on a two-point measurement for each factor) provides a quick and dirty way to initiate the exploration of the model's phase space (Lorscheid et al., 2012).
Table 6.5 summarizes the settings of our two-level factor analysis. Notice that a number of parameters with obvious importance (such as tax rate or those related to system size) were intentionally left out of the factor analysis, by fixing them at a particular value. We did this to focus the exploration on the behavior and interaction of agents: employees and employers, as well as tax authority and the government. Parameters governing the economic environment (e.g., profit rate, salary cost level, market size), as well as technical parameters, such as update frequencies, are left out of the current analysis. Tax rate and fine parameters are exceptions as they are obviously policy parameters. We kept them out of our current scope as their effect is fairly obvious. (See Chapter 5 for a discussion on the interaction of audit probability and fine.)
Also notice that the economic environment defined for this analysis is different from the one in the previous section. Here, we have 300 employees instead of 200 to seek work at the same 40 of employers competing with their products to meet the same demand (170 units per sales cycle). Obviously, these settings create stronger competition in the labor market.
Table 6.5 Parameters of the two-factorial experiments
Tested factors | |||
Parameter | Value (low, high) | Parameter | Value (low, high) |
Audit probability | 0%, 25% | Audit accuracy | 0, 0.45 |
Quality of government services to employees | 0.1, 0.9 | Quality of government services to employers | 0.1, 0.9 |
Employee job search probability | 0.01, 0.3 | Minimum tax | None, 20% |
Employee network density | 0.01, 0.3 | Employee network neighborhood size | 0, 2 |
Employer network density | 0.01, 0.3 | Employer network neighborhood size | 0, 2 |
Number of employee and employer groups | 0, 4 | ||
Fixed parameters | |||
Parameter | Value | Parameter | Value |
Tax rate | 45% | Fine | 50% |
Number of employees | 300 | Number of employers | 40 |
Chance of illness | 0.2 | Medical costs | 10 |
Minimum size of companies | 1 | Maximum size of companies | 3000 |
Employer frequency of requesting government services | 0.1 | Chance of new employer | 0.1 |
Market demand (no. of units bought) | 170 | Market update frequency (time steps) | 6 |
Salary cost | 100 | Profit rate | 1.1 |
Social network update frequency (time steps) | 12 | Estimations update frequency (time steps) | 6 |
Ratio of adaptive audits | 0% | Preference updating delta | 1 |
TAXSIM has five system-level response variables: the employment rate, the number of hidden, mixed, and legal employments and the amount of taxes collected. In the present analysis, we focus on the last four of these. The factors with the highest effects are shown on Figure 6.3. Important two-way interactions are also displayed. (The responses are evaluated based on snapshots of the system taken after 6000 time steps and averaged over 10 independent runs with the same parameter setting.)
Obviously, the four response variables studied are interrelated by definition and thus it is expected that the factors driving them would be very similar as well. This is confirmed by our results, although minor variations may and do exist.
The main observation of the analysis is that it is the interaction of the frequency of audits and the accuracy of the tax authority that has the strongest effect on all response variables. These two factors have a strong effect in their interactions with other factors as well. A third parameter with a strong influence is the quality of governmental services provided for employers. Let us now focus our attention on these identified factors of importance.
Figure 6.4(b) shows the percentage of nonlegal contracts (hidden and mixed employments combined) in case of various combinations of the two most relevant parameters. The rest of the parameters are fixed according to Tables 6.5 and 6.6. White shading stands for a fully illegal economy, while the darker shades stand for increasing levels of legality.
It is clear that for most audit probabilities and for most audit accuracies the economy is clean with nearly 100% legal contracts. However, there is a continuous region where illegal contracts exist to various degrees. At first sight it might be surprising that shadow economy may only exist at the “edges” of the parameter space, but this makes sense. While a 2% likelihood of getting audited every month only constitutes a tiny fraction of the technically meaningful parameter range, it also means that every company gets audited in every fourth year. Similarly, it is also reasonable that with an above around 40% chance of wrongdoing being discovered during an audit, it does not make sense any more for agents to cheat if there is a realistic chance to get audited. Of course, the interaction of the two parameters is clearly important. The shadow economy can prevail when both of these factors are relatively low – and it turns out that this means that none of them needs to be extremely low.
It is also worth pointing out that at practical levels of audit probability (and accuracy) the economy is not fully compliant with the current set of parameters. This means that in this region other factors may play an important role. This can also be seen from the “turbulent” nature of the transition regime at the interaction of the two parameters (more about this later).
Table 6.6 Parameter values for the analysis of the main parameters
Parameter | Value | Parameter | Value |
Minimum tax | None | ||
Employee network density | 0.1 | Employee network neighborhood size | 0 |
Employer network density | 0.1 | Employer network neighborhood size | 0 |
Number of employee and employer groups | 0 | Employee job search probability | 0.01 |
Figure 6.4(a) shows the percentage of nonlegal contacts as a function of audit probability and accuracy for the market of Section 6.3.1. Here labor competition is more lax as employers can sell enough products to employ basically all workers. (The two-level factor analysis for this market, not reported here, produces slightly different factor effects than the ones reported in Figure 6.3, but the main observations remain.)
Comparing Figure 6.4(a) and (b), we observe a significantly larger region of illicit activities in the competitive market. This is due to the fact that unemployment forces employees to accept job offers even below their compliance preferences. In both (a) and (b), parameter combinations coding low risk of discovery correspond to frequent nonlegal employment contracts. Their numbers can be significantly lowered, even to 0%, by raising the likelihood of discovery (by increasing any of the studied parameters). It is worth noting, however, that the threshold of audit probability below which illegal employment exits in significant proportions is an order of magnitude higher in case of the competitive labor market.
An important further observation from Figure 6.4 is about the nature of the transition from a hidden economy to a completely legalized labor market. As illustrated by Figures 6.5 and 6.6, this is a turbulent region of the model's phase space, where minor changes in parameter settings may result in dramatic changes in responses. The turbulent region is extended at the interaction of the two parameters, but gets narrower as the change in one factor dominates that in the other. In regions where the interaction effect is weak, we even observe sharp phase transitions. This is more pronounced in case of the competitive labor market.
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.
The experiments discussed in this section were done with one of TAXSIM's extension models. As discussed in Section 6.2.1.3, an adaptive audit strategy means that the tax authority does not select audit targets entirely at random, but prefers to check employers directly connected (in their social network) to employers previously caught with noncompliant practices. (Initial targets are selected at random and the pick from among the neighbors of previous wrongdoers is still random.) The percentage of random and adaptive audit target selection is governed by a parameter.
Table 6.7 Parameter values for the adaptive audit strategy experiments
Parameter | Value | Parameter | Value |
Minimum tax | None | ||
Employee network density | 0.02 | Employee network neighborhood size | 0 |
Employer network density | 0.1 | Employer network neighborhood size | 0 |
Number of employee and employer groups | 0 | Employee job search probability | 0.1 |
Quality of government services to employees | 0.1 | Quality of government services to employers | 0.2 |
Figure 6.8 shows the results of experiments exploring the effect of various levels of adaptive audit target selection. The horizontal axes show the ratio of random and adaptive audit selection. (The value of 1 means that every audit is selected at random, while in case of 0, all targets are selected adaptively.) On the vertical axes the numbers of the given contract types are shown. Figure 6.8(a) plots the number of hidden contracts, (b) plots the number of mixed, while (c) plots the number of legal contracts. Panels in the different rows show results for different combinations of audit frequency and audit accuracy (with both values set to 0.1, 0.2, and 0.3, respectively). The rest of the parameters are fixed as shown on Tables 6.5 and 6.7. The values plotted are snapshots after 6000 time steps and are averaged over 10 independent runs.
According to the figure, the larger the ratio of adaptive target selection (the lower the percentage of random selection), the less hidden and the more legal contracts are observed. Obviously, this trend is more pronounced when the tax authority has a larger impact on the economy, that is, when both audit frequency and accuracy are of higher values.
These results suggest that it pays off to select employers from the social neighborhood (e.g., business partners) of previous wrongdoers. It is true, however, that the current auditing strategies implemented are rather simplistic and lack empirical backing. Nonetheless, the experiments confirm the findings of Chapter 4 and show that the TAXSIM framework is capable of implementing and testing various target selection policies.
In our last set of experiments, we use another extension of TAXSIM, one that implements minimum wage policies. As discussed in Section 6.2.4.3, the impact of a minimum wage policy on the tax system is that there is a forced minimum amount of tax (that of the minimum wage) that is to be paid after every employment contract that contains a legal component.
Figure 6.9 summarizes our experiments with a minimum tax content of 16%, 30%, and 44% (second, third, and fourth column of panels, respectively). For purposes of comparison, the first column of panels shows the baseline case of no minimum wage (minimum tax rate of 0%). The first row of panels plots the percentage of illegal employment (hidden and mixed contracts combined), while middle and bottom rows of panels display the percentage of mixed and hidden contracts separately. In case of all panels, audit frequency is plotted on the horizontal axis, while accuracy is plotted on the vertical axis. The grayscale-coded values shown are snapshots after 6000 time steps and show averaged values of 10 independent runs. The values of the other parameters are fixed according to Tables 6.5 and 6.8.
Table 6.8 Parameter values for the minimum wage experiments
Parameter | Value | Parameter | Value |
Employee network density | 0.05 | Employee network neighborhood size | 0 |
Employer network density | 0.05 | Employer network neighborhood size | 0 |
Number of employee and employer groups | 0 | Employee job search probability | 0.1 |
Quality of government services to employees | 0.1 | Quality of government services to employers | 0.2 |
Our results suggest that the presence of minimum wages (and thus, a forced minimum tax rate) slightly legalizes the simulated economy in the given parameter region of TAXSIM. This is most visible from the decaying white region of the top row, in between the first and second columns. This means that we can observe low percentages of illicit activity already in combination with lower values of audit frequency and accuracy. At the same time, the slope of the transition from nonlegal to legal becomes gradually steeper as the minimum tax paid increases.
Comparing the first two columns of Figure 6.9 we see that introducing minimum wages lowers the level of mixed employment in relation to the level of hidden contracts in an economy otherwise becoming more tax compliant. This means that market players unable to pay the tax content of the minimum wage are forced to give up mixed contracts and are driven entirely to the shadow economy. The further columns of the figure reveal that this tendency is reversed with increased minimum tax rates. This is because the higher general level of taxation makes competition stronger. It is worth noting, however, that mixed employment is always rather chaotic in the region of transition, that is, in the curved band corresponding to the transition between legal and nonlegal employment in the top row. This region is full of high peaks and deep valleys, which points to the strong path dependency of the runs in this parameter region.
Our results contribute to a debate in the literature: whether higher minimum wages result in higher unemployment or not (Card and Krueger, 1995). In TAXSIM, we do not separately measure the reported employment level, but the increased level of hidden employment is clear. This corresponds to the empirical findings of Khamis (2008) and Maloney and Mendez (2004), while it is in contrast with the results of Lemos (2004) based on Brazilian data. It is important to note, however, that the decreasing number of reported contracts emerges spontaneously in TAXSIM in response to the enforced minimum amount of tax.
This chapter introduced TAXSIM, an agent-based model of tax evasion in a market sector with constant external demand. In this model the level of taxes paid is subject to an agreement between individual employers and their employees. The agreement is driven by the expected costs of evading (based on the agents' estimation of the likelihood of discovery and on the fines to be paid), by the economic situation (the savings of the employee and the market success of the employer), as well as by the agents' individual preferences (dependent, in part, on their satisfaction with the services offered by the government).
Following the description of TAXSIM using the ODD+D protocol (see Müller et al. (2013)) we demonstrated its capabilities by discussing a selection of results from using the model.
We first discussed two scenarios from Szabó et al. (2008, 2010), when policy changes are implemented during the course of the simulation. The first showed the effect of the gradual improvement of the services offered by the government, while the second analyzed the entry of a few tax-preferred employers into the market. In the first case, we found that the extended effort of the government to improve the quality of its services pays off with a gradually legalizing economy. However, neither tax income nor the number of legal employment contracts increases linearly, making the immediate observable results of the new policy dependent on the actual, often unobserved, state of the economy.
The effect of improving governmental services was further analyzed in Section 6.3.2.1, confirming our findings in a more general setting and showing that services provided to employers dominate the impact of those provided to employees (at least in the case of the strong labor competition analyzed here).
We also found that the tax preference given to “multinational employers” may lead to a segmentation of employment contracts into legal and hidden (as opposed to mixed) employments, the tax-preferred players driving their competitors toward the shadow economy.
The scenarios were followed by an exploration of the model's complex parameter space. Our factorial analysis showed that the most important factors driving the outcome were audit probability and accuracy, followed by the quality of services for employers. We could also observe, however, that at practical levels of audit probability there is ample room for other factors to influence tax compliance.
In the last two sections, we discussed two extensions of TAXSIM, demonstrating its flexibility to study policy questions at the theoretical level. In the first, we explored the impact of a different, adaptive strategy of the tax authority in selecting its audit targets. We found that even a relatively simple strategy can noticeably improve the level of compliance over a purely random audit target selection. This corresponds to the findings of Chapter 4.
With the other TAXSIM extension, we studied how minimum wage policies might affect tax compliance. In the taxation context, a minimum wage law means that there is a certain level of tax to be paid after any employment relationship containing at least one legal component. (Totally hidden contracts are not affected.) As a consequence, we found that the introduction of minimum wages drives the economy toward noncompliance by transforming mixed employment to hidden ones. However, this effect is reversed as minimum wages (i.e., their tax content) are increased.
There are many opportunities for further studies with and for the improvement of TAXSIM in the future. For example, more realistic (adaptive) audit strategies could be investigated. Another possible extension would focus on the moral costs of tax evasion. To this end more detailed models of “moral obligation” and social norms should be incorporated (Gordon, 1989; Bosco and Mittone, 1997; Lago-Penas and Lago-Penas, 2010; Méder et al., 2012). It would also be interesting to connect the quality of government services to the amount of actual taxes collected.
TAXSIM is a rich theoretical environment to experiment with the complex economics of taxation. Its uniqueness is in its unusually sophisticated structure, so that it does not only include a complex decision-making equation by employees and employers that requires the balancing of economic incentives (the amount of taxes evaded and the expected costs of discovery) with the agents' internal beliefs (based on individual and social experiences with public services) but also an information exchange among agents through their social networks. Moreover, it also makes different auditing strategies possible for the tax authority. At the same time, it is perhaps this complex structure that limits TAXSIM's wider applicability. (A mathematical analysis of the kind of Gaujal et al. (2014) remains an open challenge.) Nonetheless, it is clear that the family of TAXSIM models is able to generate a wide range of interesting and relevant emergent outcomes capable of feeding our theoretical appetite. And certainly, there are still a number of rich courses to follow.
This work benefited from grants GVOP-3.2.2-2004.07-005/3.0 and OTKA T62455 (Hungarian Government) and QosCosGrid, EMIL (FP6 STREP #033883, #033841).