10.1 Introduction

It seems Benjamin Franklin was only half right – death may be no less certain today than it was in 1789, but taxes are far from inevitable. In the United States alone, the so-called tax gap, which is the difference between the tax owed and the amount paid on time in any given tax year, amounts to a whopping $450 billion in lost revenue, much of it accounted for by individual taxpayer noncompliance. There are, of course, many innocent reasons for noncompliance, including simple ignorance or error, but a significant portion is due to deliberate, and sometimes fraudulent, activity in the form of tax shelters.

An abusive tax shelter, or scheme, involves a sequence of transactions within a network of related business entities. These transactions are specifically designed to create and transfer artificial losses to designated beneficiaries, who then claim those losses in order to reduce their overall tax liability. The associated networks are usually composed of flow-through entities such as partnerships, trusts, and S-corporations¹. Such entities do not pay tax directly, but instead pass any net income or loss to their owners. Since partnerships can themselves own shares of other partnerships, it is possible to build multitiered ownership networks of enormous complexity, rendering manual audits prohibitively difficult.

The role that large, multitiered corporate structures play in the world of tax evasion has become evidently clear with the recent Panama Papers case (Boyd, 2016), that is being analyzed with complex graph database tools. Initial investigations here indicate the extensive use of off-shore shell corporations to hide income and assets that might otherwise be taxed by their home jurisdictions. An example in point is the eighteenth century English manor bought by the American film producer Stanley Kubrick that was found to be owned by three shell holding companies. These were in turn held by trusts for his children and grandchildren further obscuring tax ownership relationships (Goodman, 2016).

Much of the existing literature on tax evasion is concerned with the economic and psychological determinants of individual taxpayer compliance (Allingham and Sandmo, 1972; Andrei et al., 2013; Bloomquist, 2011). Even highly sophisticated studies of heterogeneous and dynamic interactions between taxpayers and auditors assume a single, hypothetical tax evasion method (Balsa et al., 2006). While these models lend insight into the factors influencing agent behavior, they do not explain the structure of evasion schemes. Our own focus is rather different. Rather than try to model the decision to evade, we seek to understand the actual structure of schemes, and in particular, how that structure evolves in response to changing enforcement priorities. Hence, the fundamental unit of investigation is not about the intention to evade – but how to evade. Such knowledge would help guide audit policy toward more efficient discovery of emerging schemes.

The most sophisticated schemes are generally constructed in such a way that their constituent transactions satisfy the letter of the law. When considered as a whole, however, and in the context of the surrounding ownership network, it sometimes occurs that a particular sequence of transactions is deemed illegal by the courts. In such cases, the risk associated with the original scheme spurs the invention of novel variants. Usually, these variants exploit the same underlying mechanism, but do so in ways that skirt the new enforcement regime.

We note here that a distinction must be made between illegal tax evasion and legal tax avoidance schemes. The nuanced differences between these two types are discussed in Chapter 1. Our own work focuses on the illegal exploitation of a particular subset of the US tax code, corresponding to the availability and accessibility of data to the authors. The specific rules we focus on surround the adjustment of a quantity called “basis.” Basis is just the set point from which gains or losses on an asset are computed. Usually, the basis of an asset is just the cost of acquiring it, but there is provision for adjustment of basis under various circumstances. These basis adjustment rules are intended to allow businesses to account for things like capital expenditures, liabilities, and depreciation, but it is sometimes possible to subvert these intentions by arranging transactions whose net effect, under the rules, is to inflate the basis of certain assets artificially. Applications of this methodology to other countries should first consider the local tax laws pertaining to basis.

In what follows, we provide a description of our methodology using the ODD+D protocol (Müller et al., 2013). We emphasize here the high-level concepts and features to help drive intuition about our approach. For finer grain details please refer to the Appendix in Hemberg et al. (2016).

10.2 Overview

It is our hypothesis that every known scheme can ultimately be represented according to the following taxonomy: a set of assets; a set of tax entities (including partnerships, individual taxpayers, and trusts); a directed network indicating the initial ownership structure connecting entities to other entities and assets; and finally, a sequence of pairwise transactions in which assets are exchanged between entities. Since our goal is to discover the likely forms of emerging schemes, and since most new schemes are constructed from older versions that use the same underlying mechanism, one usually has a good notion as to the first three components of the taxonomy. The problem of discovering new candidate schemes thus reduces to the problem of searching the space of possible pairwise transactions in the “neighborhood” of an existing one.

The “best” schemes are those that afford the largest reduction in tax liability with the smallest possible risk. Viewed in this way, we are faced with a classic optimization problem on the space of pairwise transactions. This space has a natural syntactic structure that lends itself to search using a variant of genetic algorithms (GAs) known as grammatical evolution (GE) (Warner et al., 2014). Our team has built a functioning, end-to-end GE codebase that has already proved capable of finding transaction sequences corresponding to two known schemes, namely Installment-sale Bogus Optional Basis (IBOB) and Distressed Asset Debt (DAD). We will describe our efforts using the IBOB scheme as an example in the upcoming sections. For further details about the DAD scheme please refer to Rosen et al. (2015). Note that GA/GEs are but one class of algorithms that can be used for co-evolutionary optimization (de Jong et al., 2007). Further investigation is required to assess the relative merits of other techniques.

In the most basic sense, genetic algorithms are procedures for managing populations of candidate solutions to a particular problem. Typically, the first step of this procedure is to evaluate the fitness of each candidate solution. In the next step, one selects some subset of the fittest members of this population, introduces a degree of random variation into these solutions by some means (usually an analog of mutation and crossover from biology), and then repeats the process on the new populations generated thereby. Note, the use of biological concepts in the context of tax compliance has been previously studied (Torgler, 2014), but mostly in determining the incentive to evade. Here, we leverage the study of incentives and propagation in Darwinian evolution to evaluate how the logistics of a tax system can be used to reduce one's tax liability. In theory, this leads to better and better candidate solutions after many repetitions.

All GA's require a procedure for mapping candidate solutions into a data structure amenable to random variation. GE provides just such a structure by affording a clean separation between a space of “genotypes” (namely, integer lists) and a corresponding space of “phenotypes” (or candidate solutions). GE uses context-free grammars to map elements of the genotype space into candidate solutions. For our purposes, candidate solutions consist of sequences of transactions that can be simulated on a network of asset and entity objects. Such simulations require a method for allocating gain and loss recursively within these networks.

In parallel to simulating the population of candidate tax evasion schemes, we also model a population of auditors (represented as an audit score sheet) to mimic the enforcement actions of the tax authorities. As we shall see in the simulation results, co-evolutionary behavior can be observed as the tax evasion schemes adapt to different audit priorities and vice versa. This is akin to biological predator–prey type population interactions where there is a need for constant adaptation of one species with another to ensure survival. Co-evolution here can occur across a continuum of scales, from the microcellular level through to the species level, depending on the specific trait that would provide an advantage. This observation, embodied in the Red Queen hypothesis (Van Valen, 1973), has also been compared to an evolutionary arms race. In the context of tax evasion, the “arms” correspond to “strategies” for either evasion or detection. The evolutionary biologist Richard Dawkins defined such evolutionary strategies as “memes” (Dawkins, 1989). An example here is the so-called Son of BOSS tax shelter that emerged in the mid-1990s after its immediate predecessor, a scheme referred to as “shorting against the box,” was rendered defunct by changes in the tax code (Wright, 2013).

We model audit policy as a collection of flagged transaction subsequences that have each been assigned a score between 0 and 1. These scores are constrained to sum to unity, and can therefore be thought of as representing the relative probability that the associated transaction will be detected and result in the assessment of a penalty. By incorporating these scores into our objective function, we are able to “prune out” undesirable transaction subsequences, and thereby guide the search toward those schemes that are less likely to be detected under a particular enforcement regime. These are, of course, precisely the schemes most likely to emerge under that regime.

We discuss these various components in greater detail in subsequent sections. We then illustrate the principles of our search methodology by referring to experiments on the IBOB scheme.

10.3 Design Concepts

The overall design concept of our system, Simulating Tax Evasion and Law through Heuristics (STEALTH), is illustrated in Figure 10.1. As discussed in Section 2, it is possible to formulate the process of constructing potential tax evasion schemes more abstractly as a search problem in a combinatorial space of transaction sequences. This space contains all the possible pairwise transactions that can occur within an initial ownership network of assets and entities. The search terminates when solutions are found whose “fitness” exceeds some predefined threshold. Hence, the outermost layer of our computational approach is basically a genetic algorithm that manages a population of candidate solutions corresponding to potential evasion schemes.

The basic structure of the algorithm is as follows. First, a random initial population of “chromosomes” is generated. In our case, these chromosomes consist of simple integer lists. By themselves, these lists are meaningless. They are useful only as a kind of seed for growing candidate schemes – in effect, they index points in the search space (though it is possible for two distinct chromosomes to produce the same transaction sequence). Because chromosomes are just integer lists, it is straightforward to introduce random variation by the action of genetic operators corresponding to mutation and crossover (see Warner et al., 2014 for more details). This variation is required in order to allow the algorithm to explore different points in the search space, and thereby discover variants of existing schemes.

Of course, in order to simulate transactions within a network, there must first be a method for converting chromosomes into candidate transaction sequences. This takes place in the genotype-to-phenotype converter module, which uses a context-free grammar to transform each integer list into a transaction sequence. The details of this process can be found in Warner et al. (2014). Once these transaction sequences have been generated, they are passed to the simulator module. The simulator parses through each transaction sequence, makes any state changes required to all involved entities and assets, and propagates any gains or losses incurred throughout the ownership network.

The simulator requires a module capable of implementing rules governing the allocation of gain and loss in complex partnership structures. The details of this module are described in depth in Rosen (2015). In addition, the simulator requires a system for representing auditing policy. This system must be capable of scoring the relative likelihoods that different transaction sequences incur audits resulting in the assessment of penalties. The output of the simulator consists of a taxable income and an audit score per each chromosome. These quantities are then combined to compute an objective function describing the fitness of the associated chromosome. The fitness values are then used as inputs to the genetic operators, which produce chromosomal variation around the fittest solutions in the population, while making sure to preserve one or two of the very best solutions unmodified for the next generation.

The simulator and its attendant subprocesses will be discussed in greater detail in the next section.

10.3.1 Simulation

The process being simulated is the implementation of a transaction sequence between taxpayers, partnerships, and other entities described by a tax return (or set of relevant returns), along with the assignment of an audit score to each sequence, given its specific traits. We represent this process by first decomposing it into inputs and outputs. That is, one can think of this process as beginning with three questions:

1. 1. Who is filing the return?
2. 2. What financial activities is the return describing?
3. 3. What is the auditor looking for?

10.3.1.1 Ownership Network

Because partnerships are composed of multiple partners, the financial documents that a partnership files reference several taxpayers and potentially other partnerships, corporations, or trusts. Therefore, we must represent this related collection of entities as shown in Figure 10.2(a). Each entity is represented by a node, each of which holds a portfolio of assets. The edges on the graph show ownership linkages between an entity and a partnership, displaying both the Fair Market Value (FMV) and outside basis of the corresponding shares, which are themselves treated as assets. Thus, the state of the network can be fully described as a set of entities, with each entity owning a set of assets, and each asset having an FMV, adjusted basis, and other contextually relevant information.

Note that, in the example featured in Figure 10.2(a), the sum of outside bases is less than the total value of the assets contributed. This apparent mismatch illustrates a very common situation that can arise in partnerships like P1; namely, the values of assets are not static, and may change after they are purchased. The outside basis remains the same (except under certain special situations), but the asset values are constantly changing. In this particular example, the assets have accrued value since they were purchased.

10.3.1.2 Transaction Sequences and Taxable Income

Given that tax returns are essentially a description of financial activity, we can represent the information that is required to be filed on a tax return as a transaction sequence. A single transaction in this context consists of a set of two entities and , and two respective assets and . Entity gives asset in exchange for asset , altering the portfolios of and , and modifying any number of associated state variables. In essence, a transaction amounts to a very specific transition of the ownership network from one state to another as illustrated in Figure 10.2(b). A sequence of transactions can thus be thought of as a sequence of order-dependent ownership network state changes.

These state changes include the production of income upon sale of various assets within the network. The simulator uses the rules governing the allocation of gains and losses through the ownership network to compute the taxable income that accrues to each entity per transaction. At the end of the simulation the quantity of income that has accrued to the particular entity of interest is passed as an input to the objective function for the corresponding chromosome. It is important to note that can, in principle, be negative.

10.3.1.3 Audit Score Sheet

Almost by definition, an auditor scans through a stack of tax returns, looking for a piece of observable information, or a joint occurrence of several pieces of observable information, that would indicate a high likelihood of suspicious activity. Thus we represent a hypothetical auditor as an audit score sheet, with the first column being a set of observable events, as well as their combined joint occurrences. That is, if we suppose that there are individually observable events, then an audit score sheet would contain rows.

The second column on the audit score sheet is a corresponding list of weights

that are referred to as audit points. Each point indicates the amount by which the overall audit likelihood score should be incremented each time that the corresponding event (or joint occurrence of events) is observed (see Table 10.1).

Observable	Points
1
2
3

At the start of simulation, the audit score is 0. As the simulation proceeds through each transaction , the score is incremented by the weight associated with the corresponding observables . At the end of a simulation an audit score is passed to the objective function.

10.3.1.4 Summary

Our simulation methodology establishes a representation of (i) the ownership network: the unit being investigated, (ii) the transaction sequence: the activity of the unit under investigation, and (iii) the audit score sheet: the behavior of the investigator. These three elements, when combined with the partnership tax calculator, form the simulation shown in Figure 10.3. The simulator produces both a measure of taxable income for all relevant entities and a score capturing the likelihood of audit.

10.3.2 Optimization

Once a method has been established for simulating transaction sequences (and the corresponding auditing process), we can begin establishing a means to search over potential financial activity and auditing policies to optimize certain objectives. In terms of the concepts defined in Section 10.3.1:

• What is an effective transaction sequence, given an initial ownership network and audit score sheet?
• What is an effective audit score sheet, given an initial ownership network and transaction sequence?

In this section, we address the question of what defines an “effective” evasion scheme or audit policy within our framework. We also briefly discuss our ability to model the co-evolutionary dynamics between evaders and auditors. This enables us to study the effect of changes in enforcement policy on the likely forms of emerging schemes.

10.3.2.1 Objective Functions

To recap, the simulation described in Section 10.3.1 produces two outputs per chromosome, given an initial ownership network; namely, the taxable income of the entity of interest, and an audit score associated with that entity's financial activity. These quantities can be combined to form “fitness functions” whose maximization defines the objectives of different agents in the tax ecosystem.

From the perspective of a tax evader, an effective scheme is one that affords the largest reduction of taxable income for the smallest risk. We capture this by stipulating a fitness function of the form

10.1

The quantity is just the income that would accrue to the evader entity if all assets to which he had any ownership rights were immediately sold at the start of simulation. We shall sometimes refer to the quantity as the “tax gap” corresponding to a particular scheme. It is clear that the goal of the tax evader is to make as large as possible, while keeping small.

By contrast, the goal of any particular enforcement regime is to choose the weights that tend to keep as small as possible for any particular population of schemes. Thus, the fitness function of an audit scorecard with respect to any particular scheme is just . The evolutionary process for the population of audit scorecards is entirely analogous to that described above for transaction sequences, the only difference being that the phenotypes in question correspond to different values of the weights .

10.3.2.2 Co-evolution

Auditors and evaders exist in a continuous state of mutual co-adaptation, with evaders adjusting their patterns of activity to accommodate perceived changes in enforcement policy, and auditors altering their priorities to target the most successful schemes. The core genetic algorithm discussed above can be adapted to capture this predator–prey dynamic by initializing two populations simultaneously: one a collection of candidate schemes, and the other a population of audit scorecards, each with different distributions of weights .

During the simulation phase, an individual is selected from each of these populations, and the corresponding fitness functions are evaluated. Specifically, each individual in the population shown on the top of Figure 10.4 represents both an initial ownership network and an associated transaction sequence. In every generation, each individual from that population selects a subset of the audit score sheet population shown at the bottom of the figure to evaluate against. The process is then repeated for the audit score sheets being compared against the ownership network–transaction sequence pair. A more detailed account can be found in Rosen (2015).

10.4 Details

We describe here the IBOB real estate tax scheme that is used as a case study for our experiments and outline the grammar from which it can be generated. The genetic algorithm parameter settings are also listed.

10.4.1 IBOB

The Installment Sale Bogus Optional Basis Transaction (IBOB) is one instance of a wider class of tax evasion strategies that rely on a mechanism known as “basis-shifting.” Such schemes are designed to decrease, defer, or eliminate any taxable income or capital gain incurred from the sale of an asset, usually an item of real estate. This is often accomplished by artificially increasing the asset's basis, a quantity equivalent to its purchase price under most circumstances.

The initial state for the IBOB scheme is shown in Figure 10.5. The subsequent transaction steps are shown in Figure 10.6(a) and (b). Suppose Jones, a real estate developer, owns a house he originally bought for $120 (i.e., the house has a basis of $120), which he now wishes to sell to another individual named Brown for $200. In order to avoid incurring $80 in capital gains upon sale of the house, Jones forms two partnerships, JonesCo and FamilyTrust, making sure to retain majority ownership () of each. He then arranges for JonesCo to create, and retain majority ownership of, yet another partnership called NewCo. Jones then contributes the house through JonesCo to NewCo, an action which does not alter the basis of the house.

Next, Jones orchestrates a transaction wherein FamilyTrust purchases JonesCo's share in NewCo for an annuity (Figure 10.6(a)). Provided JonesCo has made an election under Section 754 of the Tax Code,² this action increases the basis of the house without incurring any current tax liability. Finally, NewCo sells the house to Brown (Figure 10.6(b)) for seemingly no capital gain because the basis of the house was increased by the previous transaction.

Thus, rather than paying capital gains on the $80 from the cash sale to Brown, Jones has to pay tax on the gain incurred from the sale of JonesCo's interest in NewCo. But because it was purchased with installment payment, the tax is only paid as the payments are received, a deferral which is advantageous to Jones. Furthermore, some manifestations of this scheme involve FamilyTrust defaulting on the annuity payments, which means that no tax is ever paid.

10.4.2 Grammar

In the GE version of the genetic algorithm utilized in our approach, the compressed form of the search space is represented by a Backus–Naur form (BNF) grammar, which defines the language that describes the possible output sentences. a BNF grammar has terminal symbols, nonterminal symbols, a start symbol and production rules for rewriting nonterminal symbols. The grammar is used in a generative approach and the production rules are applied to each nonterminal symbol, beginning with the start symbol, until a complete program is formed. The list of integers (genotype) rewrites the start symbol into a sentence. An integer from the list of integers is used to choose a production rule from the current nonterminal symbol by taking the current integer input and the modulo of the current number of production choices. Each time a production from a rule with more than one production choice is selected to rewrite a nonterminal symbol, the next integer is read and the system traverses the genome. The rewriting is complete when the sentence comprises only terminal symbols.

To illustrate this logic, Figure 10.7 provides an example of how an integer list (genotype) can be converted to a sentence (phenotype) that describes a transaction between two entities that exchange assets. The parsing occurs as follows:

1. 1. We pick the first rule in the grammar as the start symbol, in this case (1) <transactions>.
2. 2. Next, expand the left most nonterminal symbol in our sentence <transactions>. We take the current integer input 3 and the modulo of the number of production choices 2, which is 1, thus we pick <transaction> the production choice at position 1 (the indexing starts at 0) and rewrite the <transactions> with <transaction>.
3. 3. Again expand the left most nonterminal symbol <transaction>. There is only one production choice here, so it is rewritten to Transaction(<entity>, <entity>, <Asset>, <Asset>).
4. 4. Again expand the left most nonterminal symbol <entity>. We take the current integer input 11 and the modulo of the number of production choices 5, which is 1, thus we pick NewCo. The sentence is now Transaction(NewCo, <entity>, <Asset>, <Asset>).
5. 5. The left most nonterminal symbol is again <entity>. We take the current integer input 10 and the modulo of the number of production choices 5, which is 0, thus we pick Brown. The sentence is now Transaction(NewCo, Brown, <Asset>, <Asset>).
6. 6. The left most nonterminal symbol is now <Asset>. We take the current integer input 4 and the modulo of the number of production choices 3, which is 1, thus we pick <Material>. The sentence is now Transaction(NewCo, Brown, <Material>, <Asset>).
7. 7. The left most nonterminal symbol is now <Material>. There are no choices for <Material> so we rewrite it with Material(200, Hotel, 1). The sentence is now Transaction(NewCo, Brown, Material(200, Hotel, 1), <Asset>).
8. 8. The left most nonterminal symbol is again <Asset>. We take the current integer input 30 and the modulo of the number of production choices 3, which is 0, thus we pick <Cash>. The sentence is now Transaction(NewCo, Brown, Material(200, Hotel, 1), <Cash>).
9. 9. The left most nonterminal symbol is now <Material>. There are no choices for <Cash> so we rewrite it with Cash(<Cvalue>). The sentence is now Transaction(NewCo, Brown, Material(200, Hotel, 1), Cash(<CValue>).
10. 10. The left most nonterminal symbol is Cash(<CValue>. We take the current integer input 7 and the modulo of the number of production choices 3, which is 1, thus we pick 200. The sentence is now Transaction(NewCo, Brown, Material(200, Hotel, 1), Cash(200)).
11. 11. There are no more nonterminal symbols left to rewrite and our string rewriting is done.

For the purpose of detecting IBOB, we initialize a network with two tax filers, Mr. Jones and Mr. Brown, and three partnerships, JonesCo, NewCo, and FamilyTrust. These entities have portfolios of assets that include Cash, an Annuity, a Hotel, and various partnership shares. The assets can have different fair market values. The BNF grammar used to define the transaction space among these entities is shown in Figure 10.8.

<transactions>::=<transactions><transaction>|<transaction>
<transaction>::=Transaction(<entity>,<entity>,<Asset>,<Asset>)
<entity>::=Brown|NewCo|Jones|JonesCo|FamilyTrust
<Asset>::=<Cash>|<Material>|<Annuity>|<PartnershipAsset>
<Cash>::=Cash(<Cvalue>)
<Material>::=Material(200,Hotel,1)
<Annuity>::=Annuity(<Avalue>,30)
<Cvalue>::=300|200|100
<Avalue>::=300|200|100
<Pname>::=NewCo|JonesCo|FamilyTrust

The first recursive rule in the grammar shows that the search space (language) is bounded only by the length of the input (genome) used to map integers to transactions. We also note that the search space can be increased and customized by altering the structure of the grammar.

10.4.3 Parameters

For the experiments considered here, audit scores are determined as the sum of four audit points between 0 and 1. The initial average distribution of audit scores in the population is shown in Table 10.2. Note a “Single Link” audit observable here refers to transactions that occur between entities that are connected through a single direct ownership relationship, such as between Jones and JonesCo as shown in Figure 10.5. “Double Link” corresponds to transactions that occur between entities that have an ownership relationship 2 hops apart, such as between Jones and NewCo as shown in Figure 10.6. The value of each audit point can be thought of as the relative importance of the associated behavior to the auditor (the reasons for the numerical values of the three audit score sheets are explained in Section 10.5).

Audit observable	LimitedAudit	EffectiveAudit	CoEvolution
iBOB	0	0.25	0.25
Annuity	0.33	0.25	0.25
Single link	0.33	0.25	0.25
Double link	0.33	0.25	0.25

We ran 100 independent iterations of the co-evolutionary GA for 100 generations each with tax scheme and audit score populations of size 100. We chose half of the tax scheme population for evaluating the fitness of the solution in the other audit score population and vice versa. The parameters that govern the GA simulation are enumerated in Table 10.3.

Parameter	Description	Value
Mutation rate	Probability of integer change in individual	0.1
Crossover rate	Probability of combining two individual integer strings	0.7
Tournament size	Number of competitors when determining most fit individuals
Number chosen	Fraction of other population that each individual is tested against
Population size	Number of individuals in each population	100
Generations	Number of times populations are evaluated	100

The GA parameters in Table 10.3 were chosen through trial and error. Since our focus is on understanding the dynamics between taxpayers and auditors, parameters were not calibrated to achieve an optimal result for either side. Thus the specific parameters need only demonstrate the co-evolutionary relationship between the two agent types, which is easily obtained by the above parameters. We discuss next the experiments based on these initializations.

10.5 Experiments

We conducted a number of experiments to verify that the co-evolutionary dynamics of our simulation are consistent and sufficient enough to find existing tax schemes. To first order, we expect that when schemes evolve to accommodate existing audit priorities, the audit points will themselves evolve to detect the new evasion behavior. This should result in either convergent or oscillatory dynamics.

10.5.1 Experiment LimitedAudit: Audit Observables That Do Not Detect IBOB

For this experiment, we purposefully left out audit points that can detect IBOB. Thus, once IBOB is found it will propagate through the tax scheme population on the merit of being the best tax scheme that is unauditable.

Figure 10.9 shows plots of tax scheme and audit score sheet fitness. Figure 10.9(a) shows the fitnesses of both the tax schemes and the audit scores for the best individual from each generation for a single iteration. Note that while IBOB was found in only 34% of the iterations here, we expect most iterations to converge to IBOB as the number of generations increases. The average audit point values displayed in Figure 10.9(b) show the variation in the points over time. Note here that the audit points are unchanged and in equilibrium once IBOB has been found. The average audit points of the best solutions for all the iterations are shown in Figure 10.9(c), where we see that transactions that exchange a material asset for an annuity are assigned a higher audit point.

Material-annuity transactions have a significantly higher audit point because they occur more frequently than the other two schemes. That is, any transaction in which the Hotel is exchanged for an annuity mitigates all of the taxable gain on the ultimate sale of the hotel because annuities are nontaxable. Furthermore, a double link transaction requires that a material-annuity transaction takes place because Jones has to purchase the Hotel from NewCo with an annuity. Thus, the likelihood of a tax scheme involving a material-annuity transaction is higher than the likelihood of a single- or double-linked scheme. This results in a higher average audit point assigned to material-annuity transactions because it is the most common way to mitigate taxable gain in our example.

A clear pattern emerges when IBOB is evolved: initially, the pool of tax schemes gravitates toward a network of transactions that contains suspicious activity, which the audit scores are able to detect. Only after the audit scores evolve to reduce the fitness of such schemes does IBOB become dominant.

Two distinct metastable states emerge when the basic IBOB is not found. The most common is when a suspicious scheme is evolved in an early generation, which the audit scores can effectively detect early on, causing the scheme fitness to converge toward its minimum and the audit score fitness to converge to its maximum. Alternatively, the pools of both tax schemes and audit scores oscillate with respect to each other for the duration of the run, implying a process of suspicious schemes emerging and audit scores evolving to detect them, causing another suspicious scheme to become dominant. Many runs show oscillations or long-lived transients, as these show the kind of predator–prey dynamics we expect, and illustrate that the search can sometimes get stuck in a “metastable state.”

Ultimately, the only stable configuration is one in which IBOB dominates the population – any “oscillations,” whatever the intervals between transient peaks, and whatever the number of those peaks (1, 2, 3,…) must eventually give way to IBOB.

10.5.2 Experiment EffectiveAudit: Audit Observables That Can Detect IBOB

In this experiment, we include an audit point that can detect IBOB. Thus, IBOB should not be able to propagate through the tax scheme population. Because the audit score sheets were previously unable to detect IBOB, the fitness of the tax schemes would only oscillate until a single IBOB scheme was introduced into the population, at which point it would quickly propagate.

Figure 10.10(a) displays the fitnesses of both the tax schemes and the audit score sheets from the best individual from each generation from 1 iteration. Since the audit points completely cover all transactions that can create large recognizable loss, the fitness is always minimal for the tax schemes and maximal for audit score sheets. The corresponding audit points for the iteration are all constant as shown in Figure 10.10(b). Furthermore, Figure 10.10(c) shows that the average audit points of the best individuals over all the runs correspond to the expected values at the initial state.

We conclude that the observed co-evolutionary dynamics are consistent with the expectations for this example.

10.5.3 Experiment CoEvolution: Sustained Oscillatory Dynamics Of Fitness Values

Our goal with this set of experiments was to generate sustained oscillatory dynamics, since we have shown in previous experiments that oscillations in tax scheme fitness are possible for a short amount of time before converging to equilibrium. This is a necessary step because a primary assumption underlying our model is that tax schemes and audit scores sheets are engaged in a perpetual co-evolutionary process in which no global attractor exists. Because the audit score sheets were unable to detect IBOB in experiment LimitedAudit, the fitness of the tax schemes would only oscillate until a single IBOB scheme was introduced into the population, at which point it would quickly propagate. At the same time, simply allowing the audit score sheets to detect IBOB would result in rapidly convergent dynamics, as demonstrated in experiment EffectiveAudit.

To generate sustaining oscillations, we augment the audit score sheets to assign the lowest audit point a value of 0, so that there will always be at least one scheme that is not detectable by the auditor. Our hypothesis is that once the population of audit score sheets begins to converge, a tax scheme will evolve that utilizes the type of behavior that is currently not detectable by the majority of audit score sheets. The effective tax scheme will propagate within its population until the audit score sheets gradually evolve to detect the now dominant behavior.

Figure 10.11(a) displays the fitnesses of both the tax schemes and the audit scores from the best individual from each generation during a single iteration. In this scenario, since the audit points cannot completely cover all the transactions that can create large deductible loss, the fitness oscillates between minimal for the tax schemes and maximal for audit score sheets and vice versa. The audit points corresponding to this iteration also oscillate as shown in Figure 10.11(b). In Figure 10.11(c) we see for the reasons listed in Section 10.5.1 that the highest average audit points of the best individuals over all the iterations are for transactions involving annuities.

In Figure 10.11, there is at first a high level of fitness among tax schemes across all runs, but the initial dominant scheme is quickly detected by the corresponding audit score sheet population, which decreases the overall fitness. Over time, new tax schemes emerge in some of the runs that are initially not detectable by the corresponding audit score sheet population, which generates a rapid upward surge in tax scheme fitness. The audit score sheets eventually evolve to detect the type of behavior that is present in the new dominant tax schemes, but the process is more gradual. These results confirm our hypothesis that under the correct conditions, sustained oscillatory dynamics in the fitness of tax schemes are possible.

While this experiment was designed to generate oscillatory behavior, the results are promising because they show realistic dynamics between the tax schemes and the corresponding auditing priorities. Specifically, we can see that once a single new tax scheme that is not currently detectable by the auditor emerges, it propagates throughout the population very quickly, as evidenced by the steep upward slope in the average scheme fitness plot. Conversely, the audit score sheets take a longer time to adapt to the new tax scheme.

10.6 Discussion

We have demonstrated an end-to-end methodology that automates the discovery of tax evasion schemes given a set of assets, tax entities, auditing policies, and quantitative risk-reward scoring measures. A core capability developed here was the representation of tax schemes as a sequence of asset exchanges between entities. The IBOB scheme that motivated this approach deliberately arranges transactions between tax entities in order to artificially increase the basis of certain assets prior to their disposition. Our approach successfully captured the IBOB scheme and showed how a sequence of individually legal transactions can result in a fraudulent outcome. While IBOB and other similar schemes can seem simple enough to audit effectively once they are discovered, the ability of tax shelter promoters to construct vast partnership structures tends to obscure the underlying mechanism of evasion. By encoding the quantitative nature of partnership taxation into a representative system, we can traverse such transformative possibilities in a manner that mimics the brainstorming process of tax shelter promoters.

This approach to detecting tax evasion schemes using a combinatorial search of transaction sequences in a genetic algorithm-based agent model is a departure from existing data-mining and machine learning techniques, both supervised and nonsupervised. Supervised techniques require as input a known pattern of evasion (labeled data), against which the parameters of a statistical algorithm can be trained (DeBarr and Eyler-Walker, 2006). This tuned algorithm can then process data corresponding to a set of new unclassified transactions and return an evasion risk measure. In contrast, our approach requires only an objective scoring methodology to rank scheme fitness and does not need any training data. Statistical algorithms also require a significant variety of labeled data to ensure robustness to the numerous combinations of tax entities, assets, and transactions that may occur. This variety is often difficult to achieve. An even larger concern is that of “overfitting,” where the algorithm may not be able to detect schemes with minor variations from those used for training purposes. Alternatively, nonsupervised machine learning techniques do not require a priori known patterns of evasion. While this may appear favorable, categorizing evasion is based here on a measure of anomaly from a baseline. This approach can suffer from high false positive rates when a suitable normative state cannot be defined.

We propose our methodology for tax scheme detection not as a replacement, but as a complement to existing data-mining techniques. In particular, we envision an iterative process that begins with manual brainstorming by subject matter experts (SMEs) to help identify combinations of entities, assets, sections of the tax code, and audit points of specific interest. Insights from past examinations and/or expectations about areas of future evasion can help guide this brainstorm. Transaction sequences can then be randomly initialized using identified asset and entity elements.

Alternatively, transaction sequences specific to a known fraudulent scheme can be set as the starting point. The subsequent schemes evolved by the search process should be examined by SMEs to validate their potential practical effect. If required, the audit plan can be updated to guide the search process further. Once a new scheme type is verified for efficacy, data-mining techniques can be employed to test for their existence. Moreover, these new scheme variants can be incorporated into existing training data sets to help calibrate the underlying statistical algorithms. This process can be repeated by integrating observations from the data into the initial conditions for the subsequent search.

An additional use-case for this methodology is to conduct “what–if” scenarios. The relative merits of different audit plan criteria can be compared in terms of the relative fitness of the different tax schemes that emerge. Similarly, the impact of different tax policy changes could also be examined. The goal with all these efforts is to help anticipate and scope the downstream impact of an enforcement policy prior to its deployment. As before, this methodology can help complement existing manual table-top strategy gaming and red-team/blue-team exercises designed for this purpose (Mirkovic et al., 2008).

While we have demonstrated significant success with this approach, there are certain limitations that hinder broader applicability. The specific sections of the tax code we considered were reducible to first-order logic statements. For example, the calculation of an asset's inside/outside basis follows a complicated, yet fairly consistent and unambiguous, set of rules. In general, however, the tax code consists of many definitions, relationships, and exceptions that require semantic parsing, a process that can be ambiguous and inconsistent. Issues of interpretation are often only resolved in a court of law. As a workaround, expert rules can be specified in the audit plan to help direct the search toward or away from certain outcomes. Advances in natural language processing techniques (Moens et al., 2007) could also be considered to supplement first-order logic calculations and allow for more complex scenarios to be explored.

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