7.1.1 Taxpayer Dataset

To preserve taxpayer anonymity and yet facilitate model verification and validation, the IRCM uses a dataset of artificial taxpayers. The dataset of artificial taxpayers was created by substituting cases from the US IRS Statistics of Income (SOI) Public Use File (PUF) for actual tax returns of the 85,000 taxpayers featuring in the study area. Although most fields in the PUF are derived from tax forms, SOI modifies the data in order to protect the identity of individuals. Substitution was performed by first partitioning tax return and PUF records and selecting (with replacement) the PUF record that most closely matches each taxpayer record in the study area. Further details on the statistical matching algorithm are provided in Bloomquist (2012). Table 7.1 compares the resulting dataset of artificial taxpayers to the actual tax return data by major income and offset item.

	Actual data			Artificial data		Percent
Income item	N (non-zero)	Sum ($1000)		N (non-zero)	Sum ($1000)	differencein sums (%)
Wages	72,058	$2,744,170		71,773	$2,738,049
Interest	47,768	$138,156		42,582	$125,803
Dividends	22,951	$77,716		19,590	$65,905
Tax refunds	14,955	$6,098		10,764	$7,287	19.5
Alimony	238	$2,748		155	$2,071
Schedule C	8,728	$92,480		7,610	$90,104
Capital gains	17,636	$95,117		14,520	$89,043
Other gains	930	$81		690	$802	887.6
IRA	6,820	$68,681		5,315	$59,328
Pensions	18,604	$277,083		16,597	$269,574
Schedule E	8,769	$116,042		7,185	$120,370	3.7
Schedule F	1,143	$1,154		841	$2,252	95.2
Unemp. comp.	6,203	$19,783		4,774	$15,311
Social security	8,461	$73,374		7,821	$68,003
Other income	4,576	$9,194		4,573	$222
Total AGI	84,842	$3,695,035		84,846	$3,635,509
Deductions	84,851	$731,363		84,907	$743,302	1.6
Exemptions	75,870	$455,524		75,905	$453,310

From Table 7.1 it can be seen that for the largest line items (e.g., wages, interest, Schedule C income, capital gains, pension income, Schedule E income, deductions, exemptions, and total adjusted gross income (AGI)) there is close agreement in the number of returns (with non-zero values) and total dollar amount.⁴ In addition, in 20 of 21 postal code zones that make up the study region (not shown in Table 7.1), the percentage difference in Total AGI between the actual and artificial data is in low single digits (Bloomquist, 2012).

7.1.2 Agents

Figure 7.1 graphically displays the IRCM agent architecture.⁵ A single Region is composed of multiple non-overlapping zones (e.g., a postal code zone). Each Zone is the place of residence for a group of filers. Each Zone also includes any tax preparers and employers operating within its borders. A Preparer agent prepares tax returns for its Filer clients. Employer agents represent firms having one or more employee tax filers. The TaxReturn class defines the characteristics of all tax returns, which are reviewed by a tax agency (an instance of the TaxAgency class) and may be selected for an audit.

The interaction between filers and the tax agency is illustrated in Figure 7.2.⁶ The filer either self-prepares or uses a paid preparer. The tax agency reviews all filed tax returns to determine if any discrepancies are present on items having third-party information reporting. If a return is audited and underreporting is detected (or automated review reveals misreporting) the detected misreported amount is recorded. In each time period, individuals reassess how much income and/or offsets they will report in the next time period, but only for items having little or no third-party information reporting (mainly business and investment-related income). If audited, the filer may re-evaluate reporting on all major income and offset items, including those items with extensive information reporting (e.g., wage income).

7.1.3 Tax Agency

One of the important enforcement functions of the tax agency is to conduct taxpayer audits. In the IRCM, the user specifies the number of audits to perform⁷ and the tax agency selects returns to audit and completes the audit before the next tax return is filed. The assumption that tax audits are completed prior to filing the next tax return is an abstraction from reality. Typically, there is a two-year lag from the time a taxpayer files a return, the return is selected for audit, and the audit is completed. However, since audits are conducted on a continuous basis, the assumption that audits are completed during the same filing year is not believed to be a significant departure from real-world conditions.

The IRCM provides three ways to select tax returns for audit: simple random selection, fixed number, and constrained maximum yield. By default, the IRCM uses simple random selection. For the other two audit selection methods, the model randomly selects tax returns to audit from 17 pre-specified classes based on selected return characteristics: deduction type (standard or itemized), reported business income (or not), income greater than (or less than or equal to) $100,000, and preparation mode (self or paid-preparer). The final audit class is defined as taxpayers with zero-reported taxable income. Under fixed audit selection, the user specifies the number of audits in each of the 17 categories (with any unallocated audits selected randomly). The constrained maximum yield audit strategy attempts to increase the total amount of tax collected given a fixed number (including zero) of non-random audits. This is accomplished by identifying, at each time step, the audit class with the lowest and the highest average yield (average yield = tax collected/number of audits performed). The tax agency reallocates a single audit case from the class with the lowest yield to the class with the highest yield. The process of reallocating a single audit case for the next time step continues until the minimum coverage for the lowest yielding audit class is reached. The tax agency then repeats this same process with the second lowest yielding audit class and so on. Similarly, if the user-specified maximum coverage rate is reached the tax agency reallocates audits to the second highest yielding class, and so on.

In addition to performing audits, the tax agency in the IRCM also performs automatic checks of taxpayer reported income using available third-party information documents. In fact, although infrequently discussed in the academic literature on tax evasion, the most effective means for promoting high levels of voluntary compliance is, in fact, the existence of third-party information reporting. Figure 7.3 displays the relationship between reporting non-compliance and amount of information reporting for a weighted representative sample of TY 2006 US individual taxpayers (Black et al., 2012). In Figure 7.3, the “Underreporting Gap” refers to the dollar amount of underreported tax and “net misreporting percentage” (NMP) is a measure that allows for the comparison of relative non-compliance among the various line items.⁸ Wage and salary income is least likely to be misreported (NMP equal to 1%) because it is subject to both third-party information reporting and withholding. Items subject to third-party information reporting, but not to withholding (e.g., pension income, social security income, and interest and dividend income), have an NMP of 8%. Items subject to partial reporting by third parties (e.g., capital gains) have a still higher NMP of 11%. Lastly, items not subject to withholding or third-party information reporting (e.g., sole proprietor income and “other” income) are the least visible and, therefore, are most likely to be misreported. The NMP for this group of line items is 56%. The main conclusion to be drawn from Figure 7.3 is that non-compliance is most prevalent where the opportunities for underreporting are greatest.⁹

The IRCM is able to explore the impact of a change in information reporting on income items either directly by changing the default values for information coverage and/or withholding or indirectly by mapping the reporting characteristics of one item based on the reporting behavior of the taxpayer on another line item. Under the direct method, the user changes the information coverage and withholding parameters for one or more line items using drop-down menus and check boxes. With this approach, the reporting behavior of all taxpayers is potentially changed (with random variation) to reflect the new information reporting for the selected line item(s). Under the indirect approach, the user tells the IRCM to assign user reporting behavior for one line item to another line item. For example, let us say the analyst wants to use the indirect approach to apply observed reporting behavior for dividend income (with substantial information reporting) to capital gains income (with only some information reporting). The IRCM determines the new capital gains reporting behavior for each filer as follows:

1. 1. If the filer has dividend income, then assume that the current reporting rate for this filer's dividend income applies to capital gains income.
2. 2. If the filer does not have dividend income, then query the members of the filer's neighbor reference group to see if someone has dividend income. Use the reporting characteristics of the first neighbor reference group member with dividend income.
3. 3. If no one in the filer's neighbor reference group has dividend income, then query the members of the filer's coworker reference group. Use the first coworker's dividend income reporting behavior, if one is found.
4. 4. If no coworker has dividend income (or the filer has no coworkers, i.e., self-employed), then query the clients of the filer's tax preparer (if not self-prepared). Use the first client's dividend income reporting behavior, if one is found.
5. 5. If no neighbor, coworker, or preparer client has dividend income, randomly query other filers in the region until someone with dividend income is found. Use the dividend income reporting characteristics of the randomly selected filer as this filer's capital gains reporting characteristics.

Once the user finishes specifying the level of information reporting for selected line items, IRCM uses these up-dated parameters to recalculate reported amounts prior to running a simulation. Figure 7.4 shows the IRCM's Information Reporting Parameters Screen that allows a user to make changes to information reporting and withholding for the major income line items.

7.1.4 Taxpayer Reporting Behavior

In the IRCM, taxpayer reporting behavior is modeled using either the SOI reporting regime (default) or the rule-based reporting regime. When the SOI reporting regime is selected, the IRCM uses values from the PUF data to instantiate filer reported income and offset amounts. The SOI reporting regime option is useful for performing model validation, for example, by comparing the line item NMPs calculated by the model to NMPs in published IRS studies on the tax gap (Internal Revenue Service, 2007). The SOI reporting regime also provides a benchmark for model calibration (discussed later in this chapter). The baseline reporting rate calculated using the SOI reporting regime is assumed to be the individual filer's preferred reporting behavior given the enforcement environment in effect at time = 0. If never audited or if the filer's coworkers or neighbors are never audited, then the baseline reporting rate on each line item remains unchanged throughout the filing “lifetime” of the individual.

By selecting the rule-based reporting regime the user tells the IRCM to determine filer reported amounts and baseline reporting behavior using six user-specified parameters. The user sets the values of these parameters using sliders on the Filer Parameters screen (Figure 7.5). The top three sliders set the probability of misreporting success for income and offset items characterized by the extent of third-party information reporting (No Information Reporting, Some Information Reporting, or Substantial Information Reporting). For example, if the Substantial Information Reporting slider is set to a value of 10, then the model assumes 10% of filers believe that misreporting on items with substantial information reporting will be successful and 90% of filers hold the opinion that misreporting will not succeed. This difference in perception among filers may stem from different levels of knowledge and experience or due to qualitative differences in information reporting within a given income or offset line item.

The second row of sliders in the Reporting Regime section of the Filer Parameters screen defines additional influences on filers' reporting behavior. The “Withholding marginal impact” slider sets the marginal impact of withholding on reporting compliance. For example, Figure 7.3 above suggests that the marginal impact of withholding is between 80 and 90% based on the reduction in NMP from 8% for items subject to substantial misreporting (e.g., unemployment compensation, dividends and interest income) to an NMP of 1% for wage and salary income.¹⁰ The “% deontological filers” slider sets the percentage of filers whose reporting compliance is motivated by non-economic factors. While the term “deontological” suggests that the primary motivating principle is duty-based influences, equity or personal integrity can be included here as well. If this slider is set to a value of 30, then IRCM randomly selects 30% of filers to become deontological filers. Such filers are assumed to fully and accurately report all income and offset items.¹¹ Finally, the slider de minimis amount is used to set a minimum threshold amount for reporting for items with no information reporting. If the calculated reported amount for a given live item falls below the de minimis threshold, the filer is assumed to report zero for that item. More detail on the procedure the IRCM uses to derive line item-specific reporting rates is available in Bloomquist (2012).

7.1.5 Filer Behavioral Response to Tax Audit

Since taxpayers cannot know for certain that actions they take (or not take) will cause the tax agency to select their tax return for an audit, the reporting behavior of these taxpayers is modeled as a partially observable Markov decision process (POMDP) (Ghallab et al., 2004).

A POMDP is a five-tuple where:

• is a finite set of states (audited or not audited)
• is a finite set of compliance responses (perfect, increase, decrease, no change)
• is a probability distribution where for each , if there exists and such that , we have
• is the cost/reward (or expected cost/reward) experience from transition to state from state with transition probability . The quantity is the probability that if response is taken in state , then state will result. For example, if a taxpayer decides to increase compliance following a tax audit, one can infer that the action is being taken in order to reduce the probability of being selected for an audit (and the associated costs) in future time periods.
• is a set of observations with probabilities , for any , , and . represents the probability of observing in state after taking response . Finally, it is required that the sum of probabilities over the set of observations is 1, that is, .

Since the observations in a POMDP represent probability distributions, rather than exact states of the system, the probability distributions are called belief states and are updated using Bayes rule. The use of Bayes rule implies that the probabilities represented by are not static but change as knowledge of the enforcement environment changes.

In the IRCM, neither the belief states () nor the cost functions () of individual filers are modeled explicitly but are implied by filers' stochastically modeled “choices.” Stochastic choice modeling is used since relatively little is known about how taxpayers perceive the tax enforcement environment and what factors motivate changes in observed behavior.

Figure 7.6 graphically illustrates the POMDP for the filer's response to a tax audit. The two states are not audited () and audited (). A taxpayer is in one of these two states in each time period. The filer's belief about the probability of audit is defined as , implying that a filer's perceived probability of being selected for a tax audit depends on her belief about how the baseline audit probability () changes with a change in reporting behavior (response) .

In Figure 7.6 it is assumed no change in reporting compliance, an increase in reporting compliance, decrease in reporting compliance and perfect reporting compliance.¹² If not audited in time , the filer may start or increase underreporting in time on income subject to little or no information reporting, assuming the filer has such income from one or more sources. If the filer is audited in time , the decision to select a response is determined in the IRCM by a random draw and the user-specified probabilities . Although the IRCM models the filer's response as a stochastic process, actual filers are presumed to select an action based on their (heterogeneous and non-stationary) beliefs about the expected cost associated with that action.

7.1.6 Model Execution

The steps followed in executing a simulation using the IRCM are shown in Figure 7.7. The model reads tax return data for the population of artificial taxpayers and instantiates agents. During instantiation, the IRCM estimates a true amount for the largest income and offset items. The true amount is the amount reported plus imputed misreporting.¹³ Imputed amounts are based on audit results from the TY 2001 National Research Program (NRP) study. Details of the imputation methodology are described in Bloomquist (2012).

Each time step represents one filing cycle (year). Tax calculations are performed twice for all taxpayers, first using reported amounts and again using estimated true amounts. The difference in calculated tax using true and reported amounts is the tax gap for each filer. By default, the IRCM assumes that the difference between the true and reported tax amounts is the amount identified by the tax auditor. An option is provided to account for underreporting not detected by examiners.¹⁴

Tax audits are performed at the penultimate step in each time loop. During wrap up, the tax agency issues notices to taxpayers who are not audited but where computer checking of tax returns against information documents detects some underreporting.¹⁵ In addition, filers who stop filing, either because they leave the region or because they no longer have an obligation to file, are replaced by a new filer having identical income and network relationships as the “stop filer” being replaced, but with reporting behavior and memory reset to baseline levels (i.e., no memory of a prior audit experience or audits of reference group members, if that option is selected). The reporting behavior of filers who are not “stop filers” is also updated at each time step, as is the audit selection strategy of the tax agency.¹⁶ Finally, data collection occurs during the wrap-up phase. When the user-specified number of time steps has completed the model generates output in the form of tables and charts that can be reviewed and saved for further analysis.¹⁷

7A.4.1 Basic Principles

People exhibit heterogeneous reporting behaviors when filing their tax returns. Some appear to behave as rational decision makers, others comply out of a sense of duty or fear, and some pattern their reporting behavior by taking cues from family and friends. In addition to varying motivational factors, taxpayers have different opportunities for evasion based largely on the source of their income. Finally, taxpayers learn through repeated interactions with other taxpayers and with paid preparers what types of behaviors are more likely to draw the tax agency's attention. Analytical models in the tradition of Allingham and Sandmo (1972) and Srinivasan (1973) assume that taxpayers are independent, rational, and self-interested actors motivated to comply solely due to probability of detection and associated fines. However, empirical evidence from laboratory experiments, field studies, and random taxpayer audits suggests that a variety of noneconomic considerations also influence taxpayer reporting decisions. Agent-based models, such as the IRCM, are capable of incorporating both rational and behavioral motivations in a heterogeneous population of taxpayers.

7A.4.2 Emergence

The main emergent feature is a stochastically stable level of compliance (for major line items and total tax) that reflects user-specified assumptions for the level, quality, and effectiveness of tax agency enforcement activities and individuals' behavioral and filing characteristics.

7A.4.3 Adaptation

Filers adapt their reporting behavior to the perceived enforcement environment as determined from repeated interactions with the tax agency and (optionally) with their neighbors and coworkers.

7A.4.4 Objectives

The overall objective for each filer is to achieve a level of tax compliance consistent with their perception of the tax enforcement environment as well as their individual behavioral and filing characteristics.

7A.4.5 Learning

Filers may adjust their reporting behavior if they are audited or someone they know (e.g., a neighbor or coworker) is audited. This learning behavior is modeled as a partially observable Markov decision process (POMDP) , where

• is a finite set of states (audited or not audited)
• is a finite set of compliance responses (perfect, increase, decrease, no change)
• is a probability distribution where for each , if there exists and such that , we have
• is the cost/reward (or expected cost/reward) experience from transition to state from state with transition probability . The quantity is the probability that if response is taken in state , then state will result. For example, if a taxpayer decides to increase compliance following a tax audit, one can infer that the action is being taken in order to reduce the probability of being selected for an audit (and the associated costs) in future time periods.
• is a set of observations with probabilities , for any , , and . represents the probability of observing in state after taking response .

The IRCM does not explicitly model costs () and belief states () but assumes that these are implicit in the stochastically determined “choices” made by filers. These elements could be added to the model when better data on taxpayer decision-making becomes available. The IRCM allows users to provide independent sets of choice probabilities () to reflect different degrees of responsiveness by filers to a tax audit of themselves or someone in a reference group (see Section B.4.10).

7A.4.6 Prediction

The IRCM makes no predictions about future taxpayer behavior but simply models the presumed behavior of taxpayers given certain enforcement conditions.

7A.4.7 Sensing

Sensing occurs when filers become aware that someone in either their coworker or neighbor reference groups has been audited. This “sensing” is achieved by a filer polling her reference group members. If a reference group member has been audited, it is assumed that this information is openly communicated to all other reference group members. Lastly, the tax agency can use audits as a sensing mechanism if the CMY selection strategy is used.

7A.4.8 Interaction

The main types of interactions in the model that can potentially influence the behavior of individuals include (i) tax agency audits of filers and (ii) filers polling members of their reference groups to determine if someone was audited in the previous time period. Implied interactions occur between tax preparers and their clients. However, these preparer–client “interactions” are implied only because they appear as differences in estimated coefficients used to impute misreported amounts for paid prepared and self-prepared taxpayers.

7A.4.9 Stochasticity

Stochasticity is an integral feature of an IRCM. One way the model uses stochasticity is to determine which filers become “stop filers” at each time step. If the stop filer option is activated (the default setting) a uniform random number is drawn and compared to a fixed probability of becoming a stop filer as determined from analyzing filing behavior in the study area. Stop filer probabilities are specific to filing status. Another use of stochasticity is determining which filers are audited at each time step. Audit cases may be selected completely at random or by using one of two targeted strategies. The IRCM has 17 pre-determined audit classes used for targeted audits. These audit classes are groups of filers that share certain characteristics. These include filing status (single, married filing joint/qualified widow(er), head of household, married filing separate, dependent filer), children at home (yes/no), itemized or standard deduction, adjusted gross income (AGI) greater than the median (by filing status), and wage income more than one-half of AGI. Targeted audits may either be fixed in number or use a search algorithm (i.e., CMY) that assigns cases to audit classes with the highest average tax yield. A third use of stochasticity involves modeling filers' response to being audited. The user defines a vector of response probabilities (e.g., perfect compliance, increase compliance, decrease compliance, no change) and the model generates a uniform random number to determine which category of response the filer “selects.” When the rule-based reporting regime is selected, the IRCM uses a stochastic process to assign line item reporting behavior to each taxpayer. The model first determines if a filer is a “deontological” filer meaning that the filer has perfect compliance. If a line item is subject to information reporting and/or withholding the IRCM determines how much the filer will report using separate random draws for information reporting and withholding, depending on which conditions apply. Stochasticity is also involved in the process of imputing misreported income and offset amounts. These values are imputed from estimated equations that are fit to empirical cumulative distribution functions (ECDFs). Uniform [0, 1] random numbers are generated and used to select imputed amounts from these equations. Finally, creating reference groups involves stochasticity. Members of a filer's coworker and neighbor reference groups may be structured as either random or “small world” networks. In the former, reference group members are assigned using random selection from a filer's coworkers and neighbors. The process of creating “small world” networks is the same as random except one individual (the “hub”) is known to all of a firm's employees or residents of a given zone. The “hub” is determined by random selection.

7A.4.10 Collectives

There are two types of filer reference groups: neighbor and coworker. These are determined at the time of instantiation. Both groups assume the same (user specified) fixed size. If the “stop filer” option is activated (the default setting), then reference group stop filers are replaced over time; however, this does not affect group size or member relationships. Preparer networks are a third type of collective that may be optionally specified. At present, preparer networks only become relevant for scenarios that simulate a preparer-based tax scheme.

7A.4.11 Observation

The IRCM generates an output in the form of tables and figures. These can be copied and pasted into other applications for further analysis. The main interface screen also has a “map” of the study region and component zones. Options are provided that allow a user to drill down to view model output for individual preparers and employers by zone. This capability is especially useful for model verification and validation.