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Measuring the Tax Gap. Brian Erard B. Erard & Associates Outline of Presentation. Tax Gap Overview Measures based on random audits Sample design and considerations Application of design-based measures Application of model-based measures

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measuring the tax gap

Measuring the Tax Gap

Brian Erard

B. Erard & Associates

outline of presentation
Outline of Presentation
  • Tax Gap Overview
  • Measures based on random audits
    • Sample design and considerations
    • Application of design-based measures
    • Application of model-based measures
  • Measures based on operational audit data
  • Measures based on comparisons of surveys and administrative data
  • Other creative approaches
conceptual issues
Conceptual Issues
  • How is the tax gap defined?
  • What are its components?
  • Why attempt measure it?
  • How does it compare to the underground economy?
  • How broad a scope should the measure cover?
how is the t ax gap defined
How is the tax gap defined?
  • Gross – the difference between the tax that taxpayers should pay and the tax they actually pay on a timely basis
  • Net – the difference between the gross tax gap and taxes collected through enforcement and late payments
what are its components
What are its components
  • Non-filing – taxes owed but not reported and paid on a timely basis by non-registrants/non-filers (and late filers)
  • Underreporting – taxes attributable to underreporting of actual liabilities on timely filed tax returns
  • Underpayment – taxes that are reported but not paid on a timely basis
    • This component often can be accurately assessed from administrative records
how is true tax liability defined
How is true tax liability defined?
  • The liability that would be recommended based on the interpretation of a fully informed tax official?
  • The actual liability that is assessed following the resolution of any disputed amounts between the taxpayer and the tax agency?
  • The liability that would be assessed if it were to be assessed by an impartial court of law?
why attempt to measure the tax gap
Why attempt to measure the tax gap?
  • Collection of tax revenue is the primary function of a tax administration
    • Accountability: Helpful for evaluating the degree to which the tax administration is successful
    • Disaggregation of the tax gap is helpful for understanding the sources and potential underlying causes of tax compliance
what is the underground economy ue
What is the underground economy (UE)?
  • Underground/black/hidden/unobserved economy
    • Broadest concept: Subset of all economic activity (from both legal and illegal sources/market and non-market) that goes unrecorded in official statistics
    • Typical concept: Difference between total market-based income (legal and illegal) and recorded GDP
how does ue differ from tax gap
How does UE differ from tax gap?
  • Not all unrecorded income is taxable (due to filing thresholds, exemptions, and certain deductions)
  • Some taxable income sources are not counted in UE measures (such as capital gains and various transfers)
  • A sizeable portion of the tax gap is attributable to aggressive use of tax credits, depreciation rules, transfer pricing, and other provisions rather than direct underreporting of income
  • The tax gap includes taxes on income that have been reported but not paid
  • Recorded GDP actually accounts for some sources of unreported income
  • Conceptually, the UE includes income from illegal activities (drugs, gambling, prostitution) that is typically excluded from tax gap measurement
  • The UE is even harder to measure!
scope of tax gap measurement
Scope of tax gap measurement
  • Ideally, a broad monetary measure encompassing all taxes and all forms of non-compliance
  • As a practical matter, it may be too costly or difficult to develop a reasonably accurate broad measure
    • A large scale random audit programme may exhaust a large share of a tax administration’s compliance resources
  • Alternatives for a narrower scope include:
    • Focus on certain key taxes
    • Focus on compliance rates rather than compliance levels
    • Focus on indicators of non-compliance rather than direct measures
uses and m isuses of tax gap
Uses and misuses of tax gap
  • Uses
    • Reasonably good indicator of the order of magnitude of tax non-compliance
    • Helpful for identifying key sources of non-compliance
    • Underlying data can be useful for risk assessment
  • Misuses
    • Short-term trend analysis
    • Performance evaluation
digression on closing the tax gap
Digression on “closing the tax gap”
  • Public disclosure of tax gap estimates inevitably leads to demands to “close the gap”
    • Even under an optimal tax administration, it is important to recognise that some gap will exist
    • Nor is it optimal to audit until MR=MC
  • Heisenberg uncertainty principal
    • Attempts to measure the tax gap impact its size
    • Attempts to reduce the tax gap impact the tax base
how can we measure evasion
How can we measure evasion?
  • Audit Data
    • Random
    • Operational
    • Combined operational and random
  • Measures based on comparisons of surveys and administrative data
  • Other creative approaches
designing random audit studies
Designing random audit studies
  • Scope
  • Scale
  • Sampling strategy
  • Data collection
  • May be interested in a particular tax or tax issue
    • Individual income tax, Corporate income tax, VAT
    • Specific credits, deductions, or income sources
  • May be interested in a particular taxpayer segment
    • Self-employed taxpayers, employers, high wealth individuals
    • For instance, one may want to investigate compliance by small businesses with all taxes (income tax, VAT/sales tax, employment taxes, etc.)
  • The appropriate scale of the programme depends on factors such as:
    • What is being measured (e.g., rates or dollar amounts)
    • Planned method of estimation: design-based or model-based
    • Desired precision for key estimates
    • Other planned uses for the data (e.g., risk scoring)
evolution of irs random audit programs taxpayer compliance measurement program tcmp
Evolution of IRS random audit programs: Taxpayer Compliance Measurement Program (TCMP)
  • Line-by-line audits of a stratified random sample of about 50,000 individual income tax returns
  • Conducted approximately every 3 years from TY 1963 until TY 1988
    • Also occasional studies of other taxes (employment, small corporations, partnerships, individual non-filers)
  • Primary uses were:
    • Development of audit selection criteria
    • Measurement of tax gap
    • Research
13 years later ty 2001 national research program nrp
13 years later … TY 2001 National Research Program (NRP)
  • Stratified random sample of 45,000 individual returns for TY 2001
  • Advertised as “kinder and gentler” than TCMP
    • About 10% of returns accepted without examination or with only a correspondence examination
    • Not all line items examined
      • Some routinely examined – e.g., self-employment returns
      • Some examined only at discretion of “classifier” or examiner
  • Case building materials provided in advance
  • For TY 2001, had a small “calibration sample” of returns audited in a manner similar to old TCMP program
    • Useful for evaluating non-compliance on line items that were not routinely examined
nrp redesign
NRP redesign
  • Smaller annual studies of individual income tax
    • Most recently for tax years 2006, 2007, 2008
    • About 14,000 returns per year
  • No longer a calibration sample
  • Some recent studies of other taxes
    • S-corporations (tax years 2003 and 2004, 5,000 returns)
    • Employment tax (2008-2010, 6,000 returns)
design challenges
Design challenges
  • Mandatory vs. discretionary examination of line items
  • Intensity of probes for unreported income sources
  • Examination of related entities
  • Adjustments following disputes and appeals
  • If detection controlled estimation is to be employed, ensuring sufficient examiners who have each done a reasonable number of audits of the return items of interest
some best practices for random audit studies
Some best practices for random audit studies
  • Non-sampling errors can plague a random audit study. The following practices help to prevent such errors:
    • Appropriate support and training of examiners and other staff – buy-in by examiners is crucial
    • Provide examiners with relevant case-building information
    • Design procedures to distinguish reports on the wrong line item from reports of an incorrect amount
    • Have good procedures for recording, validating, and correcting data
    • Record details on which specific line items or issues have been examined and which have not
    • Provide adequate supervision
  • It is also useful to consider what auxiliary information to collect to aid research
random sampling design based estimation
Random sampling: design-based estimation
  • Design-based estimation is very common in survey work. Under this approach:
    • The variables of interest in the population are treated as fixed but unknown numbers
    • Estimates are computed based on a randomly drawn sample from this population (typically, these estimates are the sample analogues of the population characteristics of interest)
    • The properties of the estimates (such as their means and variances) are derived using information only about the selection probabilities for the observations in the sample (i.e., the approach is non-parametric)
estimating the rate of non compliance
Estimating the rate of non-compliance
  • Canada Processing Review Programme
    • Approach is to contact a random sample of individual taxpayers who have claimed certain credits or deductions to request receipts to verify their claims
    • The results are used to measure the rates of non-compliance on these items and to develop targeting criteria for future verification work
  • Canada Core Audit Programme
    • Approach is to randomly audit various SME segments for selected tax issues to estimate rates of material non-compliance and assess risks
simple random sampling srs
Simple random sampling (SRS)
  • One starts with a sample frame
    • For this example, the frame is all tax returns in a given year that claimed at least one specified credit or deduction
  • Under SRS, one randomly chooses returns from the sample frame in such a way that every possible sample of size n that can be drawn from the N returns in the population has an equal chance of selection
point and interval estimation
Point and interval estimation

Let p = unknown population proportion of returns with an improper claim

n = sample size

= number of sampled returns found to have an improper claim

Then is the point estimate of the rate of non-compliance

The following is a confidence interval for p:

The term is known as the margin of error (m)

For a 95% confidence interval,

how large should the sample be
How large should the samplebe?

Suppose we want to draw a random sample to estimate the rate of non-compliance with a margin of error m=.03 (for a 95% level of confidence). Since

we can calculate n as:

Of course, we don’t know p. The worst case scenario for precision is p=1/2, in which case:

some notes
Some notes
  • If the population size N is relatively small, a somewhat smaller sample will be required. (We are ignoring the FPC factor

point estimate)

  • If we are confident that the true rate p is far from ½, we can use a smaller sample
estimating the magnitude of non compliance
Estimating the magnitude of non-compliance
  • Example: Kleven et al. (2011)
    • As part of this study, a random sample of Danish taxpayers were selected for rather comprehensive audits of their personal tax returns
    • The study was used for various purposes, including developing an estimate of overall tax underreporting
point estimation
Point estimation

represent the overall magnitudes of tax underreporting on the N returns in the population

represent the overall magnitudes of tax underreporting on the n returns in a SRS from the population

represents the mean level of tax underreporting in the population

represents the aggregate level of tax underreporting in the population

Our respective point estimates of the mean and aggregate levels of tax underreporting in the population are:

interval estimation
Interval estimation

The population standard deviation of tax underreporting is defined as:

The interval estimates for the mean and aggregate levels of tax underreporting are, respectively:

how large should the sample be1
How large should the sample be?

Suppose we want our margin of error for the mean level of tax underreporting to be £50, and we believe that is roughly 2,000. Since

, we compute:

Similarly, suppose that there are 1 million taxpayers and we want our margin of error for the aggregate level of tax underreporting to be £50 million. Since , we compute:

stratified random sampling
Stratified random sampling
  • So far, we have considered SRS. However, often it is preferable to use a stratified random sample.
  • One should do so if:
    • Reasonably precise estimates are desired for certain subgroups of the population; or
    • The mean value of the variable of interest is likely to differ substantially across different subgroups
  • For instance, separate sampling strata were defined for employment status (self-employed or not self-employed), return complexity, and region in the Denmark study
estimation with a stratified random sample
Estimation with a stratified random sample

Under stratified random sampling, we divide the population into H distinct strata. The population count within the hthstratum is Nhand the total population count is

The population mean is defined as:

A simple random sample of size nhis drawn from each stratum, and the sample mean for the hth stratum is

This serves as an estimate of the population stratum mean . The estimate of the overall population mean is computed as:


sample weights
Sample weights
  • To simplify computation of sample statistics, one often constructs sample weights, which are defined as the inverse of the sampling rate within a stratum: for all taxpayers i in stratum h
  • So, for instance, the estimate of the population mean is computed as a weighted average over the entire sample:
stratified sampling strategies
Stratified sampling strategies
  • Proportional allocation: sample each stratum in proportion to its size in the population:
  • Optimal allocation: choose stratum sample sizes to maximise precision for a given overall sample size n
    • Suppose the cost of examining a return in stratum h is ch
    • Then the optimal allocation sets
estimating rates vs magnitudes
Estimating rates vs. magnitudes
  • Estimation of rates of non-compliance tends to require a modest sized random sample (1,000 observations or less) for reasonable precision
  • The distribution of the magnitude of tax non-compliance tends to be highly skewed, resulting in a large population standard deviation
    • As a consequence, rather large samples are typically required for adequate precision in estimating magnitudes
model based approaches with random audit data
Model-based approaches with random audit data
  • Under a model-based approach, one specifies a relationship between the variable of interest (non-compliance) and its potential determinants
  • The model generally imposes functional form and distributional assumptions (parametric approach)
  • The quality of the estimates depends not only on the sample design but also the validity of the modelling assumptions
why use a model based approach
Why use a model-based approach?
  • To control for measurement errors, such as:
    • The failure to fully detect non-compliance
    • Conflation of deliberate and unintentional errors
  • To improve one’s understanding of what drives compliance behaviour and to predict future behaviour
  • Potentially, to improve the precision of tax gap estimates (if the underlying modelling assumptions are reasonably valid)
old irs approach
Old IRS Approach
  • Long ago, a study of randomly audited returns from TY 1976 found, with the aid of third party returns not available to the original examiners, that for every dollar of underreporting discovered for certain income items, another $2.28 went undiscovered
  • Based on this study, the IRS routinely applied a “multiplier” of 3.28 to detected unreported sources not subject to third-party reporting when estimating the tax gap
what we see
What we see
  • Random audit studies such as the TCMP and NRP tell us about audit assessments on different sources of income and offsets
  • So, they give us an idea of how much additional tax might be assessed if everyone received a fairly intensive audit
  • They also indicate what sorts of income and deduction items are commonly associated with compliance problems
what we don t see
What we don’t see
  • The objective of tax evasion is to conceal one’s actual tax liability…
  • Not infrequently, this is done so well that examiners are unable to uncover all of the cheating that is present on a return
  • So audit assessments allow us to observe most of the unintentional errors and much of the deliberate cheating that is fairly easy to identify
  • However, they show us only a portion of the deliberate cheating that is hard to uncover
how to measure what we can t see
How to measure what we can’t see
  • Intuitively, some examiners are better at uncovering noncompliance than others
    • Some might be globally superior on all return issues; others may have a comparative advantage on particular issues
  • If we knew the relative abilities of different examiners on a given issue or line item, we could “scale up” what was detected by a given examiner to approximate what the best examiner would have found if (s)he had done the audit
detection controlled estimation dce
Detection Controlled Estimation (DCE)
  • A statistical methodology to account for detection errors on examinations and inspections
  • Original methodology developed by Jonathan Feinstein
    • Rand (1991), J. of Law & Economics (1990)
  • Improved and extended approach for use with NRP data in collaboration with Jonathan
Now suppose we are able to break down the results for each of three examiners who were assigned similar returns:
dce tobit model pdf of
DCE tobit model: pdf of

When A = 0, just like DCE probit case:

Pr(A=0) =

When A>0, p.d.f. is sum of expressions for 2 separate kinds of detection outcomes:

1. Perfect detection:

2. Partial detection: account for all D rates 0 to 1:

The 1/D term in the integral is the Jacobianof the transformation from N to A

extensions of approach
Extensions of approach
  • Model the probability and magnitude of non-compliance using separate equations
  • Account for skewness in distribution of non-compliance
  • Account for role of third-party information reports
  • Employ separate models for each income source
  • Account for cases where an income source was not examined during the audit
  • Separately model the case where an income source has not been reported on the return
  • Pool data from multiple tax years
  • Incorporate results into a micro-simulation model
developing detection controlled estimates
Developing detection controlled estimates
  • The estimated parameters of the DCE model are used to predict the actual level of non-compliance (N) on each return conditional on the detected level (A)
  • These estimates can be aggregated across returns to estimate overall misreporting by income source
  • A tax calculator can be applied to estimates of unreported income to compute the tax gap
  • One can also use the results to derive implicit DCE multipliers
confidence intervals
Confidence intervals
  • Our aggregate estimate of underreported income is


  • Approach 1: Delta method
    • , where
    • G is estimated gradient vector
    • is estimated covariance matrix of
  • Approach 2: Simulation
    • Draw M random samples of parameter vector from a distribution with mean and covariance
    • For each draw, compute an estimate of S
    • Sort the sample values of S and use the ndand 1-nd percentiles as the upper and lower bounds
notes on dce methodology
Notes on DCE methodology
  • Relies on variation across examiners in their performance at uncovering unreported income
    • The method essentially scales up performance of all examiners to reflect what the best examiner would have found
    • Sometimes there are not sufficient examiners who have each audited an income source on a reasonable number of returns. One can do some pooling in such cases
  • To help insure model identification, it is desirable not too have much overlap between the explanatory variable sets XN and XD
  • Use separate equations to describe the probability and magnitude of non-compliance
  • Account for undetected non-compliance
tax gap estimation with operational audit data
Tax gap estimation with operational audit data
  • Operational audits are generally undertaken on returns where substantial non-compliance is deemed likely
  • This creates a classic sample selection problem
    • The audited returns are unlikely to be representative of unaudited returns
sample selection example
Sample selection example
  • During WWII, engineers routinely examined damage to returning bombers
    • They reasoned that those areas that were consistently shot up would benefit from more reinforcement
  • Their concern, of course, was improving the odds that an aircraft would return successfully; yet the sample consisted only of aircraft that did return
  • Abraham Wald insightfully turned the “common wisdom" on its head
how to control for sample selection bias
How to control for sample selection bias
  • Statistical models of sample selection
    • In research for the IRS, I have used this approach to estimate the estate tax gap and also to investigate underreporting of self-employment income
  • Statistical matching
statistical models of sample selection
Statistical models of sample selection
  • The selected sample may differ from the general population in terms of both observed and unobserved characteristics
  • Under this approach, one attempts to account for both the observed and unobserved differences
  • One does this by jointly modelling the determinants of the outcome variable of interest and the sample selection process
estimation issues
Estimation issues
  • It is very important to have at least one regressor in XAthat is excluded from X
  • Results can be sensitive to distributional assumptions, so it is important to evaluate whether the specification is adequate
  • Performance will tend to be better when most returns have at least a small chance of being selected for audit
  • The estimation results may be used to predict, for each unaudited return, the magnitude of non-compliance that would have been discovered if the return had been audited
statistical matching
Statistical matching
  • Attempt to control for observed differences between operational audit sample and unaudited returns
  • No attempt to control for unobserved differences
    • Likely to work best with a detailed data base that includes the most important factors impacting whether a return is selected for an operational audit
  • Often used to evaluate treatment effects
    • But it can be used to impute, say, non-compliance from operationally audited returns to unaudited returns
key assumptions
Key assumptions
  • Let

A = audit indicator (A=1 if audited, 0 otherwise)

N = Non-compliance if not audited

X = set of explanatory variables

1. A|X (conditional independence or unconfoundedness

2. 0 < (common support)

3. X is exogenous (not influenced by A)

relationship between statistical matching and random assignment
Relationship between statistical matching and random assignment
  • Random assignment
    • Distribution of both measured and unmeasured variables balanced across groups
    • Common support condition always holds
  • Matching
    • Only distribution of measured variables balanced across groups
    • Common support condition may fail for some values of X
relationship between statistical matching and regression analysis
Relationship between statistical matching and regression analysis
  • Matching is non-parametric
    • No need to assume functional forms (linearity, additive errors, normality, etc.)
  • Common support requirement avoids the extrapolation problem in regression
    • Identifying effects by projecting into regions where no data points exist
matching approaches
Matching approaches
  • Exact match on X
    • Useful if small number of qualitative variables in X
  • Inexact match on X
    • A distance metric is used to find one or more audited returns that have similar X values to each audited return
  • Propensity score matching
    • Idea is to reduce dimensionality of the problem by matching on a single index:
    • Rosenbaum and Rubin (1963) showed that if

then A|

propensity score estimation approach
Propensity score estimation approach


  • Estimate “propensity score” using probit or logit
  • Match audited and unaudited returns by propensity score
  • Impute a value N to each unaudited return based on the observed value(s) of the matched audited return(s)
propensity score matching issues
Propensity score matching issues
  • Various approaches to match observations
    • Nearest neighbour, caliper, kernel, local linear, etc.
  • Without replacement or with replacement?
    • Without replacement yields lower variation, but at price of higher potential bias
    • Without replacement also sensitive to order in which observations are matched
    • With replacement is preferable if relatively few audited returns are similar to unaudited returns
  • Balancing conditions: want
    • Good to break into 5 or so strata and verify mean values of X within each stratum are similar for audited and unaudited returns
choice based sample
Choice-based sample
  • If the sampling probability depends on whether return was audited (e.g., oversampling of audited returns), one can
    • Perform an unweighted logit analysis to estimate parameter vector
    • Perform an unweighted logit analysis and match observations using the estimated log odds ratio:
  • Alternatively, one can perform weighted logit (or probit) and use usual propensity score
creative and interesting power law application
Creative and interesting power law application
  • Zipf’s Law postulates that the size (S) or frequency of an observation is inversely proportional to its rank (R):
    • It has many applications (size of cities, frequency of words in a book, income rankings, corporation size, number of visits to websites, etc.)
    • It is “power law” relationship (also known as Pareto) and often fits the upper tail of a distribution well
  • Bloomquist, Hamilton, and Pope (2013) fit a size-rank regression to operational audit results to estimate overall non-compliance among very large corporations (over US$250 million)
size rank regression for non compliance
Size-rank regression for non-compliance
  • Excluding some of the smallest operational audit adjustment cases, they fit the regression:

where represents the audit adjustment and

represents the rank of

  • They then use the estimated regression relationship to predict overall non-compliance in the population
possible issues for further exploration
Possible issues for further exploration
  • Zipf’s Law seems unlikely to hold towards the bottom of the size-rank distribution in the population where non-compliance is zero or negative (i.e., overstatements of income)
  • The ranks of observations within the estimation sample will tend to be more concentrated than the ranks of the same observations in the population
    • It is not clear how much this impacts predictions
  • The results may be somewhat sensitive to the chosen adjustment amount threshold for inclusion in the size-rank regression
  • Approach is relatively simple to apply and it accounts the important fact that a relatively small number of extreme cases account for the bulk of non-compliance
  • Approach yields an aggregate estimate
    • It does not facilitate an analysis of the determinants of underreporting
    • In principle, though, one could extend the approach to derive separate aggregate estimates for different income sources or for different categories of corporations (industry, public/private, national/international, etc.)
combining operational and random audit data
Combining operational and random audit data

Ideally, “round out” operational audit with some random audits of untargeted returns (and, ideally, non-targeted issues)

Not selected for Operational Audit

Selected for Operational Audit

issues with operational random sample
Issues with operational-random sample
  • Based on a study I performed for the IRS:
    • Design-based estimation of such a sample is not very promising – one needs a rather large random component to obtain reasonable precision
    • Model-based estimation that incorporates sample weights is known to provide a degree of protection from misspecification. However, weighted estimation adversely impacts precision, especially when weights vary substantially in the sample.
    • Although unweighted model-based estimation can lead to incorrect inferences if the modelling assumptions are invalid, a well-specified model can achieve superior precision in a combined sample with a large number of targeted audits and relatively few untargeted ones.
  • It would seem ideal to integrate random sampling into an operational audit selection program
value of a udit data for targeting non compliance
Value of audit data for targeting non-compliance
  • Random audit findings can be used to devise audit selection strategies
    • NRP and DIF-selection in U.S.
  • Operational audit findings alone are not adequate for developing audit selection criteria
    • Tunnel vision
  • A combined operational-random sample may be a viable alternative
survey discrepancies
Survey discrepancies
  • Surveys that directly ask about tax evasion are not especially useful
    • Although there has been some success with asking about informal sector employment (e.g., Lemieux et al., 1994)
  • Comparison of survey reports on income or expenditure with tax data more promising
    • Informal supplier evasion
    • “Nanny Tax” evasion
    • Non-filers
u s informal suppliers
U.S. informal suppliers
  • The IRS defines informal suppliers as “individuals who provide products or services through informal arrangements which frequently involve cash-related transactions or ‘off the books’ accounting practice”
  • Owing in large part to the lack of a ‘paper trail’ tax non-compliance among informal suppliers can be especially difficult to detect
past irs methodology
Past IRS methodology
  • In the past, the IRS commissioned a special survey of consumer purchases that attempted to assess informal earnings based on reported expenditures on informally supplied goods and services
  • It was not clear how successful this research was in distinguishing informally from formally supplied goods and services
a new approach
A new approach
  • Jim Alm and I took a different approach. Rather than rely on a dubious distinction between formal and informal sales, we identified 12 industries where informal suppliers are prevalent (food vendors, direct sales, construction, landscaping, personal services, etc.)
  • We then compared reported self-employment earnings in these industries from a large national survey to tax return reports from these same industries
  • Our approach attempts to account for all earnings in these industries from self-employment, including that earned through moonlighting
  • Our results yield a higher level of non-compliance in these industries than NRP-auditors were able to uncover through intensive audits of tax returns
  • At the same time, our estimates are somewhat lower than the DCE-adjusted NRP estimates.
    • This makes sense, since some self-employed individuals may not be fully forthcoming about their earnings, even on an anonymous national survey
who s minding the nanny tax
Who’s minding the Nanny Tax?
  • In the U.S. households are responsible for paying various employment taxes when they pay more than a nominal amount for the services of a domestic employee (nannies, housekeepers, home health aides, cooks, butlers, chauffeurs, groundskeepers, etc.)
  • Household employers are required to file Schedule H with their income tax returns to report all such payments
  • Together, federal and state employment taxes amount to more than 20% of domestic employee compensation
compliance study methodology
Compliance study methodology
  • To examine compliance with Nanny Taxes, I used a large national survey to identify individuals who report that their longest job held during the year was from domestic employment in a household
  • Based on their reported earnings from this job, I estimated how many Nanny Tax returns should have been filed
  • The results indicate that only 1 in 4 domestic employers actually file and pay Nanny Taxes, and that in aggregate, only about half of the federal taxes due are actually paid
validation of estimates
Validation of estimates
  • Concerns with the methodology include:
    • Moonlighters are excluded
    • Some domestic workers are likely to be reluctant to report their earnings on the survey
  • As a validation exercise, I used a national consumer expenditure survey to investigate how much household reported spending on in-home child care and house cleaning
    • The results suggest non-compliance is even worse, perhaps as high as 70% of taxes due
individual income tax filing rate estimation
Individual income tax filing rate estimation
  • IRS is interested in measuring the trend in the voluntary filing rate (VFR), defined as the ratio of timely filed required returns to required returns
  • I worked with Alan Plumley and Mark Payne of the IRS to develop an improved filing rate measure
measuring the numerator of the vfr
Measuring the numerator of the VFR
  • To measure the numerator of the VFR, a large representative sample of filed individual returns was analyzed to estimate the number of timely filed required returns
    • Some filed returns are not required
    • In the process of distinguishing required from non-required returns, we discovered that IRS instructions on who must file are incomplete
    • Our findings led to a change in IRS instructions to clarify that the gross income concept for filing purposes disregards all losses
estimation of denominator of vfr
Estimation of denominator of VFR
  • We relied on a large national survey to identify households that appeared to have a filing requirement
  • To address underreporting of certain income sources on the survey, we imputed additional self-employment earnings, pensions, and social security to various households
    • The imputations were based on an econometric analysis of 3rd party reports (for pensions and social security) and tax returns (for self-employment earnings)

The bump in the filing rate in TY2007 coincides with the “Economic Stimulus Payment” (worth $300 per family member), suggesting that this one-time benefit encouraged many ghosts to file a return in that year.

idea to evaluate the determinants of filing compliance calibrated probit
Idea to evaluate the determinants of filing compliance – “calibrated probit”

Tax return data: =1 for all observations i = 1,…,

Survey data: is unknown for all observations j = 1,…,n

Survey weights: (Overall population of filers and non-filers)

Constrained estimation of parameters:

Maximize s.t.

other creative approaches for measuring non compliance
Other creative approaches for measuring non-compliance
  • Searching for non-filers in Jamaica
  • Searching for traces of evasion
    • In consumption behaviour
    • In litter
searching for non filers in jamaica
Searching for non-filers in Jamaica
  • Prior to the 1986 reform, Jamaica had high marginal tax rates, but many credits and loopholes
  • Wage earners were taxed via PAYE withholding, while self-employed were required to file a return
alm bahl and murray 1991 methodology
Alm, Bahl, and Murray (1991) methodology
  • The authors sampled 12,000 names from a master population list based on third-party sources of information (telephone directories, trade association lists, etc.) on workers in 9 industries (service stations, customs brokerages, auto repair, auto parts, hair care, real estate, contractors, transport, beverage and spirits outlets)
  • A similar approach was used to sample 600 professionals (accountants, architects, attorneys, doctors, etc.)
  • The sampled names were matched against Jamaica Income Tax Department records to check filing and withholding status
  • Only 23% of professionals and 11% percent of non-professionals in the selected industries filed a return or had any income withheld
  • Focusing on the non-professionals, assuming that the characteristics of those who filed were the same as those who did not file, the amount of undeclared income was 28.0 percent of reported income, costing the government 38.8 percent of actual income taxes collected
searching for traces of evasion in consumption behaviour
Searching for traces of evasion in consumption behaviour
  • Since consumption behaviour tends to be closely linked to income, the idea is to infer underreporting of income in cases where consumption appears to be excessive in relation to income
    • Pissarides and Weber (1989)
    • Feldman and Slemrod (2007)
    • Fu (2008)
pissarides and weber 1989
Pissarides and Weber (1989)

Assume food expenditures and wages are reported accurately on national survey, but not income from self-employment

Estimate a consumption function:

where lnY = reported income

SE = dummy variable for self-employment

Z = demographic controls

Data source: 1982 Family Expenditure Survey – diary records for food consumption used

Actual SE income could then estimated as exp( (the actual analysis they use is a bit more complex)

  • The estimated coefficient of the SE dummy () is about 0.10, while the estimated mpc () is roughly 0.25, implying that actual self-employment income is about exp(.10/.25)=1.5 times as large as the reported amount (33% underreporting)
  • Possible issues
    • The self-employed may be more prone to eating out, buying meals for their clients, etc.
    • What the self-employed report as earnings on a survey may be different than what they report on their tax returns
feldman and slemrod 2007
Feldman and Slemrod (2007)
  • Apply a similar approach to measure tax evasion in U.S. by self-employed, but with charitable donations used in place of food expenditures
    • Since charitable contributions are only reported by itemizers, authors have to control for price of giving in their analysis
  • The data source is a large public use sample of federal individual income tax return data (both cross-sectional and longitudinal)
  • The key assumption is that self-employment status does not impact the true propensity to make donations
fu 2008
Fu (2008)
  • Instead of “inverting” a consumption function to predict true income, Fu searches for discrepancies between income reported on Canadian individual tax returns and an imputed measure of overall consumption and savings
  • Data sources
    • Regression on Survey of Household Spending (SHS) used to develop prediction formulae for consumption and savings
    • Prediction formula applied to Survey of Financial Security (SFS) to impute consumption and savings
      • SFS already has detailed information on income reported on tax returns
consumption regression
Consumption regression

Total household consumption regression:

where Z = common consumption sources on the2 surveys

X = demographic factors, reported income, mortgage

to income ratio, and rent to income ratio

Separate approaches attempted with and without including durable consumption

  • Even just imputing $8/day for food, clothing, and transportation on top of ongoing expenses in SFS implies 8% of wage earners and 20% of self-employed have an income statement discrepancy
  • Using SHS to impute consumption yields an estimated incidence of underreporting of 25% for non self-employed and 60% for self-employed (higher if durable consumption is included)
  • Income measure in two data sources may differ; not clear how this impacts imputations, which include income as an explanatory variable
  • Method assumes that consumption and savings self-reports are accurate
  • Imputations at the individual level likely to be rather noisy
    • Some sensitivity analysis was done
searching for traces of non compliance in litter
Searching for traces of non-compliance in litter
  • In 2007, state and local cigarette taxes in Chicago in were $2.68 per pack higher than in neighboring counties and over $3.10 higher than in the bordering state of Indiana
  • Cigarette packages are required to have tax stamps affixed to them to demonstrate that required taxes have been paid
  • Smokers in Chicago have incentives to purchase cigarettes from lower tax jurisdictions directly or from smugglers and/or Native American reservations
merriman 2010 methodology
Merriman (2010) methodology
  • Students worked in teams to find and collect littered cigarette packs in randomly selected representative tracts in Chicago and some neighbouring locations
  • The location of each pack was logged along with information about the presence or absence of tax stamps from different jurisdictions
  • 75% of sampled cigarette packs from the Chicago area did not have a Chicago tax stamp (indicating the packs were purchased from other lower tax counties or states, or from contraband suppliers)
  • The share of packs with a Chicago tax stamp was lowest in Chicago neighbourhoods close to the lower cigarette tax state (Indiana)
  • More generally, regression analysis indicated that the share of Chicago tax stamps in a location was negatively associated with the distance to a lower tax jurisdiction and with the level of tax savings
selected empirical approaches
Selected empirical approaches
  • Econometric models using random audit data
  • Aggregate panel data on tax reporting by state/jurisdiction, supplemented by socio-economic variables
  • Lab Experiments
  • Field Experiments
  • Agent-Based Models
econometric models using random audit data
Econometric models using random audit data
  • NRP Study Findings
    • Tax rates, income: hard to identify in a cross-section; Feinstein (1991) pools 2 years and finds tax rate positively related to non-compliance and income not significant
    • Tax Preparers: Klepper et al. (1991) find preparers enforce unambiguous tax rules and exploit ambiguous ones; Erard (1993) finds preparers (especially CPAs and attorneys) are associated with greater non-compliance
    • Prior Audits: Erard (1992) finds weak evidence that audits positively impact future reporting behaviour
    • Demographics: elderly less likely to cheat; married more likely
aggregate panel data findings
Aggregate panel data findings
  • Dubin et al. (1990), Plumley (1996), Dubin (2007) find very large general deterrent effect of audit rates
  • Plumley, Erard, and Snaidauf (2011) find predictions sensitive to specification decisions:
    • Trend vs. year dummies
    • Time period
    • Dynamics
lab experiments
Lab experiments
  • Can test theoretical predictions/hypotheses in a controlled setting
    • Isolate a particular factor to change, holding all other factors constant
  • However, the test is somewhat weak in that setting is artificial (external validity is unclear):
    • Salience: hard to capture moral and social influences, real world costs and benefits – I might cheat on taxes in a lab setting (just a game from my perspective), but much more inclined to be honest in actual practice
lab experiment findings
Lab experiment findings
  • Many studies by Alm et al. on myriad of factors
  • Impact of some key factors on compliance:
    • Tax rates -
    • Audit rates + (modest)
    • Fine rates + (small)
    • Positive inducements +
    • Vote over use of tax revenue (public good) +
  • Replication of experiments across different countries indicates that cultural factors/experience impact behaviour
field experiment slemrod et al 2001
Field experiment: Slemrod et al. (2001)
  • Randomised field experiment in Minnesota – treatment sample told in advance their returns would be “closely examined”; DIF-in-DIF analysis of reported taxes before/after treatment
    • Low and middle income/high opportunity groups big increase reported taxes
    • High income/high opportunity group results “perverse”
dif in dif approach
DIF-in-DIF approach

 =


of the




t = -1

t = 0

t = 1



field experiment kleven et al 2011
Field experiment Kleven et al. (2011)
  • Denmark: large scale (40,000 taxpayers) randomised field experiment; DIF-in-DIF on reported adjustments to income on pre-populated returns
    • Case 1: Threat of audit letters sent to a treatment group
      • Significant improvement in reporting of self-reported income (income not subject to 3rd party reports)
    • Case 2: Randomly audited and non-audited taxpayers in 2007 investigated for change in reported income in subsequent year
      • Significant improvement in compliance associated with prior audit in 2007
agent based models abms
Agent-Based Models (ABMs)
  • Bloomquist (2012) simulates tax compliance within a large community of taxpayers, employers, and tax preparers
  • Assumes certain behavioral rules for the various “agents”
  • Allows communication among social networks
  • One simulation experiment involves testing impact of alternative audit selection strategies on taxpayer reporting. The results illustrate that targeted audits tend to be more effective at improving compliance
  • Strengths: allows analysis of complex social interactions and behaviors that are not analytically tractable
  • Weakness: Little existing evidence to guide behavioral rules practiced by different agents