Office of Tax Analysis

Technical Paper 12

May 2023

U.S. Treasury Individual Income Tax Model

Robert Gillette, Siva Anantham

Will Boning, Michael Cooper

Rachel Costello, Julie-Anne Cronin

Portia DeFilippes, John Eiler

Geoff Gee, Kye Lippold

Ithai Lurie, Ankur Patel

OTA Technical Papers is an occasional series of reports on the research, models, and data sets 

developed to inform and improve Treasury’s tax policy analysis. The papers are works in 

progress and subject to revision. Views and opinions expressed are those of the authors and do 

not necessarily represent official Treasury positions or policy. OTA Technical Papers are 

distributed in order to document OTA analytic methods and data and invite discussion and 

suggestions for revision and improvement. Comments are welcome and should be directed to the 

authors. OTA Papers may be quoted without additional permission.
U.S. Treasury Individual Income Tax Model

Robert Gillette,

1 Siva Anantham

Will Boning, Michael Cooper

Rachel Costello, Julie-Anne Cronin

Portia DeFilippes, John Eiler

Geoff Gee, Kye Lippold

Ithai Lurie, Ankur Patel

May 2023

All authors, U.S. Department of the Treasury

This paper provides a detailed description of Treasury’s Individual Income Tax 

model (ITM). The ITM is the central model used in the analysis of individual tax 

liabilities under current law and any proposed changes to current law. Building, 

maintaining and continually improving this model as new data and modeling 

techniques become available is the task of the Economic Modeling and Computer 

Applications Staff of the Office of Tax Analysis.

Any taxpayer data used in this research was kept in a secured Treasury or IRS data repository, 

and all results have been reviewed to ensure that no confidential information is disclosed.

1 Robert Gillette: Office of Tax Analysis, U.S. Department of the Treasury, Robert.Gillette@treasury.gov
1. INTRODUCTION

The staff of the Treasury Department’s Office of Tax Analysis (OTA) has the dual responsibility 

of forecasting Federal tax receipts and of analyzing the revenue, distribution, and other 

economic impacts of tax legislation. The analysis of a proposed change in the tax law must 

answer many questions, such as: how tax revenues will change in future years; how the change 

is likely to affect the distribution of tax burdens or the distribution of income after tax; how 

efficiently the change will operate in achieving its objective; and what effect the change is likely 

to have on private economic decisions. One of the most useful tools developed, maintained, 

and employed by OTA to estimate and evaluate individual income taxes is the Individual Income 

Tax Model (ITM). 

The ITM is used for many types of analyses including the following: 

Estimating Revenue Effects for Proposed Tax Changes. To examine the effects of a single tax 

provision or set of tax provisions, the ITM simulates two tax regimes (normally referred to as 

Plan X and Plan Y) that only differ by the provision or set of provisions being examined. Thus, 

the ITM estimates tax liability and various tax values (such as the number of taxpayers claiming 

certain itemized deductions and the level of those deductions) under Plan X and Plan Y and the 

change in tax liability and tax values. Plan X does not need to be current law, so that, for 

example, the ITM can be used to estimate the additional revenue effect of a particular 

provision in a multi-provision proposal.

Estimating Interactions Among Provisions. It may be important to estimate the 

interrelationships between various individual income tax provisions in a proposed tax change or 

under current law. Because of the interactions between provisions, a revenue estimate for 

multiple provisions, each estimated separately, will not necessarily add up to the revenue 

estimate for all provisions estimated simultaneously. For example, changing tax rates will affect 

the values of deductions, and changing the levels of deductions will affect the amount of 
2 

revenue generated by the rate structure. Using the ITM, an analyst can estimate the revenue 

change from the change in statutory rates alone and from the change in the level of deductions 

alone and then also estimate the combined effect of changing both statutory rates and the level 

of deductions.

Sensitivity Analysis. Often, an important consideration in policy analysis is how responsive the 

tax system is to certain tax parameters. Using the ITM, the analyst can determine the change in 

tax liabilities due to a change in a tax parameter. The analyst may also be interested in the 

sensitivity of the tax system to economic variables. For example, the analyst can get a sense of 

how interest rates affect certain tax variables by adjusting interest income and interest expense 

items.

Estimates of Average Marginal Tax Rates. One of the most useful attributes of the ITM is its 

ability to estimate average marginal tax rates. To obtain marginal tax rates, the Federal income 

tax liability under a given tax regime is calculated for each return on the ITM. Then, the value of 

an income source is increased by a small amount (usually one percent). The ITM recalculates 

the tax liability for each return and the change in tax associated with the change in income. The 

tax and income changes are summed over all returns, and their ratio computed to give the 

average marginal tax rate for that income source. This gives a rate that is weighted by the 

amount of the particular income source appearing on each return. Alternatively, the marginal 

tax rate for each return can be multiplied by that return’s sample weight. This provides an 

average marginal tax rate that is weighted the number of returns (or the number of returns 

with that particular type of income).

Distributional Analysis. The ITM is also used extensively for distributional analysis.1 For 

example, policymakers may be interested in how individual income tax liabilities, and changes 

in these liabilities are distributed among the population. Standard ITM output includes the 

distribution of tax liabilities across adjusted gross income (AGI) class for tax units (including 

1 See Cronin (2022) for a discussion of Treasury’s Distributional Analysis Methodology and Distribution Model 

(DM). The DM is an extension of the ITM. The ITM can be used alone for certain types of distributional analysis, 

such as those based on AGI.
3 

current non-filers). An additional feature of the ITM is that it can associate “parent” returns in 

the Individual and Sole Proprietorship (INSOLE) sample with the returns of their dependents 

who file. The dependent filers included directly in the INSOLE are then replaced with these 

“dependents-of-INSOLE” filers to avoid double-counting. This option allows constructing

distributions of tax liabilities across families of associated tax units. Because the ITM uses 

microdata, the effects of tax reform can be seen on almost any subgroup of the population that 

is adequately represented in the sample (such as elderly tax units or tax units with children). 

Estimating Winners and Losers. A common policy question that arises with any tax reform 

proposal is who would win and who would lose if the proposal were enacted. A winner is 

usually defined as a tax return or family that pays less tax, while a loser is a return or family that 

pays more tax. The model can also estimate the number of returns or families who are 

removed from the tax rolls (tax liability changes from positive to non-positive) and the number 

who were previously non-taxable but must pay some tax under the proposal.

2 Standard ITM 

output includes the number of winning returns, number of losing returns, and the number of 

unaffected returns. The output also includes the number of tax returns who are either removed 

or added to the income tax rolls.

Analysis of Other Taxes. The ITM is also used to analyze other taxes, such as the levels and 

distribution of Federal payroll taxes, and Federal estate and gift taxes. 

Special Cross-Tabulations. The ITM’s use of microdata also allows cross tabulations to be made 

on any set of variables before and after a tax change. Frequently, the analyst may want to know 

how a particular subgroup of the population fares under a tax proposal. The analyst often 

wants information on the levels of certain variables before and after the proposal (e.g., the 

level of medical expenses deducted). The ITM is a highly flexible tool for addressing such 

questions.

The first version of the ITM was built in 1963. Since then, there have been over 20 versions of 

the ITM with a new version being released approximately every three years. During this period, 

2 The ITM includes a non-filer sample. The methodology for non-filers is discussed in Section 2. 
4 

the ITM has been used to analyze and estimate the effects of thousands of proposed changes 

to the tax code. The staff at OTA continue to improve the ITM as new data and modeling 

techniques become available. To capture a relatively settled version of the model, this 

document describes the version of the ITM based on returns for Tax Year 2016 that was used 

for the Fiscal Year 2021 to Fiscal Year 2023 budgets.3

In general, the ITM is comprised of five main components, each of which is discussed in detail in 

separate sections of this paper. Summaries of each section are given below. 

Section 2: Population. To capture the full revenue and distributional effects of current and 

potential tax policies, the ITM population aims to include all those who could have individual 

income tax or payroll tax liability or who could receive individual income tax credits. The ITM 

represents the population with stratified random samples of both tax filers and families or 

individuals who do not file (non-filers). The filer sample is based on the Individual and Sole 

Proprietorship (INSOLE) data file prepared by the Statistics of Income Division of the Internal 

Revenue Service. The non-filer sample is chosen using a sampling design that mirrors the 

sampling design of the INSOLE. The non-filer sample is reweighted to match the mix of 

demographic characteristics of non-filers identified in matched Census CPS-tax return data. For 

the 2016-based ITM, the non-filer sample is then reweighted again to reflect a non-filer count 

derived from tax data and information provided by the Social Security Administration (SSA).

4

Section 3: Data. This section discusses the tax and non-tax variables used to estimate tax 

liabilities. This data includes variables available on the INSOLE file, data directly matched from 

information returns such as wage splits for joint filers, data directly matched from other 

sources, such as age from social security records, and data that is imputed or extracted using 

3 More precisely, this document reflects changes made to the 2016-based ITM through calendar year 2022. In 

2022, OTA began development of a version of the model based on data from Tax Year 2019, which was used in 

preparing the Fiscal Year 2024 budget estimates. Several areas of the 2019-based model are in active development 

as of early 2023, including the population represented, deduction imputations, and health insurance coverage 

information. This document describes the more stable 2016-based version of the ITM. 4 The non-filer count targets for future years used in extrapolation are derived from a modified version of the 

Social Security Area Population (SSAP) forecast from SSA. The 2019-based ITM replaced the use of microdata to 

estimate non-filer totals for the base year with the base year modified SSAP.
5 

various sources such as itemized deduction levels for non-itemizers. 

Section 4: Extrapolation. To estimate the future effects of tax laws and tax law changes as well 

as to forecast individual income tax receipts over the ten-year budget window, the ITM 

extrapolates the level and distribution of income, deductions, and other tax variables to future 

years. 

Section 5: Estimating Tax Liabilities. The ITM’s tax calculator is a computer program that can

simulate changes in tax liabilities arising from changes in any of the underlying variables or 

parameters. The overall program can be conceptually divided into three steps. In the first step, 

the program sequentially reads the data file of income tax returns. In the second step, the 

program uses a set of tax calculators to determine a series of tax values for each return. These 

values are aggregated and retained for the third step of the program, which prints the values in 

tabular and/or spreadsheet form. Included in this section are OTA’s estimating assumptions for 

running the model, including assumptions concerning compliance, feedback effects, and 

behavior. 

Section 6 concludes. 

2. ITM POPULATION

2.1 The Ideal ITM Population 

To support estimates of the revenue effects and distributional impacts of a broad range of 

individual tax policies, the ideal ITM population would represent everyone liable for Federal 

individual taxes or eligible for Federal individual credits, as well as their dependents. For 

analysis of reasonably likely alternative tax policies, the ITM population would ideally also 

include people who would be liable for Federal individual taxes or eligible for Federal individual 

credits under those policies. 

Common uses of the ITM include people who do not currently file tax returns (non-filers), so 
6

non-filers would be included in the ideal ITM population. Income and payroll taxes are withheld 

from non-filers’ wages. Changes to refundable credits or the standard deduction could change 

who files, while distributional analysis aims to include all US families regardless of whether they 

file.

One exhaustive description of the ideal ITM population is:

1. All U.S. citizens, regardless of where they live. 

2. All non-citizens, regardless of immigration status, who live on a long-term basis in the 

U.S.

3. Non-citizens who do not live in the U.S. on a long-term basis but who have U.S.-source 

income.

2.2 Departures from the Ideal Population

The 2016-based ITM departs from the ideal population to balance providing accurate estimates 

against data and modeling challenges. While the model captures all people who file or are 

claimed as dependents on tax returns, the non-filing population used for this version of the ITM 

is limited to individuals in families who would have been required to file if they had sufficient 

income and who lived on a long-term basis in the 50 U.S. States or the District of Columbia (plus 

armed forces abroad). The ITM population thus excludes two groups of non-filers regardless of 

total income: residents of U.S. territories who do not file Federal income tax returns, and 

foreigners without Social Security income who have US-source income but do not file Federal 

income tax returns. These groups are excluded because modeling responses of these non-filers 

is technically challenging (given their lack of connection to the existing tax system), and their 

responses are not relevant to most tax reforms (which do not focus on changes to taxation in 

territories or abroad). Considering how best to model these groups is one of several areas in 

which OTA is working to improve the ITM.

2.3 Constructing Microdata to Represent the Population

The microdata that represent the population are constructed using the 2016 Individual and Sole 
7 

Proprietorship (INSOLE) file to represent filers and a supplemental sample to represent nonfilers. 

Filers. The 2016-based ITM uses the 2016 INSOLE file to represent filers. This file represents 

148.6 million filed returns (including dependent returns) and 290.4 million people.

Non-Filers. As detailed in Appendix I, OTA uses information returns and records of births and 

deaths provided by the Social Security Administration to IRS to estimate that the total non-filing 

population for 2016 was approximately 39.5 million people.

5 Demographics for the non-filing 

population are estimated from U.S. Census linked Current Population Survey - tax data. 

As Appendix II explains in greater depth, OTA constructs records on the ITM that represent nonfilers from a sample of non-filers who appear on information returns. This sample is then 

reweighted to match the total count and estimated demographics of the full population of nonfilers, including those who do not appear on information returns. OTA identified 95,000 

potential non-filing Continuous Work History Sample (CWHS)6 records. Removing those who 

would likely not have a filing obligation reduced this sample to 40,000 records. OTA then used 

2016 Form 1095 data to construct the tax-unit (family) structure for this sample. However, only 

75 percent of the sample had a 2016 Form 1095 and Form 1095 does not always contain

information on marital status. As a result, certain records for singles were paired to create 

additional joint non-filers. In the end, 34,000 unweighted tax units were reweighted to 

represent the 39.5 million people (31.5 million tax units) that OTA estimates were non-filers in 

2016. 

2.4 The Target Population Total: Adjusted Social Security Area Population

To account for population growth and demographic change between the base year and each 

year in the budget window, the ITM uses a target population. The 2016-based ITM target 

5 The 2019-based version of the ITM instead uses an adjusted version of the Social Security Area Population to 

estimate the number of non-filers in the base year. 6 The CWHS is a random sample of individuals included in the INSOLE file if they file. Selection is based on the last 

four digits of their social security number.
8 

population is an adjusted version of the Social Security Area Population (SSAP) forecast 

provided by the Social Security Administration (SSA).

7 SSA produces population projections for 

the SSAP8, which includes everyone living in the 50 U.S. States and the District of Columbia 

(including U.S. armed forces overseas, who are treated as though they live in the States), U.S. 

citizens living abroad, non-citizens living in U.S. territories, and non-citizens living abroad who 

are insured for Social Security benefits. Compared to the ideal population, the SSAP is too 

narrow because it does not include all non-residents with potential U.S. tax liability. The SSAP is 

also broader than the population used for the 2016-based ITM because it includes people living 

in U.S. territories who do not file Federal income tax returns, so OTA adjusts the SSAP to 

remove them. The population totals by age are used in the extrapolation routine described in 

Section 4 below. 

3. DATA

ITM data includes individual income tax data sent by the taxpayer to the IRS (Form 1040), 

information returns which include SSNs sent by other entities to the IRS, data linked by SSN 

from the Social Security Administration (e.g., date of birth and death), and data imputed from 

other sources such as the Survey of Consumer Finances. 

3.1 Base Year Tax Data

As discussed in Section 2, the tax data sample is the 2016 INSOLE, which is also used to prepare 

the SOI tabulation of tax return statistics, “Individual Tax Returns” or IRS Publication 1304. The 

ITM weights this sample to represent the filing population in each year. 

Generally, the INSOLE is a stratified random sample. At the heart of the sample is a purely 

random component, known as the Continuous Work History sample (CWHS). The last four digits 

7 The 2014-based version of the ITM used estimates of the U.S. resident population from the Census Bureau, but 

the SSAP is closer to the ideal ITM population. The 2019-based model in use for the FY2024 budget continues to 

use the SSAP for extrapolation. 8 See “The 2016 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and 

Federal Disability Insurance Trust Funds,” table V.A2: https://www.ssa.gov/oact/tr/2016/index.html. 
9 

of an individual’s SSN are randomly assigned by SSA. The CWHS are drawn from 10 unique 4- 

digit endings. Any individual with one of the ten 4-digit endings is included in the INSOLE 

sample every year. The sample is then stratified by income and other characteristics to ensure 

coverage of a broad range of tax situations. Strata that would otherwise have low 

representation using only the CWHS data are oversampled and the weights for these individuals 

are lower. In general, the CWHS returns have weights of 1,000 and the highest income 

individuals have weights of 1 (all are included in the sample). More information on the sample 

design and underlying data can be found on the SOI website.9 

3.2 Data and Imputations from Information Returns

The ITM incorporates data from numerous information returns associated with the taxpayers in 

the INSOLE file. While there are differences in how information return types are incorporated 

into the ITM, there is a general procedure common to all of them:

1) Information returns are matched to the 1040 using a record identification number 

assigned to the tax return and related documents by SOI at the return level and SSNs 

(including ITINs) at the individual level.

2) To the extent aggregate amounts do not match, the 1040 amounts are assumed to 

represent the true values and the information returns are used to allocate amounts 

among individuals on the return (such as splits between primary and secondary 

filers) and also to add details (e.g., how many information returns per person).

3) Where needed, OTA makes ad hoc adjustments, such as dropping duplicates and 

adjusting or deleting implausible values. The exact techniques used vary by 

information return.

9 SOI can be found at https://www.irs.gov/statistics. The 2016 sample documentation is at 

https://www.irs.gov/pub/irs-soi/16indescofsample.pdf. 
10

Certain information returns are used to create variables that are needed for detailed analysis 

using the ITM. These include information returns related to earnings, Social Security benefits, 

retirement benefits and education benefits. Each is discussed below.

Wage Splits. The INSOLE data report the combined wages of both the primary and secondary on 

a return, whether or not both have earnings. Individual wages are needed to calculate payroll 

taxes, retirement contributions, and dependent care benefits. The following procedure 

describes how Form W-2 data is used to allocate total taxable wages reported on Form 1040 

(WAS) between wages earned by the primary taxpayer (WASP) and wages earned by the 

secondary earner (WASS), for returns of married couples filing jointly: 

For all returns without a spouse present (i.e., all non-joint returns) WASP=WAS and WASS=0. 

For notation purposes, the sum of taxable wages earned by the primary as reported on Forms 

W-2 is W2P; the corresponding value for the spouse is W2S.

W2P and W2S amounts are determined based on SSN matches from the Form 1040 sample to 

Forms W-2. Any duplicates are dropped, and W-2 fields are aggregated across all unique 

employee-employer pairings. The two aggregated employer W-2s (per taxpayer) with the 

highest-wage are retained on model, with all aggregated box details. The majority of 1040 wage 

dollars (97%) is captured by the top two highest-wage W-2’s per taxpayer.

For married filing jointly tax returns, the W2P and W2S amounts are used to determine their 

wage split. This wage split is applied to the 1040 wage value (WAS).

Most of the 1040 wage dollars not captured by W2P + W2S, 1.7% out of the total of 3%, are 

from returns with no corresponding Form W-2s found. For these returns, the wage split 

between the primary and secondary is imputed. The first stage of the imputation is a probit to 

determine the likelihood of having a secondary worker; this is based on total taxable wages, 

number of dependents, and age of youngest taxpayers. If a secondary worker is likely, a logit 

regression determines their ratio of primary versus secondary earnings. For any return that is 

not married filing jointly or determined to be unlikely to have a secondary earner, all WAS is 

attributed to the primary taxpayer.
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Social Security Benefits. The ITM also uses data available from the SSA-1099 and RRB-1099 

information returns to allocate gross Social Security payments (SSINC, which includes both 

Social Security and Railroad Retirement benefits) into four subcategories for the primary 

taxpayer, as well as the secondary taxpayer if the tax unit is married and both spouses receive 

forms 1099. These categories are (1) Social Security retirement benefits, (2) Social Security 

disability benefits, (3) Railroad Retirement benefits, and (4) Railroad Retirement disability 

benefits. The following procedure explains how the gross benefits are allocated:

The Form SSA 1099s matched to the Form 1040 sample are slotted into the four categories 

outlined above, based on their Payer ID and trust fund code. This match accurately captures 

94% of SSINC. For 6% of SSINC reported, 1099s exist but do not aggregate to the same total 

declared on the 1040. For this population, the categories are calibrated to match SSINC while 

maintaining their respective ratios found on existing 1099s. For the remaining <1%, an 

imputation is performed, using the 94% of sample of taxpayers successfully matched to 1099s, 

to determine the probability that a taxpayer has a given benefit, based on AGI and ages.

Retirement Contributions. The ITM uses data available on Form 5498 and Form W-2 (deferred 

compensation) to maintain information on both the primary and secondary taxpayers’ 

contributions towards individual retirement accounts. This information includes Roth Individual 

Retirement Account (IRA), Traditional IRA, SEP, Simple, and defined benefit contributions, as 

well as their fair market values and any rollover amounts. The following outlines the process 

used to clean this data:

All Forms 5498 and W-2 are matched to the sample based on record identification numbers and 

SSNs. Duplicate, amended, and corrected returns are cleaned and aggregated by taxpayer and 

tax return. Form 5498 box details include excess contributions, rollovers, and conversions. 

There are clearly defined rules on contribution limits depending on the type of account and 

taxpayer characteristics, such as age. The tax law for the given year is applied to the aggregated 

data to more accurately capture contributions separate from the other amounts listed above. 

For example, if the maximum Roth contribution for an individual is $5,500 and the individual 

reports a contribution of $6,000, the contribution is reduced to $5,500 to account for the 
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excess contribution reported.

Higher Education. Using a combination of information from the Form 1098-T information 

return, as well a supplementary information from the National Postsecondary Student Aid 

Study (NPSAS) and the Integrated Postsecondary Education Data System (IPEDS), the ITM

creates information pertaining to a student’s estimated tuition and grants related to higher 

education, undergraduate versus graduate status, class year, and institution information. The 

process of creating this data is as follows:

The Form 1098-T is matched to the Form 1040 sample based on SSNs, and the top two forms 

for highest qualified tuition are retained. Qualified tuition being defined as the maximum of 

payments received and amount billed on a given 1098-T. Using an IPEDS dataset, information 

pertaining to the institution is merged onto each Form 1098-T. Using a combination of the halftime and graduate indicators on the Form 1098-T, as well as educational tax benefits claimed 

on the 1040, each student is given a corresponding half-time and graduate status. 

For SSNs with evidence of student status on the Form 1040 but missing a Form 1098-T, halftime and graduate status is imputed based on probabilities constructed from NPSAS and tax 

return characteristics. In addition, institutional information is imputed from the IPEDS dataset.

For all students, a class year imputation is performed, based on data provided by NPSAS as well 

as AGI, dependency status, educational tax benefits claimed, and half-time and graduate 

indicators.

Lastly, based on information reported on Form 1098-T and on Forms 8863 and 8917 attached 

to Form 1040, an estimate of qualified tuition and gross grants received is constructed. For 

those students without a Form 1098-T, an imputation is performed based on the NPSAS data, 

educational tax benefit claimed, dependency status, AGI, as well as half-time and graduate 

indicators.

Other Information Returns. The ITM uses information based on the following additional 

information returns, with minimal cleaning:
13

• Form 5498-SA: Contributions to a Health Savings Account (HSA), Archer, Medicare & 

Choice Medical Savings Account (MSA) 

• Form 1099-SA/MSA: Distributions from an HSA, Archer MSA, or Medicare Advantage 

MSA

• Form 1099-Q: Payments from Qualified Education 

• Form 1098: Mortgage Interest Statement

• Form 1098-E: Student Loan Interest Statement

• Form 1099-R: Distributions from Pensions, Annuities, Retirement or Profit-Sharing Plans, 

IRA, Insurance Contracts

3.3 Imputations

Some tax proposals are concerned with demographic, income, or deduction items that are not 

part of the income tax structure that existed in 2016 or did not appear on particular tax returns 

for various reasons. Analysis of proposed tax changes concerning these items using the ITM

requires imputing missing data to individual tax returns. OTA imputes age, itemized deductions 

for non-itemizers, health coverage for all units, and wealth for all units. Each imputation is 

discussed in detail.

Date of Birth, Age and SSN for Work. Many tax provisions and proposals include age 

requirements or require that an individual or dependent have an SSN that is valid for work. OTA 

imputes age and checks SSNs using a file that includes all valid SSNs and Taxpayer Identification 

Numbers, dates of birth, and dates of death that is maintained by the Social Security 

Administration and provided to IRS. 

Imputation of Itemized Deductions to Non-Itemizers. Changes in tax law may lead individuals 

who do not itemize deductions in the base year to itemize deductions. To model such changes, 

the following itemized deductions are imputed for non-itemizers: 

• Total medical expenses, 

• State and local income taxes, 

• Real estate taxes, 
14

• Personal property taxes, 

• Total home mortgage interest expenses, 

• Investment interest expenses, 

• Total charitable contributions, 

• Fully deductible miscellaneous expenses, 

• Miscellaneous expenses that are subject to the 2% AGI floor, and

• Total casualty and theft losses.

A key problem encountered when imputing itemized deductions is the lack of information 

about the behavior of the non-itemizing population. The methodology employed by OTA 

assumes that the non-itemizing population behaves no differently than the itemizing 

population. In addition, the imputation assumes that itemized deductions expressed as a share 

of non-negative AGI have a multivariate normal distribution truncated at zero. Given these 

assumptions, a version of the expectation-maximization (EM) algorithm can be used to 

estimate the levels for non-itemizers. The EM algorithm iterates between forming an 

expectation of the missing values and then calculating the maximum likelihood estimate of the 

imputation model given the previously formed expectations. This application of the EM 

algorithm was originally presented as one technique for imputing missing at-random data and 

developed by Little and Rubin (1987) in their work on missing data.

There are, however, several additional refinements used for the non-itemizer imputations. 

First, dependent filers (tax filers who are claimed as a dependent by another tax return) are

assumed to have zero expenses and excluded from the imputation process. Second, since not 

everyone has all forms of itemized deductions, the presence of a specific itemized deduction for 

a non-itemizer is determined by an indicator vector whose values are determined by an 

"equivalent" itemizer. A hot deck procedure is used to determine equivalence within an AGI 

class. Returns from states without an individual income tax are assigned no state and local 

income tax.

10 Similarly, returns from states without personal property taxes are assigned no

10 State is determined using the INSOLE state code.
15

personal property tax.

Next, imputed values of home mortgage interest are overwritten using Form 1098 Mortgage 

Interest Statements (nonitemizers receive these information returns). Also, the total number of 

returns with a home mortgage interest expense is reduced to match the number of 

owner-occupied houses with mortgages reported in the American Housing Survey (AHS).11

Further, any non-itemizer with home mortgage interest expense is also imputed a real estate 

tax value. The number of returns imputed a real estate tax value is also restricted so that the 

total number of returns with real estate taxes, including itemizers, equals the number of 

owner-occupied houses in the United States as reported in the AHS. The dollar amounts are 

adjusted to equal the total amount of real estate taxes paid as reported in the AHS.12 Finally, 

the age distribution of homeowners and mortgage payers is adjusted to match data reported in 

the AHS.

The imputed amounts of charitable contributions and state and local income taxes are also 

adjusted to match aggregate forecasts. In the case of charitable contributions, imputed 

amounts for non-itemizers are adjusted so that total charitable contributions (itemizer plus 

non-itemizer) match the amount reported by Giving U.S.A. The imputed amounts of state and 

local income taxes are adjusted to match values reported by the U.S. Census Bureau’s Annual 

Survey of State and Local Government Finances.

Finally, since the itemized deductions for non-itemizers must (under the assumption that 

taxpayers optimize) be less than the standard deduction, the total imputed value of itemized 

deductions is adjusted to fall below the level of the standard deduction. A value between 1/2 of 

the standard deduction and the full standard deduction is randomly assigned to each 

non-itemizer. If the initial value of deductions is greater than the standard deduction, then each 

deduction is reduced, pro-rata, so that the new total equals the assigned value.

11 Some taxpayers receive a Form 1098 for mortgage interest paid on rental property. Returns reporting mortgage 

interest expense on Schedule E (rental), Schedule C, or Schedule F were dropped first.

12 The AHS does not directly report the total amount of real estate taxes paid on owner-occupied housing units. 

This can be estimated from the AHS table “Monthly Cost Paid for Real Estate Taxes”.
16

Health Insurance Coverage and Premiums. Beginning with tax year 2015, all insurers (including 

self-insured employers, private insurers, and government entities) are required to report 

information about each enrollee’s health insurance offers and coverage to the enrollee and the 

IRS using Form 1095 information returns. There are three forms in the 1095 series: Form 1095-

A "Health Insurance Marketplace Statement," Form 1095-B "Health Coverage," and Form 1095-

C "Employer-Provided Health Insurance Offer and Coverage." Individuals may receive more 

than one form in this series. OTA uses the information on these forms to assign a type of 

insurance coverage to each individual on the ITM. The coverage types are Marketplace, 

uninsured (no indication of coverage on the 1095 series), employer-sponsored coverage, nongroup private coverage outside the Marketplace (off-exchange), and Medicare or other public 

coverage. 

Marketplace premiums are imputed using information from Forms 1095-A and 8962 (Premium 

Tax Credit). Employer sponsored insurance premiums are imputed using months of coverage 

from Forms 1095-B/C and premium data from Form W-2 (where large employers are required 

to report the total premium for policies provided to employees each year). Appendix III 

provides more information on these imputations.

Wealth.OTA imputes wealth to each tax unit on the ITM. This part of the ITM program is 

referred to as the Wealth Module (WM). The primary uses of the WM are to forecast estate tax 

liability and to conduct policy analyses involving the estate tax and the taxation of wealth and 

unrealized capital gains more generally. The WM imputes SOI estate tax data and Survey of 

Consumer Finance data to the ITM. The SOI estate tax data covers all decedents who had a 

filing requirement, generally high wealth estates. The SCF data provides wealth information for 

tax units below the estate tax filing threshold. The WM imputes for each tax return on the ITM 

values of assets (namely, stocks, bonds, other financial assets, real estate assets (other than 

home values), business assets, retirement assets (other than IRAs), and other assets), liabilities 

(namely, mortgage debt and other debt), unrealized capital gains. Home values are imputed by 

grossing up real estate taxes using local property tax rates. Information returns provide the fair 

market value of IRAs. Appendix IV provides more information on the WM.
17

Pass-Through Income. Income for certain business entities, namely partnerships and Scorporations, is passed through the entity and taxed at the individual level. The pass-through 

entity must file a Form K-1, either a Form 1065 (partnership) or a Form 1120-S (S-corporation) 

with the IRS. These forms are matched by Employer Identification Number (EIN) and SSN to the 

tax units on the ITM. For individuals with more than one source of pass-through income, up to 

10 partnership and up to 10 S-corporation returns are attached to the individual return.

Appendix V provides more information on this imputation.

4. EXTRAPOLATION

To accurately forecast the effects of proposed changes in the tax code, the ITM is extrapolated 

to future years. Currently, OTA generates an extrapolated database for every year in the budget 

forecast. The extrapolated databases depend on assumptions about economic growth. 

4.1 General Approach

As discussed in Gillette (1989), there are two approaches by which cross-sectional tax data can 

be extrapolated. The database can be reweighted so that the individual variables on each tax 

return are adjusted together in order to achieve some set of aggregate and/or distributional 

targets. Reweighting changes the number of tax returns represented by each return in the 

database. Alternatively, the individual variables on the database can be adjusted with varying 

growth factors to match a set of economic or demographic targets. 

The reweighting approach has the advantage of preserving significant correlations between the 

various items on a return, such as the likelihood of owning a home and having retirement 

income and children. The multiple growth factor approach has the advantage of allowing the 

composition of income or itemized deductions to vary over time; it also allows the means of 

particular variables to vary over time. 

OTA’s current approach is a hybrid of the reweighting and multiple growth factor approaches. 

For example, when the sample is extrapolated over ten years, a 35-year-old married man with 
18

two children and no sources of income other than wages and interest in the first year (call him 

record 1 with weight x) still represents a 35-year-old married man with two children and 

income solely from wages and interest in the tenth year (still record 1 but now with weight y). 

However, because we allow for differential growth factors, record 1 may have a different ratio 

of wages to interest in the tenth year relative to the first year. 

The sections that follow detail the targets and formal procedure used in the ITM’s hybrid 

approach. 

4.2 Targets

OTA typically conducts two major budget exercises per year: the Administration’s Annual (or 

winter) Budget and the Midsession Review. Each budget exercise’s window is generally ten 

years beginning the year after the current fiscal year and the extrapolation is updated for each 

exercise to account for the latest economic forecast. The Office of Management and Budget 

(OMB) provides OTA with an economic forecast of income levels, employment, inflation levels, 

interest rates, and other important macroeconomic variables for each budget exercise. 

The ITM also requires forecasts of tax-relevant macroeconomic aggregates not included in 

OMB’s economic assumptions. For example, the ITM requires taxable interest, while the OMB 

provides total interest. Each target is forecast using the OMB assumptions, population 

projections from the SSA, and historical data on the target variable and variables in the OMB 

assumptions. 

The tax-relevant aggregate forecasts are called targets, because the ITM’s extrapolation 

procedure is constrained to hit these targets in each year of the forecast. There are 84 targeted 

variables including: 

35 Return (or Individual) Count Targets Including: filing status (4 classes), age (11 classes), total

exemptions, elderly exemptions, AGI over $1 million (4 classes), returns with interest income, 

returns with sole proprietor income, returns with AGI under certain poverty thresholds (3 

classes), insurance statuses (6 classes), returns with health savings accounts, returns with 
19

unemployment compensation, and returns with self-employed unemployment compensation. 

49 Dollar Amounts Targets Including: total wages, total qualified dividends in AGI, total 

nonqualified dividends in AGI, total interest, total pensions in AGI, total unemployment 

insurance compensation, total Social Security income in AGI, total sole proprietorship income, 

total net positive Schedule E income (4 sources of income), total net negative Schedule E 

income (4 types of income), total positive capital gains by income class (9 income classes), total 

modified AGI by income class (15 income classes), total tax exempt interest, total discharge of 

mortgage debt, total ESI premiums, total non-filer income (5 sources of income) and total selfemployed unemployment compensation.

4.3 Procedure

The extrapolation process consists of two stages. The first stage adjusts items on a tax return 

whereas the second stage adjusts a return’s weight to hit aggregate yearly targets based on 

OMB and other forecasts. Stage I imposes growth factors that reflect per-capita real and 

inflationary growth on a set of dollar items in the database. Stage II reflects more complicated 

trends by adjusting the weights of each return to hit target amounts for a selected set of 

variables, while minimizing a nonlinear loss function where large changes in weights cost 

disproportionately more than small ones. The net effect of this process ensures that the ITM’s 

extrapolated database is consistent with forecasted aggregate economic measures such as 

national income, inflation, and population. 

In Stage I, dollar variables on the database are adjusted for per-capita growth. The various 

income, deduction, and credit items on each return are multiplied by factors based on 

per-capita growth rates estimated from OMB’s economic forecasts. We allow differential 

growth rates for income variables where growth has historically varied across the income 

distribution. For example, if we expect average wage income to grow by 10% and we expect 

high-wage returns to capture most of that growth, then we apply different factors across the 

wage distribution to meet those two beliefs about the future economy. For the 2016-based 

ITM, we adjust dollar values by one of roughly 40 growth factors. 
20

Following Stage I, Stage II begins by directly adjusting the weights with growth factors reflecting 

expected changes in return counts by filing status. Stage II then recalculates the ITM’s 

endogenous variables. These variables are transformations or combinations of other variables 

such that the tax return is internally consistent and consistent with the tax law. For example, 

after growing individual dollar fields the ITM recalculates adjusted gross income for the tax 

return. Alternatively, it might limit the contribution to a retirement account, such as a 

traditional IRA, to reflect that year’s tax law. 

Stage II then adjusts the sample weights so that all income and demographic targets are 

simultaneously achieved. The targets, as listed above, are variables likely to impact distribution 

and revenue estimates. Additional or alternative targets are possible and often discussed. 

However, OTA research has shown that adding additional targets does not necessarily improve 

the extrapolation (Gillette 1989). Also, adding more targets will eventually lead to nonconvergence of the extrapolation routines. The extrapolation process is akin to inflating a 

balloon, with the targets forcing the balloon to fit a certain shape. Adding targets leads the 

balloon to bulge in an unconstrained dimension. These bulges may prove more problematic 

than the original justification for the additional target.

With several hundred thousand records and a limited number of targets, there is no unique 

solution to the problem of adjusting the weights to hit the extrapolation targets. The problem 

amounts to solving a number of linear equations equal to the number of targets, where the 

number of independent variables equals the number of records in the INSOLE file. Clearly, some 

criterion must be developed for choosing one of the many solutions. The ITM’s criterion is 

stated in terms of an objective function, whose arguments include the new sample weights. 

Simply stated, the new weights are chosen to hit the targets while minimizing the objective 

function. 

The convergence algorithm is summarized as follows. Let the targets be represented by t(j)(j=1,

..., N), where N is the number of targets. In addition, let w(i) be the original sample weight (i=1,

..., M), where M is the number of returns, let s(i, j) be the amount of the j-th targeted item on 
21

the i-th return and let (x(i)*w(i)) be the new weight. Thus, x is the ratio of the new weight to the 

old weight.

The problem is to minimize, by choosing the x(i)’s, the objective function,

∑=

Φ

M

i

ixiw

1

))((*)( , 

subject to the constraints

( ) )(),(*)(*)(

1

jtjisiwix

M

i

∑ = =

for each target t(j) (j=1,...,N). 

This is achieved by introducing Lagrange multipliers λ(j) (j=1,...,N) and seeking an extremum for 

the Lagrangian:

∑ ∑ = =

= −Φ

N

j

M

i

zjixiwP

1 1

λ *)())((*)( , 

where,

( ) )(),(*)(*)(

1

jtjisiwixz

M

i

= ∑ − =

. 

The partial derivatives of P are:

( ) )(),(*)(*)( )( 1

jtjisiwix j

P

M

i

= − ∂

∂ ∑= λ (1)

(for each j), and
22















 −Φ= ∂

∂ ∑=

N

j

jisjixiw ix

P

1

),(*)())(('*)( )( λ (2)

(for each i). 

Setting these equal to zero gives a set of simultaneous nonlinear equations, one for each target 

and one for each return, which can be solved for the x(i)’s and λ (j)’s. The first step in the 

solution is to use the group of equations to express the x(i)’s in terms of the λ(j)’s. 

For each i, setting the partial derivatives in (2) equal to zero implies:

0),(*)())(('

1

−Φ ∑ = =

N

j

λ jisjix . 

Solving for x(i) yields:















 Φ= ∑=

− N

j

ix jisj

1

1 λ ),(*)()'()( . 

Setting the partials derivatives in (1) equal to zero and substituting the above values for the 

x(i)’s results in: 

0)(),(*)(*),(*)()'(

1 1

1 =−





























 ∑ ∑ Φ = =

− jtjisiwjisj

M

i

N

j

λ (3)

(for each j).

This is a set of N equations that can be solved for λ(j). Then the x(i)’s from the equation can be 

determined given a specific distortion function Φ.

The following distortion function was chosen:

( ) 2 44 −+=Φ − xxx . 
23

There are many possible distortion functions that could be chosen, but functions of this class have 

several desirable features:

( ) =Φ 01 , 

so there is no distortion when the weight is not changed. Further,

Limox ( ) x x Lim∞ ( ) x ∞=Φ=Φ , 

so weights too far from 1 are not tolerated. Finally,

( ) Φ=Φ ( ) 1 xx , 

so the distortion function is symmetric with respect to both increases and decreases in the 

weights (i.e., it is as distorting to multiply a weight by 4 as it is to divide it by 4).

Unfortunately, the resulting system of equations is, in general, nonlinear and cannot be solved 

explicitly. For the particular choice of Φ the system cannot even be written explicitly, as (Φ’)-1

cannot be expressed in terms of simple functions. Still, OTA has written a fairly general 

algorithm for calculating numeric solutions to the distortion equation specified. The user 

specifies the function Φ, whereupon the machine constructs tables of values for Φ, Φ’, and 

(Φ’)-1. Any further reference to Φ is interpreted in terms of the table of values.

The algorithm begins with a set of initial guesses for the λ(j)’s. The initial value of each λ(j) is 

1.0. Then the left sides of the equations in (3) are computed, which requires one pass through 

the file of returns. At the same time, the Jacobean matrix is computed (which shows the effects 

of small changes in the λ(j)’s on the values of the left sides of the equations). With this 

information it is possible to select an improved guess for the λ(j)’s for use in the next pass. 

Normally, five to ten iterations will be sufficient to enable the algorithm to converge on the 

targets within the limit of accuracy of the computer.

The process of convergence is interesting to follow, since the left sides of the equations 
24

represent the amounts by which the targets will be missed if the process is stopped with the 

current values of the λ(j)’s. Thus, while the λ(j)’s converge on their correct values, one can 

watch the entire file converge on its targets. In general, if convergence problems are 

encountered in applying the algorithm, it is generally the result of the target forecast being 

inconsistent and alternative targets are chosen 

The final output of Stage II is a data file that contains a new return weight for each record on 

the file. A different file is created for each extrapolation year and for each set of growth factors 

and targets.

5. THE INDIVIDUAL INCOME TAX MODEL PROGRAM

The ITM consists of tens of thousands of lines of code in Python, Stata, SAS, and Fortran. The 

core tax calculator is written in Fortran and submitted via Python, while Python 

(Numpy/Pandas), Stata, and SAS are used to produce the input files for the ITM. Output tables 

are provided both as text (log files) and Excel spreadsheets. A standard ITM run spanning the 

budget window (10 years) will take 2 to 3 minutes to run while more complex runs such as 

those producing marginal tax rate tables can take 5 to 7 minutes.

The sections that follow present the major components of the ITM program. The first section 

briefly describes the overall design of the ITM program. We then discuss the operating 

assumptions used in ITM runs and the general limitations of the program. 

5.1 ITM Program Design

A typical ITM run compares two tax regimes of tax parameters and code that we label Plan X 

and Plan Y. Plan X is a baseline chosen for comparison. Typically, this is the tax law currently in 

effect. Plan Y represents the proposal or alternative that OTA wishes to simulate. For most 

proposals, the number of differences between Plan X and Plan Y is small in relation to the total 

number of tax parameters in Plan X. The program takes advantage of this fact by setting the 

default to be the case where no differences exist between Plan X and Plan Y (i.e., Plan X = Plan 
25

Y). This assumption normally simplifies the model preparation for the user, who has only to 

specify how Plan Y differs from Plan X.

An ITM flowchart is depicted in Figure 1. On the left is a high-level overview of the process 

broken into three steps: (1) calculating tax parameters such as rates and income breaks for the 

relevant years, (2) looping over tax families13 to process return- and family-level data, and (3) 

summarizing/printing the simulation’s results. Moving to the right, the second step is broken 

out into more detail. A tax family consists of the primary non-dependent tax return plus any 

returns filed by dependents on that return. The right side of Figure 1 shows two loops over the 

family’s returns. The first loop is primarily concerned with loading the INSOLE and 

administrative data that references a particular base year (2016 as of this document) and 

adjusting it to target a year. The targeting during the first loop assumes a continuation of the 

tax law as of the base year. The second loop applies data adjustments that reflect behavior 

from tax law enacted after the base year, simulates a proposal’s tax behavior, and tallies results 

at the return level. Processing a family in two loops allows tax behavior across returns in the 

family; e.g., choices in the nondependent return affect the dependent returns. 

At the heart of the ITM are two versions of the tax calculator, one each for Plan X and Plan Y. 

Each calculator takes information from each potential tax-filing unit in the data file and 

calculates that unit's Federal individual income tax liability under the appropriate tax plan. 

While most fields are taken directly from tax and information returns with an adjustment to 

move the data from the base to target year, the tax calculator also computes the values of 

several variables that affect tax liability. Note that the calculator does not endogenously 

determine total levels of capital gains (or losses), IRA contributions, or Social Security income. 

The calculator only determines the portion of these items included in AGI. 

13 A tax family consists of all of the family members that file on one tax return.
26

Figure 1: ITM Flow Diagram

Loop over 

returns in the 

tax family

Calculate Tax Parameters

Read in tax and information return 

Adjust and create variables

Extrapolate data to target year

Read/calculate baseline behavior

Calculate Plan X

Calculate Plan Y

Tabulate return data

Loop over 

returns in the 

tax family

Loop over 

all tax 

families

Print Results and Tables
27

5.2 Modeling Assumptions

To make the modeling tractable, the ITM calculator makes several assumptions. These 

assumptions are discussed below. Of note, the ITM is only one tool that analysts use to 

estimate a response to tax changes. Analysts are aware of the ITM assumptions and limitations 

and can change the assumptions or make off-model adjustments to the ITM output.

Optimization. The ITM assumes all filers choose tax options that minimize their Federal

individual income tax liabilities. The model does not include state calculators and does not 

optimize the sum of state and Federal income taxes. Note that to the extent that certain 

taxpayers appear eligible but do not claim certain credits under Plan X, the tax model flags 

these individuals as not taking the credit and would not, generally, switch them under Plan Y. 

However, analysts may decide to model a change in take-up if appropriate for a specific 

proposal. 

Compliance. The ITM assumes taxpayers are compliant and have correctly reported their 

income and expenses. The information given by the taxpayer on their tax form is assumed to be 

accurate and is used by the tax calculator. While the IRS automatically checks for certain errors 

and the INSOLE file is edited to address inconsistencies within the tax form, the INSOLE is not 

generally a post-audit file. 

Compliance Costs. The ITM assumes that compliance costs are zero. For example, it assumes 

that taxpayers who take the standard deduction would have total itemized deductions below 

the standard deduction amount. It does not allow a taxpayer to choose not to itemize because 

of the added effort required to itemize deductions. This simplifying assumption avoids the 

challenges involved in modeling the relationship between compliance costs and tax rules. When 

considering a proposal with significant compliance costs, the analyst may choose to make an 

“off-model” adjustment to the ITM output to reflect the compliance costs.

Feedback Effects. Estimates for years after the year of the sample data are inherently less 

reliable than estimates for the year of the data. Given the representativeness of the sample, 

the estimates will be valid under the assumption that the proposal under analysis has no 
28

significant feedback effects on important variables exogenous to the ITM (e.g., the level and 

distribution of income and itemized deductions). Clearly, the degree to which data can be 

assumed exogenous depends on the nature of the proposal, e.g., taxation of all realized capital 

gains as ordinary income is much more likely to have feedback effects than changes in the zerobracket amount. Even when feedback is suspected, however, ignoring it is often a useful

starting point.

Behavioral Responses. The ITM incorporates “micro” behavioral responses to changes in the tax 

code but does not include behavioral responses that would change the macroeconomic 

forecast. It automatically applies tax minimizing choices like the decision to itemize., On 

occasion, the analyst may explicitly define a behavioral response to a particular change in the 

tax code. For example, the ITM can use specified price and income elasticities of charitable 

giving to model how a particular change in the tax code affects charitable contributions. 

Similarly, estimates using the ITM can use price elasticities to adjust the level of capital gains 

realizations in response to changes in the tax rate on capital gains. The ITM also considers 

responses that do not expand or contract GDP, but merely change the level of taxable income.

For example, if a proposal increases premiums for employer-sponsored health insurance (which 

is excluded from taxable wages), the model holds total compensation (wages plus health 

insurance premiums) fixed but captures the fact that taxable compensation and thus tax 

revenue will be lower under the proposal.

5.4 Program Limitations

The tax calculator is quite robust and can trace through most interactions between any income 

source and the various provisions of the tax code. However, it does have limitations. These 

include:

Certain Missing Calculations. The ITM calculator does not simulate the effects of 

changes in tax law on several small but important provisions in the tax code. Among 

these are state and local tax refunds, the foreign tax credit, certain general business 

credits, and depreciation expenses. The ITM takes the values of these variables as given, 
29

though changes in these variables may be captured by other OTA models or off-model 

and then provided to the ITM as inputs. 

Certain Missing Behavioral Responses. The calculator does not capture changes in 

individual behavior in response to changes in disposable income or prices. For example, 

the ITM does not by default capture changes in charitable giving due to changes in tax 

rates or incomes. Such changes are usually captured by making off-model adjustments, 

although the ITM is sometimes used to apply a behavioral adjustment on an ad hoc 

basis. 

Imputation Errors. Simulations often require imputed data (data not contained on 

original tax returns but necessary in computing tax liability under one or more plans). 

Although every effort is made to correctly impute data items, errors are unavoidable. 

Within any simulation, variables containing imputed data will interact with other 

variables in the model. To the extent that imputation errors were made to one or more 

variables in some systematic way, the results of simulations will be biased. 

Missing Dynamics. Many of the imputations for non-itemizers are based on values of 

variables on tax returns such as AGI. For example, the imputation for state and local 

income tax deductions is based, in part, on AGI. Therefore, these imputations should be 

adjusted when the base variables change. For simplicity, such adjustments are not 

made.

While these limitations are easy to identify, they are difficult to correct within the ITM. These 

limitations, however, may be corrected much more easily "off model." That is, if the analyst 

believes the ITM does not accurately portray the effects of a tax law change, they may adjust 

the output provided by the ITM. 

6. CONCLUSION

As discussed in this paper, the ITM is the central model used by the Office of Tax Analysis to 
30

analyze individual tax liabilities under current law and any proposed changes to current law. In 

addition to the ITM, the office also maintains corporate tax models, a foreign tax model, a 

depreciation model, tax receipts models, and a distribution model (Cronin 2022). Building, 

maintaining and continually improving these models as new data and modeling techniques 

become available is the task of the Economic Modeling and Computer Application (EMCA) Staff 

of the Office of Tax Analysis. 

As tax provisions have expanded to cover more economic situations, the EMCA staff has added 

modules to the ITM. Modules for health, wealth, education, and retirement have become more 

sophisticated over time, allowing analysts to better understand the interrelationships among 

new and existing provisions and to present more detailed analysis. 

OTA has also been expanding the ITM to include weighting schemes to represent Federal tax 

liabilities by state (Fisher and Lin 2015) and to represent tax liabilities by race and ethnicity 

(Fisher 2023, Cronin, DeFilippes and Fisher 2023). Understanding tax liabilities by state and by 

race and ethnicity allows OTA to answer a broader array of questions regarding the fairness of 

tax burdens.
31

APPENDIX I: ESTIMATING THE SIZE OF THE ITM POPULATION FOR 2016

This appendix describes how OTA estimated the total size and non-filer demographics of the 

2016 population used for the 2016-based ITM.

The 2016 Individual and Sole Proprietorship (INSOLE) file represents 148,606,578 filed returns 

(including dependent returns) and 290,404,266 people (being sure to not double count 

dependent filers). Only 144,168,019 of these returns were filed for tax year (TY) 2016 or 2015 

(representing 282,561,164 people). All the other 4,438,559 returns (and 7,848,102 people) 

were filed for prior tax years (1999 through 2013). The ITM assumes that these prior year 

returns represent future late filers for TY 2016. For example, TY 2015 returns filed during 

processing year (PY) 2017 (when the 2016 INSOLE was compiled) are a proxy for TY 2016 

returns that were expected to be filed in PY 2018. Because these prior year returns proxy for 

future late filers, care is needed to avoid double-counting late filers.

The basis for the ITM’s non-filer sample is a database containing the population of information 

returns.

14 OTA identified Continuous Work History Sample (CWHS) Social Security Numbers 

(SSNs) with information returns for TY 2016 that were not present on the 2016 INSOLE file. OTA 

also requires that each non-filer was not present on a 2016 tax return as of the construction of 

the 2016-based ITM in the spring of 2019 and that each non-filer does not have a recorded date 

of death prior to 2016. About 36,488,000 non-filing individuals were identified as non-filers 

using this data and methodology (assuming a weight of 1,000 for each person). A detailed 

outline of the steps used to construct the 2016 non-filer file is provided in Appendix II.

Combining the INSOLE population with the non-filer population yields a total tax-based 

population of 326,897,000. This population estimate double counts certain non-filers and omits 

others (those who do not appear on information returns). The rest of this section will focus on 

the double count problem that results from having a group of returns on the INSOLE file that 

proxy for people who file a return in PY 2016 or later. 

14OTA uses several information returns to construct non-filers: Forms W-2, 1099-SSA, 1099-INT, 1099-DIV, 1099-

MISC, etc.
32

Many of the prior year filers on the 2016 INSOLE also file a TY 2016 return in the 2016 INSOLE. 

People on prior year returns that do not also file a 2016 return are not double counted because 

these SSNs are all excluded from the SSN list used to generate the non-filer sample. Essentially, 

these prior year returns on the 2016 INSOLE represent themselves as future late filers for TY 

2016. People on prior year returns that also file a 2016 return cannot represent themselves and

must instead represent other non-filers who are expected to eventually file a late return for TY 

2016. Because these SSNs were included in the SSN list to generate the non-filer sample, these 

people/returns represent the portion of the already sampled 36,488,000 non-filers that we 

expect to eventually file a return in future processing years. As a result, the 36,488,000 nonfilers need to be reduced to account for these prior year returns that also file a 2016 tax return 

on the 2016 INSOLE. 

Out of the 4,438,559 prior year returns (7,848,102 people) on the 2016 INSOLE, 3,281,167 also 

filed a 2016 return (5,752,199 people). This implies that the non-filer sample is too large by 

5,752,199 people. This suggests a total ITM population of 321,145,067. To represent the correct 

population total, the weight applied to non-filer records in the CWHS sample is reduced from

1,000 to 842.

OTA used population data following the method of Heim, Lurie, and Pearce (2017) to obtain 

upper and lower bounds that provide a check on the estimate of the total 2016 ITM population. 

This method identifies 318,283,000 people who appear on a 2016 tax return or information 

return in the population data. This count is a lower bound because it may not contain some 

dependents or spouses who did not appear on TY 2016 tax returns or information returns as of 

the construction of the 2016-based ITM in 2019 but who would appear on late-filed TY 2016 tax 

returns filed after 2019.

15 Upper bound estimates of the number of such dependents and 

spouses come from late-filed returns from pre-2016 tax years contained in the 2016 INSOLE. 

There are about 2,445,000 such dependents and 1,080,000 such spouses. These estimates are 

an upper bound because some such dependents and spouses appear on 2016 information 

15As was the case with the INSOLE-based population counts outlined above, the CDW-based methodology also 

misses people who do not appear on tax returns or information returns.
33

returns and thus are already included in the lower bound count. Adding these additional 

dependents and spouses to the lower bound gives an upper bound for the total population 

appearing on tax returns or information returns of 321,808,000 people. The total 2016 ITM 

population estimate of 321,245,067 is between the upper and lower bound estimates obtained 

from this method.
34

APPENDIX II: IDENTIFYING AND CONSTRUCTING 2016 NON-FILERS

The 2016-based version of the ITM models a non-filer population that consists of individuals 

who did not file an individual income tax return but who would have had an individual income 

tax filing obligation if they had sufficient income.

16 Many, but not all, such individuals have 

income and payroll tax withheld from wages reported on Form W-2. The 2016-based model 

creates this non-filer population in four steps. The first step assembles a pool of potential nonfiling individuals to represent all non-filers in 2016. The second step narrows that pool to 

exclude those who may be deceased, may have filed after the INSOLE sample of filers was 

constructed, and who should not appear in the non-filer population for other similar reasons. In 

the third step, the pool of representative individuals is formed into tax return units (adding 

spouses and dependents where appropriate). The final step weights the sample to represents 

the estimated demographics and total count of non-filers. 

Step 1: Identifying Potential Non-Filers. The Continuous Work History (CWHS) sample forms the 

purely random component of the tax filer sample (INSOLE file). The non-filer sample follows the 

same random design.

CWHS individuals include anyone with one of 1 of 10 4-digit SSN endings. For example, for SSN 

xxx-xx-yyyy, yyyy is the 4-digit ending. There are 10 unique, unvarying values for yyyy that are 

followed over time and make up the CWHS sample. Anytime a CWHS individual files a return in 

any year, they are included in the INSOLE. Because the last four digits of an SSN are randomly 

assigned, the CWHS records form a purely random sample, each record represents 1,000 filers; 

has a weight of 1,000 (10 of 9,999 possible 4-digit endings, since SSA does not assign 0000 

endings). 17

16 The 2016-based ITM also limits the non-filer population to those living on a long-term basis within the 50 U.S. 

States and District of Columbia or in the armed forces abroad. The scope of the population of non-filers to model is 

an area of active model development in the 2019-based ITM. 17 The INSOLE file also includes an oversample of certain low probability returns, such as those with high income. 

This is done to improve the estimates of tax provisions which would otherwise have too small a sample from which 

to get a reliable estimate. Thus, the INSOLE is a stratified random sample. Certain low probability strata are over 

oversampled. The sample of taxpayers with 1 of the CWHS ending digits forms the base and random oversampling 

fills out each strata to achieve an efficient number of unweighted returns in each strata.
35

All potential members of the non-filer sample will likewise have 1 of the 10 4-digit SSN endings. 

Thus, the sample that represents non-filers uses the same sampling design as the sample that 

represents filers. If an individual has one of the CWHS ending digits and interacts with the tax 

system either by filing an individual income tax return, or by receiving or being present on an 

individual income tax return or an information return, then they will be part of the ITM 

sample.18 

To find CWHS records that did not file but might have had a filing obligation if they had 

sufficient income, OTA assembles a pool of records for all potential non-filers gleaned from two

data sources: 

1) SOI-provided information returns for those with CWHS ending digits and,

2) A TY 2016 file constructed by OTA using the population of Forms 1095. 

The first source contains 307,000 records for approximately 92,000 unique SSNs that were not 

associated with an individual income tax return filed for 2016. Over 50 types of information 

returns were included in the information returns population data from SOI in 2016 and all were 

used to search for potential non-filers. Most records meeting the criteria were from the 

following types of information returns: W-2 Wage and Tax Statements, 1095-B Health 

Coverage, 1099-B Proceeds from Broker and Barter Exchanges, SSA-1099 Social Security Benefit 

Statement, 1099-INT Interest Income, and 1099-R Distributions from Pensions, Annuities, IRA. 

The second data source, the population of Forms 1095, identifies CWHS individuals who were 

not the recipient of a Form 1095 (health insurance coverage form) but were listed as covered 

on a Form 1095 received by someone who was not in the CWHS.

19 This source identifies an 

additional 3,000 potential non-filers.

18 The ITM represents people who do not appear on information returns by increasing the weights applied to nonfilers who appear on information returns to represent the full estimated total population of non-filers. 19 The population data also contain some Forms 1095 provided to CWHS members that do not appear in the SOIprovided information returns file, perhaps because the 1095s arrived after the SOI file was constructed. 
36

In total, the initial pool contains around 95,000 potential non-filing individuals. 

Step 2: Refining the Sample. OTA narrows the pool of potential non-filing individuals to those 

likely to meet the population definition used for the 2016-based ITM. The reasons individuals 

are removed from the pool and approximate counts are:

1. Drop those who appear as a primary or secondary filer on a Tax Year 2016 Form 1040 in 

the population data as of the construction of the 2016-based ITM in calendar year 2019. 

These are late filers captured by the population data but not the INSOLE (4,000 records).

2. Drop those who appear as dependents on a Tax Year 2016 Form 1040 in the population 

data as of calendar year 2019 (35,000 records). 

3. Drop those whose SSNs are not verified in information on SSNs, dates of birth, and dates 

of death provided to the IRS by the SSA (2,000 records). 

4. Drop those with a date of death before 2016 (5,000 records).

5. Drop those whose date of birth is after 2016, who were older than 105 years, or who 

are missing a date of birth (less than 500 records)

6. Drop those whose date of birth indicates they are younger than 19 (4,000 eliminations) 

7. Drop those who appear to be foreign residents (appear on Form 1042-S or 8288-A) (less 

than 500 records).

8. Drop those who appear to be residents of Puerto Rico, the U.S. Virgin Islands or another 

U.S. Territory (2,000 records)

9. Other (2,000 records)

After these refinements, the sample contains 40,000 records. 

Step 3: Forming Tax Units. OTA uses Forms 1095 (A, B, and C) to form tax units (add secondary 

filers and children). Forms 1095 provide SSNs and names of covered family members. This 
37

matches approximately 75% of the non-filer records to a Form 1095, and thereby approximates 

filing status (single, joint, or head of household) and the number of dependents. OTA also 

attaches information returns, such as Form 1098-T information forms, using the population 

data and ages from the file provided by the SSA to the attached secondaries and dependents. 

This information is used to exclude people who appear on the same Form 1095 but would not 

be dependents for tax purposes (such as children age 19-25 who are not students). 

Unfortunately, some Forms 1095 do not show spouses (such as those filed for Medicare 

recipients), and 10,000 individuals in the non-filer sample do not have Form 1095s. OTA 

imputes joint filers to a fraction of these returns by “marrying” individuals, assigning a share of 

single returns to instead be spouses on other returns. 

After adjusting the totals for these “marriages”, there are about 34,000 total non-filer tax units.

Step 4: Targets and Weights. As described in Appendix I, OTA’s estimate of the total 2016 ITM 

population contains 39.5 million people and 31.5 million families not represented by the 2016 

INSOLE. The demographics of these non-filers were estimated from U.S. Census Current 

Population Survey data linked to tax returns. From these estimates, the non-filer population 

contains 1.8 children (ages 0 to 18) and 2.0 million dependents of any age. Even after 

“marrying” some individuals, the non-filer sample contained too few joint and head of 

household non-filers and too many single non-filers relative to the estimated demographics and 

total ITM population. OTA corrects this imbalance by multiplying the weight on joint and head 

of household tax units by 1.5 and the weight on single tax units by 0.9. 

Table A1 shows counts of unweighted non-filer records and weighted non-filer tax units, nonfiler dependents, and non-filer primary and secondary filers over the age of 65 by filing status 

and dependents, by filing status and age, and by family size. Most non-filers are single. Few 

have dependents. This pattern is consistent with the greater incentives to file (even when not 

required to do so) that much larger refundable credits provide to families with children than to

low-income households without children. Around a third of non-filer tax units have a primary 

filer over age 65, consistent with lower income among retirees and the exclusion of some Social 
38

Security income from filing requirements. 

Table A1

Non-filers in 2016 

ITM

Unweighted

Non-Filer 

Records

Non-filer 

units

(weighted) 

(millions)

Non-filer

Dependents

(weighted)

(millions)

Non-filer 

Primaries

Age 65+

(weighted)

(millions)

Non-filer 

Secondaries

Age 65+

(weighted)

(millions)

All 34,000 31.5 2.0 11.0 1.7

By Filing Status and Dependents

Single, no dep. 27,000 24.5 0 9.3 0

Joint, no dep. 6,000 5.7 0 1.7 1.7

Joint, with dep. * 0.4 0.7 ** **

HoH, with dep. 1,000 0.9 1.2 ** 0

By Filing Status and Age

a Single, <65 17,000 15.2 0 0 0

b Single, 65+ 10,000 9.3 0 9.3 0

c Joint, both <65 4,000 4.1 0.7 0 0

d Joint, one 65+ 1,000 0.6 ** .3 .3

e Joint, both 65+ 1,000 1.4 ** 1.4 1.4

f HoH, <65 1,000 0.8 1.2 0 0

g HoH, 65+ * ** ** ** 0

By Family Size

Family size 1 27,000 24.5 0 9.3 0

Family size 2 6,000 6.2 0.6 1.7 1.7

Family size 3+ * 0.4 0.6 ** **

*Less than 500 unweighted

**Less than 50,000 weighted

“HoH” is “Head of Household” filing status
39

APPENDIX III: HEALTH MODULE

The health module of the ITM estimates health insurance coverage to model a tax unit’s 

changes in tax liability arising from changes to health-related tax provisions, such as the 

Premium Tax Credit (PTC) for Marketplace coverage and the exclusion of employer-sponsored 

insurance (ESI) from taxable compensation.

Coverage Assignments

Beginning with tax year 2015, all insurers (including self-insured employers, private insurers, 

and government entities) are required to report months of health insurance coverage to 

enrollees and the IRS using Form 1095. Although the 2016 ITM mostly includes people who filed 

for tax year 2016, the base data for the model uses all taxpayers who filed in processing year 

2017, some of whom filed for earlier years. OTA used Form 1095 coverage information from 

2016 for taxpayers who filed tax year 2016 returns, and year 2015 coverage information for all 

other taxpayers. The coverage of the tax units for the model is merged from OTA’s populationlevel health insurance coverage data, as described by Lurie and Pearce (2021).

OTA’s measure of coverage is based on a hierarchical assignment of coverage on a monthly 

basis. We used the following hierarchy: Marketplace, employer-sponsored coverage, non-group 

private coverage outside the Marketplace (off-exchange), public coverage (Medicare, Medicaid, 

VA healthcare, and other public sources), and uninsured (no indication of 1095 coverage). As 

noted by Lurie and Pearce (2021), the number of uninsured people using the Form 1095 

measure alone is much higher than in survey data. However, there is an indicator on the Form 

1040 for 2016 where some people without Form 1095 coverage report having full year 

coverage (to claim an exemption from the individual mandate penalty that was in effect at that 

time). Instead of imputing coverage to those individuals to try and match survey information,

we assign those people into a separate coverage group called “unverified” coverage. Not having 

third-party reported information about coverage for those people suggests that even if they do 

truly have coverage, it is somewhat different from people who have coverage reported on a

1095. The unverified coverage group represents about 26 million person-years of coverage in 
40

2016. Other coverage totals include 156 million in ESI, 7.6 million in off-exchange coverage, 101 

million in public, 25.8 million uninsured and 9.9 million people in marketplace coverage. 

It is important to note that Form 1095s are sent for what we like to refer to as “major medical” 

coverage. For example, 1095 information is not sent for retiree coverage that is secondary to 

Medicare (also known as a “wraparound” policy), or short-term limited duration (STLD) plans. 

OTA does not impute these types of policies unless necessary for specific proposals. 

Premium Imputations

Marketplace Premiums. To compute the PTC, OTA uses Form 1095A and Form 8962 to calculate 

the monthly Marketplace premiums and monthly Second Lowest-Cost Silver Plan (SLCSP) 

associated with each return. When Form 8962 data was available, OTA used that information 

first. The PTC uses an income concept of Modified Adjusted Gross Income (MAGI) relative to 

the Federal Poverty Level (FPL), which we computed using Form 1040 income and household 

size information. 

The Advance Premium Tax Credit (APTC) depends on the “Advance MAGI” taxpayers reported 

to the Marketplace as their projected income for the year. This information is not available on 

tax returns, but one can calculate the implied income reported by using the APTC and SLCSP 

taxpayers received (from the 1095A) and the number of people on the return (assumed to be 

the same at Marketplace signup and on the 1040). However, this imputation is not exact--a 

taxpayer’s family size may change during the year, and taxpayers with different values of 

Advance MAGI may qualify for the same APTC in certain cases. Consistent with this, OTA 

identified some taxpayers with imputed Advance MAGI below 100% of FPL in states that did not 

expand Medicaid and below 138% of FPL in expansion states, most of whom would not have 

received the APTC if the imputed Advance MAGI were correct. OTA edited the imputed 

Advance MAGI variable to ensure the MAGI to FPL ratio is in the right range. 

ESI Premiums. As noted earlier, large employers are required to report the total premium for 

ESI policies provided to employees each year on Form W-2. However, because some employees 

begin or leave employment mid-year, the Form W-2 reports premiums that in many cases do 
41

not represent a full-year premium. Also, reported premiums could be for the worker alone or 

for a policy with family members. Using the coverage information from Form 1095 for ESI policy 

holders, OTA can observe the number of people covered by the policy and the number of 

months the policyholder held the policy. Using that information combined with W-2 premiums 

enables OTA to calculate an annualized measure of premiums for W-2s. As shown by Lurie and 

Miller (2022), the shape of the premium distribution by family size from the tax data closely 

matches the premium distribution from the MEPS-IC, which helps validate the tax-based 

premiums. OTA then used tax-based premiums to impute ESI premiums to policies without W-2 

premium information (using a random draw from the premium distribution by family size).

One issue OTA has encountered is that the total of implied ESI premiums from tax data is

different from total premiums in the MEPS-IC. This is not surprising because the two data 

sources include different types of ESI premiums. Accounting for MEPS-IC not having federal 

policies (and Tricare) and OTA not having “wraparound” policies suggest that OTA and MEPS-IC 

totals are fairly close.

Extrapolation

The steps above result in coverage and premium assignments for 2016 data. The ITM 

extrapolates the 2016 data through the budget window by reweighting returns and adjusting 

dollar values on each return to hit targets based on OMB’s economic forecasts. Targeted counts 

include the number of tax-filing and non-filing units by filing status and by income relative to 

the poverty level; we assume that the ratio of advance to final MAGI for each return remains 

constant throughout the budget window. In addition, targets for the number of subsidized and 

unsubsidized persons in the Marketplace were obtained from the Department of Health and 

Human Services’ Office of the Actuary (OACT). Similarly, targets for the number of people with 

ESI coverage, non-group coverage outside of the Marketplace, and uninsured status were 

constructed from National Health Expenditure Accounts (NHE) growth rates for these 

categories. For premium growth, OTA used OACT projected growth rates for Marketplace 

premiums and NHE projections of total ESI premiums to grow reported 2016 premiums to 

future levels. Premium tax credit estimates for the Budget period are obtained using the 
42

projected distribution of returns by coverage, premiums, and incomes.

Estimating Alternative Health Policies

When modeling changes to ESI or Marketplace subsidies, it is important to consider how 

taxpayers will change their choice of coverage in response to the policy. For example, the 

expansion of PTC subsidies in the American Rescue Plan was projected to cause some uninsured 

individuals to start buying coverage on the Marketplace. For the 2016 base year ITM, OTA has 

used its Simulation of the Health Insurance Market (SHIM) model to project how the 

distribution of coverage by income will change in response to policies, and then impute 

corresponding changes in coverage status for people in the ITM. The model assigns new

Marketplace enrollees a premium (equal to the SLCSP value for their location, age and family 

size), computes their MAGI to FPL ratio (assuming advance MAGI will be equal to final MAGI), 

and computes total PTC spending for the new enrollees. Similarly, if individuals leave ESI 

coverage, the model captures the long-run shift of the value of their ESI exclusion from 

nontaxable to taxable compensation. These capabilities help the ITM provide accurate 

budgetary estimates of changes to health provisions in the tax code.
43

APPENDIX IV: WEALTH MODULE

OTA’s Wealth Module (WM) imputes wealth to individuals on the ITM. The primary uses of 

imputed wealth values are to forecast estate tax liability and to conduct policy analyses 

involving the estate tax. Because, in general, estate tax returns are filed only by estates above 

the filing threshold, they are of limited use in estimating proposals that involve changing the 

filing threshold. The WM provides estimates of wealth for taxpayers below the estate tax filing 

threshold, which directly addresses this shortcoming. 

Briefly, the WM imputes for each tax return on the ITM values of assets (namely, stocks, bonds, 

other financial assets, real estate assets, business assets, retirement assets, and other assets), 

liabilities (namely, mortgage debt and other debt), unrealized capital gains (namely for home 

values, stocks, and business assets) and the holding periods associated with these assets and 

liabilities. 

The remainder of this document describes the primary data sources and imputation 

methodologies used in the construction of the WM and describes how the various data files 

were merged and extrapolated. The WM for the 2016-based model described in this 

documentation was based on return information for tax years 2013 and 2014.

Primary Data Sources

The WM’s estimates combine data from the following core data sets:

• INSOLE2013 – The WM is based on estate tax returns for individuals who died in 2014. The 

tax year 2013 Income and Sole Proprietorship (INSOLE) file from the Statistics of Income 

Division (SOI) of the Internal Revenue Service (IRS) provided the core sample of taxpayers 

on which the WM is based because it is the last tax year for which individuals who died in 

2014 report a full year of income.
44

o Real estate assets were derived directly from INSOLE data by capitalizing property 

taxes paid (found on Schedule A of Form 1040 for individuals who itemize their 

deductions) using ZIP code-level property tax rates. These property tax rates were 

obtained from the 2008 American Community Survey, produced by the U.S. Census 

Bureau. Property taxes for non-itemizers were imputed using an expectationmaximization (EM) algorithm. Roughly, the shares of income that itemizers spent on 

itemized expenses such as property taxes and charitable contributions were 

calculated, and a covariance matrix of these shares was constructed. This covariance 

structure was then applied to non-itemizers to impute their values of property taxes 

paid. (A match randomly chosen from an itemizing near neighbor return was used to 

determine the presence of a particular deduction.) The algorithm iterated until 

aggregate targets for property taxes paid from the U.S. Census Bureau’s 2013 

American Housing Survey were reached. 

o Information on defined contribution plan assets was obtained directly from the ITM. 

IRA assets were obtained by matching tax records on the ITM to the Form 5498 “IRA 

Contribution Information”. Assets for other types of defined contribution plans were 

imputed using information on contributions from Form W-2 and other sources. 

o Information on defined benefit plan benefits was obtained directly from the ITM, 

which in turn was imputed using accrued retirement benefits reported in the 2014 

Survey of Consumer Finances (SCF); Form 5500, Annual Return/Report of Employee 

Benefit Plan, data; the Department of Labor’s Private Pension Plan Bulletin Abstract 

(2014); and various publications related to pension benefits for government 

employees. The flow of benefits obtained from these sources was converted into 

defined benefit plan assets by using the U.S. Treasury’s Second Segment Rate in a 

present-discounted-value calculation. 

• ESTATE2014_SOI – The 2014 estate tax sample from SOI was used to provide data on total 

assets and liabilities, as well as asset components (other than for real estate and retirement 

assets) for returns that could be matched to the INSOLE2013.
45

• ESTATE2014_POPULATION – This dataset, containing the entire population of estate tax 

filers who died in 2014, was used to provide data on total assets and liabilities for additional 

returns to be matched to the INSOLE2013, the last complete year tax return. (Detailed asset 

data is not available in the population file.)

• DECEDENTS (2014) – This dataset, the population of 2014 decedents from the Social 

Security Administration, was matched with INSOLE and estate tax returns to develop a 

model that predicted, conditional on income, age, and marital status, the probability of 

each living income taxpayer’s having wealth above or below $5 million.

• SCF2013 – The 2013 SCF was used to impute asset and liability components (other than for 

real estate and retirement assets) for those taxpayers with imputed wealth below $5 

million. It was also used to impute basis for selected assets from both the SCF and on estate 

tax returns.

• MORTALITY RATE – In order to calculate unrealized gains held at death and expected estate 

and gift tax revenues, mortality rates were required. Mortality rates based on age, sex, and 

income were estimated by merging the SSA Decedent data with the population of tax 

returns (including non-filers) to create the Mortality Rate dataset. The average mortality 

rate was estimated for 72 cells: 3 income groups by 2 sexes by 12 age groups.

Imputation Method

There are a number of methods for imputing values from one dataset to another, each with 

certain advantages and disadvantages. Except where noted, the WM uses hot decking or a 

closely related method called predictive mean matching (PMM) to impute values.

The basic hot decking method begins by using available categorical variables to group all 

observations in both the donor and recipient datasets into discrete cells. Any continuous 

variables used to create cells must first be converted into discrete categories. Next, each 

recipient observation is randomly matched to a donor observation in the same cell, after which 

all values to be imputed for that recipient observation are imputed from the same donor.
46

PMM is a more general case of the hot decking imputation. In this case, some or all of the 

variables used to create the cells are instead used in a regression. The predicted values from 

the regression are then used within each cell to match recipients and donors. Generally, the 

match is not the closest one, but rather is randomly chosen from a fixed number of the closest 

matches (generally known as k-nearest neighbors). While regression was used as part of the 

PMM process, the predicted values were only used for matching purposes, and never to 

directly impute values.

Choosing between a hot deck or PMM method at different stages of the WM creation generally 

depends on practical issues. Using the PMM version of Stata’s “mi” (multiple imputation) 

command is fairly automated and easy to program, but it also has some tradeoffs. If a large 

number of cells are used, one might end up with cells containing too few donors. But if a 

smaller number of cells is used, the speed of computation is unfeasibly long. Conversely, pure 

hot decking must be manually programmed in Stata, but it is generally fast and robust. Hence, 

PMM was generally used if it worked well and quickly; otherwise, pure hot decking was used.

In contrast to hot decking or PMM that uses regression analysis to match recipients and donors, 

pure regression-based methods use regression results from the donor dataset to directly 

impute values in the recipient dataset. The primary advantage of pure regression-based 

methods is that they are straightforward to apply. 

Nevertheless, hot decking (and PMM) methods were the main methods used to construct the 

WM because they have two key advantages. The first is that they only use actual values from 

the donor data set. For example, most of the imputed variables represent dollar values that are 

non-negative and not excessively large. In other words, with hot decking, one is constrained to 

imputing reasonable values as only those are contained in the donor set. With pure regressionbased techniques, it is common to get negative or unreasonably large imputed values.

Second, most of the imputations involved simultaneous imputations of multiple values from a 

donor observation to a recipient observation. Hot decking preserves the covariance structure of 

the imputed data. Conversely, with regression methods it is necessary to perform sequential 
47

imputation of the imputed variables, making it much more difficult to preserve the covariance 

structure.

The main disadvantage of hot decking (and PMM) methods in our imputation was that the 

donor data set was smaller than the recipient data set. As a consequence, donor cells had to be 

reused.20 

Imputation Procedure

The first step in the WM is to create a single data set containing wealth values for individual 

taxpayers across the wealth distribution. Estate tax returns are used for taxpayers with wealth 

in excess of the filing thresholds and the Survey of Consumer Finances is used for taxpayers 

with wealth below the filing thresholds.

When available, the estate tax data are generally preferred to SCF data. The former represents 

reported tax values, and taxpayers are legally liable for any false claims. In contrast, the latter 

contains data that are voluntarily provided, and there are no penalties for misrepresentation. 

While estate taxpayers do have an incentive to minimize asset values, the primary purpose of 

the WM is to calculate estate and gift tax revenues, which will generally reflect those reported 

values.

Estate tax returns are required to be filed for all decedents with gross estates above $5.34 

million in 2014. Estate tax data are also available for many decedents with gross estates 

between $3 million and $5.34 million, as those estates sometimes file returns due to portability 

of the spousal exemption21 and Generation-Skipping Tax (GST) elections. Additionally, returns 

are required to be filed for some decedents with a gross estate below $5.34 million because 

they have made gifts prior to death. Nevertheless, because coverage below the $5.34 million 

20 See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3130338/ for more details about hot decking and 

predictive mean matching. 21 Since 2010, the portability rule allows any unused lifetime estate and gift tax exemption of a deceased spouse to 

be transferred to the surviving spouse, ensuring it isn't lost. While predicted values based on the SCF were not 

compared with the actual values from the estate tax returns because of sampling issues, the resulting distribution 

is smooth at the $5.34 million net worth threshold. 
48

threshold is difficult to determine, we used data from the SCF to impute asset and liability 

values when the imputed net worth is below the threshold.

The SCF-based dataset was prepared by aggregating wealth into seven asset categories (real 

estate, bonds, stocks, business, retirement, other financial and other non-financial) and two 

liability categories (mortgage debt and other debt). These categories were chosen so that 

variables in both the SCF-based and estate tax-based datasets could be aggregated into 

comparable categories. Preparation of the SCF-based dataset also involved calculating basis in 

percentage terms for real estate assets, stocks, and business assets by dividing the reported 

cost price of aggregated assets by the reported market value of aggregated assets. 

Preparation of the estate tax dataset similarly required aggregation into the above asset and 

liability categories. It also required combining the population data (ESTATE2014_POPULATION)

that lacked detail on assets and liabilities with the sample data (ESTATE2014_SOI) that contain 

those details. To impute this detail to the population, a simple hot deck from the SOI sample to 

the population data was performed, with cells consisting of income, age, and marital status.

Before merging the INSOLE2013 with the SCF-based and estate tax-based datasets, it was 

necessary first to impute a binary variable indicating if a taxpayer in the INSOLE file had a net 

worth above or below $5.34 million. This was done by merging the 2013 INSOLE to the 

population of decedents from 2014 and the population of estate tax returns from 2014. A logit 

model was estimated on INSOLE decedents with capital income (interest, dividends, etc.), 

retirement balances (IRA, SEP, etc.), and marital status as covariates. This model was then used 

to predict if the net worth of non-decedents was above or below $5.34 million.

Conditional on this predicted net worth indicator, asset and debt components were imputed via 

hot decking to INSOLE2013 from either the SCF-based dataset if predicted net worth was below 

$5.34 million or the estate-based dataset if predicted net worth was above $5.34 million. Basis 

for each type of asset, measured as a percentage of asset values, were imputed via hot decking 

to the entire INSOLE13 using the SCF-based dataset since the estate-based dataset does not 
49

contain information on basis.22

Figure A1 shows a general diagram of the matching that leads to the estimation of 2013 wealth 

in 2013. 

Figure A1: Files Used to Merge INSOLE2013 Data to Non-INSOLE Data

Calibration and Extrapolation

In order to create the 2016 WM, we hot decked the asset and liability data created from the 

INSOLE2013 to INSOLE2016, using total income, age, marital status, interest income, dividend 

income, and property taxes to create the cells for the hot decking. We limited our imputation to 

these 6 control variables since increasing the number of control variables causes the number of 

22 For the purposes of imputing asset and debt components, the 2013 SCF file was truncated to exclude individuals 

with reported net worth exceeding $5.34m since the combined estate tax file was used to impute these 

components for taxpayers with predicted net worth above this level. For the purposes of imputing basis for each 

type of asset, the entire 2013 SCF file was used to impure these components for all taxpayer records in the 

INSOLE2013. 

ESTATE2014_POP

(population)

SCF2013

ESTATE2014_SOI

(sample)

Combined Estate 

Truncated SCF 

2013 Wealth

INSOLE2013

DECEDENTS

POPULATION
50

cells to grow exponentially, which in turn leads to empty donor cells. Hence, while our 

methodology assigns tax-preferred retirement wealth to only those with tax-preferred 

retirement savings, housing wealth to only homeowners, stocks holdings to those with dividend 

income and bond holdings to those with interest income, it does not assign business assets 

necessarily to those with business income.

After asset and liability fields were created, they were calibrated to produce an estate tax 

estimate comparable to the reported tax revenues for tax years 2015 and 2016 both in 

aggregate and by gross estate size and marital status class, which consists of ten cells (5 gross 

estate size groups and 2 marital status groups). The latter necessitated the use of both 2015 

and 2016 due to the small size of the estate tax sample. (The basis of assets is determined by 

taking the calibrated asset values and then applying imputed basis percentages from the SCF. 

The basis is also adjusted to be consistent with existing revenue estimates from taxing capital 

gains at death. 

At each budget cycle, all monetary amounts in the WM are grown at the GDP growth rate on 

the ITM plus an additional 0.1 percent a year, which is in line with the growth in historical 

receipts for the estate and gift tax. Non-monetary fields such as expected mortality (conditional 

on age, sex, and income), as well as basis (as a percentage of asset value), are held constant 

across all years.
51

APPENDIX V: PASS-THROUGH INCOME

The K-1 information return has the partner’s/shareholder’s tax id (SSN) as well as the entity’s 

tax id (EIN). So, both SSN and EIN already exist on the K-1. Edited K-1s are available for INSOLE 

taxpayers and their dependents. We add EIN-level data, using the EIN from the K-1, by 

matching the EIN to CDW files; in this way, we are able to attach entity-level information (such 

as total assets and interest deduction) to a particular K-1.

We keep information for as many as 10 partnership K-1s plus as many as 10 S-Corp K-1s for 

each INSOLE return. The INSOLE only has aggregated Schedule E data. So, we are matching as 

many as 20 K-1s in order to identify the source of the Schedule E income. Among INSOLE 

returns with non-zero schedule E income or loss, there are a number of returns with more than 

10 K-1s. For these returns, we rank the K-1s by the absolute value of income or loss (active 

income + passive income + abs(active loss) + abs(passive loss)) and add the EIN level data for 

the top 10. 

The entity-level information is also used to define a “business” flag which may be used at the 

discretion of the analyst.23

In total, 27 fields are extracted from the population files for Forms 1065 and 1120S. These 

include the NAICS industry code, total assets, gross receipts, net receipts, various deductions 

and types of compensation. In addition, 12 more entity-level fields are created by aggregating 

K-1 information by EIN (so, all K-1s found in the population file for given tax-year & EIN, rolledup to the EIN-level). These aggregated fields include ordinary income, dividends, interest, net 

long-term gains or losses, net short-term gains or losses, real estate, other rental, and a count 

of the number of K-1s aggregated.

23 One example of a non-business is where individuals or entities form partnerships to re-distribute earnings that 

are passed through from other partnerships. These entities are conduits that merely redistribute funds. For further 

information, see Knittel et. al. (2016). 
52

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