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In US, governments from the federal government to states and local, their
revenue structure relies heavily upon the personal income tax (PIT).
The income tax accounts for almost 50 percent of total federal government
receipts, for New York, it is almost 60 percent of state tax receipts.
PIT liability is the amount which taxpayers actually owe based on total earnings
during a given tax year, according to tax law.
Although the individual income tax has many complexities, its basic structure is
straightforward. Taxpayers add up their income from various sources (net of
exclusions), subtract standard or itemized deductions and personal exemptions
to determine taxable income, apply the schedule of graduated tax rates to
determine their tax liability (how much they owe), and subtract various credits to
determine their final tax liability.
One of the complexities is the existence of the alternative minimum tax (AMT), a
parallel system of individual income taxation with its own set of income types,
exclusions, exemptions, and tax rates. For example, in tax year 2000, the top
statutory rate for the regular income tax was 39.6 percent; for the AMT, it was 28
percent. Taxpayers in effect pay the greater of the taxes calculated under the two
systems. Although only about 1 percent of taxpayer pay tax in 1999 under the
AMT, it is projected that under current law, that share will rise to roughly 15
percent in the next 10 years. That increase is projected to occur principally
because the two systems treat differently the effects of changes in income
caused by inflation.
There are 4 major steps in forecast of Personal Income Tax as indicated in the
figure 1: a sample of historical individual tax payers; Macro income components
models; Micro-simulation model of tax liabilities; and Cash collection models;
Micro simulation model uses individuals' income tax returns compiled annually
by tax agencies. For example, for New York, the most recent database contains
a sample of more than 500,000 tax returns for tax year 2012, collected by the
Tax Department. The data include all of the basic information from those returns
for that year.
When the government processes the tax returns, it also designs a sample which
can be used to study tax payers’ behavior. This sample is used in the PIT
forecast. Since the tax rate structure is progressive, the macro-level forecast is
Figure 1
Personal Income Tax Forecasting System
1. Historical Personal
Income Tax Study
2. Income
Tax Law
Total Liability
4. Cash
Estimated Payments
Income Tax
Long form
Short form
not very useful, since the same amount increase in personal income will result in
different amount of tax liabilities, which is depending on the income distribution.
The sample is a collection of all the information on the tax forms, and the sample
weights are chosen so that the total aggregates (like number of tax returns, total
income, and total liabilities) are equal to the actual numbers. Samples can also
be stratified to reflect sub-total constraints.
The underlying assumption is that many of the basic characteristics of filers in the
most recently available tax year will persist through the immediate future. But the
number of taxpayers and relative importance of various subgroups of taxpayers
will change over that time, as will the kinds of income they receive. Hence, to
simulate conditions in a projection year using the database of tax returns from a
past year, we must adjust ("age") the database to reflect projected changes in
the number of returns and in the amount of income and deductions for each
return. That aging is accomplished by changing the weights in the sample--the
total number of returns that each sample return represents--and the incomes on
the returns.
Income Distribution
The tax system is progressive, so growth in revenues depends on the degree to
which growth in total income comes from an increase in the number of tax
returns or from an increase in income per return. If growth in total income occurs
more because of increases in income per taxpayer than because of increases in
the number of taxpayers, then more of the additional income will be earned by
taxpayers who face higher tax rates. Different household characteristics, such as
age and number of children, affect tax liability, so demographic changes
influence income tax receipts. Various features of the tax code imply that
different effective tax rates apply to different sources of income. Thus, as the
different sources of income change relative to each other, they must be
accounted for explicitly to produce a reliable projection of tax liability.
Adjusting for Demographics
In its first step to age the database, we use population projections and
employment figures from our macroeconomic projection to adjust the total
number of returns filed each year. The weight that applies to each subgroup
generally changes as its relative share of the population changes. For example,
compared with younger individuals, older people tend to earn a greater share of
their income from capital and less from labor. Also, between 2005 and 2012, the
population age 50 or over is expected to increase much faster than the younger
population. Thus, for demographic reasons alone, returns with a high share of
capital income should grow more quickly over that period than returns with a high
share of labor income.
AGI and Its Components
In projecting the base for the individual income tax, we must keep track of which
types of income go to which types of taxpayer. That is, it must estimate what
share of total wages and salaries, rent, interest, dividends, or proprietors' income
goes to taxpayers who file returns singly, jointly, or as a head of household,
broken down by income.
In this step to age the database, we extrapolate the reported income and
deductions on each return using different techniques. The extrapolation process
first requires that each type of income or other item found on tax returns (other
than those calculated by formula) be matched with a corresponding measure that
DOB projects in the aggregate. Changes in that corresponding measure should
track changes in the associated tax-return measure historically and be expected
to track them during the projection period. The extrapolation process then
involves calculating the increase in income necessary on each return, given the
first step of demographic aging, so that in the aggregate, the amounts on tax
returns grow at the same rate as the corresponding measures.
The macroeconomic projection, especially its variables from the national income
and product accounts, provides the basis for extrapolating many tax-return
measures. Those macroeconomic variables include wages and salaries,
personal dividend income, and interest income (only the monetary portion, which
excludes imputed interest). Each of those macroeconomic variables has a direct
counterpart on tax returns, but sometimes they do not match
Annual data pertaining to the number of tax returns and the components of
adjusted gross income are obtained from samples mentioned above. Singleequation econometric models are used to project the future number of returns, as
well as all the components of income. In almost all cases, the data series on the
components are found to be nonstationary. Therefore, to avoid being misled by
spurious regression results, a logarithmic transformation is performed and then
first-differenced for all series for which at least 20 observations are available.
Dummy variables are incorporated into models where anomalies in the data are
thought to be the product of sampling error. Detailed descriptions of the models
for the number of returns and for the major components of NYSAGI, other than
wages, are presented below. All estimation results presented below are based
on tax return data from a sample of State taxpayers through the 2003 tax year,
made available by the New York State Department of Taxation and Finance.
Micro-Simulation Model
The micro-simulation approach to project liabilities from individual income taxes
is very common. This type of models use historical patterns of payment to project
how those liabilities will be paid over time as receipts. The micro-simulation
approach uses a sample of tax returns that represents the diversity of
households in an economy. It applies a projection of different types of taxable
income and adjustments to income based on comparable measures from the
macroeconomic projection. It then calculates how much those households will
owe in taxes on those incomes. Finally, it converts those calendar year tax
liabilities into expected payments by fiscal year.
Tax Liability and Cash Payments
Although significant risks necessarily remain in any estimates of income tax
liability, estimation of the level of tax liability for a particular tax year leads, with a
high degree of confidence, to the approximate level of cash receipts that can be
expected for the particular tax year.
Forecast AGI and Its Components
Elasticity is a common measure of the sensitivity of one economic variable to
changes in another. The percent change in the value of an economic variable in
response to the percent change in real U.S. GDP yields the elasticity measure.
Typically, PIT liability has a higher elasticity value than NYSAGI, while NYSAGI
has a higher elasticity value with respect to changes in overall economic
conditions (as measured by GDP) than personal income. The responsiveness of
NYSAGI to economic trends tends to be higher than that of personal income
because NYSAGI measures the taxable components of income, including
realized capital gains and losses. These are not included in the NIPA concept of
personal income since they do not add to the value of current production.1 Unlike
indicators such as GDP and employment, which have relatively stable bases,
income from capital gains realizations can fall dramatically if taxpayers refrain
from selling financial assets due to depressed market conditions or if taxpayers
are carrying forward losses from prior years. In 2001 and 2002, income from
positive capital gains realizations declined dramatically at rates of 50 percent and
27 percent, respectively, in response to the downturn in the economy and the
financial markets (see Table 1). DOB’s estimate suggests a strong positive
response of capital gains income to the upturn in economic activity in 2004.
Moreover, NYSAGI can fluctuate due to statutory changes in the definition of
taxable income, as well as due to taxpayers’ strategic responses to such
PIT liability is even more elastic than NYSAGI, primarily due to the
progressivity of the State tax system. The volatile components of taxable
income, such as bonuses and capital gains realizations, tend to be concentrated
among the State’s high-income taxpayers, who are also taxed at the highest
marginal tax rate. While the top one percent of taxpayers, ranked by their
NYSAGI, accounted for 31.4 percent of adjusted gross income in 2003, they
accounted for fully 72.7 percent of capital gains realizations (see Figure 2).
Growth in those components usually increases the average, or effective, tax rate
and contributes to the elasticity of the response of liability to income changes.
Liability also tends to grow faster than taxable income because as incomes grow
over time, taxpayers are pushed into higher tax brackets, which also raises the
effective tax rate. This impact is exacerbated in New York by provisions in State
statute that recapture the benefits of lower tax rates in the tax tables for high
income taxpayers.
However, any transaction cost generated by such a sale would add value to current production and would therefore be
included in personal income.
Indicators of New York State Tax Base
Growth Rate Comparison
PIT Liability
Personal Income
* Growth rates for PIT liability and NYSAGI for 2004 are staff estimates. PIT
liability growth rates are at 2002 law.
Source: NYS Department of Taxation and Finance; Moody's;
DOB staff estimates.
Tax Returns
The number of tax returns is expected to vary with the number of
households that earn any kind of income during the year. The number of such
households, in turn, should be closely associated with the number of individuals
who are either self-employed, employed by others, or earn taxable income from a
source other than labor. Since most taxable income is earned as wages and
salaries and thus related to employment, total State payroll employment, which is
forecast within DOB/N.Y., is a key input to this model.
New Yorkers can earn taxable income from sources other than payroll
employment, such as self-employment and real and financial assets.
Self-employment is expected to be closely related to proprietors’ income, a
component of the NIPA definition of State personal income that is available from
BEA and forecast within DOB/N.Y. Another component of personal income that
is forecast within DOB/N.Y., State property income, includes interest, dividend,
and rental income. The DOB tax return model incorporates the sum of
proprietors’ and property income for New York, deflated by the consumer price
index for New York as constructed by DOB.
A one-time upward shift in the number of tax returns is observed in 1987,
believed to be related to the Tax Reform Act of 1986. Beginning in 1987, the
two-earner deduction for married couples was eliminated, reducing the incentive
for married couples to file joint tax returns. To capture this effect, a dummy
variable for 1987 is added to the model. A dummy variable for 2000 is also
included to account for a change in the way tax returns were processed and
sampled starting that year. The equation specification is shown in Table 1.
 ln RETt  0.00221  0.430  ln NYSEMPt  0.0980  ln((PROPNY  YENTNY ) / CPINY )t 
0.0186 D87t  0.0378 D00t
Adjusted R 2  0.897
Number of tax returns
Total State employment
State property income
State proprietors’ income
Consumer Price Index for New York
Dummy variable for 1987 tax law change
Dummy variable for 2000 processing changes
New York State’s positive capital gains realizations forecasting model
incorporates those factors that are most likely to influence realization behavior:
expected and actual tax law changes, equity market activity, and, as of this
forecasting cycle, real estate market activity. Realization behavior appears to
exhibit two types of responses to changes in tax law: a transitory response to an
expected change in the law and a steady-state response to an actual change.
For example, if the tax rate is expected to rise next year, then taxpayers may
realize additional gains this year, in order to take advantage of the lower rate.
However, in the long run, the higher tax rate should result in a lower level of
current realizations, all things being equal. Based on Miller and Ozanne (2000),
the transitory response variable is specified as the square of the difference
between the rate expected to take effect next period and the current period rate,
with the sign of the difference preserved. The long-term or steady-state
response variable is the actual tax rate.
The growth in realizations is also expected to be directly related to growth
in equity prices. To capture the effect of equity prices, the average price of all
stocks traded is incorporated into the model. Forecasts of the average stock
price are based on the forecast for the S&P 500 from DOB/U.S. A measure of
real estate market activity has been added to the model in acknowledgement of
another large and possibly growing contributor to capital gains realizations: real
estate transactions. Taxpayers can exempt gains from the sale of a primary
residence of up to $250,000 ($500,000 if filing jointly), but all other capital gains
from real estate transactions are fully taxable. Conditions in the real estate
market are captured by including New York State real estate transfer tax
collections. The model specification is shown in Table 2.
Two years of dramatic declines in equity prices resulted in very large loss
carryover amounts that appear not to have diminished in 2003 despite
considerable growth in capital gains realizations. These carryover losses pose
significant risk to the model forecast, particularly because of the lack of historical
experience with respect to the magnitude of the loss carryover amounts.
Adjustments are made to the capital gains forecast to balance these risks.
 ln CGt  0.0604  6.33  TRSTX t  2.65  PRMTX t  1.38  ln EQTYPt  0.449  ln RETTt
 0.326 D90t
Adjusted R  0.818
Positive capital gains realizations
Transitory tax measure
Permanent tax rate
Average price of stocks traded
Real estate transfer tax collections
Dummy variable for 1990
The largest component of New York’s positive partnership, S corporation,
rent, royalty, estate and trust gains (PSG) is partnership income, much of which
originates within the finance industry. Therefore, growth in PSG is believed to be
related closely to overall economic conditions, as represented by real U.S. GDP,
as well as to the performance of the stock market, as represented by the S&P
An almost equally large contributor to this income category is income from
closely held corporations organized under subchapter S of the Internal Revenue
Code, and known as S corporations. Selection of S corporation status allows
firms to pass earnings through to a limited number of shareholders and to avoid
corporate taxation. Empirical work shows that the differential between personal
income tax and corporate income tax rates can significantly affect election of
S corporation status.2 As more firms choose S corporation status over
C corporation status, which is taxed under the corporate franchise tax, personal
income increases, all else equal. Consequently, DOB’s forecast model includes
the difference between the corporate franchise tax rate and the maximum
See, for example, Carroll and Joulfaian (1997).
marginal personal income tax rate, where the rates are composites of both State
and Federal rates.
Changes in tax law are believed to account for some of the volatility in
PSG. The enactment of the Tax Reform Act of 1986, which created additional
incentives to elect S corporation status, is likely to have resulted in an unusually
high rate of growth in this component of income in the late 1980s. In particular,
we observe an unusually high rate of growth in this component in 1988 that was
followed by extremely low growth in 1989. Possible explanations are the
expectation of a large tax increase after 1988, or an increase in the fee for
electing S corporation status in 1989. This effect is captured by a dummy
variable that assumes a value of one for 1988 and minus one for 1989. The
equation specification is shown in Table 3.
 ln PSGt  0.000317  0.477  MTRt  0.264  ln JSt  2.23  ln GDPt  0.228 D88 _ 89 t
Adjusted R  0.840
Partnership, S corporation, rent, royalty, estate and trust income
Difference between corporate and personal income maximum marginal tax rates
Standard and Poor’s 500 stock index
Real U.S. GDP
Dummy variable, 1 for 1988, -1 for 1989
Dividend income is expected to rise with the fortunes of publicly held U.S.
firms, which, in turn, are expected to vary with the business cycle. For example,
during the State’s last recession, dividend income declined for four consecutive
years from 1989 to 1992. Because a strong (or weak) economy, as measured by
growth in real U.S. gross domestic product, might have a sustained impact on the
payout of dividends, the impact of the business cycle on dividend income is
modeled as a polynomial lag of real U.S. GDP. In a polynomial lag estimation,
the coefficients on the various lags of GDP are estimated as functions of the
length of the lag. As specified in the model shown in Table 4, the coefficient on
the ith lag of GDP is equal to - 0.131 i + 0.18 i 2. Thus, the coefficient on the
second lag (i=2) of GDP is 0.457 = - 0.131·2 + 0.18·4.
Dividend income is also thought to be associated with firms’ expectations
pertaining to their future profitability, which is expected to be tied to the future
strength of the economy. Because interest rates incorporate inflation
expectations, which in turn incorporate expectations regarding the future strength
of the economy, they represent a proxy for the latter. Interest rates are
represented by the rate on the 10-year Treasury note.
Historically, State dividend income has ranged from a decline of 6 percent
in 1991 to an increase of 22 percent in 1981, proving much more variable than
U.S. dividend income, a component of the NIPA definition of U.S. personal
income. This may suggest the importance of factors affecting the way taxpayers
report their income, rather than changes in the payment of dividends by firms.
The most obvious impact of a change in the tax law occurred in 1988, when
reported dividend income grew 21.8 percent, followed by a decline of 2.6 percent
the following year. A dummy variable is included to control for what is assumed
to be the impact of the Tax Reform Act of 1986 on the reporting of taxable
dividend income. A dummy variable is also included to capture the extraordinary
impact of recessions (1975, 1990, 1991, 1992, 2001, 2002) beyond what is
captured by fluctuations in real U.S. GDP.
 ln DIVt  0.0367  TRATE10t  0.209  ln JSt  0.0488  ln GDPt 1  0.457  ln GDPt 2
1.22  ln GDPt 3  0.127 DREC t  0.121 D88 _ 89 t
Adjusted R  0.683
Dividend income
Interest rate on 10-year Treasury notes
Standard and Poor’s 500 stock Index
Real U.S. GDP
Recession dummy variable
Dummy variable, 1 for 1988, -1 for 1989
For a given amount of assets, an increase in interest rates will increase
interest income. DOB’s interest income forecasting model is based on this
simple concept and accordingly includes the 10-year Treasury rate. In addition,
the overall trend in taxable interest income for New York is found to closely track
that of U.S. interest income, another component of the NIPA definition of U.S.
personal income. However, taxable interest income for New York is much more
volatile than the latter measure. For the period from 1976 to 2002, the average
growth rate for U.S. interest income was 8.0 percent, with a standard deviation of
8.4 percentage points. In contrast, New York’s interest income over the same
period averaged 4.8 percent growth, with a standard deviation of over 14.7
percentage points. The additional volatility in the New York series could be
related to the behavioral response of State taxpayers to past changes in the tax
law, as well as to sampling error. Dummy variables are included to capture
extraordinary declines in 1992 and 2002 beyond what would have been expected
due to the changes in interest rates. The model specification is shown in Table
 ln INTt   0.0168  0.967  ln USINTt  0.0389  TRATE10t  0.204 D92 t  0.214 D02 t
Adjusted R  0.816
Interest income
U.S. interest income (NIPA definition)
Interest rate on 10-year Treasury notes
Dummy variable for 1992
Dummy variable for 2002
Business income combines income earned and reported as a result of
operating a business or practicing a profession as a sole proprietor, or from
operating a farm. Such income is expected to vary with the overall strength of
the State and national economies. The inclusion in the model of State
proprietors’ income, a component of the NIPA definition of New York personal
income, which is forecast within DOB/N.Y., insures consistency between DOB’s
New York forecast and the forecast of this component of NYSAGI. Real U.S.
GDP, forecast under DOB/U.S., captures the impact of the national business
cycle, which might not be captured by the NIPA definition of State proprietors’
income. In addition, a dummy variable is included to capture the downward shift
in reported business income growth for the period from 1989 onward, perhaps
due to new firms registering as S corporations rather than sole proprietorships, in
order to take advantage of more favorable laws pertaining to liability. The
equation specification is shown in Table 6.
 ln BUSt  0.0873  0.349  ln BUSt -1  0.297  ln YENTNYt  1.68  ln GDPt
 0.102 D89 t
Adjusted R 2  0.647
Sole proprietor and farm income
State proprietor income (NIPA definition)
Real U.S. GDP
Dummy variable for 1989 onward
Pension income includes payments from retirement plans, life insurance
annuity contracts, profit-sharing plans, military retirement pay, and employee
savings plans. Pension income is linked to growth in the New York State
population and to long-term interest rates, suggesting that firms base the level of
pension and life-insurance benefits they offer to employees on their expectations
of future profitability, which are tied to the future strength of the economy. As
indicated above, interest rates represent a proxy for the latter. Pension income
has grown steadily over the years with a growing New York State population,
although the growth rate has declined considerably over time. While the average
annual growth rate between 1978 and 1989 was 13.4 percent, it fell to 7.6
percent between 1990 and 2002. This coincides with a decline in the 10-year
Treasury rate from 10.3 percent in the earlier years to 6.3 percent in the later
years. The equation specification is shown in Table 7.
 ln PEN t   4.45  ln NRNYt  0.0129  TRATE10t -1  0.660 AR1 0.0866 D89 t  0.152 D94 t
Adjusted R  0.684
New York State population
Pension income
Interest rate on 10-year Treasury notes
First order autoregressive term
Dummy variable for 1989
Dummy variable for 1994
Because the State has a progressive tax system, the distribution of
income across taxpayers helps determine total income tax liability. Out-year
estimation of the income distribution is risky since the share of income earned
among the wealthiest taxpayers can fluctuate dramatically with such factors as
the business cycle, the condition of financial markets, and changes in federal and
state tax treatment. As incomes rise, some taxpayers move into higher income
tax brackets, increasing the effective tax rate and the amount of liability
generated from a given amount of adjusted gross income. The opposite occurs
as incomes fall. The effective tax rate fell from a high of 4.76 percent in 2000 to
a low of 4.43 percent in 2002 without any significant changes in tax law. As the
economy and equity markets improved, and income tax rates for high-income
taxpayers were increased in 2003, the effective tax rate climbed to 4.66. DOB
estimates that without the tax law change, the effective tax rate would have fallen
slightly to 4.40 percent largely because of a 6.5 percent decline in bonuses. In
2004, the effective tax rate is estimated to have increased to 4.84 percent under
current law, and 4.56 percent under 2002 tax law. The temporary increase in tax
rates for high-income taxpayers will be reversed in 2006, which will diminish the
liability generated from NYSAGI. The decline in liability in 2006 will be
compounded if the projected reduction in real estate transactions lowers capital
gains realizations, since capital gains income is highly concentrated among the
wealthiest taxpayers who are also subject to the tax rate reduction.
The rising stock market created thousands of millionaires in the late 1990s,
causing the share of total personal income tax liability accounted for by highincome taxpayers— those reporting NYSAGI of $200,000 or more — to grow
rapidly during that period.3 While the collapse of the equity markets in 2000 and
2001 led to a noticeable decline in returns filed by high-income taxpayers, the 9.0
percent average annual growth rate in high-income returns between 1992 and
2003 far outpaced the 0.9 percent overall growth in returns (see Figure 3). In
2003, high-income taxpayers represented a mere 2.8 percent of all taxpayers but
accounted for 33.5 percent of NYSAGI and 48.8 percent of personal income tax
liability (see Figure 4). The increasing concentration of liability among highincome taxpayers increases the elasticity of total liability with respect to tax rate
changes that affect high-income taxpayers.
In 1995, 6,910 New York taxpayers had federal adjusted gross incomes of $1,000,000 or more. This
number skyrocketed to 48,856 taxpayers in 2000. Between 1999 and 2000 alone, the number of
millionaires almost doubled from 25,537 to 48,856.
Total Returns
Total Liability (right scale)
Total Liability 2002 Law
(right scale)
Total Liability
($ Billions)
Number of Returns
Figure 3
New York State High-Income Tax Returns
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Source: NYS Department of Taxation and Finance; DOB staff estimates.
Figure 4
High-Income Taxpayers as Percent
of Total Returns and Liability
As % of Total Liability (right scale)
As % of Total Liability 2002 Law
(right scale)
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Source: NYS Department of Taxation and Finance; DOB staff estimates.
Liability (percent)
Returns (percent)
As % of Total Returns
1993 VERSUS 2003
Number of
Total ($ in millions)
Top 1% (percent share)
Top 5% (percent share)
Top 10% (percent share)
Top 25% (percent share)
Total ($ in millions)
Top 1% (percent share)
Top 5% (percent share)
Top 10% (percent share)
Top 25% (percent share)
Note: Returns are ranked on the basis of gross income and are based on weighted statistical sample of all tax returns.
Source: NYS Department of Taxation and Finance; DOB staff estimates.
Table 2 indicates that trends in both wage and non-wage income are
responsible for the increasing concentration of liability since the early 1990s.
The share of non-wage income accruing to the top 25 percent of taxpayers grew
5.6 percentage points between 1993 and 2003, while the wage share grew 3.2
percentage points. Much of the growth in non-wage income during the 1990s
has been in capital gains realizations and partnership/S corporation income,
which tend to accrue primarily to high-income filers. Although wage income is
more evenly distributed across taxpayers than non-wage income, the gains in
wages earned since 1993 have accrued disproportionately to the top filers.
Figure 5 compares the composition of NYSAGI for all taxpayers for 2002, the
second year of the State’s recession, to that for the 2006 tax year, based on
Budget Division projections. The figure shows a substantial shift in income from
wages to net capital gains realizations over the period.4 By 2006, net capital
gains income is projected to contribute 11.2 percent to NYSAGI, up from 4.4
percent in 2002. Net capital gains realizations peaked at 12.2 percent of
NYSAGI in 2000 at the height of the stock market bubble, and again in 2005 at
the same share with the estimated peak of the real estate market boom. The
wage share is expected to decrease from 80.2 percent in 2002 to 74.0 percent in
2006. Business and farm income is predicted to decrease slightly from 3.8
percent to 3.4 percent while, net partnership income is expected to increase from
6.4 percent of NYSAGI to 6.8 percent over the period.
Net capital gains and partnership/S corporation income in these figures are net of the corresponding
aggregate losses.
Figure 5
Composition of NYSAGI for All Taxpayers
NYSAGI: $459,919 M
NYSAGI: $599,872 M
Int & Div
Net Cap
Note: Both capital gains and partnership/S corporation gains income are net of losses.
Source: NYS Department of Taxation and Finance; DOB staff estimates.
The composition of NYSAGI for high-income taxpayers differs noticeably
from that of all other taxpayers (see Figure 6). In particular, the wage share is
more than 20 percentage points lower, while net capital gains and
partnership/S corporation income make up a much larger share among highincome taxpayers than for taxpayers overall.5 Their share of net capital gains
realizations is projected to increase from 11.7 percent in 2002 to 23.6 percent in
2006. Meanwhile, their shares for partnership/S corporation income and
particularly wages are projected to fall.
Although tax return data do not differentiate bonus income from non-bonus income, it can be surmised that
bonus income represents a much larger share of taxable income among high-income taxpayers than among
low-income taxpayers.
Figure 6
Composition of NYSAGI for High-Income Taxpayers
NYSAGI: $150,594 M
NYSAGI: $261,930 M
Int & Div
Net Cap
Note: Both capital gains and partnership/S corporation gains income are net of losses.
Source: NYS Department of Taxation and Finance; DOB staff estimates.
The Division of the Budget uses forecasting models to project future
values for the components of New York State adjusted gross income (NYSAGI).
By and large, these models presume that the historical relationships between the
components of income and a number of key economic indicators are useful for
projecting their future behavior, and that these relationships are stable and can
be estimated using standard statistical methods. Since all statistical models are
simplifications of complex relationships, they are subject to model
misspecification error. In addition, there are risks associated with the forecasts
for the exogenous economic indicators. Even if a model is well specified and the
future values of the exogenous inputs can be predicted with certainty, a statistical
forecast remains subject to error. There is always a component that cannot be
captured by the model, which is simply ascribed to random variation. And the
estimated parameters of the model are themselves random variables and, as
such, subject to estimation error.
The tool used by the Division of the Budget for presenting the risk to the
forecast is the fan chart. Fan charts display prediction intervals as shown in the
sample chart below (see Figure 1). It is estimated that with 90 percent
probability, future values will fall into the shaded area of the fan. Each band
within the shaded area reflects five percent probability regions. The chart "fans
out" over time to reflect the increasing uncertainty and growing risk as the
forecast departs further from the base year. Not only does the fan chart
graphically depict the risks associated with a point forecast as time progresses,
but it also highlights how realizations that are quite far from the point estimate
can have a reasonably high likelihood of occurring. Fan charts can exhibit
skewness that reflects more downside or upside risk to the forecast, and the
costs associated with erring on either side.
Fan Chart for Partnership/S Corporation Income Growth
90 percent prediction intervals
Monte Carlo Mean
DOB Forecast
Percent change
Note: With 90 percent probability, actual growth will fall into the shaded region. Bands represent 5 percent probability regions.
Source: NYS Department of Taxation and Finance; DOB staff estimates.
Fan Chart for Capital Gains Income Growth
90 percent prediction interval
Monte Carlo Mean
DOB Forecast
Percent change
Note: With 90 percent probability, capital gains growth will fall within the shaded
region. Bands represent 5 percent probability regions.
Source: NYS Department of Taxation and Finance; DOB staff estimates.
Monte Carlo Simulation Study
The fan charts used by DOB are based on means and standard deviations
derived from another tool, the Monte Carlo simulation study. For a given model
specification and a given set of exogenous inputs, Monte Carlo simulation
studies evaluate the risk to the forecast due to variation in the dependent variable
that cannot be explained by the model, as well as the random variation in the
model parameters. By assumption, the model errors are considered to be draws
from a normally distributed random variable with mean zero. For purposes of the
simulation, the model parameters are also considered to be random variables
that are distributed as multivariate normal. The standard deviation of the
regression errors, and the means and standard deviations of the parameter
distribution are derived from the regression analysis.
In order to simulate values for the dependent variable, a random number
generator is used to generate a value for the model error and values for the
parameters from each of the above probability distributions. Based on these
draws and values from the input data set, which for purposes of the simulation is
assumed to be fixed, the model is solved for the dependent variable. This
"experiment" is typically repeated thousands of times, yielding thousands of
simulated values for each observation of the dependent variable. The means
and standard deviations of these simulated values provide the starting point for
the fan chart.
The Fan Chart: Theoretical Underpinnings
To capture the notion of asymmetric risk, the fan chart used by DOB is
based on a two-piece normal distribution for each of the forecast years following
an approach due to Wallis (1999). A two-piece normal distribution of the form
 A exp[( x   )2 / 2 12 ] x  
f ( x)  
 A exp[( x   ) / 2 2 ] x  
with A  ( 2 (1   2 ) / 2)1 , is formed by combining halves of two normal
distributions having the same mean but different standard deviations, with
parameters (  , 1 ) and (  , 2 ) , and scaling them to give the common value f (  ).
If  1   2 , the two-piece normal has positive skewness with the mean and median
exceeding the mode. A smooth distribution f ( x) arises from scaling the
discontinuous distribution f ( z ) to the left of μ using 2 1 /( 1   2 ) and the original
distribution f ( z ) to the right of μ using 2 2 /( 1   2 ).
f ( x), f ( z )
____ two halves of normal distributions with mean
and standard deviations  1 and  2 .
------ two-piece normal distribution with mean  .
x, z
One can determine the cutoff values for the smooth probability density
function f ( x) from the underlying standard normal cumulative distribution
functions by recalling the scaling factors. For    1 ( 1   2 ) , i.e. to the left of μ,
the point of the two-piece normal distribution defined by Prob( X  x ) = is the
same as the point that is defined by Prob(Z  z ) = , with
 ( 1   2 )
2 1
x   1 z  
Likewise, for (1   )   2 ( 1   2 ) , i.e. to the right of μ, the point of the twopiece normal distribution that is defined by Prob( X  x ) = is the same as the
point that is defined by Prob( Z  z ) = , with
 ( 1   2 )
2 2
x1   1 z1  
For the two-piece normal distribution, the mode remains at μ. The median
of the distribution can be determined as the value defined by Prob( X  x ) =0.5 .
The mean of the two-piece normal distribution depends on the skewness of the
distribution and can be calculated as:
E( X )   
( 2  1 )
The Fan Chart: Choice of Parameters
In constructing its fan charts, DOB uses means from the Monte Carlo
simulation study as the mean, μ, of the two underlying normal distributions. As
mentioned above, if the two-piece normal distribution is skewed, the Monte Carlo
mean becomes the mode or most likely outcome of the distribution and will differ
from the median and the mean. In the sample fan chart above, the mode is
displayed as the crossed line. Except for in extremely skewed cases the mode
tends to fall close to the middle of the central 10 percent prediction interval. As
Britton et al. (1998) point out in their discussion of the inflation fan chart by the
Bank of England, the difference between the mean and the mode provides a
measure of the skewness of the distribution. Given the skewness parameter, γ,
DOB determines the two standard deviations,  1 and  2 , as  1 = (1+ )
and  2 = (1- ) , where  is the standard deviation from the Monte Carlo
simulation study.
By definition, the mean of the distribution is the weighted average of the
realizations of the variable under all possible scenarios, with the weights
corresponding to the probability or likelihood of each scenario. In its forecasts,
DOB aims to assess and incorporate the likely risks. Though no attempt is made
to strictly calculate the probability weighted average, the forecast will be
considered a close approximation of the mean. Thus the skewness parameter,
γ, is determined as the difference between DOB's forecast and the Monte Carlo
mean. DOB's fan chart shows central prediction intervals with equal tail
probabilities. For example, the region in the darkest two slivers represents the
ten percent region in the center of the distribution. DOB adds regions with 5
percent probability on either side of the central interval to obtain the next
prediction interval. If the distribution is skewed, the corresponding 5 percent
prediction intervals will include different ranges of growth rates at the top and the
bottom, thus leading to an asymmetric fan chart.
The 5 percent prediction regions encompass increasingly wider ranges of
growth rates as one moves away from the center because the probability density
of the two-piece normal distribution decreases as one moves further the tails.
Thus the limiting probability for any single outcome to occur is higher for the
central prediction regions than for intervals further out because a smaller range
of outcomes shares the same cumulative probability. Over time, risks become
cumulative and uncertainties grow. DOB uses its own forecast history to
determine the degree to which σ1 and σ2 need to be adjusted upward to maintain
the appropriate probability regions.
Liabilities and Cash
Tax Liability and Cash Payments.
Although significant risks necessarily remain in any estimates of income tax
liability, estimation of the level of tax liability for a particular tax year leads, with a
high degree of confidence, to the approximate level of cash receipts that can be
expected for the particular tax year. The consistency in this relationship is shown
in the graph below.
PIT Liability vs. PIT Cash Receipts
1982 to 2006 Tax Years
Cash Receipts
($ in billions)
($ in billions)
Despite the strong relationship between tax-year liability and cash
receipts, estimation of cash payments is subject to an important complication that
pervades forecasts for the Executive Budget and other State Financial Plan
updates. This complication is determining the portions of tax-year liability that
will occur in particular State fiscal years. Income tax prepayments — withholding
tax and quarterly estimated tax payments — tend to be received not long after
income is earned. For example, most withholding tax payments and quarterly
estimated tax payments for the 2005 tax year will be received before the end of
the 2005-06 State fiscal year. Settlement payments — those payments received
when taxpayers file final returns for a tax year — tend to be received in the next
State fiscal year after the end of a tax year. Thus, settlement payments for the
2005 tax year will be received largely in the 2006-07 fiscal year. Some
settlement payments (known as prior-year payments) are received later and can
occur in a subsequent fiscal year. Such payments for the 2005 tax year can be
received in fiscal year 2006-07 or a later fiscal year.
As is evident in the graph below showing net settlement payments for the
1983 through 2005 tax years, the amount of liability received in the settlement
can vary widely from year to year. In most years, the net settlement has been
very negative, with State settlement outlays (such as refunds and offsets) far
exceeding taxpayer settlement payments (such as those sent with returns and
extension requests). There have been some important exceptions to this pattern
— most notably during times of tax reform (in 1986 and 1988), in times of rapid
economic growth, and during periods with large increases in non-wage income.
Income Tax Settlement
1983 to Present
Tax Year
($ in billions)
Note: The settlement is comprised of extension payments plus final return payments minus refunds and the
state-city offset.
Several different settlement patterns have occurred in recent years. With
the rapid growth of the New York economy in the late 1990s, the settlement
became much less negative than it traditionally had been. This pattern,
accompanying the strongly growing economy, resulted generally from
prepayment growth rates that fell short of liability growth rates, leading to the
need for increased settlement payments with filed returns. With the weak
economy of 2001 and 2002, taxpayers, in aggregate, dramatically reduced their
settlement payments and the total settlement became very negative again, with
the net amount paid out by the State exceeding $2 billion for the 2002 tax year.
Due to the temporary tax increases enacted by the Legislature in 2003, the net
settlement payout by the State is estimated to have remained negative but below
$600 million for the 2004 tax year, and to become positive at $190 million for tax
year 2005. This expected net settlement increase will reflect the need of highincome taxpayers to add to their settlement payments to cover liability increases
that were not collected through added prepayments, due to continued
extraordinary growth in non-wage income.
The Role of Micro-simulation in Estimating Liability
Use the spreadsheet to explain the issue
After aggregate AGI targets are set and decomposed into deciles for the largest
components, the results can be incorporated into a micro-simulation model that
generates forecasts of PIT liability for future years. Forecasters can also use
micro-simulation to estimate the impact of tax policy proposals on overall liability
and on different taxpayer groups. Examples of such proposals include changes
in the standard deduction or exemption amounts, changes in the tax rate
schedule, and changes in various tax credits.
The process of forecasting liability proceeds in two steps. The first step is to
sequentially “advance” or “trend” the most recent study file into future tax years.
Thus, the 2010 study file forms the base for the 2011 trended dataset, which in
turn becomes the base for creating the 2012 trended dataset, and so on. Once
done for any given year, the analyst can submit the new trended dataset to the
second step, which is the computation of tax liability under existing tax law for
that year. This second step is essentially the application of a PIT tax liability
calculator that follows the structure of the state tax form.
In New York, residents and nonresidents are trended separately. In the first step
of the trending process for residents, taxpayer record weights are advanced by
the projected growth in the total number of resident returns. In the second step,
the major components of gross income are advanced by the projected decilespecific growth rates, discounted for the growth in the total number of returns.
For New York, these resident income components include wages, positive capital
gains realizations, positive PSG, dividends, interest, and business income; for
nonresidents, only taxable wages are advanced by the decile-specific growth
At this point, weighted sums for the major income components may not be
precisely equal to the aggregate AGI targets developed in the section, “Projecting
Aggregate Component Growth.” Thus, in the third step, the forecaster adjusts
the individual taxpayer record weights yet again to ensure that the targets are
met precisely. The method used to determine the size of these adjustments
follows the U.S. Treasury Department methodology (Cilke 1994). Define xi to be
the adjustment factor for weight class i. This adjustment acts as a scaling factor,
such that if xi  1 , then the new weight is exactly equal to the original weight;
xi  1 implies that the new weight is greater than the original weight, while xi  1
implies that the new weight is less than the original weight, for weight class i .
In theory, there are an infinite number of sets of adjustments that would serve the
purpose. The Treasury Department methodology chooses the unique set that
guarantees that the targets are met with the smallest possible deviations from the
original weights. This is accomplished by constructing a "loss function", (xi),
such that (1)  0 , i.e., the penalty is zero if there is no adjustment, and
lim ( x)  lim  ( x)   , i.e., upward and downward adjustments to the existing
x 
x 0
weights are equally penalized. Again, following the Treasury Department, we
choose the following functional form for (xi),
( xi )  xi 4  xi 4  2
where xi is the adjustment to the existing weight for the ith weight class. The
analyst's goal is to choose weight adjustments that minimize the weighted sum of
these "losses" subject to meeting the aggregate income targets. This goal
implies a Lagrangean function of the following form:
i 1
j 1
i 1
L    ni wi ( xi4  xi4  2)     j ( y j   xi wi yij )
I is the number of weight classes,
ni is the number of records in the ith weight class,
wi is the existing weight for the ith weight class,
J is the number of major income components for which decile growth rates are
j is the Lagrange multiplier for the jth major income component,
yj is the aggregate target for the jth major income component, and
yij is the unweighted total for the jth major income component for the ith weight
Note that (1)  0 implies that the set {xi} that solves the minimization problem
can be expected to be close to one. Taking partial derivatives with respect to xi
and  j and rearranging produces the following first order conditions:
4ni wi ( xi 3  xi 5 )    j wi yij  0
j 1
xw y
i 1
 yj
j  1,..., J
Equation (3) is nonlinear and has no analytical solution. Therefore, an iterative
numerical process is employed to simultaneously solve the above set of
In the final step of the trending process, forecasters trend forward the remaining
components of taxpayer income at the rates projected by the aggregate AGI
models, discounted by the growth in the total number of returns. The entire
procedure is repeated for nonresidents, except that decile-specific rates are
applied only to taxable wages. Thus, J = 1 and the minimization of the objective
function is constrained only by the need to satisfy the aggregate nonresident
wage target. The final trended dataset forms the base for trending forward to the
following year.
Liability Estimation
Once a trended dataset has been created, it can then be submitted to the
“liability calculator.” This component of the micro-simulation emulates the
calculations done by the tax filer in completing a state tax form by making use of
all of the available information on each taxpayer’s record to compute state AGI,
allowable deductions and exemptions, taxable income, and all of the various
allowable credits in order to compute that taxpayer’s total tax liability under the
pertaining state tax law. Total state liability is the weighted sum over all of the
individual taxpayer records in the dataset, where the sum of the weights
corresponds to the size of the total taxpaying population of the state.
Typically, certain tax law provisions are scheduled to change during the
projection period. For example, the major provisions of the 2001 Economic
Growth and Reconciliation Tax Act are scheduled to sunset at the end of 2010.
Thus, the parameters used in the tax calculator portion of the micro-simulation
model must be consistent with the tax law in effect for the year being simulated.
The analyst can simulate the impact of alternative tax regimes on liability by
adjusting model parameters, such as tax rates, and repeating the tax calculating
process. The capacity to alter tax law parameters makes the micro-simulation
model a useful tool for estimating the impact of alternative tax policy proposals,
as well as the sensitivity of liability estimates to alternative economic forecast
scenarios. Thus, it is important to create the capability to easily alter these
parameters when constructing the micro-simulation model.