tax base elasticities: a multi-state analysis of long-run and short-run dynamics
TRANSCRIPT
Tax Base Elasticities: A Multi-State Analysisof Long-Run and Short-Run Dynamics
Donald Bruce,* William F. Fox,{ and M. H. Tuttle{
We examine the relative dynamic responses of state personal tax revenues and sales tax bases tochanges in state personal income. Our econometric analysis, which includes separate analyses oflong-run and short-run dynamics for each state, permits the estimation of asymmetric short-runresponses depending upon the relationship between current and expected tax base growth.Results indicate that the average long-run elasticity for income taxes is more than double thatfor sales taxes. Most states have asymmetric short-run income elasticities, which are againgreater for income taxes than for sales taxes. However, a joint analysis of long- and short-rundynamics reveals that neither tax is universally more volatile. After calculating state-specificincome elasticities for both taxes, we employ cross-section regression techniques to explain thevariation in elasticities across states. Several policy factors are found to be important, includingelements of tax bases and rate structures.
JEL Codes: H2, H7
1. Introduction
Generating ;sufficient revenue to finance government service delivery is arguably the most
important characteristic of state tax systems because revenue collection is the primary purpose
for most taxation. Despite this obvious point, collections often remain in the back seat of any
economic analysis, with efficiency and equity frequently receiving the most analytical attention.
Revenue is frequently introduced either as a constraint in maximization problems or by
assumption, while other aspects of the tax system are analyzed. Further, the analyses are often
static, meaning government revenue is only considered in a single year, with no consideration
given to the dynamics of revenue performance.
The poor fiscal performance of most states from 2001 through 2003 has at least
temporarily brought revenue issues to the forefront. States have had difficulty in financ-
ing legislated budgets—or in some cases, even maintaining past spending levels.1 Un-
fortunately, the emphasis of many political discussions has been on meeting current revenue
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* Center for Business and Economic Research, 105 Temple Court, University of Tennessee, Knoxville, TN 37996-
4334, USA; E-mail [email protected]; corresponding author.
{ Center for Business and Economic Research, 101 Temple Court, University of Tennessee, Knoxville, TN 37996-
4334, USA; E-mail [email protected].
{ Department of Economics and International Business, 237A Smith-Hutson Building, Sam Houston State
University, Huntsville, TX 77341, USA; E-mail [email protected].
The authors thank Mohammed Mohsin, Robert Ebel, Robert Strauss, John Mikesell, and three anonymous
referees for very helpful comments and John Deskins for very valuable research assistance.
Received September 2004; accepted February 2006.1 See Jenny (2002) for an example of the problems that states have confronted.
Southern Economic Journal 2006, 73(2), 000–000
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goals without considering whether the revenue system is structured to collect sufficient
revenue over the long term.2 Much debate can be expected during the next several years on
the design of tax structures that can best prevent recurrence of similar fiscal crises. A clear
understanding of the dynamic properties of revenue structures is necessary so that tax
structures can be adapted to ensure they generate appropriate revenue growth in the future.3
This paper fills this gap by analyzing the factors that determine the dynamic performance
of revenue systems. This is achieved by estimating long-run and short-run income elasti-
cities for personal income taxes and general sales taxes for every state. Then, the factors that
explain the elasticity differences across states are examined to discern the implications for tax
policy.
The primary focus in this paper is on the income elasticities of the two major tax sources
relied upon by state governments, the sales and the personal income taxes. Combined, these
taxes generated 66.7% of all state tax revenue in 2004.4 Reliance on these tax instruments varies
both over time and across states. In 2004, state sales taxes raised between 14.5% of tax revenue
in Vermont and 61.3% in Tennessee.5 In 2004, state personal income taxes raised between
17.4% of revenue in North Dakota and 70.0% in Oregon. Across all states, the income tax has
grown dramatically as a share of state tax revenue, rising from 17.3% in 1967 to 33.1% in 2004.
The sales tax has also risen, although at a less robust rate, growing from 28.6% of state tax
revenue in 1967 to 33.6% in 2004.
State tax structures can be envisioned much like personal portfolios. Revenue growth and
volatility are parallels to the risk-reward framework for the portfolio, but we have little
information on the way in which growth occurs. Current experience illustrates the parallel,
since many states have seen that an adequate long-term growth rate is not necessarily sufficient
to ensure that service delivery will be properly financed on an annual basis. Further, depending
upon the particular economic environment, tax revenue growth may slow (or accelerate) more
radically than would appear consistent with long-run relationships between personal income
and revenue growth. Again, the rapidity with which revenue growth slowed for the states
during 2001 appeared to be radically different from the slow pace with which revenue growth
recovered in the 2003 to 2005 time period. Tax and financing structures must be able to pro-
vide adequate revenues during the wide array of different economic environments that may
arise. Thus, this paper not only investigates long-run elasticities but also estimates short-run
elasticities for every state and seeks to determine the differences between the short- and long-
run elasticities. Further, the econometric specifications are designed to consider whether short-
run elasticities are asymmetric, since revenues may be more responsive in certain economic
environments. Based on this information, states can not only enhance the design of their tax
structures, but they can also use careful resource planning, such as rainy day funds, to smooth
expenditures during downturns.
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2 One example is the strong tendency for states to partially correct their revenue shortfalls with increases in specific taxes
on tobacco products. Forty states have raised their cigarette tax rates a total of 63 times since 2000. See http://
www.taxadmin.org/fta/rate/cig_inc02.html.3 There is no intent in this study to identify the appropriate size of government. Revenue growth is deemed appropriate if
it is sufficient to fund the publicly desired level of expenditures as determined through the political process.4 U.S. Bureau of the Census, State Tax Collections, 2004. See also http://www.census.gov/govs/www/statetax.html.5 All percentages in this paragraph refer to states that impose the tax being discussed. State tax shares are taken from
information provided by the Federation of Tax Administrators at http://www.taxadmin.org/fta/rate/04taxdis.html.
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2. Literature Review
The literature on income elasticities and stability of state and local taxes has a long history,
though it is relatively sparse. In the seminal paper in this literature, Groves and Kahn (1952)
estimate state and local revenue elasticities and recognize that elasticities need not be constant
over time. Fox and Campbell (1984) estimate the sales tax elasticity for ten disaggregated
taxable sales categories and find the elasticities vary by sales category, average 0.59 over the
long term, and are widely variable on an annual basis. Variation occurs as the income elasticity
for taxable durable goods categories declines in recessions and rises in expansions and moves
in the opposition direction for nondurable goods. Otsuka and Braun (1999) use a random
coefficient model and generally confirm the Fox and Campbell results.
Dye and McGuire (1991) examine the elasticity and stability of both the individual in-
come and sales taxes. They conclude that the components of both the income (by income class)
and sales (by type of consumption) tax structures vary significantly and that both flat and pro-
gressive income taxes are likely to grow faster than either a broad or a narrow-based sales tax.
Sobel and Holcombe (1996) build on the Dye and McGuire analysis through the use of
time series techniques and by examining more tax instruments. A key limitation of both Dye
and McGuire and Sobel and Holcombe, however, is that their analyses rely on stylized rather
than actual tax structures. For example, Sobel and Holcombe proxy the sales tax base with
national total retail sales and nonfood retail sales. However, retail sales differ dramatically
from the sales tax bases imposed by states. Several states exempt some retail purchases be-
sides food (such as gasoline and clothing), tax a varying number of services and tax many
business purchases.6 Also, state income tax bases have very different exemption and deduction
structures and often exclude certain forms of income. For example, pension income is exempt in
many states. Differences between the actual tax base used in a state and the stylized tax bases
seen by economists occur for many reasons, including political, economic development, and
administrative factors.
The rate structures also differ from those implicit in the analyses of the earlier studies.
Many states impose multiple sales tax rates and complicated progressive income tax regimes.
Thus, earlier research is useful as exploratory steps, but fails to investigate how actual tax
structures respond to economic growth, how specific tax structure characteristics alter the
underlying elasticities, and how these relationships change over time.
This paper extends the literature on state revenue elasticities in three important ways.
First, tax elasticities are estimated for each state using actual tax base data. Thus, the estimated
relationships between bases and personal income result from the response of legislated tax bases
and rates to changing income, and the resulting wide differences across states illustrate how
important policy decisions are to the final outcome. These estimates are much more useful for
understanding the underlying determinants of tax base growth. Second, both short-run and
long-run elasticities are measured, and the short-run elasticities are allowed to be asymmetric
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6 The actual tax structures differ widely by state from the very broad base used by Hawaii, representing 108.2% of state
personal income, to the narrow base imposed in states such as Massachusetts and New Jersey, representing about 30%
of personal income. Values are drawn from calculations prepared by the authors using data from State Government
Finances, U.S. Bureau of the Census and tax rates obtained from various sources. See Ring (1999) for state estimates of
the extent to which business purchases are included in the base. An overview of state taxation of services as well as
exemptions for certain categories of tangible goods is provided by the Federation of Tax Administrators at http://
www.taxadmin.org/fta/rate/tax_stru.html. We return to these issues below.
Tax Base Elasticities 0
based on the direction of underlying disequilibrium. Third, the study directly examines the
determinants of the variation in elasticities across states. This allows states to better understand
what policy decisions affect revenue responses and what state characteristics cause revenues to
grow differently across states.
3. Econometric Specification
Several steps are required to estimate the long-run elasticities, short-run elasticities, and
any asymmetries that may exist in the short run. This section describes the econometric
methods used to estimate the tax elasticities. First, we estimate long-run elasticities using
a single-equation cointegration technique, namely Dynamic Ordinary Least Squares (DOLS)
(Stock and Watson 1993).7 These estimated elasticities measure the long-run, stable
relationships between state tax bases and state personal income. Next, we estimate short-run
elasticities and speed of adjustment parameters for each tax instrument via an error correction
model, which restricts the tax base to adjust toward the estimated long-term relationship. This
method follows that employed by Sobel and Holcombe (1996). We further contribute to the
current literature by introducing a model that allows and tests for asymmetric responses in both
the short-run tax base elasticity and long-run speed of adjustment for each state. Finally, we
estimate cross-sectional regressions to examine the possible determinants of these elasticities.
Long-Run Income Elasticities
Over long time periods, sales and personal income tax bases in each state depend upon the
level of state personal income as follows:
Bit ~ f i I i
t
� �ð1Þ
In Equation 1, for state i in year t, B denotes the natural log of the current period tax
measure and I denotes the natural log of personal income. Caution must be observed when
using time-series data to estimate relationships such as this, since the use of non-stationary
time-series observations may produce spurious results.8 Augmented Dickey-Fuller (ADF) tests
(Dickey and Fuller 1981) suggest that the natural logs of sales tax bases, personal income tax
revenues, and personal income in each state contain a unit root, or are non-stationary.9
However, the risk of spurious regression is eliminated if the variables in question tend to move
together over a long period of time (i.e., if they are cointegrated). Although the presence of
cointegration removes the problem of spurious regression, several other problems can arise in
the context of time series regression via OLS. These problems include serial correlation, non-
normally distributed residuals, and endogeneity.10 Personal income shares a theoretical long-
run relationship with both the sales tax base and the personal income tax base, mitigating the
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7 See Ludvigson and Steindel (1999) for an example of the use of this technique.8 See Granger and Newbold (1974).9 From the ADF tests, all series appear to be integrated of order one and first-difference stationary. All ADF results are
available from the authors upon request.10 While the lack of a suitable instrumental variable precludes thorough testing for endogeneity, we provide evidence of
serial correlation in the analysis that follows.
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possibility of spurious regression. We further correct for the deficiencies of OLS by using
DOLS to estimate the long-run elasticity of each tax base with respect to personal income. The
DOLS specification, which provides a correction for bias and serial correlation, is as follows:
Bit ~ bi
0 z bi1I i
t zXj
g~{j
cigDI i
tzg z Qit ð2Þ
Equation 2 is estimated separately for each tax base, and the long-run elasticity of the specific
tax base with respect to personal income in state i is given by b1.11 The j leads and lags of the
change in personal income represent the DOLS correction to adjust for possible endogeneity
and autocorrelation.12 We use standard delta notation to denote first differences of our key
variables.
Symmetric Short-Run Elasticities
Changes in long-run equilibrium tax bases caused by changes in personal income may not
be fully realized until after an adjustment period. More importantly, stability between tax bases
and personal income need not hold in the short run; any differences between short and long-run
income elasticities create deviations between the long-run equilibrium base and the current
period base. Therefore, actual bases from either tax for state i (denoted by Bt) may be above or
below the long-run equilibrium value (denoted by Bt*) in any period. In Equation 3, the current
period value of e measures the deviations of the respective actual tax base in period t from its
long-run equilibrium value. These short-run deviations occur when the immediate effect of
a change in personal income is different from the long-run effect.
Bit ~ Bi�
t ~ eit ~ Bi
t { bi0 { bi
1I it ð3Þ
Thus, two short-run effects can exist in any time period: tax bases can respond to changes
in personal income and tax bases can adjust according to the disequilibrium (e) that exists at the
beginning of the period. The selected econometric approach must capture both of these short-
run effects, and this is achieved with an error-correction model (ECM):
Bit { Bi
t{1 ~ ai0 z ai
1 I it { I i
t{1
� �z ai
2 eit{1 z mi
t ð4Þ
The ECM involves separate regressors to measure each of these effects. The a1 parameter in
Equation 4 captures the immediate, intra-period effects of a change in personal income; it is
a measure of the short-run income elasticity.
One point of interest is how the short-run tax base elasticities differ from the long-run
elasticities. The econometric specification used here allows for direct comparison between the
two. The short-run tax base response to personal income changes is smaller or greater than the
long-run response according to whether a1 is less than or greater than b1. Another interesting
question is how fast tax bases move toward a new long-run equilibrium brought about by
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11 In Equations 2–5, B denotes the natural log of the current period tax measure and I denotes the natural log of
personal income.12 The appropriate number of leads and lags varies between states and is determined using the Schwarz Bayesian
Criterion (1978). Standard errors in this paper are calculated using the method of Newey and West (1987).
Tax Base Elasticities 0
changes in personal income. The a2 parameter in Equation 4 measures the size of adjustment of
the tax base to its long-run equilibrium value, and gives the percentage of disequilibrium that
is removed in every period.13 Therefore, the larger the absolute value of this adjustment
parameter, the faster the tax base moves toward its long-run value.
Asymmetric Short-Run Income Elasticities
The short-run elasticity in Equation 4 is the same regardless of whether the respective tax
base measure is below (et less than zero) or above (et greater than zero) its long-run equilibrium
value. However, it is reasonable to expect that either tax base could exhibit an asymmetric
response as a result of state structural considerations, differences in household behavior, or
other factors.
The ECM can be modified to allow for the presence of any asymmetry, as shown in
Equation 5:
DBit ~ ai
0 z ai1DI i
t z hi1 DBi
t � DI it
� �z ai
2 eit{1 z hi
2 DBit{1 � ei
t{1
� �z ni
t ð5Þ
A dummy variable (DBt) is inserted to identify the tax measure’s position relative to its
equilibrium value.14 This dummy equals zero if the respective tax measure is below its long-run
equilibrium value and one if it is above equilibrium.15 The model specification given by
Equation 5 allows for separate measurement of an asymmetric short-run elasticity and
adjustment parameter.
The revised econometric method provides the ability to estimate differences between short-
run and long-run elasticities and determine whether the short-run elasticities vary according to
the projected future growth in taxes. For example, the respective tax base measure will adjust
upward in the future if it is below long-run equilibrium (et less than zero). Examining whether
h1 is statistically different from zero allows a test of whether this upward adjustment is different
relative to the downward future adjustment when bases are above equilibrium. Asymmetry in
the long-run adjustment of either tax base is determined by the statistical significance of h2.
4. Data Issues
We use annual time series data for 1967 through 2000 to estimate all long-run and short-
run elasticities and adjustment parameters separately for the sales and income tax for each
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13 The total disequilibrium removed after t periods is given by 1 2 (1 + a2)t.14 Here, a modified version of the method developed by Granger and Lee (1989) is employed. Granger and Lee separate
the error-correction term into its positive and negative elements. Here, a dummy is added to signify the positive and
negative elements of the error-correction term to measure any asymmetries in the short-run adjustment and to allow
for the measurement of any asymmetries in the short-run elasticity. See Cook, Holly, and Turner (1999) for another
application. For an additional method, see Enders and Siklos (2001).15 Specifically, DBt takes the value of zero when et is less than zero and one when it is above zero. While this strategy
identifies asymmetry on the basis of base/revenue growth relative to personal income growth, a potentially more easily
interpretable approach would define asymmetry on the basis of income fluctuations in isolation. Experimentation with
such approaches (e.g., where DBttakes the value of one in times of recession or relatively slow income growth) left us
unable to identify any asymmetry at all. This is likely because there were not enough recession or slow growth years
with which to identify asymmetric responses.
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state. Selection of the dependent variables for the sales and income taxes is a key decision in the
analysis. As we have noted, much previous work has relied upon national proxies for state tax
bases. There are two main reasons why we choose to use actual state data rather than national
proxies. First, our approach allows us to develop state-specific elasticity estimates and to
investigate the causes of the wide differences in estimated elasticities across the states. It seems
very likely that elasticities would vary with state-specific tax base characteristics, such as
progressive income tax rates or the extent to which services are taxed by the sales tax. Long-run
elasticities may also be affected by the causes of economic growth, which might be influenced
by the state economic structure. State-specific tax estimates are necessary to study issues such as
how the elasticity is affected by the interplay between the differing state economies and tax
performance. This would not be possible with national proxies.
Second, and more importantly, extensive differences exist between any possible proxies
and the actual bases observed in each state. As a result, state-specific data are necessary to
measure elasticities in the context of the actual tax institutions used across the United States.
State structures also differ so greatly that it is necessary to estimate each state’s elas-
ticity independently. The most significant difference is that approximately 40% of the sales
tax is paid on intermediate purchases (Ring 1999), and this portion of the base will not be
reflected in national consumption proxies used by other analysts. Various components of
retail sales or consumption (from national income accounts) do not include these inter-
mediate purchases, which are large shares of the sales tax base in every state.16 This is not to say
that taxation of intermediate purchases is good tax policy, but it is a large part of actual tax
bases, and it is not possible to examine actual sales tax elasticities with this part of the base
excluded.
State treatment of consumer purchases also differs widely from measures of consumption
in the economic data. For example, 30 states exempt food for consumption at home, seven
exempt some clothing, all but one exempt prescription drugs, 10 exempt nonprescription drugs,
and states tax between 14 (Colorado) and 160 (Hawaii) of the 168 categories of services
enumerated by the Federation of Tax Administrators (FTA).17 The problem is exacerbated
by the radical differences in state definitions of taxable food, clothing, services, and other
transactions.
Figure 1 illustrates the importance of the sales tax base choice.18 Personal consumption
has risen during the time series, from about 62% to 70% of GDP. Retail sales have been slightly
volatile but are nearly the same share of GDP at the beginning and end of the panel. The simple
average of all statss’ actual sales tax bases, on the other hand, is consistently much larger than
retail sales (because the taxation of business inputs and services exceeds exemption of goods)
but has declined from 53.2% of GDP in 1979 to 40.1% in 2003. Observation of these data series
evidences the definitional differences between actual sales tax bases and economic data and
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16 As a general rule, states exempt goods purchased for resale and goods that become component parts of other goods.
This means that states frequently tax a range of intermediate purchases including computers, software, cash registers,
services, packaging and many other items.17 See the wealth of state tax rule information provided by the FTA at http://www.taxadmin.org/fta/rate/tax_stru.html.18 Data in Figure 1 are taken from: retail sales, U.S. Department of Commerce, Advanced Monthly Sales for Retail and
Food Services; consumption, National Income Accounts, Bureau of Economic Analysis; and state sales tax bases are
drawn from calculations prepared by the authors using data from State Government Finances, U.S. Bureau of the
Census and tax rates obtained from various sources.
Tax Base Elasticities 0
how these series are diverging over time.19 Differences in state definitions of the actual tax base
are even broader than the divergence from economic data. Hawaii’s tax base was 92.6% of
GSP in 2000, while Rhode Island’s base was only 27.5% of GSP in the same year. Proxies
cannot reasonably be used to account for the differences arising from state-specific policy
choices.
Similar cross-state differences exist for the income tax. Twenty-seven states start
calculation of the personal income tax with federal adjusted gross income, leaving the state
free to set deductions and exemptions, if any are used at all, according to state preferences. Ten
states start with federal taxable income, meaning federal exemptions and deductions are
accepted. Four states do not explicitly start with a federal definition of income.20 In every case,
states make adjustments to income after the starting point. For example, all but three states
allow some personal exemption, but the amounts vary significantly. Some states exempt all or
part of pension income. States do not allow deduction of state income taxes, but eight states
allow deduction of federal income tax paid. Tax structures in 14 states are at least partially
indexed for inflation. National proxies, such as personal income or GSP, cannot allow for
these cross-state differences, and at best can be seen as some type of average income across
states that does not capture actual tax institutions. Further, these measures often do not include
capital gains and some other forms of non-labor income that have been an important part of
taxable income. National tax measures, such as adjusted gross income or taxable income, are
closer to state tax measures. However, these proxies cannot account for the differences in state
practice.
State data on the income and sales tax bases, the preferred dependent variables, are
unfortunately not directly available. Actual state sales tax bases are measured here as state sales
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19 Likely causes of the decline in state sales tax bases over time include policy decisions to narrow the base (such as new
exemptions of food for consumption at home), different growth rates of taxable and nontaxable transactions, and
inability of states to collect the tax on rapidly growing remote sales.
Figure 1. Personal Consumption, General Sales, and Retail Sales as a Percentage of GDP
20 Again, see the FTA resources at http://www.taxadmin.org/fta/rate/inc_stp.html.
0 Bruce, Fox, and Tuttle
tax revenue divided by the general state sales tax rate.21 While many states impose rates that
differ from the general rate on a narrow set of transactions, the resulting difference between the
estimated and actual bases will be very small. In fact, the only variation from the actual tax
base could arise because tax credits could alter the timing of sales tax receipts between fiscal
years. The income tax is measured here using actual revenues rather than the base because 35
states impose progressive rates and the quotient obtained by dividing income tax revenue by
the maximum rate will differ significantly from the actual income tax base.22 Based on the
significant limitations of alternative tax base proxies, we believe that our resulting elasticity
estimates are much better measures of actual state relationships than would be obtained using
non-tax proxies for tax bases.
State tax revenue data are drawn from the U.S. Census,23 with each tax base measure
adjusted for inflation using the GDP deflator. Specifically, we estimate the relationships
between inflation-adjusted tax bases and inflation-adjusted personal income. Factors besides
personal income that can influence the pattern of tax bases, such as legislated base changes, are
taken into account in our cross-section analysis.24
5. Empirical Results
Long-Run Income Elasticities
We estimate Equations 2 and 5 separately for each state and provide average parameter
estimates across the states for the sales tax in Table 1 and the income tax in Table 2. State-
specific estimates are shown in Figures 2 and 3 and Tables 3 and 4. The average parameter
estimates appear very reasonable, but there are significant differences across the states, as
expected. The average long-run income tax elasticity is 1.832, which is more than twice the
average sales tax elasticity. The difference between the average long-run sales tax and income
tax elasticities is statistically significant at the 99% level of confidence. Both are significantly
different from one, with income tax revenues growing significantly faster than personal income
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21 This approach has been used in a number of other papers. See Mikesell (2004) for an example.22 The resulting coefficient estimates from these types of regressions are often termed buoyancy measures rather than
elasticities because the relationship between the dependent variable—revenues—and personal income includes
influences from rate and base changes. However, in our cross-section analysis we separate out the effects of base and
rate changes on the elasticity estimates and simulate the elasticities for each state net of rate changes.23 Tax revenue data used in this paper are taken from U.S. Bureau of the Census, State Government Finances, annual.
See also http://www.census.gov/govs/www/state.html.24 Another important issue that we are not able to explore in this framework is the possible spatial relationships between
state tax base elasticities, or the notion that one state’s elasticities are related to those in similar or surrounding states.
Such an analysis would be a worthwhile addition to the literature but is left for future research.
Table 1. Average State Sales Tax Elasticities
Mean Variance
Long-run sales tax elasticity 0.811 0.048Short-run sales tax elasticity above equilibrium 1.804 7.179Short-run sales tax elasticity below equilibrium 0.149 0.880Sales tax adjustment parameter above equilibrium 20.332 0.054Sales tax adjustment parameter below equilibrium 20.513 0.150
Tax Base Elasticities 0
and sales tax bases growing slower than personal income. The long-run income tax elasticity
estimate is greater than the long-run sales tax elasticity estimate in every state that employs
both taxes (see Tables 3 and 4).25,26 The relative sizes of the long-run elasticities are consistent
with the change in the share of revenues raised by these two taxes.
The highest sales tax elasticity, at 1.365, occurs in Massachusetts, and the lowest, at 0.339,
occurs in North Dakota (see Table 3 and Figure 2). Only nine states have sales tax elasticities
above 1.0, and in four cases the difference from 1.0 is statistically significant. Individual state
income tax elasticities vary widely (see Table 4 and Figure 3). The estimate for the income tax
elasticity is only below 1.0 in two states, North Dakota and Vermont, and is only significantly
below 1.0 in North Dakota.27 Thirteen states have income tax elasticities above two, and in five
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27 The North Dakota elasticity is not significantly different from zero.
Table 2. Average State Income Tax Elasticities
Mean Variance
Long-run personal income tax elasticity 1.832 0.427Short-run personal income tax elasticity above equilibrium 2.663 5.014Short-run personal income tax elasticity below equilibrium 0.217 2.180Personal income tax adjustment parameter above equilibrium 20.618 0.192Personal income tax adjustment parameter below equilibrium 20.411 0.090
Figure 2. Long-Run Sales Tax Elasticities
25 No sales tax elasticity is calculated for Indiana because personal income and sales tax revenues are not cointegrated.
No income tax elasticity is calculated for Connecticut because the tax was only introduced in 1991, leaving only a short
time series of revenue data.26 This result continues to hold for all states except Massachusetts when we adjust the income tax elasticities for rate
changes using the cross-section results. Adjusted elasticities are provided in Appendix 2.
0 Bruce, Fox, and Tuttle
cases the elasticity is significantly above two. As shown in Figure 4, the distribution of income
tax elasticities is much wider than for the sales tax.
It is difficult to compare our results with earlier research because those studies used
different econometric methods and generally relied on national proxies rather than state-level
analysis. A comparison with Dye and McGuire (1991) is particularly difficult because they
estimate growth rates for various tax alternatives and components of the base rather than
elasticities. Our income tax elasticity estimates for the average state are higher than Sobel and
Holcombe (1996) find for the national proxies, and 34 of 40 states have a higher long-run
elasticity than their national estimate. This is expected given our use of relatively more variable
state-specific data. Our average sales tax estimate, on the other hand, is in the middle of those
presented by Sobel and Holcombe. With that said, we find essentially no state to have sales tax
elasticity as high as their high-end estimate.
Short-Run Elasticities and Adjustment Parameters
Short-run estimates are generated using the error correction model that allows for
asymmetric income elasticities and rates of adjustment when the above and below equilibrium
estimates are significantly different (Equation 5). Otherwise, the coefficients are from the
symmetric model (Equation 4). The primary focus from a policy perspective is on the collection
of revenues within a fiscal year rather than on the more narrowly defined relationship between
bases and income. As previously described, the change in bases during any year is the net of two
effects: (1) the change in bases in response to any change in personal income and (2) the
adjustment to eliminate any existing disequilibrium. Thus, it is important to evaluate both
effects and how they interact. As the results are discussed, each effect is considered separately
and then the net impact is evaluated.
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:00 11 Cust # 240184
Figure 3. Long-Run Personal Income Tax Elasticities
Tax Base Elasticities 0
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Table 3. Sales Tax Elasticities
Long-Run
Elasticity
Short-Run Elasticities Speed of Adjustment
When Current
Revenue Value is
below Long-Run
Equilibrium
When Current
Revenue Value is
above Long-Run
Equilibrium
When Current
Revenue Value is
below Long-Run
Equilibrium
When Current
Revenue Value is
above Long-Run
Equilibrium
Alabama 0.712** 0.050 1.120** 20.152 20.152Arizona 0.744** 21.232** 1.452** 20.742** 20.742**Arkansas 0.835** 0.323 1.398** 20.915** 20.113California 0.833** 21.408** 1.146** 21.874** 20.193Colorado 0.781** 1.869** 1.869** 20.183* 20.183*Connecticut 1.242** 1.152** 2.781** 20.168* 20.168*Florida 0.926** 20.049 1.445** 20.528** 20.528**Georgia 0.708** 0.171 1.209** 20.263** 20.263**Hawaii 1.110** 0.629** 1.285** 20.476** 20.476**Idaho 0.847** 0.665** 1.456** 20.246** 20.246**Illinois 0.871** 0.028 0.028 20.226 20.226Indiana — 0.723* 0.723* — —Iowa 0.374** 20.056 0.853** 20.850** 20.850**Kentucky 0.654** 0.826** 0.826** 20.255** 20.255**Kansas 0.630** 0.466* 0.466* 20.119 20.119Louisiana 0.514** 20.347 1.531** 20.182* 20.182*Maine 0.904** 20.857 1.047 20.380** 20.380**Maryland 0.767** 1.162** 1.162** 20.154 20.154Massachusetts 1.365** 0.354 2.375** 20.320** 20.320**Michigan 0.772** 20.017 1.713** 20.511** 20.511**Minnesota 0.876** 20.226 0.903** 21.082** 20.409*Mississippi 0.486** 20.188 1.340** 20.262* 20.262*Missouri 0.639** 22.192** 0.907* 20.612** 20.612**Nebraska 0.431* 0.191 18.779** 20.905** 20.905**Nevada 0.781** 20.500 1.600** 20.506** 20.506**New Jersey 1.049** 20.297 1.552** 20.601** 20.601**New Mexico 0.924** 20.628 3.070** 21.188** 20.399*New York 0.750** 0.128 1.571** 20.438** 20.438**North Carolina 0.874** 0.501 1.820** 21.045** 20.124North Dakota 0.339 0.256 20.506* 20.483** 0.260Ohio 1.033** 1.802** 1.802** 20.357** 20.357**Oklahoma 0.695** 1.890** 1.890** 20.124* 20.124*Pennsylvania 1.069** 1.504** 1.504** 20.216** 20.216**Rhode Island 0.531** 0.515 1.848** 20.124 20.124South Carolina 0.773** 21.150 1.143** 20.510** 20.510**South Dakota 1.145** 0.471** 0.471** 20.562** 20.562**Tennessee 0.716** 0.308 1.271** 20.240* 20.240*Texas 0.997** 1.580** 1.580** 20.749** 20.749**Utah 0.873** 21.544 1.780** 20.234** 20.234**Virginia 0.800** 20.645 0.826** 20.293** 20.293**Vermont 0.735** 0.779 2.289** 20.840** 20.061Washington 0.740** 0.045 1.722** 21.404** 20.546**West Virginia 1.013** 21.146 3.295** 20.829** 20.106Wisconsin 1.113** 20.623 1.373 20.289** 20.289**Wyoming 0.720** 1.443** 1.443** 20.134 20.134
Bold, italicized, and underlined type indicate statistically significant differences from one, two, and three, respectively,
at the 5% level. Bold type for speed of adjustment results indicates that the coefficient is not statistically different from 21.0.
* Statistically significant differences from zero at the 10% level.
** Statistically significant differences from zero at the 5% level.
0 Bruce, Fox, and Tuttle
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:12 13 Cust # 240184
Table 4. Personal Income Tax Elasticities
Long-Run
Elasticity
Short-Run Elasticities Speed of Adjustment
When Current
Revenue Value is
Below Long-Run
Equilibrium
When Current
Revenue Value is
Above Long-Run
Equilibrium
When Current
Revenue Value is
Below Long-Run
Equilibrium
When Current
Revenue Value is
Above Long-Run
Equilibrium
Alabama 1.823** 1.393** 3.009** 20.221 21.216**Arizona 1.140** 0.768** 0.768** 20.271** 20.271**Arkansas 2.102** 0.833 0.833 20.508** 20.508**California 1.749** 21.536 3.223** 20.718** 20.718**Colorado 1.256** 21.040 0.962* 20.181* 20.181*Delaware 1.018** 20.885 1.088* 20.174* 20.174*Georgia 1.690** 0.130 1.199** 20.172** 20.172**Hawaii 1.320** 20.786 2.013** 20.667** 20.667**Idaho 1.565** 20.001 2.382** 20.683** 20.683**Illinois 1.565** 0.298 2.882** 21.017** 21.017**Indiana 2.435** 20.783 1.702** 0.445 20.611**Iowa 2.349** 1.176** 22.679 20.256** 20.256**Kentucky 2.600** 0.465 0.465 0.015 0.015Kansas 2.260** 0.461 6.223** 20.609** 20.609**Louisiana 2.272** 1.123 8.938** 20.292* 21.176**Maine 2.873** 0.403 2.639** 20.051 21.638**Maryland 1.183** 0.510* 1.986** 20.814** 20.814**Massachusetts 1.415** 0.538 1.660** 20.248** 21.548**Michigan 1.879** 0.570 3.210** 20.366** 20.366**Minnesota 1.320** 20.128 2.300** 20.262 20.930**Mississippi 1.910** 2.400** 2.400** 20.563** 20.563**Missouri 2.292** 0.046 6.242** 20.370** 21.784**Montana 1.604** 20.486 2.313** 20.392** 20.392**Nebraska 2.491** 1.170* 1.170* 20.811** 20.811**New Jersey 2.016** 20.195 2.031** 20.470** 20.470**New Mexico 3.024** 26.223 8.370* 20.207** 20.207**New York 1.295** 21.169* 2.160** 20.309** 20.309**North Carolina 1.545** 0.767** 2.505** 20.265** 21.181**North Dakota 0.809 0.197 0.197 20.298** 20.298**Ohio 3.983** 22.479 2.529* 20.956** 20.136Oklahoma 2.613** 1.731** 4.250** 20.434** 20.434**Oregon 1.440** 0.100 4.333** 20.991** 20.991**Pennsylvania 1.431** 2.042** 5.736** 20.312** 0.064Rhode Island 1.756** 2.344** 2.344** 20.841** 20.311*South Carolina 1.564** 1.536** 1.536** 20.550** 20.550**Utah 1.477** 1.379** 1.379** 20.827** 20.827**Virginia 1.474** 0.140 1.775** 20.655** 20.655**Vermont 0.974** 0.218 0.218 20.549** 20.549**West Virginia 2.569** 1.681* 4.770** 20.296** 20.296**Wisconsin 1.215** 0.186 2.534** 20.485** 20.485**
Bold, italicized, and underlined type indicate statistically significant differences from one, two, and three,
respectively, at the 5% level. Bold type for speed of adjustment results indicates that the coefficient is not statistically
different from 21.0.
* Statistically significant differences from zero at the 10% level.
** Statistically significant differences from zero at the 5% level.
Tax Base Elasticities 0
Sales Tax Results
Consider sales tax effects arising from a change in personal income (elasticity response).
As shown in Table 1, the mean short-run sales tax elasticity is much greater when the base is
above equilibrium (1.80) than when it is below equilibrium (0.15). Estimates for individual
states differ widely, and in most states, an asymmetric base elasticity is found. Only 11 states
have symmetric short-run sales tax elasticities, with the other 33 states having different short-
run elasticities depending on the direction of disequilibrium (see Table 3).28 The short-run
above-equilibrium elasticity is only below the long-run elasticity in three states: Illinois, Kansas,
and South Dakota. Tax bases respond slowly to an increase in personal income when they are
below the long-run level. The base (and tax revenues) is most likely to be below equilibrium
during a recession or sluggish economic growth period, so the low elasticity suggests that the
revenue rebound will not be affected very much by whether personal income growth during the
recovery is rapid or slow. Yet, the high above-equilibrium short-run elasticities provide
evidence that the base is more responsive to a change in personal income when it is adjusting
downward toward its long-run value.
Second, consider the adjustment to the long-run equilibrium. The speed of adjustment
coefficient is negative on average both when the base is above and below expectations
(Table 1), but the effect is to reduce the base when it is above expectations and raise it when it is
below expectations (see Equation 3).29 Of course, the effect of adjustment on the actual base is
greater when the base is farther from equilibrium (since the effect is the coefficient times the
disequilibrium). The average below-equilibrium adjustment parameter is greater in absolute
value than the average above-equilibrium adjustment parameter suggesting a greater response
to disequilibrium below expectations, but the two parameters are only significantly different in
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:14 14 Cust # 240184
Figure 4. Long-Run Elasticities
28 The revenue elasticity for the sales tax in North Dakota is excluded here.29 Positive adjustment parameters are estimated for several states for both the income and sales taxes but the parameters
are never statistically different from zero.
0 Bruce, Fox, and Tuttle
nine states. Thus, the amount of disequilibrium eliminated in each year is generally the same
whether revenues are above or below equilibrium.
The below-equilibrium and above-equilibrium adjustment parameters are not significantly
different from 21.0 for twelve and four states, respectively, indicating that the disequilibrium is
entirely eliminated for these states in the following year. It takes more than one year to
eliminate disequilibrium in all other states. A relationship appears to exist between the size of
the short-run elasticity and the rate of adjustment. The adjustment parameter and short-run
elasticity are positively correlated (0.362) when the base is below expectations and are
negatively correlated (20.370) when the base is above expectations, and both of these
correlation coefficients are statistically significantly different from zero at the 95% level.
The dynamic base change in any year is the combination of the elasticity response and the
adjustment to disequilibrium. Figure 5 illustrates the dynamic sales tax response in two states.30
Panels A and B show the simulated below-equilibrium response when the base begins 1% below
equilibrium and when real personal income grows by 1%. The long-run equilibrium base index
rises by 0.712 in Alabama and by 0.833 in Arkansas because of the one-percent income growth.
Yet, the actual base grows slowly in Alabama because the short-run elasticity is very small
(0.05) and the adjustment coefficient is very low (20.152), meaning little of the preexisting
disequilibrium is eliminated in each year and much of the disequilibrium remains after ten
years. Conversely, Arkansas has a somewhat larger short-run elasticity (0.323) and adjusts to
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:21 15 Cust # 240184
Figure 5. Dynamic Sales Tax Responses—A Comparison between Alabama and Arkansas
30 These simulations examine the effect of a one-time increase in personal income.
Tax Base Elasticities 0
disequilibrium more rapidly (20.915). The entire disequilibrium is nearly eliminated after two
years. In the case of a similar income increase when both states are above equilibrium (see
Panels C and D), both states overshoot the expected base increase, and neither fully eliminates
the disequilibrium after ten years.
Several conclusions can be made about the dynamics of sales tax base responses. First,
states are affected very differently by cyclical and trend growth conditions, since the parameter
estimates differ widely by state. Second, tax bases grow less than would be expected from the
short-run elasticity when above equilibrium and faster than would be expected when below
equilibrium because of the adjustment to any preexisting disequilibrium. Results for the short-
run below-equilibrium elasticities and the adjustment parameters are consistent with the res-
ponse of durable goods purchases and business input purchases in the early stages of economic
recovery, depending more on the degree to which expenditure levels have fallen below long-run
equilibrium than on the speed with which income recovers. Another conclusion is that the
relative size of the two effects can vary, depending on how fast personal income changes and
how far tax bases are from their long-run equilibrium. This means the simple relationship
between income and base growth could take any sign. For example, the base could decline as
income rises (when above equilibrium) if the extent of disequilibrium is large relative to the in-
come growth or if the adjustment parameter is large relative to the short-run elasticity. Further,
the statistical estimates indicate that the adjustment parameter is much greater relative to the
short-run elasticity when the base is below expectations than when it is above expectations.
Thus, revenues are much more likely to rise noticeably above expectations (at least for a short
time) than to fall below them. This general logic applies to the income tax results that follow.
Income Tax Results
The pattern of income tax responses is similar to the sales tax (see Tables 2 and 4). Thirty
states have statistically different short-run elasticities depending on whether the base is above
or below equilibrium, while the remaining ten states have symmetric elasticities. The mean
above-equilibrium short-run elasticity (2.66) is much greater than either the long-run elasticity
(1.83) or the below-equilibrium short-run elasticity (0.22). The short-run above-equilibrium
elasticity is below the long-run elasticity in 12 states.
The average short-run sales and income tax elasticities are very similar and not
significantly different when the bases are below their respective long-run equilibrium values.31
As noted above, both taxes have short-run elasticities that are very small when the base is below
equilibrium. Further, while the average short-run elasticities differ by nearly 0.9 when the base
is above expectations, the standard deviations are relatively large, so this difference is not
statistically significant. One distinction between the income and sales tax results is that the
speed of adjustment is greater above equilibrium for the income tax (i.e., the absolute value of
the adjustment coefficient is greater above equilibrium than below equilibrium).
Nonetheless, the adjustment parameters for the income tax are the same for most states,
with only 11 states having a different adjustment parameter when above and below equilibrium.
The above-equilibrium adjustment parameter is not statistically different from 21.0 for 12
states and the below-equilibrium adjustment parameter is not statistically different from 21.0
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:27 16 Cust # 240184
31 The associated p-value is 0.79.
0 Bruce, Fox, and Tuttle
for nine states, suggesting that the entire disequilibrium is eliminated in one year for these
states.
Very different income tax responses are found across the states. For example, Louisiana
has a very high response to personal income growth when the base is above equilibrium, but the
entire disequilibrium is eliminated in the following year.32 On the other hand, New Mexico has
very high elasticity without the rapid adjustment to equilibrium.
6. Which Tax Is More Volatile?
Overall, the estimates do not provide a firm conclusion as to whether the sales or the
income tax is more volatile, with the conclusion depending upon the definition of volatility. The
income tax has a higher long-run elasticity, but that simply means that revenues grow faster
over long periods of time—it tells little about whether the growth path is volatile. Nonetheless,
discussions of volatility have often focused on the long-run elasticity. Volatility is inherently
a short-run issue and is best considered in the context of how an actual tax base (or revenue)
performs relative to its long-run equilibrium value and how much it fluctuates around the
equilibrium during short time periods or different segments of the business cycle.
Conditions when tax bases (and revenues) will be above or below expectations can be
parallel to specific economic environments, though not precisely. Both sales tax bases and
income tax revenues are likely to be above long-run equilibrium during strong growth periods,
such as the late 1990s. The base and revenues are likely to be below long-run equilibrium during
the latter stages of a recession or economic slowdown, as during the early years of the 2000s.
Thus, both taxes will respond gradually as income begins to grow more rapidly at the end of the
economic slowdown, but the total rise in the tax measure will be larger in cases when the extent
of disequilibrium has gotten to be relatively large (because of the adjustment parameter).
Figure 6 illustrates dynamic responses of both the income and sales tax bases for periods
above and below equilibrium using average state parameter estimates and similar assumptions
to Figure 5. The long-run income tax response to a one-percent income increase is twice as
large as for the sales tax, as determined by the long-run elasticities. Given that the short-run
below-equilibrium elasticities are approximately the same, the income tax response will be
much further below equilibrium than the sales tax response (Panels A and B of Figure 6). In
this sense, the income tax is more volatile. However, adjustment to the new equilibrium takes
approximately the same time for both taxes (the income tax takes slightly longer), leaving the
question of relative volatility unanswered.
Differences between the two taxes are also evident in the above-equilibrium scenarios in
Panels C and D of Figure 6. First, it should be noted that the relative extent of disequilibrium
will be greater for the sales tax than for the income tax because the difference between the
short-run above-equilibrium elasticity and the long-run elasticity is greater for the sales tax
(1.804 vs. 0.811) than for the income tax (2.663 vs. 1.832). However, the adjustment para-
meter is larger for the income tax (20.618 vs. 20.332), so the reaction to any amount of
disequilibrium will be greater for the income tax. As shown in Figure 6, the sales tax has the
greater increase relative to the new equilibrium, suggesting that the sales tax can be the more
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:28 17 Cust # 240184
32 The point estimate for the adjustment parameter is not significantly different from 21.0.
Tax Base Elasticities 0
volatile tax in above-equilibrium scenarios. The sales tax base adjusts to the new equilibrium
more slowly than the income tax. In sum, the answer to the question of relative volatility
depends upon the particular economic situation at hand.
7. Causes of State Variation in Base Elasticities
While the preceding analysis sheds important light on the differences in tax base elasticities
both across states and over time, the chosen econometric methodology is not designed to
explain the resulting cross-state differences. Toward that end, we now turn to estimates of
cross-section OLS regressions to determine whether the estimated cross-state differences in tax
base elasticities can be explained by observable factors. We estimate separate cross-section
regressions for each vector of estimated parameters (i.e., long-run elasticities, short-run
elasticities, and adjustment parameters for each of the two taxes), but only provide detailed
models of the long-run elasticity models here.
Equation Structure
The regression structure is not drawn from a formal theoretical framework, but is a policy
experiment to provide greater relevance to the findings by identifying features that are
associated with cross-state differences in the elasticities. Quite simply, we are seeking to identify
what factors are related to elasticity differences using four categories of regressors: tax structure
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:28 18 Cust # 240184
Figure 6. Dynamic Tax Responses—Analysis of Sample Means
0 Bruce, Fox, and Tuttle
characteristics, demographic factors, political characteristics, and measures of state economic
structures.33 The variables are listed with summary statistics in Appendix 1.
An important issue is what values to use as regressors, since the elasticities were estimated
using 33 years of data. In order to make these results as useful as possible in a policy context,
our baseline analysis uses regressors defined mostly as of the most recent year (1999) of our
data. Our motivation for doing this is that states are better able to make use of results drawn
from recent data (most closely related to the current environment) than if we were to explain
cross-sectional variation in elasticities using data from an earlier period. Recognizing that this
is temporally misaligned with the underlying elasticities, we also provide results where most
variables are entered as changes between 1970 and 1999.
We include six characteristics of state income tax structures in our income tax regressions:
the income threshold at which the highest marginal tax rate is imposed, a dummy variable for
whether a state-level earned-income tax credit exists, the share of the tax base represented by
capital gains, a series of four dummy variables to measure the taxation of pensions, a measure
of the overall progressivity of the income tax rate schedule, and the average annual change in
the highest marginal income tax rate between 1970 and 1999. More specifically, our pension
taxability dummies control for the total or partial exemption of government or private
pensions. Our progressivity measure is calculated as the change in the effective tax rate over an
income range from $10,000 below to $10,000 above the state’s median income level. Our
inclusion of the average change over time in the highest marginal tax rate is necessitated by our
use of tax revenue rather than tax base as the dependent variable in the income tax elasticity
estimates, and the coefficient is expected to have a positive sign. Including this variable will
allow us to essentially adjust our elasticity estimates for tax rate changes during our period of
analysis. We expect the income threshold to be negatively associated and progressivity to be
positively related with the elasticity because these variables account for how rapidly taxpayer
liabilities grow as their incomes rise. The influence of an earned income credit is less
straightforward to predict, however, as the relationship between income and tax liability varies
depending on shares of taxpayers in the phase-in and phase-out ranges of the credit. Inclusions
of pension income will be positively related to the elasticity if pension income is growing faster
than other forms of income, and negatively related otherwise.
We include two separate tax variables in our regressions of sales tax parameters. The first is
the sales tax base as a percent of personal income. The sign is expected to be positive because
a broader tax base, as given by a larger value of this variable, is an indicator that a state relies
more heavily on taxation of services. The second is a measure of the extent to which the sales tax is
levied on consumers, drawn from the estimates developed by Ring (1999). We do not have an
a priori expectation on this coefficient. We do not include the change in the sales tax rate over time
because we use tax base rather than tax revenue in our calculation of the sales tax elasticities.
These estimated elasticities are, therefore, immune to the effects of rate changes (i.e., the elasticity
of our tax base measure with respect to the tax rate is, by construction of our base measure, zero).
Our list of demographic variables in all regressions includes median income, the per-
centage of the population under 18 years of age, and the percentage of the population over
65 years of age. We control for political factors using a series of dummy variables for the
Southern Economic Journal soec-73-02-12.3d 31/7/06 13:47:34 19 Cust # 240184
33 Note that we have not included controls for spatial correlation in these regressions, although we suspect that a state’s
elasticity estimates might be related to the economic and policy environments in other states. Such an analysis, while
interesting, relevant, and fruitful, is again left for future research.
Tax Base Elasticities 0
Governor’s political party, as well as the majority party in the state’s legislature. State economic
conditions enter the regressions via measures of the share of Gross State Product (GSP) in
mining, in services, in agriculture, and in manufacturing; average annual employment growth
over the study period; and the standard deviation of employment growth. It is generally diffi-
cult to impose a priori expectations on many of these variables, so we use empirical techniques
to determine whether any relationships exist between these variables and the elasticities.
Long-Run Income Tax Estimates
As shown in the first column of results in Table 5, many of the variables are statistically
significant at the 90% level in our baseline long-run income tax elasticity model, revealing that
the wide differences in income tax elasticities can often be explained by variation in the included
regressors. For example, the long-run income elasticity is higher in states where the maximum
tax bracket occurs at lower income levels (the coefficient is negative). Of course, like any
regression coefficient, this result holds the degree of progressivity around median income (and
all other variables in the model) constant. Given a level of progressivity, our finding that states
with lower top-bracket thresholds have higher long-run income elasticities is perhaps un-
surprising, since an increase in income would lead to a relatively larger increase in taxes paid in
those states. This result is seen only with the 1999 specification, and not with the 1970–1999
changes specification.
Failure to tax pensions generally lowers the elasticity, suggesting that pension income is rising
faster than other forms of income. The one exception in both models is partial exemption of private
pension income. Some states have chosen to exclude pension income during the study period, so the
coefficient may be capturing both the fall in elasticity as the base was narrowed and the effects that
failure to tax pensions has on the elasticity. The result cannot be interpreted to mean that the
elasticity going forward will be lower for states that have already excluded pensions.
The change in tax rates is positively related to the long-run elasticity in both models,
providing the anticipated finding that revenues grow faster when rates are increased and slower
when rates are decreased. Of the states that imposed an income tax throughout the entire study
period, 16 raised their maximum income tax rate and 14 decreased their rate, with the average
annual change being an increase of 0.3%. Thus, the average income tax elasticity was increased
by 0.09 as a result of rate changes, leaving the average income tax elasticity adjusted for rate
changes still about twice as large as the average sales tax elasticity.34
In terms of state demographic characteristics, our 1999 specification reveals that long-run
income tax elasticities are higher in states with a larger share of their population either under
age 18 or over age 65. Also, for the 1999 model, higher median incomes translate into lower
long-run income elasticities for the personal income tax. Moving to state economic factors, we
find that long-run income tax elasticities tend to be lower in states with significant resource-
based economies, whether agriculture or mining, but the coefficients are only of marginal
significance. A large agricultural sector results in a large reduction in the elasticity, providing
evidence that tax systems respond slowly to economic expansion of this sector. This finding is
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34 The effect of rate changes can be very important to some states and the adjusted elasticities for each state are presented
in Appendix 2. This calculation uses the coefficient on the tax rate change variable in Table 5 with the change in tax
rates for each state to estimate the income tax base elasticity holding all else constant. The general finding is that
elasticities moved closer to the mean, but they are still statistically different from the mean long-run sales tax elasticity.
0 Bruce, Fox, and Tuttle
consistent with the propensity of states to allow specialized treatment and low effective rates on
income generated in the agriculture sector.35 It may also reveal that credits and loss carry-
forwards from slow economic periods allow taxable income in the agriculture sector to respond
slowly as the economy improves. In any event, if all else is equal, the resource-intensive states
have less revenue-elastic tax systems than other states. More volatile employment growth, on
the other hand, tends to result in higher income tax elasticity in both models.
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Table 5. Cross-Sectional Analysis of Long-Run Elasticities
Variable
1999 Values
Income Sales
Lowest income in highest PITbracket ($ thousand)a
20.003** (0.001)
EITC dummy 20.273 (0.173)Capital gains/personal income 17.253 (11.523)Progressivity at median income 87.567 (56.813)Partial exemption for
government pensions20.920** (0.392)
Total exemption forgovernment pensions
20.656* (0.314)
Partial exemption for private pensions 0.792** (0.294)Total exemption for private pensions 20.768* (0.398)Average change in top PIT
rate (1970–1999)25.723* (12.132)
ST base/personal income 0.952** (0.451)Consumer share of ST 0.012* (0.006)Percentage of population
under 18 years of agea33.490** (7.856) 0.477 (2.913)
Percentage of populationover 65 years of ageb
27.771** (8.233) 1.854 (3.030)
Median income ($ thousands)a 20.052** (0.021) 0.017** (0.007)Republican legislature 0.660* (0.353) 0.119 (0.128)Democratic legislature 20.284 (0.262) 0.180 (0.121)Republican governor 20.329 (0.300) 0.026 (0.078)Mining share of GSPb 29.560 (7.270) 3.677 (2.398)Average annual employment
growth (1970–1999)24.808 (9.670) 0.471 (2.010)
Standard deviation of employmentgrowth (1970–1999)
23.860** (10.624) 0.548 (4.486)
Manufacturing share of GSPb 21.065 (2.689) 1.768 (1.347)Services share of GSPb 218.081 (17.737) 5.585 (3.966)Agriculture share of GSPb 235.335 (21.218) 4.669 (6.815)Constant 24.657 (4.140) 23.220 (1.903)N 35 43R2 0.601 0.060
Entries are ordinary least-squares regression coefficients with White (1980) standard errors in parentheses.a Variable enters 1970–1999 Changes specifications as the change from 1970 to 1999.b Vanable enters 1979–1999 Changes specifications as the average change from 1970 to 1999.
* Statistically significant at 10% and above.
** Statistically significant at 5% and above.
35 The authors thank John Mikesell for making this observation.
Tax Base Elasticities 0
Long-Run Sales Tax Elasticities
Unlike the analysis of the long-run personal income tax elasticities, most variables are not
statistically significant in the sales tax elasticity regressions, as shown in the second and fourth
columns of Table 5. One likely explanation is that the range of sales tax elasticities is much
smaller than for the income tax, meaning there is less variation to be explained (see Figure 4).
Also, it is more difficult to summarize important sales tax base differences quantitatively.
Despite this general lack of statistical significance, we find in our 1999 specification that
a broader sales tax base results in higher sales tax elasticity. Given the rapid growth in the
service sector as a share of personal income during the study period, and the fact that greater
taxation of services is responsible for much of the state variation in base breadth, this find-
ing suggests that taxation of more services results in a higher elasticity.36 Quite simply,
consumption of services has been more elastic than consumption of goods over the past several
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Table 5. Extended
1970–1999 Changes
Income Sales
1.935 (359.289)
20.395 (0.275)2739.067** (289.629)
433.921 (1916.552)21.039** (0.447)
20.306 (0.374)
0.576 (0.350)20.557 (0.420)30.602** (12.405)
21.967** (0.836)20.006 (0.005)
22.785 (3.787) 0.386 (1.103)
20.334 (0.983) 20.070 (0.304)
215.467 (12.968) 1.730 (4.460)0.515* (0.254) 20.047 (0.108)
20.136 (0.289) 0.021 (0.125)0.011 (0.333) 0.007 (0.086)
25.313 (3.592) 0.738 (1.360)28.002 (8.158) 0.972 (2.234)
26.263* (12.747) 22.250 (6.265)
38.594 (105.490) 224.319 (31.092)245.028* (23.391) 24.984 (5.645)
0.738 (22.500) 1.806 (4.705)5.343** (1.869) 1.288** (0.618)
35 430.517 0.047
0 Bruce, Fox, and Tuttle
decades. Alternatively, our 1970–1999 changes model reveals that states in which the change in
sales tax base breadth has been most extensive between 1970 and 1999 tend to have lower
elasticities. The sales tax base in every state declined relative to personal income during our
study period, meaning that states with the greatest base decline tend to have a more elastic sales
tax.37 Decisions by many states during our study period to exempt food for consumption at
home are probably the largest policy-driven narrowing of the bases. Thus, the finding can be
interpreted to mean that exemption of relatively slow-growing food from the base is likely to
increase the sales tax elasticity.
States where a higher share of the sales tax is incident on consumers tend to have higher
elasticities in the 1999 model. One possible explanation for this is that states have high
consumer shares because they have exempted a significant amount of business transactions
during the study period.38 The only other statistically significant result from our regressions of
long-run sales tax elasticities is that median income is found to have a significant and positive
influence on the long-run sales tax elasticity, again only in the 1999 model.
We also estimate similar regressions of all short-run parameters, with the only difference
being our inclusion of the corresponding long-run elasticity as a regressor. To summarize the
many findings of this exercise, we are largely unable to identify many policy variables that are
associated with short-run elasticities and adjustment parameters.
8. Conclusions
As states continue to experience financial hardship due to the flagging revenue
performance of major state taxes, many are tempted to adjust their revenue structure in order
to stave off future instability. In such a policy environment, it is important to understand the
comparative dynamics of various taxes. States’ failure to consider such dynamics in the mid-
1990s helped create their subsequent problems, as a number of states reduced their tax rates or
bases during the robust revenue growth years of the late 1990s, apparently believing that the
existing short-run revenue conditions reflected the underlying long-run revenue environment.
Our research expands upon the earlier literature by estimating long-run income elasticities
of the two major state taxes (personal income and sales), by separately identifying short-run
elasticities, and by allowing variation in the dynamic adjustment of the tax base in response to
personal income changes. Further, we examine the various determinants of the cross-state
variation in all estimated parameters. These results allow for a more in-depth understanding of
state revenue performance and much better insight into the relationship between short-run and
long-run revenue fluctuations.
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38 One reviewer observed that a higher consumer share might translate into lesser taxation of business, which could
stimulate economic growth.
37 The difference in these results highlights the policy applicability of the 1999 model. While the sales tax base breadth
variable (along with other variables entered as changes over the 30-year span) serves as more of a control variable in
the 1970–1999 changes model, it functions as a policy variable in the 1999 model in that states can broaden their sales
tax bases in order to increase the elasticity of the tax.
36 This result was confirmed in a separate regression where we measured base breadth via the number of taxable services
in each state.
Tax Base Elasticities 0
To summarize the many results of this empirical exercise, we first find that the average
long-run income elasticity of state personal income tax bases is more than double that for sales
taxes. Short-run elasticities are found to exhibit asymmetry in most states. Specifically, they are
higher than long-run elasticities when the current tax base is above the long-run equilibrium,
and lower when the current tax base is below equilibrium. Estimated adjustment parameters
indicate that any short-run disequilibrium is quickly alleviated for both taxes in many states.
Contrary to conventional wisdom, neither the personal income tax nor the sales tax
emerges as the universally more volatile tax. While income elasticities are generally larger for
the income tax in both the long run and the short run, a careful assessment of relative volatility
must consider the interaction of long-run elasticities, short-run elasticities, the extent of
preexisting disequilibrium, and the relative speed of adjustment toward the new equilibrium.
The sales tax can actually be the more volatile tax in certain scenarios.
After controlling for state demographic and economic characteristics, we find that
a number of state-specific policy elements are important factors of state variation in estimated
elasticities. Over the long run, personal income taxes are more income-elastic in states where the
maximum tax bracket occurs at lower income levels, pensions are taxed, the rate structure is
more progressive around the median income level, and the top rate has increased by a larger
percentage. In terms of the sales tax, states with broader bases and with larger shares being paid
by consumers have higher income elasticities.
Consequently, these results indicate that states have a number of options for increasing the
overall income elasticity of their tax structures. They can simply shift away from lower-
elasticity taxes (e.g., the sales tax) toward higher-elasticity taxes (e.g., the personal income tax),
or they can work within their existing tax portfolio by adjusting these policy elements.
However, increasing a revenue system’s elasticity does not necessarily increase its volatility.
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Appendix 1Summary Statistics and Source Notes for Cross-Sectional Regression Variables
Variable Mean Std. Dev. Minimum Maximum
ST base/personal income 0.463 0.153 0.252 1.108Consumer share of ST 59.422 8.892 28.000 89.000Lowest income in highest PIT bracket 59,344 78,977 0 300,000EITC dummy 0.220 0.418 0 1Capital gains/personal income 0.060 0.020 0.026 0.123Progressivity at median income 0.003 0.002 0 0.008Partial exemption for government pensions 0.463 0.505 0 1Total exemption for government pensions 0.268 0.449 0 1Partial exemption for private pensions 0.488 0.506 0 1Total exemption for private pensions 0.073 0.264 0 1Percentage of population under 18 years of age 0.257 0.017 0.223 0.322Percentage of population over 65 years of age 0.125 0.019 0.057 0.176Median income 58,500 7,701 44,947 75,505Republican legislature 0.400 0.495 0 1Democratic legislature 0.380 0.490 0 1Republican governor 0.620 0.490 0 1Mining share of GSP 0.017 0.034 0 0.161Average annual employment growth (1970–1999) 0.035 0.023 0.006 0.129Standard deviation of employment growth
(1970–1999)0.026 0.011 0.015 0.061
0 Bruce, Fox, and Tuttle
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Variable Mean Std. Dev. Minimum Maximum
Manufacturing share of GSP 0.162 0.064 0.030 0.316Services share of GSP 0.160 0.027 0.085 0.240Agriculture share of GSP 0.015 0.011 0.003 0.055Average change in top PIT rate (1970–1999) 0.003 0.012 20.025 0.032
Variable Source
ST base/personal income U.S. Bureau of Economic AnalysisConsumer share of ST Ring (1999)Lowest income in highest PIT bracket State Tax Handbook, Commerce ClearinghouseEITC dummy Center for Budget and Policy PrioritiesCapital gains/personal income Internal Revenue Service and Bureau of Economic
AnalysisProgressivity at median income Authors’ calculations based on median income and
tax ratesPartial exemption for government
pensionsFederation of Tax Administrators at http://
assets.aarp.org/rgcenter/econ/ib55_sstax.pdfTotal exemption for government pensions Federation of Tax Administrators at http://
assets.aarp.org/rgcenter/econ/ib55_sstax.pdfPartial exemption for private pensions Federation of Tax Administrators at http://
assets.aarp.org/rgcenter/econ/ib55_sstax.pdfTotal exemption for private pensions Federation of Tax Administrators at http://
assets.aarp.org/rgcenter/econ/ib55_sstax.pdfPercentage of population under 18 years
of ageU.S. Bureau of the Census
Percentage of population over 65 yearsof age
U.S. Bureau of the Census
Median income Statistical Abstract of the United States, U.S.Bureau of the Census
Republican legislature Statistical Abstract of the United States, U.S.Bureau of the Census
Democratic legislature Statistical Abstract of the United States, U.S.Bureau of the Census
Republican governor Statistical Abstract of the United States, U.S.Bureau of the Census
Mining share of GSP Authors’ calculations based on Regional AccountsData, Bureau of Economic Analysis
Average annual employment growth(1970–1999)
Bureau of Labor Statistics
Standard deviation of employmentgrowth (1970–1999)
Bureau of Labor Statistics
Manufacturing share of GSP Authors’ calculations based on Regional AccountsData, Bureau of Economic Analysis
Services share of GSP Authors’ calculations based on Regional AccountsData, Bureau of Economic Analysis
Agriculture share of GSP Authors’ calculations based on Regional AccountsData, Bureau of Economic Analysis
Average change in top PIT rate(1970–1999)
Authors’ calculations based on data from StateTax Handbook, Commerce Clearinghouse
Appendix 1. Continued
Tax Base Elasticities 0
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Appendix 2Long-Run PIT Elasticities Adjusted for Rate Changes
Unadjusted Adjusted
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Tax Base Elasticities 0
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0 Bruce, Fox, and Tuttle