Tax base elasticities: a multi-state analysis of long-run and short-run dynamics.

Tuttle, M.H.

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 financing legislated budgets--or in some cases, even maintaining past spending levels. (1) Unfortunately, the emphasis of many political discussions has been on meeting current revenue 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 elasticities 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 of 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 provide 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.

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 income 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 progressive 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 besides 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 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:

[B.sup.i.sub.t] = [f.sup.i] ([I.sup.i.sub.t]). (1)

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 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:

[B.sup.i.sub.t] = [[beta].sup.i.sub.0] + [[beta].sup.i.sub.1][I.sup.i.sub.t] + [j.summation over (g = -j)] [[gamma].sup.i.sub.g][DELTA][I.sup.i.sub.t+g] + [[theta].sup.i.sub.t]. (2)

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 [[beta].sub.1]. (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 [B.sub.t]) may be above or below the long-run equilibrium value (denoted by [B.sup.*.sub.t]) 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.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

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 ([epsilon]) that exists at the beginning of the period. The selected econometric approach must capture both of these shortrun effects, and this is achieved with an error-correction model (ECM):

[B.sup.i.sub.t] - [B.sup.i.sub.t-1] = [[alpha].sup.i.sub.0] + [[alpha].sup.i.sub.1](I.sup.i.sub.t] - [I.sup.i.sub.t-1]) + [[alpha].sup.i.sub.2][[epsilon].sup.i.sub.t-1] + [[mu].sup.i.sub.t]. (4)

The ECM involves separate regressors to measure each of these effects. The [[alpha].sub.1] 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 [[alpha].sub.1] is less than or greater than [[beta].sub.1]. Another interesting question is how fast tax bases move toward a new long-run equilibrium brought about by changes in personal income. The [[alpha].sub.2] 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 ([[epsilon].sub.t] less than zero) or above ([[epsilon].sub.t] at 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:

[DELTA][B.sup.i.sub.t] = [[alpha].sup.i.sub.0] + [[alpha].sup.i.sub.1][DELTA][I.sup.i.sub.t] + [[theta].sup.i.sub.1]([DB.sup.i.sub.t] * [DELTA][I.sup.i.sub.t]) + [[alpha].sup.i.sub.2] + [[epsilon].sup.i.sub.t-1] + [[theta].sup.i.sub.2]([DB.sup.i.sub.t-1] * [[epsilon].sup.i.sub.t-1]) + [v.sup.i.sub.t]. (5)

A dummy variable ([DB.sub.t]) 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 shortrun 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 ([[epsilon].sub.t] less than zero). Examining whether [[theta].sub.1] 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 [[theta].sub.2].

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 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 elasticity 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 intermediate 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 states' 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 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.

[FIGURE 1 OMITTED]

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 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 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.

[FIGURES 2-3 OMITTED]

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 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.

[FIGURE 4 OMITTED]

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.

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 shortrun 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 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 - 1.0 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 (-0.370) 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 (-0.152), 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 disequilibrium more rapidly (-0.915). 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.

[FIGURE 5 OMITTED]

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 shortrun below-equilibrium elasticities and the adjustment parameters are consistent with the response 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 income 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 -1.0 for 12 states and the below-equilibrium adjustment parameter is not statistically different from -1.0 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.

[FIGURE 6 OMITTED]

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 parameter is larger for the income tax (-0.618 vs. -0.332), 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 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 characteristics, demographic factors, political characteristics, and measures of state economic structures. (33) The variables are listed with summary statistics in Appendix A.

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 percentage 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 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 difficult 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 unsurprising, 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 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.

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 finding 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 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.

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.

Appendix A
Summary Statistics and Source Notes for Cross-Sectional Regression

Variable Mean Std. Dev.

ST base/personal income 0.463 0.153
Consumer share of ST 59.422 8.892
Lowest income in highest PIT bracket 59,344 78,977
EITC dummy 0.220 0.418
Capital gains/personal income 0.060 0.020
Progressivity at median income 0.003 0.002
Partial exemption for government pensions 0.463 0.505
Total exemption for government pensions 0.268 0.449
Partial exemption for private pensions 0.488 0.506
Total exemption for private pensions 0.073 0.264
Percentage of population under 18 years of age 0.257 0.017
Percentage of population over 65 years of age 0.125 0.019
Median income 58,500 7,701
Republican legislature 0.400 0.495
Democratic legislature 0.380 0.490
Republican governor 0.620 0.490
Mining share of GSP 0.017 0.034
Average annual employment growth (1970-1999) 0.035 0.023
Standard deviation of employment growth
 (1970-1999) 0.026 0.011
Manufacturing share of GSP 0.162 0.064
Services share of GSP 0.160 0.027
Agriculture share of GSP 0.015 0.011
Average change in top PIT rate (1970-1999) 0.003 0.012

Variable Minimum Maximum

ST base/personal income 0.252 1.108
Consumer share of ST 28.000 89.000
Lowest income in highest PIT bracket 0 300,000
EITC dummy 0 1
Capital gains/personal income 0.026 0.123
Progressivity at median income 0 0.008
Partial exemption for government pensions 0 1
Total exemption for government pensions 0 1
Partial exemption for private pensions 0 1
Total exemption for private pensions 0 1
Percentage of population under 18 years of age 0.223 0.322
Percentage of population over 65 years of age 0.057 0.176
Median income 44,947 75,505
Republican legislature 0 1
Democratic legislature 0 1
Republican governor 0 1
Mining share of GSP 0 0.161
Average annual employment growth (1970-1999) 0.006 0.129
Standard deviation of employment growth
 (1970-1999) 0.015 0.061
Manufacturing share of GSP 0.030 0.316
Services share of GSP 0.085 0.240
Agriculture share of GSP 0.003 0.055
Average change in top PIT rate (1970-1999) -0.025 0.032

Variable Source

ST base/personal income U.S. Bureau of Economic Analysis
Consumer share of ST Ring (1999)
Lowest income in highest PIT State Tax Handbook, Commerce
 bracket Clearinghouse
EITC dummy Center for Budget and Policy Priorities
Capital gains/personalx Internal Revenue Service and Bureau of
 over Economic Analysis
Progressivity at median Authors' calculations based on median
 income income and tax rates
Partial exemption for Federation of Tax Administrators at
 government pensions http://assets.aarp.org/rgcenter/
 econ/ib55_sstax.pdf
Total exemption for Federation of Tax Administrators at
 government pensions http://assets.aarp.org/rgcenter/
 econ/ib55_sstax.pdf
Partial exemption for Federation of Tax Administrators at
 private pensions http://assets.aarp.org/rgcenter/
 econ/ib55_sstax.pdf
Total exemption for private Federation of Tax Administrators at
 pensions http://assets.aarp.org/rgcenter/
 econ/ib55_sstax.pdf
Percentage of population U.S. Bureau of the Census
 under 18 years of age
Percentage of population U.S. Bureau of the Census
 over 65 years of age
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
 Accounts Data, Bureau of Economic
 Analysis
Average annual employment Bureau of Labor Statistics
 growth (1970-1999)
Standard deviation of Bureau of Labor Statistics
 employment growth
 (1970-1999)
Manufacturing share of GSP Authors' calculations based on
 Regional Accounts Data, Bureau of
 Economic Analysis
Services share of GSP Authors' calculations based on Regional
 Accounts Data, Bureau of Economic
 Analysis
Agriculture share of GSP Authors' calculations based on Regional
 Accounts Data, Bureau of Economic
 Analysis
Average change in top PIT Authors' calculations based on data
 rate (1970-1999) from State Tax Handbook, Commerce
 Clearinghouse

Appendix B
Long-Run PIT Elasticities Adjusted for Rate Changes

 Unadjusted Adjusted

Alabama 1.82 1.82
Arizona 1.14 1.55
Arkansas 2.10 1.79
California 1.75 1.82
Colorado 1.26 1.17
Georgia 1.69 1.69
Hawaii 1.32 1.41
Idaho 1.57 1.65
Illinois 1.57 1.40
Indiana 2.44 1.95
Iowa 2.35 1.86
Kansas 2.26 2.27
Kentucky 2.60 2.60
Louisiana 2.27 2.27
Maine 2.87 2.55
Maryland 1.18 1.21
Massachusetts 1.42 1.05
Michigan 1.88 1.40
Minnesota 1.32 1.64
Mississippi 1.91 1.71
Missouri 2.29 1.92
Montana 1.60 1.60
Nebraska 2.49 3.10
New Jersey 2.02 1.16
New Mexico 3.02 3.11
New York 1.30 1.95
North Carolina 1.55 1.45
North Dakota 0.81 0.59
Ohio 3.98 3.38
Oklahoma 2.61 2.47
Oregon 1.44 1.54
Pennsylvania 1.43 1.25
Rhode Island 1.76 1.22
South Carolina 1.56 1.56
Utah 1.48 1.41
Vermont 0.97 0.97
Virginia 1.47 1.35
West Virginia 2.57 2.42
Wisconsin 1.22 1.57
Average 1.85 1.76
Std. Dev. 0.648 0.611

Unadjusted elasticities are taken from Table 4.

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.

References

Cook, Steven, Sean Holly, and Paul Turner. 1999. DSHY revisited: The role of asymmetries. Applied Economics 31:775-8.

Dickey, David A., and Wayne A. Fuller. 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49:1057-72.

Dye, Richard F., and Therese J. McGuire. 1991. Growth and variability of state individual income and general sales taxes. National Tax Journal 44:55-66.

Enders, Walter, and Pierre L. Siklos. 2001. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19:166-76.

Fox, William F., and Charles Campbell. 1984. Stability of the state sales tax income elasticity. National Tax Journal 37:201-12.

Granger, Clive W. J., and Tae-Hwy Lee. 1989. Investigation of production, sales, and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Econometrics 4:S145-S159.

Granger, Clive W. J., and Paul Newbold. 1974. Spurious regression in econometrics. Journal of Econometrics 2:111-20.

Groves, Harold M., and C. Harry Kahn. 1952. The stability of state and local tax yields. American Economic Review 42:87-102.

Jenny, Nicholas W. 2002. State tax revenue decline accelerates. State Tax Notes 26:169.

Ludvigson, Sydney, and Charles Steindel. 1999. How important is the stock market effect on consumption? Federal Reserve Bank of New York Economic Policy Review 5:29-51.

Mikesell, John L. 2004. State retail sales tax burdens, reliance, and breadth in fiscal 2003. State Tax Notes 33:125.

Newey, Whitney K., and Kenneth D. West. 1987. A simple, positive semi-definite, heteroskedasticity and autocorretation consistent covariance matrix. Econometrica 55, 1987:703-08.

Otsuka, Yasuji, and Bradley M. Braun. 1999. The random coefficient approach for estimating tax revenue stability and growth. Public Finance Review 27:665-76.

Ring, Raymond J., Jr. 1999. Consumer's share and producer's share of the general sales tax. National Tax Journal 52:79-90.

Schwarz, Gideon. 1978. Estimating the dimension of a model. The Annals of Statistics 6:461-4.

Sobel, Russell S., and Randall G. Holcombe. 1996. Measuring the growth and variability of tax bases over the business cycle. National Tax Journal 49:535-52.

Stock, James H., and Mark W. Watson. 1993. A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61:783-820.

U.S. Bureau of the Census. State Tax Collections. Various years.

(1) See Jenny (2002) for an example of the problems that states have confronted.

(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.

(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.

(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.

(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).

(13) The total disequilibrium removed after t periods is given by 1 - [(1 + [[alpha].sub.2]).sup.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, [DB.sub.t] takes the value of zero when [[epsilon].sub.1] 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 [DB.sub.t] takes 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.

(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.

(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.

(20) Again, see the FTA resources at http://www.taxadmin.org/fta/rate/inc_stp.html.

(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.

(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 B.

(27) The North Dakota elasticity is not significantly different from zero.

(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

(30) These simulations examine the effect of a one-time increase in personal income.

(31) The associated p-value is 0.79.

(32) The point estimate for the adjustment parameter is not significantly different from -1.0.

(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.

(34) The effect of rate changes can be very important to some states and the adjusted elasticities for each state are presented in Appendix B. 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.

(35) The authors thank John Mikesell for making this observation.

(36) This result was confirmed in a separate regression where we measured base breadth via the number of taxable services in each state.

(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.

(38) One reviewer observed that a higher consumer share might translate into lesser taxation of business, which could stimulate economic growth.

Donald Bruce, Center for Business and Economic Research, 105 Temple Court, University of Tennessee, Knoxville, TN 37996-4334, USA; E-mail dbruce@utk.edu; corresponding author.

William F. Fox, Center for Business and Economic Research, 101 Temple Court, University of Tennessee, Knoxville, TN 37996-4334, USA; E-mail billfox@utk.edu.

M. H. Tuttle, Department of Economics and International Business, 237A Smith-Hutson Building, Sam Houston State University, Huntsville, TX 77341, USA; E-mail mht001@shsu.edu.

Table 1. Average State Sales Tax Elasticities

 Mean Variance

Long-run sales tax elasticity 0.811 0.048
Short-run sales tax elasticity above equilibrium 1.804 7.179
Short-run sales tax elasticity below equilibrium 0.149 0.880
Sales tax adjustment parameter above equilibrium -0.332 0.054
Sales tax adjustment parameter below equilibrium -0.513 0.150

Table 2. Average State Income Tax Elasticities

 Mean Variance

Long-run personal income tax elasticity 1.832 0.427
Short-run personal income tax elasticity above
 equilibrium 2.663 5.014
Short-run personal income tax elasticity below
 equilibrium 0.217 2.180
Personal income tax adjustment parameter above
 equilibrium -0.618 0.192
Personal income tax adjustment parameter below
 equilibrium -0.411 0.090

Table 3. Sales Tax Elasticities

 Short-Run Elasticities

 Long-Run When Current When Current
 Elasticity Revenue Value is Revenue Value is
 below Long-Run above Long-Run
 Equilibrium Equilibrium

Alabama 0.712 ** 0.050# 1.120# **
Arizona 0.744 ** -1.232 ** 1.452#^ **
Arkansas 0.835 ** 0.323 1.398#^ **
California 0.833 ** -1.408 ** 1.146# **
Colorado 0.781 ** 1.869^ ** 1.869^ **
Connecticut 1.242 ** 1.152# ** 2.781^~ **
Florida 0.926 ** -0.049 1.445#^ **
Georgia 0.708 ** 0.171 1.209# **
Hawaii 1.110 ** 0.629 ** 1.285# **
Idaho 0.847 ** 0.665# ** 1.456#^ **
Illinois 0.871# ** 0.028# 0.028#
Indiana -- 0.723 * 0.723 *
Iowa 0.374 ** -0.056 0.853# **
Kentucky 0.654 ** 0.826# ** 0.826# **
Kansas 0.630 ** 0.466# * 0.466# *
Louisiana 0.514 ** -0.347 1.531#^ **
Maine 0.904 ** -0.857 1.047^
Maryland 0.767 ** 1.162# ** 1.162#^ **
Massachusetts 1.365 ** 0.354# 2.375^~ **
Michigan 0.772 ** -0.017 1.713#^ **
Minnesota 0.876 ** -0.226 0.903# **
Mississippi 0.486 ** -0.188# 1.340#^ **
Missouri 0.639 ** -2.192 ** 0.907# *
Nebraska 0.431 * 0.191 18.779 **
Nevada 0.781 ** -0.500 1.600#^ **
New Jersey 1.049# ** -0.297 1.552#^ **
New Mexico 0.924# ** -0.628# 3.070^~ **
New York 0.750 0.128 1.571 **
North Carolina 0.874 0.501# 1.820^ **
North Dakota 0.339 0.256^ -0.506 *
Ohio 1.033# ** 1.802^ ** 1.802^ **
Oklahoma 0.695 ** 1.890^ ** 1.890^ **
Pennsylvania 1.069# ** 1.504#^ ** 1.504#^ **
Rhode Island 0.531 ** 0.515# 1.848 **
South Carolina 0.773 ** -1.150# 1.143# **
South Dakota 1.145 ** 0.471 ** 0.471# **
Tennessee 0.716 ** 0.308 1.271# **
Texas 0.997# ** 1.580 ** 1.580#^ **
Utah 0.873 ** -1.544 1.780^ **
Virginia 0.800 ** -0.645 0.826# **
Vermont 0.735 ** 0.779#^ 2.289^~ **
Washington 0.740 ** 0.045# 1.722#^ **
West Virginia 1.013# ** -1.146#^ 3.295#^ **
Wisconsin 1.113# ** -0.623# 1.373^~
Wyoming 0.720# ** 1.443#^ ** 1.443#^ **

 Speed of Adjustment

 When Current When Current
 Revenue Value is Revenue Value is
 below Long-Run above Long-Run
 Equilibrium Equilibrium

Alabama -0.152 -0.152
Arizona -0.742@ ** -0.742@ **
Arkansas -0.915@ ** -0.113
California -1.874@ ** -0.193
Colorado -0.183 * -0.183 *
Connecticut -0.168 * -0.168 *
Florida -0.528 ** -0.528 **
Georgia -0.263 ** -0.263 **
Hawaii -0.476 ** -0.476 **
Idaho -0.246 ** -0.246 **
Illinois -0.226 -0.226
Indiana -- --
Iowa -0.850@ ** -0.850@ **
Kentucky -0.255 ** -0.255 **
Kansas -0.119 -0.119
Louisiana -0.182 -0.182 *
Maine -0.380 ** -0.380 **
Maryland -0.154 -0.154
Massachusetts -0.320 ** -0.320 **
Michigan -0.511 ** -0.511 **
Minnesota -1.082@ ** -0.409 *
Mississippi -0.262 * -0.262 *
Missouri -0.612 ** -0.612 **
Nebraska -0.905@ ** -0.905@ **
Nevada -0.506 ** -0.506 **
New Jersey -0.601 ** -0.601 **
New Mexico -1.188@ ** -0.399 *
New York -0.438 ** -0.438 **
North Carolina -1.045 ** -0.124
North Dakota -0.483 ** 0.260
Ohio -0.357 ** -0.357 **
Oklahoma -0.124 * -0.124 *
Pennsylvania -0.216 ** -0.216 **
Rhode Island -0.124 -0.124
South Carolina -0.510 ** -0.510 **
South Dakota -0.562 ** -0.562 **
Tennessee -0.240 * -0.240 *
Texas -0.749@ ** -0.749@ **
Utah -0.234 ** -0.234 **
Virginia -0.293 ** -0.293 **
Vermont -0.840@ ** -0.061
Washington -1.404@ ** -0.546 **
West Virginia -0.829@ ** -0.106
Wisconsin -0.289 ** -0.289 **
Wyoming -0.134 -0.134

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 -1.0.

* Statistically significant differences from zero at the 10% level.

** Statistically significant differences from zero at the 5% level.

Note: Indicate statistically significant differences from one at the
5% level indicated with #.

Note: Indicate statistically significant differences from two at the
5% level ^.

Note: Indicate statistically significant differences from three at
the 5% level ~.

Note: Speed of adjustment results indicates that the coefficient is
not statistically different from -1.0 indicated with @.

Table 4. Personal Income Tax Elasticities

 Short-Run Elasticities

 When Current When Current
 Revenue Value is Revenue Value is
 Long-Run Below Long-Run Above Long-Run
 Elasticity Equilibrium Equilibrium

Alabama 1.823 ** 1.393#^ ** 3.009^~ **
Arizona 1.140#^ ** 0.768# ** 0.768# **
Arkansas 2.102 ** 0.833# 0.833#
California 1.749 ** -1.536# 3.223~ **
Colorado 1.256 ** -1.040 0.962#^ *
Delaware 1.018# ** -0.885 1.088#^ *
Georgia 1.690 ** 0.130# 1.199#^ **
Hawaii 1.320 ** -0.786 2.013^ **
Idaho 1.565 ** -0.001 2.382^~ **
Illinois 1.565 ** 0.298# 2.882^~ **
Indiana 2.435 ** -0.783 1.702#^ **
Iowa 2.349 ** 1.176#^ ** -2.679#
Kentucky 2.600 ** 0.465# 0.465#
Kansas 2.260 ** 0.461# 6.223^~ **
Louisiana 2.272 ** 1.123#^~ 8.938 **
Maine 2.873~ ** 0.403# 2.639^~ **
Maryland 1.183 ** 0.510# * 1.986^ **
Massachusetts 1.415 ** 0.538# 1.660#^ **
Michigan 1.879^ ** 0.570 3.210^~ **
Minnesota 1.320 ** -0.128 2.300#^ **
Mississippi 1.910 ** 2.400#^~ ** 2.400#^ **
Missouri 2.292 ** 0.046# 6.242 **
Montana 1.604 ** -0.486#^ 2.313^~ **
Nebraska 2.491 ** 1.170#^ * 1.170#^ *
New Jersey 2.016^ ** -0.195# 2.031#^~ **
New Mexico 3.024^~ ** -6.223#^~ 8.370#^~ *
New York 1.295 ** -1.169 * 2.160^~ **
North Carolina 1.545 ** 0.767# ** 2.505^~ **
North Dakota 0.809#^ 0.197# 0.197#
Ohio 3.983~ ** -2.479 2.529#^~ *
Oklahoma 2.613 ** 1.731#^ ** 4.250~ **
Oregon 1.440 ** 0.100# 4.333^~ **
Pennsylvania 1.431 ** 2.042#^ ** 5.736 **
Rhode Island 1.756 ** 2.344^ ** 2.344^~ **
South Carolina 1.564 ** 1.536#^ ** 1.536#^ **
Utah 1.477 ** 1.379#^ ** 1.379#^ **
Virginia 1.474 ** 0.140# 1.775^ **
Vermont 0.974# ** 0.218#^ 0.218#^
West Virginia 2.569 ** 1.681#^~ * 4.770~ **
Wisconsin 1.215 ** 0.186# 2.534^~ **

 Speed of Adjustment

 When Current When Current
 Revenue Value is Revenue Value is
 Below Long-Run Above Long-Run
 Equilibrium Equilibrium

Alabama -0.221 -1.216@ **
Arizona -0.271 ** -0.271 **
Arkansas -0.508 ** -0.508 **
California -0.718 ** -0.718 **
Colorado -0.181 * -0.181
Delaware -0.174 * -0.174 *
Georgia -0.172 ** -0.172 **
Hawaii -0.667 ** -0.667 **
Idaho -0.683@ ** -0.683@ **
Illinois -1.017@ ** -1.017@ **
Indiana 0.445 -0.611@ **
Iowa -0.256 ** -0.256 **
Kentucky 0.015 0.015
Kansas -0.609 ** -0.609 **
Louisiana -0.292 * -1.176@ **
Maine -0.051@ -1.638 **
Maryland -0.814 ** -0.814 **
Massachusetts -0.248 ** -1.548@ **
Michigan -0.366 ** -0.366 **
Minnesota -0.262 -0.930@ **
Mississippi -0.563 ** -0.563 **
Missouri -0.370 ** -1.784 **
Montana -0.392 ** -0.392 **
Nebraska -0.811@ ** -0.811@ **
New Jersey -0.470 ** -0.470 **
New Mexico -0.207 ** -0.207 **
New York -0.309 ** -0.309 **
North Carolina -0.265 ** -1.181@ **
North Dakota -0.298 ** -0.298 **
Ohio -0.956@ ** -0.136
Oklahoma -0.434 ** -0.434 **
Oregon -0.991@ ** -0.991@ **
Pennsylvania -0.312 ** 0.064
Rhode Island -0.841@ ** -0.311 *
South Carolina -0.550 ** -0.550 **
Utah -0.827@ ** -0.827@ **
Virginia -0.655@ ** -0.655@ **
Vermont -0.549 ** -0.549 **
West Virginia -0.296 ** -0.296 **
Wisconsin -0.485 ** -0.485 **

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 -1.0.

* Statistically significant differences from zero at the 10% level.

** Statistically significant differences from zero at the 5% level.

Note: Indicate statistically significant differences from one at the
5% level indicated with #.

Note: Indicate statistically significant differences from two at the
5% level indicated with ^.

Note: Indicate statistically significant differences from three at the
5% level indicated with ~.

Note: Speed of adjustment results indicates that the coefficient is
not statistically different from -1.0. indicated with @.

Table 5. Cross-Sectional Analysis of Long-Run Elasticities

 1999 Values

Variable Income Sales

Lowest income in highest
 PIT bracket
 ($ thousand) (a) -0.003 ** (0.001)
EITC dummy -0.273
Capital gains/personal
 income 17.253
Progressivity at median
 income 87.567
Partial exemption for
 government pensions -0.920 ** (0.392)
Total exemption for
 government pensions -0.656 * (0.314)
Partial exemption for
 private pensions 0.792 ** (0.294)
Total exemption for private
 pensions -0.768 * (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 age (a) 33.490 ** (7.856) 0.477 (2.913)
Percentage of population
 over 65 years of age (b) 27.771 ** (8.233) 1.854 (3.030)
Median income
 ($ thousands) (a) -0.052 ** (0.021) 0.017 ** (0.007)
Republican legislature 0.660 * (0.353) 0.119 (0.128)
Democratic legislature -0.284 (0.262) 0.180 (0.121)
Republican governor -0.329 (0.300) 0.026 (0.078)
Mining share of GSP (b) -9.560 (7.270) 3.677 (2.398)
Average annual employment
 growth (1970-1999) -4.808 (9.670) 0.471 (2.010)
Standard deviation of
 employment growth
 (1970-1999) 23.860 ** (10.624) 0.548 (4.486)
Manufacturing share of
 GSP (b) -1.065 (2.689) 1.768 (1.347)
Services share of GSP (b) -18.081 (17.737) 5.585 (3.966)
Agriculture share of
 GSP (b) -35.335 (21.218) 4.669 (6.815)
Constant -4.657 (4.140) -3.220 (1.903)
N 35 43
[R.sup.2] 0.601 0.060

 1970-1999 Changes

Variable Income Sales

Lowest income in highest
 PIT bracket
 ($ thousand) (a) 1.935 (359.289)
EITC dummy -0.395 (0.275)
Capital gains/personal
 income -739.067 ** (289.629)
Progressivity at median
 income 433.921 (1916.552)
Partial exemption for
 government pensions -1.039 ** (0.447)
Total exemption for
 government pensions -0.306 (0.374)
Partial exemption for
 private pensions 0.576 (0.350)
Total exemption for private
 pensions -0.557 (0.420)
Average change in top PIT
 rate (1970-1999) 30.602 ** (12.405)
ST base/personal income -1.967 ** (0.836)
Consumer share of ST -0.006 (0.005)
Percentage of population
 under 18 years of age (a) -2.785 (3.787) 0.386 (1.103)
Percentage of population
 over 65 years of age (b) -0.334 (0.983) -0.070 (0.304)
Median income
 ($ thousands) (a) -15.467 (12.968) 1.730 (4.460)
Republican legislature 0.515 * (0.254) -0.047 (0.108)
Democratic legislature -0.136 (0.289) 0.021 (0.125)
Republican governor 0.011 (0.333) 0.007 (0.086)
Mining share of GSP (b) -5.313 (3.592) 0.738 (1.360)
Average annual employment
 growth (1970-1999) -8.002 (8.158) 0.972 (2.234)
Standard deviation of
 employment growth
 (1970-1999) 26.263 * (12.747) -2.25 (6.265)
Manufacturing share of
 GSP (b) 38.594 (105.490) -24.319 (31.092)
Services share of GSP (b) -45.028 * (23.391) -4.984 (5.645)
Agriculture share of
 GSP (b) 0.738 (22.500) 1.806 (4.705)
Constant 5.343 ** (1.869) 1.288 ** (0.618)
N 35 43
[R.sup.2] 0.517 0.047

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) Variable 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.