Preliminary: Comments Welcome Tax Structure and Revenue Instability: The Great Recession and the States

The Great Recession had the most severe impact on state tax revenues of any downturn since the Great Depression. We hypothesize that states with more progressive tax structures are more vulnerable to economic downturns, and that progressivity and income volatility may interact to amplify the recession’s fiscal impact. We find that, while potential revenue exposure is greater in more progressive states, the most important source of variation was differences in income concentration and capital gains shares in the top 5 percent of taxpayers. Though the interaction between income volatility and high tax burdens at the top did produce large decreases in tax revenue in a few states, tax progressivity accounted for little of the overall interstate variation in revenue volatility. JEL codes: H24; H71

We hypothesize that variation in revenue impact across states is due to differences in the severity of the income shocks at different levels of income, the degree of income inequality, the importance of capital gains in top incomes, and the level and progressivity of tax burdens. Progressive states are likely to be more vulnerable to revenue losses in economic downturns. Progressivity and income volatility may interact to amplify the recession's fiscal impact.
To test these hypotheses, we construct a measure of potential revenue exposure by state for 2007-2009. We disaggregate revenue exposure by income quantile, summing state-specific changes in federal AGI per return by AGI quantile, multiplied by the effective tax burden by quantile. We simulate the effects of replacing state-specific economic shocks, average tax burdens, and tax progressivity with national averages. We find the variation in potential revenue exposure to be less than half as large as the variation in actual revenue changes. The dominant factor in potential revenue exposure is the shock to a state's tax base, particularly for the top 5 percent of filing units.
We then estimate a multiple regression model of revenue changes as a function of the components of revenue exposure and their interactions, and use the estimated coefficients to simulate the effect of a "race to the middle" for the most and least progressive states. We find that on average, states with relatively progressive tax systems are not more vulnerable to recessions than less-progressive states. While actual revenue changes are affected by both initial tax burdens and changes in AGI for the top 5 percent, the net effect depends on the interaction between these two factors. Given the weak correlation between income volatility and tax progressivity, larger drops in top incomes do not systematically lead to larger drops in tax revenue.
In sum, we find that the net effect of greater tax-base volatility at the top is not volatility-enhancing. In the majority of states, tax structures serve to dampen, not amplify revenue impacts of the change in capital gains. And surprisingly, higher tax burdens on the 80 th to 95 th percentiles of a state's income distribution tend to mitigate the recession-induced decline in tax revenues. federal aid increases, these revenue reductions have led to sharp decreases in state employment and state aid to local governments. 2 The decline in state aid, primarily to school districts, has been a major factor in the unprecedented decline in local government employment. 3 Despite the sharp overall decline, there has been considerable variation across states in the revenue impact of the recession. While 36 states had declines in state tax revenue, 12 states had increases in tax revenue during this period.  4 In the preceding decades, income has grown much rapidly at the top than for most families. 5 Have the secular increase in the concentration of income, particularly from capital gains, and the high volatility of income from capital gains increased overall state fiscal exposure to recessions? If so, have these income trends increased the vulnerability of states with higher or more progressive tax burdens, relative to those states with lower or more regressive burdens? These are the questions addressed in this paper. 6 To assess the relative impact on state revenues of the aggregate income shock versus the effects of tax progressivity, income concentration, and capital gains volatility, we decompose the sources of revenue volatility, not by separate taxes as has been done in the past (Dye, 2004), but by income level. We are able to do this by drawing on state-bystate estimates of the tax burden by income quantile from the Institute for Taxation and Economic Policy (2009) to estimate potential revenue exposure as a weighted sum of the changes in adjusted gross income (AGI) by quantile, where the weights are the effective tax burdens by quantile. This alternative approach to the study of tax volatility adds to our insight into the effect of state tax structures on the very important fiscal goal of revenue stability over time.
We find that, while potential revenue exposure is on average higher in more progressive states, the major source of variation in revenue exposure was not state tax structure, but differences across states in both their exposure to the sharp national decline in capital gains income and the state-specific severity of the great recession. Regression analysis of actual changes in state tax revenues on the components of fiscal exposure shows that the interaction between sharper drops in income among top taxpayers and higher tax burdens on these groups can potentially lead to bigger decreases in tax revenue. However, because the correlation between recession-related changes in the income of top taxpayers and the relative tax burden on top taxpayers is weak, the overall quantitative importance of tax progressivity in exacerbating the fiscal impact of the recession is small. California is the leading example of a state with a relatively progressive tax structure that suffered a large decrease not only in potential but also in actual tax revenues. However, the revenue impact of the recession was much greater in Nevada and Florida, two of the most regressive states in the U.S. The plan of the paper is as follows. Section I presents the conceptual basis for calculating revenue exposure, the steps taken to implement the concept for state taxes, and the comparison of revenue exposure to both the actual change in taxes and to counterfactual measures. The regression analysis of actual tax changes and the regression-based simulations are presented in section II. Section III concludes. Twelve states had increases in tax revenue, with an average increase of eight percent.
The biggest increases were in North Dakota and Wyoming, in both of which tax revenues grew by more than 35 percent. These two states, as well as Texas, West Virginia and South Dakota, have benefitted from significant increases in severance tax revenues on minerals.
Second, tax progressivity varies substantially across states. Drawing on multiple years of data from both the Institute for Taxation and Economic Policy (ITEP) of the Citizens for Tax Justice and other studies, Chernick (2005) shows that progressivity, defined as the ratio of the tax burden on the top 5 percent of families to the bottom 20 percent, ranges across states by almost three to one. In 2007, according to the ITEP model, the ratio of the burden on the top 5 percent to the average burden ranged from 0.94 at the 90 th percentile to 0.57 at the 10 th percentile (Institute for Taxation and Economic Policy, 2009). For the income tax, which has an important effect on state tax progressivity, the ratio ranged from 1.58 to 1.02. 7 We expect that the greater the progressivity of a state's tax system, the more volatile or elastic are tax yields, for a given cyclical shock to a state's economy. 8 The third fact is the longstanding secular trend towards increased income inequality, both for the U.S. overall and within states. National trends, particularly for the very top of the income distribution, are well documented (Saez, 2012 In and of itself, the increased concentration of income does not necessarily imply greater volatility of tax revenue over the business cycle. However, if the income of the top taxpayers is more volatile than the rest of the distribution, then by a simple compositional argument, the increased share of total income received by high-income taxpayers would imply an increase over time in the cyclical sensitivity of the state tax 7 The structure of the income tax varies widely across states. As discussed by Dye (2004), nine states have either no income tax or only a narrow-based tax. Of the 41 states that do use broad based income taxation, 19 states have either a flat rate or a rate structure that taxes most income at a single rate. In the 34 states that have a graduated rate structure, there is considerable variation in both the top rate and the degree of graduation. 8 Dietz et al (2010) argue that reliance on more cyclically sensitive taxes has increased the budgetary exposure of particular states to cyclical economic fluctuations. Boyd (2010) makes a similar point in terms of the recovery from the great recession. However, Dye (2004) did not find a significant difference between the income and the sales tax in terms of short-run revenue elasticities. 5 base for an overall economic shock of any given magnitude. If the relative volatility of the income of top taxpayers compared to lower income taxpayers is growing over time, then the cyclical volatility of the overall tax base would be increasing at an even faster pace.
Hence, the fourth pertinent fact in explaining both the mean and the variation of changes in state tax revenues pertains to the volatility of the income of top taxpayers. As discussed above, the decline in average real income per family was more than twice as Changes in capital gains realizations may also interact with tax structure, to amplify revenue fluctuations. This would occur if states with greater capital gains income tax that income at relatively high rates.
These points suggest that to analyze the revenue shock to states from the great recession, it is necessary to take account of four factors: the overall economic shock to the state's economy, the state's overall tax burden, differences in the economic shock at different positions in the state's income distribution, and the tax burdens imposed at those different positions. Differences in revenue exposure between progressive and regressive state tax systems may be reinforced (or offset) by the differential shocks by income level.
For example, if the income decline associated with the recession is concentrated among high-income taxpayers, then the potential revenue effects will be magnified for states with the most progressive systems -i.e., the highest top-bracket rates. If the income decline is concentrated among middle-or lower-income taxpayers, then states that rely more on progressive income taxation may be spared the worst effects of the recession.

B. Conceptual Measure of Exposure and Its Uses
To explain variation in the potential shock to state revenues, we measure revenue exposure in terms of the overall economic shock, differences in the magnitude of the shock across a state's income distribution, and the structure of the state's tax system.
Specifically, a state's potential revenue change in each income quantile is measured by the change in federal adjusted gross income in that quantile, multiplied by the prerecession state-specific tax burden in that quantile. The potential change in aggregate tax revenues is then computed as the weighted average of the potential revenue change by income quantile, where the weights are the shares of the aggregate tax base in each quantile. We call this measure "potential revenue exposure." Revenue exposure is calculated for all state taxes and for the income tax alone.
We then simulate the change in potential revenue exposure if each state, given its tax structure, were to experience the national average economic shock at each income quantile, or if it experienced its actual economic shock but had the national average tax structure. These counterfactual simulations allow us to analyze one at a time the effects on revenue exposure of variation across states in the economic shock, the average tax burden, and the progressivity of tax burdens.
We then turn from potential revenue exposure to actual revenue changes, estimating a set of regression models to explain changes in tax revenues from 2007 to 2009. The independent variables in this exercise are the individual components of the potential revenue exposure. We use the coefficients from our preferred specification of the tax change model to simulate the effect on state revenue changes of altering the progressivity of state tax systems, reducing top rates in the most progressive states and raising top rates in the least progressive states. In the conclusion, we use the results from the two methods of analysis --simulations of potential revenue exposure and regression estimates --to provide an overall assessment of the effect of tax progressivity on state tax revenues.

C. Actual Tax Changes, Policy Offsets, and Exposure
The change in tax revenue in state j resulting from a cyclical downturn is equal to ΔTax Revenue j = ∑ i [(ΔBase ij · Rate ij ) + (Base ij · ΔRate ij ) + (ΔBase ij · ΔRate ij )] (1) where i indexes the various state taxes. The major state tax sources are the individual income tax, the general sales tax, the corporation income tax, and excise taxes on tobacco, alcohol, and gasoline. The base change in (1) may be divided into a recession component and a policy offset.
The first term in (2) is the change in the tax base due to the recession, with policy unchanged. For the sales tax, for example, the recession-induced change in the tax base would be the decline in taxable sales.
In expression (5), the subscript q denotes the quantile of income, while t bar is the average tax burden. By definition, the average tax burden is the income share-weighted sum of the quantile tax burdens, i.e. t bar = ∑ q=1,3 t q,07 (SHR BASE) q,07 Based on available IRS data and our special focus on the effect of income changes at the high end of the income distribution, families are divided into three income quantiles: the top 5 percent, the next 15 percent, and the bottom 80 percent. The rate t q represents the effective tax burden on quantile q; i.e., the average share of income paid by families in quantile q. The empirical implementation of (5) is given by Revenue Exposure = [(t top5 /t bar ) · ΔAGI top5 /Ret top5,07 ) + (t nxt15 /t bar ) · ΔAGI nxt15 /Ret nxt15,07 ) Effective tax burdens t by income quantile in (7)  13 the 90 th percentile was at risk for a $74 increase. Notably, the standard deviation of revenue exposure is less than half that of actual tax changes. It is not surprising that actual revenue performance varies more than potential exposure, given the variation across states in the importance of policy offsets, as well as other factors such as changes in severance tax revenues, which are not included in our measure of potential revenue exposure. 13 The second panel of Table 1 shows summary statistics for the personal income tax. Six of the lower 48 states have no income tax. Not surprisingly, the income tax exposure measure tracks the actual change in income tax revenues much more closely than in the case of all taxes combined. However, the pattern from the top panel is replicated for the income tax, with mean potential income tax revenue exposure equal to -$171, 44 percent larger than the mean actual change (-$119).
The standard deviation of revenue exposure for the income tax is much closer to the standard deviation of actual income tax revenues than is the case for all taxes, as are most of the outliers. The smaller difference reflects the exclusion of revenues from mineral extraction. Moreover, seven states have zero or very low income taxes, including at least two, Florida and Nevada, that experienced exceptionally large reductions in revenues. More generally, we would expect that the relationship between the change in federal AGI in a state, which is the basis for our exposure measure, and the actual change in a state's income tax base is likely to be much stronger than the relationship between the changes in AGI and in the composite income-consumption tax base that determines the overall revenue change. Table 2 shows actual revenue changes and potential revenue exposure for the top and bottom ten percent of states, ranked according to various criteria. The first two columns compare the most progressive and least progressive states, as measured by the ratio of the tax burden on the top 5 percent to the average tax burden. As expected, both actual revenue decreases and potential revenue exposure are greater for the more progressive states. As shown in the first row of Table 2, revenues dropped by 6.7 percent for the most progressive states, but went up by 1.2 percent for the most regressive group.
Potential revenue exposure is also much closer in value to the actual revenue change for the progressive states than for the regressive states. Notably, revenue exposure is negative (predicting a decline in tax revenues) for both groups, whereas actual revenue changes were slightly positive for the regressive states. This suggests that either policy offsets or changes in types of taxes that are not well captured by the revenue exposure measure (e.g., severance taxes) were more important for the regressive states. As indicated by the "NA" in the third and fourth rows of column 2, the regressive states are distinguished from the progressive states by the absence of state income taxes.
The third and fourth columns of Table 2 compare high-and low-tax states, as measured by the average tax burden. As expected, both actual revenue reductions and potential revenue exposure are greater for the high-burden than the low-burden states. It is notable that the actual drop in revenues for high average-burden states (column 3, row 1) is substantially smaller than for the most progressive states (column 1, row 1).
Revenue exposure is also smaller for states with the highest average tax burdens than for the most progressive states, though the difference is not as great as the divergence in actual revenue changes. These comparisons suggest that a relatively high tax burden at the top of the income distribution was more important than a high overall burden in determining potential revenue exposure to the recession.
Columns 5 and 6 of Table 2 compare states with the largest actual revenue decreases and increases. Notably, revenue exposure would predict a revenue decrease for both groups. For both groups, the absolute value of the actual change in revenues is much greater than the revenue exposure measure, again reflecting state-specific factors which are not captured by the exposure measure. However, for the revenue-increase group, there is a much greater divergence between potential exposure (-$102) and the actual increases ($1031). Because mineral tax revenues are likely to play a role in this latter result, the last column of Table 2 shows revenue performance in eight states with substantial severance tax revenues. On average, these states realized an eight percent increase in tax revenues, but also had very low revenue exposure. in fiscal exposure to the great recession is the magnitude of the economic shock, rather than the rate and structure of taxation.
The lower panel of Table 3 shows the revenue exposure measures for the income tax alone. As for all taxes, the greatest reduction in the variation in income tax exposure across states is produced by imposing the national-average shock to each AGI quintile, while retaining the state-specific tax structure (lower panel, Simulation III). The percent of a state's tax filing units is more important than differences in the rest of the income distribution in explaining differences in fiscal exposure. 14 As shown below in Table 8, column (1) Table 5 presents Spearman rank correlation coefficients between actual revenue changes, potential exposure, and the various counterfactual measures of revenue exposure, both for all taxes and for the income tax alone. Revenue exposure is significantly positively correlated with actual changes in taxes. Not surprisingly, correlations are stronger for the income tax than for all state taxes. 16 The rank correlation between potential exposure and actual revenue change is virtually unchanged if all states are assumed to have the same degree of progressivity. However, imposing a uniform economic shock on all states causes the correlation between potential exposure and actual changes in revenue to become insignificant, despite the fact that the hypothetical measure with the national-average economic shock remains strongly correlated with revenue exposure. Thus, Table 5 reinforces the prior conclusion that the variation in greatrecession-induced revenue changes has been much more heavily influenced by differences in the magnitude of the economic shock than by differences in tax structure. ΔRev j =a 0 + Σ q (a 1q · ΔAGI qj + a 2q · BURD qj + a 3q · ΔAGI qj · BURD qj ) + a 4 · AVGBURD j + e j (8) In ( for the variables in (8) assume that that policy offsets are not systematically larger in states with greater potential revenue exposure (that is, the error term is uncorrelated with the components). 17 Analysis of the relationship between revenue exposure and actual revenue changes in the prior section helps to justify this assumption. In those few states with substantial revenues from severance taxes on mineral extraction, changes in mineral 17 In this respect, our model is different from that of Poterba (1994), who presents evidence for [1988][1989][1990][1991][1992] showing that the offsetting state tax response to an unexpected negative deficit shock is proportional to the magnitude of the shock. Poterba finds that there is an increase in states taxes after two years approximately equal to the shock.

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prices are also likely to impact tax revenues. To the extent that changes in extraction activity are translated into changes in income, the effects are at least partially captured by changes in the tax base (AGI). Hence, some though not all of the revenue impact of windfall increases in severance tax revenue are captured by the model. Table 6 presents descriptive statistics for the variables in the regression analyses, and Table 7 presents the analysis of the change in tax revenues. Column (1) of Table 7 includes only the measure of potential revenue exposure discussed in section I.D above.

B. Results
Not surprisingly, there is a significant positive relationship between potential exposure and the actual change in revenues, with a one dollar change in exposure implying a one dollar change in revenues. Thus, potential exposure is an unbiased predictor on average.
However, it explains only a small portion of the variation in revenue changes (adjusted R 2 = 0.12). Recall that revenue exposure is measured as ∑ q=1,3 ΔAGI q · BURD q . Hence, this measure may be thought of as a measure of the change in fiscal capacity of the state.
The estimated coefficient implies that a change in fiscal capacity is associated with an equal change in revenue outcomes, under the restriction that each quantile-specific weighted revenue exposure will have the same effect on tax revenues, regardless of the income quantile.
The next two columns in the table relax this restriction, by including as separate covariates the various terms in the fiscal exposure measure and their interaction effects.
Column (2) includes as separate covariates the change in AGI and the tax burden for the three quantiles. The only AGI change which has a significant effect on tax revenues is that for the 80 th -95 th percentiles of the AGI distribution. The tax burden effects are largely insignificant. The explanatory power of the regression, while greater than in column (1), is still weak.
Column (3) Table 8 shows   (Table 7,  In this section, we use the regression coefficients in column 3 of Table 7  Since the average tax burden is calculated as the weighted sum of the bur the three quantiles of income (with AGI shares as weights), changing the burden on t top quantile(s) will automatically change the average burden. Therefore, in the simulation exercise we also adjust the average tax burden --downward for the most progressive states, and upward for the least progressive states. Thus, we are not simulating revenue-neutral changes in progressivity, but reducing both progressivity and average tax burdens in progressive states, and doing the opposite in regressive states.
However, we are able to isolate the effect of the change in progressivity from the change in average tax burden, by decomposing the difference between the simulation and the base model into components d age tax rates. One might think of this simulation as a "race to the middle," rather than a "race to the bottom." The results are shown in Tables 9 and 10 Table 9 shows the effect of compressing burdens in the most progressive states, while the bottom panel shows the most re the s.
ity was much less important than the rece ws k gressive states.
Column 2 of Table 9 shows that the actual average change in tax revenues was  Table 2, which found that tax progressiv ssion shock in explaining revenue exposure.
Column 3 shows that model (3) in Table 7 Table 9 show the effect on the most progressive states of reducing the burdens not only on the top 5 percent but also on the next 15 percent, ag with offsetting adjustments to the average tax rate. Rather than further reducing the

Notes:
Marginal effect of a 1 percentage-point increase in tax burden on top 5%, Model 5: At the mean chg agi per return for the 12 most progressive states (burden on top 5 percent greater than 75th percentile) 68 At the mean chg agi per return for the 12 least progressive states (burden on top 5 percent less than 25th percentile) 37 Marginal effect of a 1 percentage-point increase in tax burden on next 15%, Model 5: At the mean chg agi per return for the 12 most progressive states (burden on top 5 percent greater than 75th percentile) 235 At the mean chg agi per return for the 12 least progressive states (burden on top 5 percent less than 25th percentile) 152 (1)   Table 7, Model 3.

2.
Positive values indicate that under the particular simulation the reduction in state taxes would have been smaller than the regression prediction, or the increase in state taxes would have been larger than the regression prediction.
Negative values indicate that under the particular simulation the reduction in state taxes would have been larger than the regression prediction, or the increase in state taxes under the regression prediction would have been smaller than the regression prediction. 3. The burden on the next 15% in California is at the 75th percentile nationally, so is not reduced by the simulation.