Evaluating state tax revenue variability: a portfolio approach

Abstract

This article develops a volatility model based on portfolio theory to examine state tax revenue variability. Unlike traditional parametric methods used to analyse state tax revenue variability, the portfolio approach allows the computation of a tax's share of total tax revenue that minimizes the overall variability in total state tax revenue given a state's portfolio of tax revenue sources. The model can thus be used to evaluate how closely a state's revenue portfolio is constructed to minimize variability in total state tax revenue. An empirical application of the model is conducted on a sample of US states. The volatility model presented here serves as a useful complement to parametric techniques that have been used to estimate tax revenue variability.

Notes

¹In 2000, over 61% of tax revenue in Washington came from the state's sales tax compared to only 15% in Vermont. Nearly 70% of California's total tax revenue was obtained through the personal income tax, whereas Tennessee only generated 2.5% of its total tax revenue from the personal income tax (only interest and dividends are taxed). Excise taxes accounted for 32% of total tax revenue in New Hampshire, but California obtained only 7.5% of its total tax revenue from excise taxes.

²The exemption of food from the sales tax increases the variability of sales tax revenue.

³Szakmary and Szakmary (1995) use the volatility model to answer the question of whether lottery revenues stabilize or destabilize total state revenue.

⁴Note that w* can fall outside the range 0 ≤ w*≤ 1. The conditions under which this will occur are discussed later in this article.

⁵State tax revenue data are available from the US Census, State Government Finances. The excise tax category consists of taxes on alcohol, motor fuels, tobacco, amusements, pari-mutuels, public utilities, insurance premiums and other select taxes.

⁶On average, the revenue from the ‘other’ category accounts for 10% of total state tax revenue. However, states such as Delaware, Montana and New Hampshire have a significantly higher percentage of total tax revenue coming from ‘other’ taxes (about 25%, on average).

⁷This may result in a trade-off between growth and variability. Since excise taxes, unlike income and sales taxes, are not indexed to inflation, frequent rate increases would be required to maintain a real level of excise tax revenue. In addition, the trend from a goods producing economy to a service economy does not bode well for growing sales tax revenue since services are less likely to be taxed than durable and nondurables. Thus, while sales and excise taxes are less volatile, they may also have a lower growth potential than income taxes. See Holcombe and Sobel (1997) for a discussion on tax revenue growth and variability.

⁸Consider the case of w* < 0. This implies that V _O  < cov (T, O) in Equation 5(5). Rewriting cov (T, O) as ρ _T, Oċ σ _Tċσ _O , it can be shown from V _O  < ρ _T, Oċ σ _Tċσ _O that w* < 0 when σ _T  > σ _O /ρ _T, O and ρ _T, O  > 0. Now consider the case of w* > 1. This implies that V _O  − cov(T, O) > V(T−O) in Equation 5(5). Rewriting V(T−O) as V _T  + V _O  − 2cov (T, O) and using cov(T, O) = ρ _T, Oċσ _T ċσ _O , it can be shown that w* > 1 when σ _T  < σ _O ċρ _T, O and ρ _T, O  > 0.