The robust relationship between taxes and U.S. state income growth.

[2] [Y.sub.t]/[N.sub.t] = [A.sub.t] [Q.sub.t.sup.[beta]] [([K.sub.t]/[N.sub.t]).sup.[alpha]] [([L.sub.t]/[N.sub.t]).sup.[beta]] [N.sub.t.sup.([alpha] + [beta] - 1].

This can be expressed in log form as

[3] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [y.sub.t] = [Y.sub.t]/[N.sub.t], [k.sub.t] = [K.sub.t]/[N.sub.t], and [e.sub.t] = [L.sub.t]/[N.sub.t].

Differentiating equation [3] with respect to time yields

[4] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

It follows that

[5] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [C.sub.t] = [ln([A.sub.t]) - ln([A.sub.t-L])] + [beta](Q,) ln([Q.sub.t)]--ln ([Q.sub.t-L])] and L = the length of the time period minus 1 (e.g., for a five-year period with t measuring calendar years, L = 4). (4)

Equation [5] identifies changes in capital, employment, and population as important determinants of income growth. The last term, [C.sub.t], collects the additional effects of all other variables on income growth. Within this framework, taxes can affect economic growth via two channels. First, they can directly influence capital, employment, and population growth. Second, they can influence the way capital, labor and other resources are employed--either encouraging or discouraging their most productive employment.

DATA AND ESTIMATION ISSUES

My data consist of observations on 48 U.S. states from 1970-1999. (5) I decided on this particular time period because a longer time frame would have required me to omit many variables of interest. The respective 30 years of data are grouped into six, five-year periods (1970-1974, 1975-1979, ..., 1995-1999). Data for most of these variables were collected from original data sources. (6)

Besides previously cited benefits, five-year interval data (7) offer two additional advantages over annual data: they (1) minimize errors from misspecifying lag effects, and (2) reduce measurement error due to time-specification issues. The latter arise because data can have different start and end periods within a given calendar year. For example, state income data are defined over calendar years; state fiscal data are defined over fiscal years (which are different for different states); and other variables (e.g., employment, population data) may be measured at different points within the year (beginning/middle/end). In addition, a number of variables (e.g., variables based on decennial Census data) require annual interpolation in order to get a balanced panel. The errors associated with both types of time-specification issues are mitigated by using longer-interval data.

Following equation [5], the general specification for the empirical models is (8)

[6] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where t = 1974, 1979, 1984, 1989, 1994, 1999; [DLNY.sub.t], [DLNK.sub.t], [DLNL.sub.t], and [DLNN.sub.t] are the respective difference quantifies from equation [5] multiplied by 100 (to give percent); ([X.sub.dt]- [X.sub.d,t-4]) is the change in the explanatory variable over the five-year period--where the subscript "d" represents the "differenced" form of X; and [X.sub.l,t-4] is the value of the explanatory variable at the beginning of the five-year period--with subscript "l" representing "level" form. Note that the last two terms can also be thought of as capturing the "contemporaneous" and "lagged" effects of X. (9)

A comparison of equations [5] and [6] reveals that both "differenced" and "level" forms of X are used as proxies for [C.sub.t] = [ln([A.sub.t]) - ln([A.sub.t-L])] + [beta][ln([Q.sub.t]) - In([Q.sub.t-L])]. [C.sub.t] incorporates factors that affect the growth rate of productivity. As this term appears in differences, one may question why level forms of X are included. Consider the role of education. It is likely that the stock of human capital (as distinct from the growth rate of human capital) is a determinant of the creation of new ideas, which contribute to productivity growth. This argues that level-measures of human capital, such as educational achievement, also be included as potential determinants of [C.sub.t]. Similar arguments can be made for other variables. (10)

An alternative argument for including both "differenced" and "level" variables arises when these are seen as representing "contemporaneous" and "lagged" effects. For example, taxes may have immediate effects on the allocation of resources. They may also have persistent effects, as the effort to smooth adjustment costs causes tax-induced re-allocations of resources to be delayed into future time periods.

As my measure of taxes, I use tax burden, defined as the ratio of state and local tax revenues to personal income. Tax burden is by far the most commonly employed measure of state taxation, and can be thought of as the "effective average tax rate" in a state (e.g., Helms, 1985; Mofidi and Stone, 1990; Mullen and Williams, 1994; Carroll and Wasylenko, 1994; Knight, 2000; Caplan, 2001; Yamarik, 2000, 2004; Alm and Rogers, 2005).

INITIAL EMPIRICAL RESULTS

Table 1 summarizes the initial results. The first column reports the results of estimating a narrowly specified version of equation [6]. The only explanatory variable from the set of differenced variables is the change in tax burden, TaxBurden(D); and the only explanatory variable from the set of level variables is the value of tax burden at the beginning of the period, TaxBurden(L). (11)

Both tax variables are negative and highly significant (the t-values are -4.38 and -2.25, respectively). This suggests that taxes have both an immediate and a persistent effect. The coefficient estimate for TaxBurden(D) indicates that a one percentage-point increase in tax burden over a five-year period is associated with lower real Per Capita Personal Income (PCPI) growth of 1.37 percent during that period. A further consequence arises because this increase causes future periods to commence with a higher level of taxes. This lagged effect is measured by the coefficient on TaxBurden(L): A state having an initial tax burden that is one percentage point higher than other states is estimated to have real PCPI growth that is 0.90 percent lower in subsequent five-year periods.

Two points are worth noting. First, these effects represent the net effect of taxes and spending. Since expenditure variables are omitted from the specification, and since the relationship between U.S. state expenditures and revenues is generally one-to-one, the respective coefficients should be interpreted as an increase in taxes to fund general (unspecified) expenditures. (12) Second, these estimated effects are sizeable. The mean value of the tax burden variable is 10.87, and the mean growth rate of real PCPI (DLNY) is 8.23 percent. Thus, tax variable coefficients in the range of -1.0 represent economically important relationships.

With respect to the rest of the equation, the other coefficient estimates confirm the expected result that increases in a state's capital stock (DLNK), employed labor force (DLNL), and population (DLNN) are each associated with greater income growth. Overall, the equation has good explanatory power--a result that largely persists even when the state and time fixed effects are omitted. (13)

The estimated tax impacts of column 1 hold constant any effects that taxes might have on investment, employment, and population growth. One might reasonably expect taxes to be related to these as well. Columns 2-4 report the results of investigating this hypothesis by respectively regressing each of these on the two tax variables plus state and time fixed effects. Across all three equations, we see that higher taxes are associated with lower investment, lower employment growth, and lower population growth.

Notably, there are differences in the timing of the respective estimated effects. Columns 2 and 3 report that an increase in tax burden is associated with a statistically significant decrease in investment and employment growth during the same five--year period. Beyond that period, the tax effects are smaller and statistically insignificant. In contrast, column 4 indicates that an increase in tax burden is estimated to have a negligible contemporaneous effect on population growth. However, there is some evidence to indicate that higher taxes lower population growth in later time periods (the respective p-value is 0.19). These results are consistent with expectations about how taxes might affect each of these variables: investment and employment are more easily adjusted in the short-run, while migration decisions respond more slowly and require more time to be realized.

The preceding results suggest that taxes influence state income growth via two general channels. The first channel is associated with the term, [C.sub.t], which collects changes in the efficiency of labor ([Q.sub.t]) plus the effects of other time-varying factors related to productivity ([A.sub.t]). The second channel is via the terms DLNK, DLNL, and DLNN, which incorporate the effects of taxes on investment, employment, and population growth. Ideally, one could measure the combined effect of tax burden on income growth by estimating a structural system of equations with DLNY, DLNK, DLNL, and DLNN all treated as endogenous. Unfortunately, a lack of good instruments makes this approach unfeasible. (14)