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

(7) The data are formatted in terms of five-year differences, not averages (cf. equation [5]).

(8) I do not impose the restriction that [[beta].sub.3] = ([[beta].sub.3] + [[beta].sub.2] - 1) because population growth could also be related to [C.sub.t], in which case the restriction would be violated.

(9) For an alternative derivation that arrives at a virtually identical specification, see Bassanini, Scarpetta, and Hemmings (2001).

(10) Previous studies of fiscal policy that specify income growth as the dependent variable have typically included either (1) level (cf. Helms, 1985; Chernick, 1997; Yamarick, 2000) or (2) differenced forms of the explanatory variables (cf. Evans and Karras, 1994; Garcia-Mila et al., 1996; Crain and Lee, 1999), but not both. Romans and Subrahmanyam (1979) and Mullen and Williams (1994) are the exceptions.

(11) A mathematically equivalent specification is to include the level of tax burden at the beginning and end of the period (times t-4 and t, respectively).

(12) Many empirical growth studies follow Helms (1985) and include expenditures along with tax variables, with welfare expenditures as the omitted category. In contrast, my study--along with several others (e.g., Chernick, 1997; Tomljanovich, 2004)--does not. This affects the interpretation of the estimated tax effect. In the former case, the estimated tax effect represents the effect of raising tax revenues to fund welfare expenditures. In the latter case, the estimated effect represents the effect of raising tax revenues to fund general expenditures (assuming non-tax revenues and deficit remain constant). I prefer the latter specification because it represents the more relevant policy question. Further below, I investigate the consequences of including expenditure variables in the specification.

(13) The [R.sup.2] value for the same specification without state and time fixed effects is 0.744.

(14) I estimated a model with lagged values of DLNK, DLNL, DLNN, and TaxBurden(D) as instruments. This produced a positive, but insignificant coefficient for TaxBurden(D) (p-value = 0.758). However, I rejected this approach because the first-stage estimates indicated weak correlations. For example, the partial F test for the excluded instruments in the TaxBurden(D) equation was 0.77, with a p-value of 0.511. Further, some of the other estimated coefficients were implausible, such as the finding that employment growth (DLNL) was associated with negative income growth.

(15) Note that the interpretation of this variable should not be associated with convergence, since the model is not specified in steady-state form. Rather, this variable should be interpreted as proxying for the effect of omitted, initial-value variables that affect productivity growth.

(16) The variable DLNN potentially affects income growth through two channels: (1) directly (cf. equation [5]), and (2) indirectly, through [C.sub.t]. If DLNN did not exert a separate effect via C,, then its associated coefficient would be ([[beta].sub.1] + [[beta].sub.2] - 1) (cf. equations [5] and [6]). However, this hypothesis is consistently rejected in the subsequent empirical analyses.

(17) These criteria, as well as the associated SAS/IML computer program that implements them, are described in further detail in Reed (2008).

(18) I also included squared terms for the two tax variables, to allow for nonlinear tax effects. These are jointly significant. Both estimated tax effects were monotonically negative for all observations within the sample range, except for the largest value of the TaxBurden(D) variable.

(19) The Durbin-Watson statistic is 2.15; the Jarque--Bera statistic is 5.07, with an associated p-value of 0.079.

(20) I use the modified Wald test for groupwise heteroscedasticity available in the STATA command xttest3. The corresponding sample Chi-square value is 798.30 with 48 degrees of freedom, and the associated p-value is 0.0000.

(21) use Pesaran's test for cross-sectional dependence available in the STATA command xtcsd, which is distributed asymptotically standard normal. The corresponding cross-sectional dependence (CD) statistic is -1.481 with a p-value of 0.1385. However, this test assumes that the cross-sectional correlations are all same--signed. It has low power when the cross--sectional correlations are not same-signed, which describes my data. The average, absolute value of the cross-sectional correlations is 0.375 even with the inclusion of time fixed effects. This is quite large. Accordingly, I correct some of my estimates for cross-sectional correlation even though I do not formally reject the null hypothesis of no cross-sectional dependence.

(22) Note that "White standard errors" are robust only to heteroscedasticity, and not cross-sectional correlation.

(23) The DPD estimates were obtained using STATA's xtabond2 procedure. Note that both the one-step and two-step procedures assume no cross-sectional correlation. I do not use the DPD (system) estimator because the key moment condition in the level equation requires that the "distance" between a state's initial income and its "steady-state" value be uncorrelated with the state fixed effect (cf. Roodman, 2006, page 27). This is clearly violated in endogenous growth models and likely violated in exogenous growth models.

(24) I chose this estimation procedure given that testing of the residuals produced evidence of groupwise heteroscedasticity and cross-sectional correlation.

(25) The smaller estimated coefficients for TaxBurden(D) during the1980s is consistent with the findings of Carroll and Wasylenko (1994), though their study focused on state employment.

(26) An alternative approach that estimates individual state effects without a great sacrifice in degrees of freedom is to include squared terms for both tax variables. This allows taxes to exert either positive or negative effects on income growth, depending on the value of the respective tax variable. When I did this, I found that the individual, state-specific tax effects were negative for every state for both tax variables, except for one state with a large outlier value for the TaxBurden[D] variable. I thank a referee for suggesting this approach.

(27) We cannot reject the null hypothesis that the coefficients associated with the difference and level forms of the two kinds of revenues are the same. The associated p-values for the specifications of columns 2 and 3 are 0.51 and 0.47.

(28) State Personal Income as measured by the BEA includes transfer payments.

(29) A key remaining issue is the problem of endogeneity between tax policy and economic conditions. Policymakers frequently raise taxes during economic downturns, and lower taxes during times of economic prosperity (Poterba, 1994). This generates a negative bias to estimates of contemporaneous tax effects. While this cannot explain why I find a negative, lagged effect for tax burden (cf. the coefficient for TaxBurden [L]), it may contribute to the estimated, negative effect for contemporaneous changes in the tax burden variable (cf. the coefficient for TaxBurden[D]). TABLE 1 ESTIMATION OF THE RELATIONSHIP BETWEEN TAX BURDEN AND INCOME GROWTH: INITIAL RESULTS

(1) (2)

Dep. Dep.

Variable = Variable =

DLNY DLNK DLNK 0.3304 --

(7.26) DLNL 0.4258 --

(6.70) DLNN 0.4241 --

(5.02) TaxBurden(D) -1.3660 -2.5881

(-4.38) (-2.43) TiexBurden(L) -0.8979 -0.8318

(-2.25) (-0.88) [R.sup.2] 0.850 0.345 SIC 729.84 -- AICc 815.28 -- Observations 288 288 Hypothesis Tests

State effects = 0 [chi square] = 120.46 [chi square] = 91.67

(p-value = 0.000) (p-value = 0.000)

Time effects = 0 [chi square] = 86.76 [chi square] = 90.93

(p-value = 0.000) (p-value = 0.000)

(3) (4)

Dep. Dep.

Variable = Variable =

DLNL DLNN DLNK -- -- DLNL -- -- DLNN -- -- TaxBurden(D) -0.8380 -0.0346

(-2.71) (-0.13) TiexBurden(L) -0.3143 -0.5907

(-0.85) (-1.31) [R.sup.2] 0.629 0.766 SIC -- -- AICc -- -- Observations 288 288 Hypothesis Tests

State effects = 0 [chi square] = 46.67 [chi square] = 787.22

(p-value = 0.486) (p-value = 0.000)