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

The first approach allows the endpoint of one five-year period to coincide with the beginning of the next five-year period. Following this approach, the data are divided as follows: 1970-1975, 1975-1980, 1980-1985, ..., 1995-2000. A drawback of this approach is that it forces dependency between contiguous time periods. An alternative approach keeps the endpoints and beginning points of the periods separate, but shifts the data by a year: 1971-1975, 1976-1980, ..., 1996-2000.

This analysis takes its starting point as the variable specification of column 2, Table 3, estimated with FGLS (weighting on groupwise heteroscedasticity) using robust Variance--Covariance Estimation (VCE) to address heteroscedasticity and cross-sectional correlation. (24) These results were previously reported in abbreviated form in Table 4 and are repeated in column I of Table 5. The subsequent two columns use the same variable specification and estimation procedure, but employ different cuts of the data.

Alternative cuts of the data can make a difference. For example, the estimates for Female(D) change considerably, with the respective t-values ranging from -4.38 to -1.51. The coefficients for Mining(D) and Diversity(L) also show substantial variation, even switching signs. Indeed, the coefficient for TaxBurden(L) in column 3 is less than one-half the size of the equivalent estimate in column 1, with a correspondingly large change in the respective t-statistic.

Nevertheless, these estimates provide overall confirmation of the previous tax burden results. Across the alternative time divisions of the data, the coefficients of the two tax variables are uniformly, negatively signed and statistically significant, always having a t-statistic larger than two in absolute value.

Robustness across Time Periods, Regions, and States

A possible concern with previous estimates is that the results may be driven by a few time periods, regions, or states with particularly strong relationships between tax burden and income growth, and that these may not be broadly representative for the majority of observations. Previous specifications assumed that the estimated tax effects were the same for all observations. In this section, I use interaction terms to estimate individual time period, region, and state effects.

I first check for robustness across time periods. There are a total of six five-year periods: 1970-1974, 1975-1979,1980-1984, 1985-1989, 1990-1994, 1995-1999. The variable specification for this analysis continues to use the "Best SIC Specification" from Table 3, but supplements it with time-interaction effects to capture changes in the tax burden/income growth relationship over time. Following the previous results on estimation procedures, all coefficients are estimated using FGLS (with weighting for groupwise heteroscedasticity), with a White robust estimator for heteroscedasticity and cross-sectional correlation used to calculate standard errors. I first estimate time--specific coefficients for the variable TaxBurden(D). I then repeat the robustness check by estimating time--specification coefficients for the variable TaxBurden(L).

Table 6 summarizes the results. Notably, each of the 12 time-specific coefficients is negative. Ten of the 12 are individually significant. While the pattern is not perfect, smaller estimated coefficients for TaxBurden(D) are generally accompanied by larger coefficients for TaxBurden(L), and vice versa. (25) A similar pattern is observed when I estimate region- and state--specific interaction terms. An interpretation consistent with these results is that changes in tax burden take longer to register their effects for some time periods, regions, and states. That being said, the main finding from Table 6 is that the estimated relationships between income growth, and both the differenced and level forms of tax burden, are negative for every time period.

Table 7 reports the results of a similar analysis checking for robustness across the eight BEA regions and 48 states. The top part of the table reports the results of the regional analysis: 15 of the 16 estimated tax effects are negative; ten are significant at the ten percent level. The bottom part of the table reports a summary analysis for the states: Of the 48, state-specific coefficients for TaxBurden(D), 72.9 percent are negative. Of these, 15 are statistically significant at the ten percent level, and 13 of these are negative (86.7 percent). The corresponding numbers for the TaxBurden(L) coefficients are 64.5 and 69.2 percent, respectively. Only two states (Montana and Virginia) have positive coefficients for both TaxBurden(D) and TaxBurden(L), and none of the associated coefficients are significant at the ten percent level. In contrast, 20 states have negative coefficients for both tax variables. In 11 of these cases, at least one of the tax coefficients is significant at the ten percent level.

The results of Table 7 are not as robust as those of Table 6. In general, I find that as the data are cut into finer slices, the results become less consistent. By the time I get to the state level, there are only six observations per estimated coefficient (compared to 48 observations for the time-period analyses). (26) Nevertheless, it is clear that the finding of negative and statistically significant tax effects applies widely across time periods, regions, and states; and is not driven by a few observations exerting a disproportionately strong influence.

Robustness across Alternative Specifications of Government Finances

As Helms (1985) points out, the government budget constraint should always be kept in mind when interpreting the coefficients of fiscal variables:

(Tax Revenues + Non-Tax Revenues)

- (Welfare Expenditures

+ "Productive Expenditures")

+ Deficit = 0,

where I define "Productive Expenditures" as all state and local Direct General Expenditures other than Public Welfare. Thus, an increase in taxes must be accompanied by some combination of (1) a decrease in Non-Tax Revenues (e.g., fees and federal aid), (2) an increase in Welfare Expenditures or Productive Expenditures, and (3) a decrease in the Deficit. Previous specifications did not attempt to distinguish these alternatives.

Table 8 reports the results of including variables for both differences and levels of Non-Tax Revenues and Welfare, appropriately divided by state Personal Income. In column 2, the coefficients on the tax variables should now be interpreted as estimating the effect of an increase in taxes matched by a corresponding increase in general expenditures (as a practical matter, we can ignore deficits as they are usually negligibly small compared to overall revenues and expenditures.) The tax coefficients remain negative and statistically significant.

Column 3 adds welfare variables to the specification. The tax coefficients in this specification should be interpreted as estimating the effect of an increase in taxes matched by a corresponding increase in Productive Expenditures. Again, the estimated coefficients remain negative and statistically significant. Column 4 removes the Non-Tax Revenue variables from the specification, with no change in the overall finding of negative and statistically significant tax effects.

It is interesting to note that the negative tax effects are close in size to the corresponding negative effects associated with Non-Tax Revenues. (27) This is consistent with an interpretation that both variables are measuring negative effects associated with a larger public sector, and that the added, distortionary effects of taxes are negligible.

On the other hand, the positive and statistically significant coefficients for the welfare variables are puzzling. A possible explanation is that transfer payments are almost exclusively received by state residents, and hence, contribute directly to state income. (28) In contrast, other government expenditures can be diverted outside the state's economy (e.g., as payments to out-of-state suppliers of government services or supplies), so that the corresponding stimulative spending effects may not contribute to income growth within the state.

WHY HAVE PREVIOUS STUDIES FOUND IT DIFFICULT TO ESTIMATE ROBUST TAX EFFECTS?

In this section I show that annual data produces substantially different estimates of tax effects compared to five-year interval data. This may provide an explanation for why previous studies have found it difficult to estimate robust tax effects.

Column 1 of Table 9 uses OLS to estimate an annual analogue to the variable specification of column 2 in Table 3. The data cover 1970-1999 and include the log of capital, employment, and population, along with state and annual time fixed effects and a number of other control variables. The dependent variable is the log of real PCPI. I begin by following the conventional practice of only including contemporaneous values of the explanatory variables.

In contrast to the prior results, I now estimate a positive relationship between tax burden and state incomes. A one-percentage point increase in tax burden is estimated to increase real state PCPI by 0.16 percent. Further, the coefficient is significant well below the five percent level, with a t-value of just over three.

To check the sensitivity of this result, I drop various sets of variables from the specification of column 1. Column 2 drops the capital, employment, population, and lagged income variables. Column 3 drops these, plus the control variables. Column 4 drops these, plus all fixed effects. While the tax coefficient remains positive throughout, its size and statistical significance is unstable across specifications.