THE ROBUST RELATIONSHIP BETWEEN TAXES AND STATE ECONOMIC GROWTH 1. W. Robert Reed* Abstract

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1 THE ROBUST RELATIONSHIP BETWEEN TAXES AND STATE ECONOMIC GROWTH 1 by W. Rober Reed* Absrac I esimae he relaionship beween axes and economic growh using daa from and he fory-eigh coninenal U.S. saes. I find ha axes used o fund general expendiures are associaed wih significan, negaive effecs on economic growh. This finding is generally robus across alernaive variable specificaions, alernaive esimaion procedures, alernaive ways of dividing he daa ino five-year periods, and across differen ime periods and BEA regions, hough sae-specific esimaes vary widely. I also provide an explanaion for why previous research has had difficuly idenifying his robus relaionship. Revised, April 3, 2007 * Professor, Deparmen of Economics, Universiy of Canerbury, Privae Bag 4800, Chrischurch, New Zealand. Phone: bobreednz@yahoo.com. 1 This paper is submied as a Qualiy Assured conference paper for he 2007 NZAE Meeings, Chrischurch, New Zealand.

2 I. INTRODUCTION Barik (1994a,b) has suggesed ha he inerregional elasiciy of economic aciviy wih respec o axes is beween -0.1 and -0.6.[However] he resuls are no very reliable and change depending on which variables are included in he esimaion equaion, or which ime period is analyzed. -- Michael Wasylenko (1997, p. 38) My conclusion is ha we are uncerain abou he effecs of economic developmen policies, including broad sae fiscal policy, on economic growh. How does his conclusion ranslae ino policy? My message o policy makers is ha he effecs of sae and local ax policy are so uncerain ha concern over his issue should no be a driving force in general policy decisions. -- Therese McGuire (1992, p. 458) A long-sanding research enerprise has been devoed o esimaing he effec of axes on economic growh in U.S. saes. To he exen a consensus exiss, i is ha axes used o fund ransfer paymens have small, negaive effecs on economic aciviy. When used o fund producive expendiures, he associaed ax effecs are ofen esimaed o vanish, or even become posiive (Helms, 1985; Barik, 1991; Phillips and Goss, 1995; Wasylenko, 1997). However, even his modes conclusion is dispued, since esimaed effecs vary widely across sudies (Barik, 1991; McGuire, 1992; Wasylenko, 1997). Given he scores of sudies ha have invesigaed his issue, i is surprising ha many imporan esimaion issues have no been addressed. My sudy akes up several of hese, and re-esimaes he relaionship beween axes and economic growh. I find ha axes used o fund general expendiures are associaed wih significan, negaive effecs on economic growh. Furher, I show ha hese effecs are generally robus across esimaion procedures, alernaive specificaions of he regression equaion, differen ime 1

3 divisions of he daa, and across ime periods and BEA regions. In conras, sae-specific esimaes are highly variable. I also provide a possible explanaion for why previous research has had difficuly idenifying hese effecs. My analysis addresses he following esimaion issues. Firs, i uses economic heory o derive an esimable equaion. Wih respec o specificaion of he regression equaion, heory has consequences for he following: (i) he inclusion/exclusion of labor, capial, and populaion variables along wih, or insead of, underlying parameers such as saving, depreciaion, and populaion growh raes; (ii) he inclusion/exclusion of a lagged dependen variable; and (iii) wheher o include oher explanaory variables in level or differenced forms. The Cobb-Douglas producion funcion has now become a sandard poin of deparure for models of economic growh. Sudies ha have analyzed U.S. sae fiscal policy 1 wihin his framework include Merriman (1990); Garcia-Milá and McGuire (1992); Evans and Karras (1994); Holz-Eakin (1994); Garcia-Milá, McGuire, and Porer (1996); Aschauer (2000); Yamarik (2000); and. Shioji (2001). My sudy follows sui by employing a general version of he Cobb-Douglas producion ha includes he exbook Solow model and he augmened, human capial model of Mankiw, Romer and Weil (1992) as special cases. A second specificaion issue concerns he role of ime. Much of he previous lieraure has resriced axes o have only conemporaneous effecs on economic aciviy. When dynamic effecs are incorporaed, i is usually done indirecly, hrough he 1 The subsequen discussion of previous research resrics iself o sae-level analyses in which he dependen variable is income or income growh, where income is measured eiher by Personal Income or Gross Sae Produc in eiher oal or per capia erms. 2

4 inclusion of a lagged income variable (e.g., Helms, 1985). My regression specificaions allow axes o have boh conemporaneous and lagged effecs. 2 A relaed issue concerns how o define he lengh of a ime period for ime series observaions of saes. Previous research on sae-level axes and growh has relied almos exclusively on eiher cross-secional (e.g., Romans and Subrahmanyam, 1979; Mullen and Williams, 1994; Yamarik, 2000) or annual panel daa (e.g., Helms, 1985; Crain and Lee, 1999). Cross-secional daa is undesirable because i ignores ime-varying behavior in he explanaory variables. This is paricularly a problem for axes: The average sae ax burden in 1999 was very close o is level in 1970 (cf. Reed, 2006, Figure 1), despie large variaion over ime. Cross-secional analyses also suffer from omied variable bias due o unconrolled fixed effecs -- o he exen hese are no picked up in iniial income levels. On he oher hand, annual daa is paricularly vulnerable o measuremen error bias. This is, again, of paricular relevance for ax sudies. Using wo very differen approaches, Reed and Rogers (2006, 2007) esimae ha roughly half of he annual variaion in ax burden is due o facors oher han ax policy. This bias is exacerbaed by he inclusion of sae fixed effecs. Furher, annual sae-level income daa are characerized by subsanial serial correlaion (cf. Evans and Karras, 1994). The combinaion of serial correlaion wih a lagged dependen variable produces inconsisen esimaes. 2 Tomljanovich (2004) also allows for dynamic ax effecs, bu his sudy only includes sae axes, no sae and local. The pracical implicaion of his is ha i ignores propery axes, among ohers, and locally financed public expendiures. The empirical imporance of hese is demonsraed by Helms (1985). 3

5 Muli-year inerval daa also suffer from hese problems, bu o a lesser degree: Measuremen errors are more likely o cancel ou over longer ime periods. Serial correlaion is less severe when observaions are disanced furher in ime. A few sudies have analyzed he effecs of fiscal policy using muliple-year inerval daa. These include Garcia-Milá, McGuire, and Porer (1996); Aschauer (2000), Shioji (2001), Chernick (1997), and Tomljanovich (2004), hough only he laer wo direcly sudy axes. My analysis esimaes ax effecs over hiry years using five-year inerval daa. A hird issue is he selecion of conrol variables. Growh heory is sufficienly general ha many variables are poenial deerminans of growh. Despie his, many sudies of ax effecs include no, or only a few, non-fiscal variables oher han iniial/lagged income, ime, and/or sae-fixed effecs (cf. Becsi, 1996; Tomljanovich, 2004; Yamarik, 2000). Helms (1985) includes variables for sae wages, percen unionizaion, and populaion densiy. Mullen and Williams (1994) include variables for growh of he civilian labor force, and he growh raes of privae and public capial. Only Chernick (1997) and, noably, Crain and Lee (1999) have a broad se of conrol variables. My sudy includes an exensive se of conrol variables o avoid problems of bias associaed wih omied variables. Tha being said, i is well known ha coefficien esimaes are ofen highly dependen upon he paricular se of variables included in he regression equaion (Leamer, 1985; Levine and Renel, 1992; Crain and Lee, 1999; Sali-i-Marin, 2004). To address his problem, I employ model selecion crieria o deermine variable selecion. Furher, I invesigae he robusness of my resuls o alernaive specificaions. 4

6 A fourh issue concerns he choice of esimaion procedure. Panel daa are poenially characerized by complex error srucures. Mos previous research on fiscal policy uses OLS (e.g., Garcia-Milá and McGuire, 1992; Chernick, 1997; Crain and Lee, 1999), or OLS wih sandard errors correced for general heeroscedasiciy (e.g., Aschauer, 2000; Tomljanovich, 2004) or serial correlaion (Evans and Karras, 1994). A few sudies employ feasible Generalized Leas Squares (FGLS) o address random effecs (Garcia-Milá, McGuire, and Porer, 1996; Helms, 1985; Holz-Eakin, 1994), hough his procedure is usually rejeced in favor of OLS wih fixed effecs. Dynamic panel daa (DPD) esimaors have occasionally been used o obain consisen esimaes when he regression specificaion includes boh a lagged dependen variable and fixed effecs (Holz-Eakin, 1994; Shioji, 1994). My analysis allows for a variey of serial correlaion, heeroscedasiciy, and cross-secional correlaion behaviors in he error erm. I invesigaes he robusness of esimaing ax effecs using alernaive OLS, FGLS, and DPD esimaors. A fifh issue addresses he role of influenial observaions. Poin esimaes may mask he fac ha resuls can be driven by jus a few ime periods, or jus a few saes. This is of paricular imporance o policy-makers who are ineresed in exrapolaing he resuls of empirical sudies o heir own saes and ime periods. Wih only a few excepions, previous research on ax effecs repors only average effecs: Mullen and Williams (1994) and Chernick (1997) check for (i) robusness across differen ime periods and (ii) he effec of omiing some saes from heir samples. My analysis goes furher by ineracing ax variables wih boh ime, region, and sae dummy variables o check for robusness across hese dimensions. 5

7 The paper proceeds as follows: Secion II derives a model of economic growh ha is general enough o encompass many of he models ha have been used in previous research. Secion III describes he daa and discusses associaed specificaion issues. Secion IV presens he iniial empirical resuls. Secion V checks for robusness across (i) alernaive variable specificaions, (ii) alernaive esimaion procedures, (iii) differen ime divisions of he daa, and (iv) differen ime periods, regions, and saes. Secion VI provides a possible explanaion for why my sudy finds a robus relaionship beween axes and economic growh while previous sudies have no. Secion VII concludes. II. A MODEL OF ECONOMIC GROWTH I assume ha sae income ( ) is deermined by he following general version of he Y Cobb-Douglas producion funcion, α β α β β (1) Y = A K ( L Q ) = AQ K L, where K and L are capial and employmen, Q is he efficiency of labor, and A represens oher facors ha influence sae incomes (e.g., human capial variables, facor neural produciviy deerminans). The exbook Solow model and he augmened human capial model of Mankiw, Weil, and Romer (1992) are boh special cases of Equaion (1). 3 Dividing boh sides by N gives (2) Y N = A Q β K N α L N β N ( α + β 1). This can be expressed in log form as 1 α 3 α 1 α α α The exbook Solow model is ( ) Y = K L Q = Q K 1 α β L 1. Mankiw, Romer, and Weil s α β β 1 α β α α β augmened version of he Solow model is ( ) Y = K H L Q = H Q K L. 1 6

8 (3) ln ( y ) = α ln ( k ) + β ln ( l ) + ( α + β 1) ln( N ) + ln ( A ) + β ln ( Q ) where Y y =, N K k =, and N L l =. N Differeniaing Equaion (3) wih respec o ime yields y k l N (4) = α + β + ( α + β 1) y I follows ha k l A Q + + β N A Q (5) ln (y ) ln (y -L ) α [ ln (k ) ln (k-l )] + β [ ln (l ) ln (l-l )] ( α + β 1)[ ln (N ) ln (N -L )] + C +, where C [ ln (A ) ln (A )] + [ ln (Q ) ln (Q )] = β and L = he lengh of he ime -L period minus 1 (e.g., for a five-year period wih measuring calendar years, L = 4). 4, 5, 6 Equaion (5) idenifies changes in capial, employmen, and populaion as -L imporan deerminans of economic growh. However, he las erm, C, allows a role for oher variables -- poenially many oher variables -- o affec economic growh. III. DATA AND ESTIMATION ISSUES My daa consis of observaions on 48 U.S. saes from I decided on his paricular ime period because a longer ime frame would have required me o omi many variables of ineres. The respecive hiry years of daa are grouped ino 6, five-year 4 In he subsequen empirical work, he difference in log values is muliplied by An alernaive specificaion solves for he seady sae value of y as a funcion of sae parameers, and hen inroduces convergence hrough he inclusion of a lagged value of he dependen variable. The main cos of his approach is ha i requires he imposiion of addiional resricions. 6 I also check for robusness when L = 5, so ha he endpoins and sarpoins of he respecive five-year periods coincide. 7 Alaska and Hawaii were omied, as is usual in sudies of U.S. sae economic growh. 7

9 periods ( , ,, ). Daa for mos of hese variables were colleced from original daa sources. 8 In addiion o he previously cied benefis, five-year inerval daa 9 offer he following advanages over annual daa: They (i) average ou business cycle effecs (Grier and Tullock, 1989); (ii) minimize errors from misspecifying lag effecs; and (iii) reduce ime-specificaion issues. Time-specificaion issues arise because daa can have differen sar and end periods wihin a given calendar year. For example, sae income daa are defined over calendar years; sae fiscal daa are defined over fiscal years (which are differen for differen saes); and oher variables (e.g. employmen, populaion daa) may be measured a differen poins wihin he year (beginning/middle/end). In addiion, a number of variables (e.g., variables based on decennial Census daa) require inerpolaion in order o ge a balanced panel. Following Equaion (5), he general specificaion for he empirical models is 10 : β0 + β1dlnk + β 2DLNL + β3dlnn DLNY = (6) sae fixed effecs ime fixed effecs + +, + δ X X + λ X + ε d d ( d, d, 4 ) l l, 4 l where = 1974, 1979, 1984, 1989, 1994, 1999 ; DLNY, DLNK, DLNL, and DLNN are he respecive difference quaniies from Equaion (5) muliplied by 100 (o give percen); ( X ) is he change in he explanaory variable over he five-year period d X d, 4 ( differenced form); and X l, 4 is he value of he explanaory variable a he beginning 8 The Appendix presens saisical descripions of all he variables used in his sudy. 9 The daa are formaed in erms of five-year differences, no averages (cf. Equaion [5]). 10 I do no impose he resricion ha β 3 = ( β1 + β2 1) because populaion growh could also be relaed o C, in which case he resricion would be violaed. 8

10 of he five-year period ( level form). Noe ha he las wo erms can also be hough of as capuring he conemporaneous and lagged effecs of X. 11 A comparison of Equaions (5) and (6) reveals ha he differenced and level forms of X are designed o proxy for C [ ln (A ) ln (A )] + [ ln (Q ) ln (Q )] = β. As his laer erm is in differences, one may quesion why he level form of X is also -L -L included. Consider ha C incorporaes facors ha affec he growh rae of produciviy, which is relaed o he producion of new ideas. The supply of new ideas is likely relaed o he size of he populaion. This argues for inclusion of he level form of populaion. Similar argumens can be made for oher variables. As my measure of axes, I use ax burden, defined as he raio of sae and local ax revenues o personal income. Tax burden is by far he mos commonly employed measure of sae axaion, and can be hough of as he effecive average ax rae in a sae (e.g., Helms, 1985; Mofidi and Sone, 1994; Mullen and Williams, 1994; Carroll and Wasylenko, 1994; Knigh, 2000; Caplan, 2001; Yamarik, 2000, 2004; Alm and Rogers, 2005). 12 IV. INITIAL EMPIRICAL RESULTS TABLE 1 summarizes he iniial resuls. The firs column (Equaion [7]), repors he resuls of esimaing a narrowly specified version of Equaion (6). The only explanaory variable from he se of differenced variables, {( X d, X d, 4 )} d, is he change in ax 11 For an alernaive derivaion ha arrives a a virually idenical specificaion, see Bassanini, Scarpea, and Hemmings (2001). 12 Previous sudies of fiscal policy ha specify income growh as he dependen variable have ypically included eiher (i) level (cf. Helms, 1985; Chernick, 1997; Yamarick, 2000) or (ii) differenced forms of he explanaory variables (cf. Evans and Karras, 1994; Garcia-Milá, McGuire, and Porer, 1996; Crain and Lee, 1999), bu no boh. Romans and Subrahmanyam (1979) and Mullen and Williams (1994) are excepions. 9

11 burden, TaxBurden(D); and he only explanaory variable from he se of level variables, { X l, 4} l, is he value of ax burden a he beginning of he period, TaxBurden(L). Boh ax variables are negaive and highly significan (he -values are and -2.25, respecively). This suggess ha axes have boh an immediae and a persisen effec. The coefficien esimae for TaxBurden(D) indicaes ha a one percenage-poin increase in ax burden over a five-year period is associaed wih lower real PCPI growh of 1.37 percen during ha period. In addiion, an increase in axes raises he level of ax burden, which is associaed wih lower growh in fuure ime periods. A sae having a ax burden ha is one percenage poin higher han oher saes is esimaed o have real PCPI growh ha is lower by 0.90 percen in subsequen five-year periods. Two poins are worh noing. Firs, hese effecs represen he ne effec of axes and spending. Since expendiures variables are omied from he specificaion, and since he relaionship beween U.S. sae expendiures and revenues is generally one-o-one, he respecive coefficiens should be inerpreed as an increase in axes o fund general (unspecified) expendiures. Second, hese esimaed effecs are sizeable. The mean value of he ax burden variable is 10.87, and he mean growh rae of real PCPI (DLNY) is 8.23 percen. Thus, ax variable coefficiens in he range of -1.0 represen economically imporan relaionships. Wih respec o he res of he equaion, he resuls indicae ha increases in a sae s capial sock (DLNK), employed labor force (DLNL), and populaion (DLNN) are each associaed wih greaer income growh. Overall, he equaion has good explanaory power, hough much of ha comes from he sae and ime fixed effecs The R 2 value for he same specificaion wihou sae and ime fixed effecs is

12 The esimaed ax effecs of Equaion (7) hold consan any effecs ha axes migh have on invesmen, employmen and populaion growh. One migh reasonably expec axes o be relaed o hese as well. Equaions (8) hrough (10) invesigae his by respecively regressing each of hese on he wo ax variables plus sae and ime fixed effecs. Across all hree equaions, we see ha higher axes are associaed wih lower invesmen, lower employmen growh, and lower populaion growh. Noably, here are differences in he iming of he respecive esimaed effecs. Equaions (8) and (9) repor ha an increase in ax burden is associaed wih a saisically significan decrease in invesmen and employmen growh during he same five-year period. Beyond ha period, he ax effecs are smaller and saisically insignifican. In conras, Equaion (10) indicaes ha an increase in ax burden is esimaed o have a negligible conemporaneous effec on populaion growh. However, here is some evidence o indicae ha higher axes lower populaion growh in laer ime periods (he respecive p-value is 0.19). These resuls are consisen wih expecaions abou how axes migh affec each of hese variables: invesmen and employmen are more easily adjused in he shor-run, while migraion decisions respond more slowly and require more ime o be realized. The preceding resuls sugges ha axes influence sae economic growh via wo general channels. The firs channel is associaed wih he erm, C, which collecs changes in he efficiency of labor ( relaed o produciviy ( A Q ) plus he effecs of oher ime-varying facors ). The second channel is via he erms DLNK, DLNL, and DLNN, which incorporae he effecs of axes on invesmen, employmen and populaion growh. Ideally, one could measure he combined effec of ax burden on economic 11

13 growh by esimaing a srucural sysem of equaions wih DLNY, DLNK, DLNL, and DLNN all reaed as endogenous. Unforunaely, a lack of good insrumens makes his approach unfeasible. 14 An alernaive is o esimae a reduced form version of Equaion (7), omiing he erms DLNK, DLNL, and DLNN. Equaion (11) repors he resuls of his exercise. As expeced, he combined effec of axes is esimaed o be subsanially larger. A one percenage poin increase in ax burden is associaed wih a conemporaneous, decrease of 2.59 percen in real PCPI growh. In addiion, fuure five-year growh raes are esimaed o be lower by 1.56 percen. V. ROBUSTNESS CHECKS Robusness wih respec o alernaive specificaions. One concern wih he previous se of resuls is ha he esimaed ax effecs may suffer from omied variable bias. I is hus imporan o conrol for he influence of oher variables ha may affec sae economic growh. The subsequen analysis akes Equaion (7) as is saring poin, and appends his wih heoreically appropriae conrol variables. I is clear from Equaion (5) ha a large number of variables could be included as proxies for he unobserved erm, C. Reed (2007) idenifies hiry-wo variables ha have been used or suggesed by previous sudies. Eliminaing he public secor variables (such as caegories of public spending or axes) -- since including hese would change he naure of he ax variables -- leaves hireen non-ax variables. These are idenified in TABLE 2. Each of hese can be argued o be included in differenced or level (iniial 14 I esimaed a model wih lagged values of DLNK, DLNL, DLNN, and TaxBurden(D) as insrumens, bu rejeced his approach because he firs-sage esimaes indicaed weak correlaions. 12

14 value) form. If one also allows he iniial value of income o be included as a regressor 15, and recalls ha he differenced form of he populaion variable (DLNN) is already included in he core specificaion, one obains a oal of weny-six possible conrol variables. 16 While i is likely ha many of hese variables do no really belong in he regression equaion, i is no apparen a priori which ones should be excluded. Choosing one or a few ses of conrol variables is poenially a problem, since previous lieraure (e.g., Leamer, 1985; Levine and Renel, 1992; Crain and Lee, 1999; Sali-i-Marin e al., 2004) has demonsraed ha esimaed coefficiens are ofen fragile, sensiive o he paricular composiion of condiioning variables. The problem is complicaed by he fac ha here are million ways o combine weny-six variables, each one a possible regression specificaion. I address he issue of variable specificaion in he following way. Firs, I esimae a complee specificaion ha includes all weny-six variables. Nex, I idenify and esimae he bes specificaions as deermined by boh SIC and AIC (correced version) model selecion crieria. 17 This produces hree ses of regression resuls, each of which is repored in TABLE 3 (cf. Equaion [12], [13] and [14]). 15 Noe ha he inerpreaion of his variable should no be associaed wih convergence, since he model is no specified in seady-sae form. Raher, his variable should be inerpreed as proxying for he effec of omied, iniial-value variables ha affec produciviy growh. 16 The variable DLNN poenially affecs economic growh hrough wo channels: (i) direcly (cf. Equaion [5]), and (ii) indirecly, hrough C. If DLNN did no exer a separae effec via C, hen is associaed coefficien would be ( β 1 + β2 1) (cf. Equaions [5] and [6]). However, his hypohesis is consisenly rejeced in he subsequen empirical analyses. The upsho is ha one canno esimae an analogue of Equaion (10), appended wih conrol variables, since DLNN would appear as one of he conrol variables. 17 This procedure, as well as he specific SAS program I use o implemen i, is described in furher deail in Reed (2007). 13

15 Of greaes ineres are he firs wo rows of TABLE 3. These repor he esimaed coefficiens of TaxBurden(D) and TaxBurden(L) afer including alernaive ses of conrol variables. Boh ax coefficiens are smaller in absolue value compared o Equaion (7), where he esimaed values are and -0.90, respecively. Neverheless, hey remain negaive across he expanded specificaions of Equaions (12) hrough (14). Furher, hey coninue o be highly significan. In he All Variables specificaion of Equaion (12), TaxBurden(D) and TaxBurden(L) have -saisics(p-values) of, respecively, -2.58(0.011) and -2.87(0.004). The corresponding -saisics are even higher in Equaions (13) and (14). And while hese laer wo specificaions are he produc of sequenial search, he - saisics/p-values for he wo ax variables can sill be inerpreed in he classical manner because he search procedure includes hese wo variables in every specificaion. Turning o he oher variables, I find ha he esimaed coefficiens are generally consisen wih he predicions of growh heory, or a leas no inconsisen. Focusing on he coefficiens from Equaion (13), we observe he following resuls (ignoring he disincion beween iniial levels and conemporaneous changes): higher educaional aainmen, a greaer percenage of he populaion who are of working age, a greaer percenage of he populaion ha is nonwhie, a larger populaion, a greaer reliance on agriculure, and a more unionized workforce are associaed wih higher economic growh. A larger female populaion, a larger mining secor, and greaer indusrial diversiy are associaed wih lower economic growh. Lasly, ceeris paribus, saes wih a greaer iniial value of real PCPI grow slower han oher saes. In conclusion, I find ha he significan, negaive ax effecs repored in Equaion (7) are robus o he inclusion of a wide variey of conrol variables. The nex secion 14

16 invesigaes he robusness of he relaionship beween ax burden and sae economic growh when alernaive esimaion procedures are employed. Robusness wih respec o alernaive esimaion procedures. The subsequen analysis selecs Equaion (13) as he bes of he preceding specificaions. This OLS equaion displays good properies. I has a high R 2, he key explanaory variables all have large -saisics, he Durbin-Wason saisic is close o 2, and a es of error normaliy fails o be rejeced a he 5 percen level. 18 However, here are a leas wo concerns. Firs, panel daa are ofen characerized by complex error srucures. Using he residuals from Equaion (13), I esed for (i) firsorder serial correlaion, (ii) groupwise heeroscedasiciy, and (iii) cross-secional correlaion. I found no evidence of significan serial correlaion (he esimaed value of he AR(1) parameer was -0.02). However, I rejec he hypohesis of no groupwise heeroscedasiciy 19 and find subsanial evidence of cross-secional correlaion. 20 This raises worries abou he inefficiency of he coefficien esimaes and biasedness in he esimaes of he sandard errors. 21 Unforunaely, while one can esimae an error variance-covariance marix ha allows for cross-secional correlaion, one canno inver ha marix, since N=48 > T=6. 18 The Durbin-Wason saisic is 2.15; and he Jarque-Bera saisic is 5.07, wih an associaed p-value of I use he modified Wald es for groupwise heeroscedasiciy available in he STATA command xes3. The corresponding sample Chi-square value is wih 48 degrees of freedom, and he associaed p- value is I use Pesaran s es for cross-secional dependence available in he STATA command xcsd, which is disribued asympoically sandard normal. The corresponding CD saisic is wih a p-value of However, his es assumes ha he cross-secional correlaions are all same-signed. I has low power when he cross-secional correlaions are no same-signed, which describes my daa. The average, absolue value of he cross-secional correlaions is even wih he inclusion of ime fixed effecs. This is quie large. Accordingly, I correc some of my esimaes for cross-secional correlaion even hough I do no formally rejec he null hypohesis of no cross-secional dependence. 21 Noe ha Whie sandard errors are robus only o individual heeroscedasiciy, and no cross-secional correlaion. 15

17 This precludes he use of Parks-ype feasible Generalized Leas Squares (FGLS). However, here are several alernaives. One approach is o coninue o use OLS, bu adjus he sandard errors for cross-secional correlaion; eiher by using Beck and Kaz s panel-correced sandard error procedure (Beck and Kaz, 1995), or by using a more robus esimaor of he error variance-covariance marix. Anoher is o follow-up a suggesion by Greene (2003, pages 333f.) and use FGLS, weighing on groupwise heeroscedasiciy while adjusing he sandard errors for cross-secional correlaion. Accordingly, I check for robusness of he esimaed ax effecs across he following alernaive esimaion procedures: i) OLS wih panel-correced sandard errors ii) iii) iv) OLS wih robus esimaion of he error variance-covariance marix assuming cross-secional correlaion (i.e. cluser sandard errors) FGLS (weighed on groupwise heeroscedasiciy) wih panel-correced sandard errors FGLS (weighed on groupwise heeroscedasiciy) wih panel-correced sandard errors v) FGLS (weighed on groupwise heeroscedasiciy) wih cluser sandard errors There is an addiional concern. Equaion (13) includes boh fixed effecs and a lagged form of he dependen variable as explanaory variables. This generaes correlaion beween he error erm and he lagged form of he dependen variable, causing biased coefficien esimaes (Nickell, 1981). To address his concern, I use wo dynamic panel daa (DPD) esimaors: he Arellano-Bond (difference) one-sep and wo-sep procedures The DPD esimaes were obained using STATA s xabond2 procedure. Noe ha boh he one-sep and wo-sep procedures assume no cross-secional correlaion. I do no use he DPD(sysem) esimaor because he key momen condiion in he level equaion requires ha he disance beween a sae s iniial 16

18 TABLE 4 repors he esimaes from hese alernaive esimaion procedures. For comparison s sake, he firs row duplicaes he ax burden esimaes from Equaion (13) in TABLE 3. There are wo main findings from his analysis: Boh FGLS and DPD confirm earlier resuls in ha hey produce negaive coefficien esimaes for each of he ax variables. The FGLS esimaes are similar in size o he OLS esimaes, while he DPD esimaes are generally larger (in absolue value). In addiion, he saisical significance of he ax effecs is confirmed across all alernaive esimaion procedures. Of he sixeen -saisics repored in TABLE 4, foureen imply significance a he 1 percen level, wih he remaining wo significan a he 5 and 10 percen levels. Accordingly, I conclude ha my main findings of negaive, saisically significan ax effecs are robus across alernaive esimaion procedures. Robusness across alernaive cus of he daa. The preceding analyses divide he hiry years of daa from ino six periods of five-years each: , ,, This secion looks a wo alernaive ways of dividing he daa. The firs approach allows he endpoin of one five-year period o coincide wih he beginning of he nex five-year period. Following his approach, he daa are divided as follows: , , ,, A drawback of his approach is ha i forces dependency beween coniguous ime periods. An alernaive approach keeps he endpoins and beginning poins of he periods separae, bu shifs he daa by a year: , ,, TABLE 5 repors he resuls. The firs column of TABLE 5 uses FGLS (weighing on groupwise heeroscedasiciy) wih robus VCE for cross-secional income and is seady-sae value be uncorrelaed wih he sae fixed effec (cf. Roodman, 2006, page 27). This is clearly violaed in endogenous growh models and likely violaed in exogenous growh models. 17

19 correlaion o esimae he variable specificaion of Equaion (13). 23 These resuls were previously repored in abbreviaed form in TABLE 4. The subsequen wo columns use he same esimaion procedure and variable specificaion bu employ differen cus of he daa. Alernaive cus of he daa can make a difference. For example, he esimaes for Female(D) change considerably, wih he respecive -values ranging from o The coefficiens for Mining(D) and Diversiy(L) also show subsanial variaion, even swiching signs. Indeed, he coefficien for TaxBurden(L) in Column (3) is less han half he size of he equivalen esimae in Column (1), wih a correspondingly large change in he respecive -saisic. Neverheless, hese esimaes provide overall confirmaion of he previous ax burden resuls. Across he alernaive ime divisions of he daa, he coefficiens of he wo ax variables are uniformly negaively signed and saisically significan, always having a -saisic larger han wo in absolue value. Robusness across ime periods, regions, and saes. A possible concern wih previous esimaes is ha he resuls may be driven by a few ime periods, regions, or saes wih paricularly srong relaionships beween ax burden and economic growh; and ha hese may no be broadly represenaive for he majoriy of observaions. Previous specificaions assumed ha he esimaed ax effecs were he same for all observaions. In his secion, I use ineracion erms o esimae individual ime period, region, and sae effecs. 23 I chose his esimaion procedure given ha esing of he residuals produced evidence of groupwise heeroscedasiciy and cross-secional correlaion. 18

20 I firs check for robusness across ime periods. There are a oal of 6 five-year periods: ( , , , , , ). I respecify Equaion (13) and include ime-ineracion effecs o capure changes in he ax burden/economic growh relaionship over ime. Following he previous resuls on esimaion procedures, all coefficiens are esimaed using FGLS (wih weighing for groupwise heeroscedasiciy), wih a Whie robus esimaor for cross-secional correlaion used o calculae sandard errors. I firs esimae ime-specific coefficiens for he variable TaxBurden(D). I hen repea he robusness check by esimaing imespecificaion coefficiens for he variable TaxBurden(L). TABLE 6 summarizes he resuls. Noably, each of he welve ime-specific coefficiens is negaive. Ten of he welve are individually significan. While he paern isn perfec, smaller esimaed coefficiens for TaxBurden(D) are generally accompanied by larger coefficiens for TaxBurden(L), and vice versa. 24 A similar paern is observed when I esimae region- and sae-specific ineracion erms. An inerpreaion consisen wih hese resuls is ha changes in ax burden ake longer o regiser heir effecs for some ime periods, regions, and saes. Tha being said, he main finding from TABLE 6 is ha he esimaed relaionships beween economic growh, and boh he differenced and level forms of ax burden are negaive for every ime period. TABLE 7 repors he resuls of a similar analysis checking for robusness across he eigh BEA regions and saes. The op par of he able repors he resuls of he regional analysis: Fifeen of he sixeen esimaed ax effecs are negaive; en are significan a he 10 percen level. The boom par of he able repors a summary 24 The smaller esimaed coefficiens for TaxBurden(D) during he 1980 s is consisen wih he findings of Carroll and Wasylenko (1994), hough heir sudy focused on sae employmen. 19

21 analysis for he saes: Of he fory-eigh, sae-specific coefficiens for TaxBurden(D), 72.9 percen are negaive. Of hese, fifeen are saisically significan a he 10 percen level, and hireen of hese are negaive (86.7 percen). The corresponding numbers for he TaxBurden(L) coefficiens are 64.5 and 69.2 percen, respecively. Only wo saes (Monana and Virginia) have posiive coefficiens for boh TaxBurden(D) and TaxBurden(L), and none of he associaed coefficiens are significan a he 10 percen level. In conras, weny saes have negaive coefficiens for boh ax variables. In eleven of hese cases, a leas one of he ax coefficiens is significan a he 10 percen level. The resuls of TABLE 7 are no as robus as hose of TABLE 6. In general, I find ha as he daa are cu ino finer slices, he resuls become less consisen. By he ime I ge o he sae level, here are only 6 observaions per esimaed coefficien (compared o 48 observaions for he ime-period analyses). 25 Neverheless, i is clear ha he finding of negaive and saisically significan ax effecs applies widely across ime periods, regions, and saes; and is no driven by a few observaions exering a disproporionaely srong influence. Robusness across alernaive specificaions of governmen finances. As Helms (1985) poins ou, he governmen budge consrain should always be kep in mind when inerpreing he coefficiens of fiscal variables: (Tax Revenues + Non-Tax Revenues) (Welfare Expendiures + Producive Expendiures ) + Defici = 0, 25 An alernaive approach ha esimaes individual sae effecs wihou a grea sacrifice in degrees of freedom is o include squared erms for boh ax variables. This allows axes o exer eiher posiive or negaive effecs on economic growh, depending on he value of he respecive ax variable. The respecive coefficiens can be used o solve for he hreshold level a which he effec of axes swiches signs. When I did his, I found ha all saes had esimaed negaive ax effecs for boh of he ax variables. I hank a referee for suggesing his approach. 20

22 where I define Producive Expendiures as all sae and local Direc General Expendiures oher han Public Welfare. Thus, an increase in axes mus be accompanied by some combinaion of (i) a decrease in Non-Tax Revenues (e.g., fees and federal aid), (ii) an increase in Welfare Expendiures or Producive Expendiures, and (iii) a decrease in he Defici. Previous specificaions did no aemp o disinguish hese alernaives. TABLE 8 repors he resuls of including variables for boh differences and levels of Non-Tax Revenues and Welfare, appropriaely divided by sae Personal Income. In Column (2), he coefficiens on he ax variables should now be inerpreed as esimaing he effec of an increase in axes mached by a corresponding increase in general expendiures (as a pracical maer, we can ignore deficis as hey are usually negligibly small compared o overall revenues and expendiures.) The ax coefficiens remain negaive and saisically significan. Column (3) adds welfare variables o he specificaion. The ax coefficiens in his specificaion should be inerpreed as esimaing he effec of an increase in axes mached by a corresponding increase in Producive Expendiures. Again, he esimaed coefficiens remain negaive and saisically significan. Column (4) removes he Non- Tax Revenue variables from he specificaion, wih no change in he overall finding of negaive and saisically significan ax effecs. I is ineresing o noe ha he negaive ax effecs are close in size o he corresponding negaive effecs associaed wih Non-Tax Revenues. 26 This is consisen 26 However, we canno rejec he null hypohesis ha he coefficiens associaed wih he difference and level forms of he wo kinds of revenues are he same. The associaed p-values for he specificaions of Columns (2) and (3) are 0.51 and

23 wih an inerpreaion ha boh variables are measuring negaive effecs associaed wih a larger public secor; and ha he added, disorionary effecs of axes are negligible. On he oher hand, he posiive and saisically significan coefficiens for he welfare variables are puzzling. A possible explanaion is ha ransfer paymens are almos exclusively received by sae residens, and hence conribue direcly o sae income. 27 In conras, oher governmen expendiures can be divered ouside he sae s economy (e.g., as paymens o ou-of-sae suppliers of governmen services or supplies), so ha he corresponding simulaive spending effecs may no conribue o economic growh wihin he sae. VI. WHY HAVE PREVIOUS STUDIES FOUND IT DIFFICULT TO ESTIMATE ROBUST TAX EFFECTS? In his secion I show ha annual daa produces subsanially differen esimaes of ax effecs compared o five-year inerval daa. This may provide an explanaion for why previous sudies have found i difficul o esimae robus ax effecs. Column (1) of TABLE 9 uses OLS o esimae an annual analogue o Equaion (13). The daa cover and include he log of capial, employmen, and populaion, along wih sae and annual ime fixed effecs and a number of oher conrol variables. The dependen variable is he log of real PCPI. I begin by following he convenional pracice of only including conemporaneous values of he explanaory variables. In conras o he prior resuls, I now esimae a posiive relaionship beween ax burden and sae incomes. A one-percenage poin increase in ax burden is esimaed o 27 Sae Personal Income as measured by he BEA includes ransfer paymens. 22

24 increase real sae PCPI by 0.16 percen. Furher, he coefficien is significan well below he 5 percen level, wih a -value jus over hree. To check he sensiiviy of his resul, I drop various ses of variables from he specificaion of Column (1). Column (2) drops he capial, employmen, populaion, and lagged income variables. Column (3) drops hese, plus he conrol variables. Column (4) drops hese, plus all fixed effecs. While he ax coefficien remains posiive hroughou, is size and saisical significance is unsable across specificaions. A somewha differen picure emerges when he specificaion is broadened o allow lagged effecs. Column (5) repors he resuls of adding lagged values of he ax burden variable o he specificaion of Column (1). While he conemporaneous relaionship beween ax burden and economic growh remains posiive, lagged values of ax burden are esimaed o be negaively associaed wih sae income. This suggess ha previous sudies may have failed o idenify a negaive relaionship beween axes and economic growh because hey relied on specificaions ha used annual daa and did no allow for lagged ax effecs. My analysis suggess ha ax policies ake ime o work heir full effecs on he economy. When he specificaion is sufficienly general o pick up hese effecs, a negaive relaionship beween axes and economic growh emerges. The use of annual daa may also have conribued o previous findings of coefficien insabiliy. Annual daa are more vulnerable o measuremen error bias han five-year inerval daa. Fixed effecs exacerbae he influence of measuremen errors. As demonsraed by Reed and Rogers (2006, 2007), ax burden subsanially mismeasures sae ax policy. Consequenly, i would no be surprising if esimaes of ax effecs based 23

25 on annual daa were prone o insabiliy depending on he paricular disribuion of measuremen errors in he sample. This may be an addiional reason why previous sudies have had difficuly idenifying robus ax effecs. VII. CONCLUSION Using five-year daa from and he fory-eigh coninenal saes, I find ha boh (i) conemporaneous changes and (ii) lagged levels of axes are negaively and significanly relaed o economic growh. The esimaed effecs vary depending on variable specificaion; esimaion procedure; ime period, region, and sae; and he manner in which he daa are organized ino five-year inervals. Neverheless, he finding of negaive and saisically significan ax effecs is generally robus across all of hese dimensions, wih one excepion: Sae-specific esimaes of ax effecs vary widely. This laer resul may be explained by he narrow parsing of he daa. A his level of analysis here are only six observaions per sae-specific ax coefficien. These resuls are surprising given ha previous sudies have had difficuly idenifying a robus relaionship beween sae axes and incomes. My analysis suggess ha his may be because previous sudies of sae income growh have ended o use annual daa, have differed in heir variable specificaions, and have no allowed for lagged ax effecs. When I use annual daa and resric he analysis o conemporaneous ax effecs, I esimae posiive ax effecs, bu he sizes and significances of he ax coefficien vary grealy depending on variable specificaion. When I include lagged values of he ax variable, a negaive relaionship beween axes and growh emerges. This lack of robusness is no apparen in he five-year inerval daa. This may be because he variables inerac over ime in complex ways ha are difficul o model. I 24

26 may also be ha he daa -- for definiional and measuremen reasons -- are no wellsuied o relaing o each oher a he annual level. Much work remains o be done before reliable esimaes of ax effecs can be obained. 28 However, his sudy esablishes ha here is an imporan empirical relaionship beween axes and U. S. sae economic growh. Obaining a beer undersanding of he naure and cause of ha relaionship is a poenially fruiful avenue for fuure research. I is hoped ha his sudy will simulae effors owards ha end. 28 A key remaining issue is he problem of endogeneiy beween ax policy and economic condiions. Policy makers frequenly raise axes during economic downurns, and lower axes during imes of economic prosperiy (Poerba, 1994). This generaes a negaive bias o esimaes of conemporaneous ax effecs. While his canno explain why I find a negaive, lagged effec for ax burden (cf. he coefficien for TaxBurden[L]), i may conribue o he esimaed, negaive effec for conemporaneous changes in he ax burden variable (cf. he coefficien for TaxBurden[D]). 25

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