An unbalanced spatial panel data approach to US state tax competition

An unbalanced spatial panel data approach toUS state tax competitionPeter Egger a,T ,Michael Pfaffermayr b ,Hannes Winner baIfo-Institute for Economic Research,University of Munich,and CESifo,P .O.Box 860460,Munich 81631,GermanybDepartment of Economics,University of Innsbruck,Universitaetsstrasse 15,Innsbruck A-6020,AustriaReceived 17March 2004;accepted 28March 2005Available online 13June 2005AbstractThis paper assesses spatial competition in excise taxation among US states over the time period 1975–1999.We estimate the slope and shifters of the tax reaction curves using spatial panel data methods recently proposed by Kapoor et al.(in press)[Kapoor,M.,Kelejian,H.H.,Prucha,I.R.,in press.Panel data models with spatially correlated error components.J.Econ.].D 2005Elsevier B.V .All rights reserved.Keywords:Commodity tax competition;Spatial panel data econometrics JEL classification:H87;F15;C331.IntroductionCommodity tax competition emerges if independent jurisdictions set their excise tax rates strategically to extend their tax base by attracting mobile consumers (cross-border shoppers).Recent theoretical research has taken a spatial view on this issue (see Kanbur and Keen,1993;Ohsawa,1999;Nielsen,2001).According to these models,commodity tax rates are (i)positively affected by higher commodity tax rates of neighboring/adjacent jurisdictions,suggesting upward sloping tax reaction curves;(ii)0165-1765/$-see front matter D 2005Elsevier B.V .All rights reserved.doi:10.1016/j.econlet.2005.03.002T Corresponding author.Tel.:+498992241238;fax:+4989985369.E-mail address:egger@ifo.de (P.Egger).Economics Letters 88(2005)329–335/locate/econbasepositively associated with the size of the domestic jurisdiction,indicating an upward shift of reaction curves;and (iii)affected by the (weighted)size of competing jurisdictions.1Empirically,there is only evidence on spatial commodity tax competition between US states (Rork,2003;Devereux et al.,2004),confirming upward sloping reactions curves.However,although both studies rely on panel data,they do not consider recent contributions to spatial panel data ing tax rates for gasoline,cigarettes,beer,and wine of US states between 1975and 1999,this paper provides a rigorous assessment of the above hypotheses based on spatial GMM estimation methods by Kelejian and Prucha (1999),in general,and the spatial panel data model proposed by Kapoor et al.(in press)and Kelejian and Prucha (2003),in particular.2Since these papers focus on balanced panel data,we propose an adaptation to the unbalanced case.Based on the empirical estimates,we further calculate the direct effects of a state’s tax cut on the excise rates of its neighbors as indicated by the slope of the spatial tax reaction curve,and the indirect equilibrium feedback effects through the adjustment to the new Nash equilibrium induced by such a change.2.Econometric specificationThe econometric specification of the tax reaction function is motivated by the tax competition literature (see Kanbur and Keen,1993;Ohsawa,1999;Nielsen,2001).In particular,it accounts for the spatial pattern of tax competition:s it ¼q 1W N t s ðÞi þx it b þk t þu it ;u ¼q 2W N t u þe ;e it ¼l i þm it :ð1ÞThe data are first sorted by time (t )and second by states (i ).Bold letters indicate matrices or vectors.Specifically,s denotes the vector of the respective tax rate and x >it for (k Â1)vector of the explanatory variables (comprising size,spatially weighted size,and the remaining controls)for state i at time t .Sincethe panel is unbalanced,the (N t ÂN t )spatial weighting matrix,W N t ,is specific for each year and indexed by N t .The typical row-normalized element is given by w ij =b ij /Pj =1N (b ij ).b ij =1if i p j and two states share a common border,and 0if they do not.w ij =0if i =j .Rows and columns of missing observations have been deleted.For the whole panel,the spatial weighting matrix is bloc-diagonal with typical bloc W N t .q 1represents the slope of the tax reaction function.In line with the spatial tax competition models,the excise rate of state i depends on the (weighted)neighboring states’tax rates.|q 1|b 1ensures that the tax setting is consistent with a Nash equilibrium.The errors may be likewise spatially autocorrelated (SAR)with |q 2|b 1.The hypothesis of q 2p 0can be tested by the Moran I test (see Kelejian and Prucha,2001).Fixed time effects k t capture all time-variant influences common to all1The impact of foreign jurisdiction size is ambiguous in theoretical terms,depending on the definition and measurement of size (see Kanbur and Keen,1993vs.Ohsawa,1999).2Kelejian and Prucha (2003)generalize the framework in Kapoor et al.(in press)to allow for a spatially lagged dependent variable.We are grateful to Ingmar Prucha for making the unpublished manuscript available and for helpful communications on this issue.P .Egger et al./Economics Letters 88(2005)329–335330states such as the US business cycle.In addition,we allow for fixed or random state effects l i (withl i ~iid (0,r l2),E [l i m it ]=0and E [x kit m it ]=0in the latter case)to control for time invariant heterogeneity of the states.m it is a classical error term (with m it ~iid (0,r m2)).We follow Kapoor et al.(in press)and Kelejian and Prucha (2003)in using a GMM estimator,which proceeds in several steps.Due to the imbalance of our panel,their approach has to be modified,however.The moment conditions for the unbalanced panel data case are derived in Baltagi et al.(2005).First,a consistent 2SLS within estimator of q 1and b is employed (Baltagi,2001,p.112),using second-and higher-order spatial lags of the within-transformed explanatory variables as proper instruments for (W N t s )i .Second,the corresponding generalized residuals,which include the fixed or random state-specific effects,form the basis of the GMM estimator of Kapoor et al.(in press)and Kelejian and Prucha (2003)for q 2.Assuming for the moment that the remaining parameters (and,hence,u t )are known and using thenotation ¯u ¼Wu ;¯u ¼W 2u ,the (first four)moment conditions for the GMM estimator of q 2,r m 2,and r l 2read:E u Àq 2¯u ðÞV Q u Àq 2¯u ðÞÀr 2mn ÀN ðÞÀÁ¼0E ¯u Àq 2¯u ðÞV Q ¯u Àq 2¯u ðÞðÞÀr 2m tr W V QW ðÞÀr 2l tr W V QW D 1D 1V ðÞ¼0E ¯uÀq 2¯u ðÞV Q u Àq 2¯u ðÞðÞ¼0E u Àq 2¯uðÞV P u Àq 2¯u ðÞÀn r 2l ÀN r 2m¼0where n denotes the total number of observations and N is the number of unique US states in the sample.#1=(D 1V ,D 2V ,...,D T V )V is the selector matrix of dimension n ÂN ,and D t is an N t ÂN matrix obtained from I N ,skipping the rows corresponding to states not observed in year t .Further,P =#1(#1V #1)À1#1and Q =I n ÀP ,where the latter represents the within two transformations.We use the identity matrix for weighting and an NLS procedure to solve these four equations in three unknowns (see Kapoor et al.,in press;Baltagi et al.,2005).Third,we transform the data,say z ,as follows:(i)we remove the SAR error using an Cochrane–Orcutt-type transformation:z *(qˆ2)=(I n Àq ˆ2W )z ,and (ii)we apply the GLS transformation to account for the random effects (see Wansbeek and Kapteyn,1989):z it 44ˆq 2;ˆh i¼z it 4Àˆh i ¯z :t4with h i ¼1Àffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiˆr 2mT j ˆr 2l þˆr 2ms :Lastly,we apply 2SLS on the transformed data using the optimal set of instruments H it =z it***(h ˆi ),(W N t z t ***)i ,and (W N t 2z t ***)i ,where z it ***ˆh i ¼z it Àˆh i ¯z t .Kapoor et al.(in press)and Kelejian and Prucha (2003)demonstrate that this procedure obtains consistent and asymptotically normal estimates.P .Egger et al./Economics Letters 88(2005)329–3353313.Empirical resultsTable 1presents the fixed effects (FE)and random effects (RE)estimation results for gasoline,cigarettes,beer,and wine tax rates 3The RE estimator uses the GLS weights as discussed above,while the FE estimator relies on the within-transformed data with h i =1.As is obvious from the number of covered states and observations reported in the table,imbalance is an important issue.We only report estimates using relevant instruments,which pass the F -tests in the first-stage regressions and also the Sargan overidentification test.The main findings can be summarized as follows.First and most importantly,we identify a significant positive slope coefficient of the tax reaction function for each tax rate.In absolute terms,the point estimates are smaller than one,which guarantees the existence of a Nash equilibrium.These findings are consistent with the theoretical literature and the previous studies (Rork,2003;Devereux et al.,2004).Second,in all models,qˆ2is negative and exhibits a relatively high absolute value.On average,unobserved positive stochastic shocks in one state impede tax competition in others.Third,only for cigarettes and beer,we find significant evidence for the hypothesis that domestic state size exerts a positive impact on tax rates.For the panel of wine taxes,there is even evidence for the opposite.However,we should interpret this result with care,given the low data coverage in this case.Fourth,the negative parameter estimate of spatially weighted neighbors’size (again,except for wine)lends indirect support to Kanbur and Keen’s (1993,Proposition 1,p.882)hypothesis that tax rate undercutting is attractive for small states,which,in turn,leads to a negative impact of the competitors’size on the domestic Nash commodity tax rate (see also Nielsen,2001,p.603).Fifth,a liberal political orientation exerts a negative impact on tax rate setting,if any.In line with Devereux et al.(2004),the dependency ratio coefficient tends to be significantly positive.Further,public expenditure (lagged once to avoid endogeneity problems)tends to be associated with higher tax rates as expected.Concerning the tax structure,we find mixed support for the (general)sales tax and the top income tax rate (both,again,lagged once).A negative parameter estimate of both would indicate that tax competition is limited by the overall tax burden.The reported estimates illustrate that US state-specific effects should be modelled as random.This considerably improves the efficiency,maintaining consistent parameter estimates (note that the REparameters are almost indistinguishable from their FE counterparts).The significance of qˆ1and q ˆ2makes a strong case for spatial models using the Cochrane–Orcutt-type transformation and IV estimation with the appropriate instruments (discussed above).It should be emphasized that the selection of relevant and appropriate instruments is extremely important.This issue is not addressed in Rork (2003)and Devereux et al.(2004)due to their application of maximum likelihood estimators.4Given the consistent estimates in Table 2,we can proceed and quantify the underlying estimated tax competition effects.For this purpose,we distinguish between seven different groups of US states:Middle Atlantic,Midwest,New England,Pacific Coast,Rocky Mountains,South,and Southwest (see Table 2for details on the grouping).The table is produced as follows.First,we reduce each states tax rate by one r (standard deviation),based on the entire available period.Second,we compute the overall resulting change of such an exogenous shock on the domestic tax rate,and the part of this that3Due to missing observations and small time variation,the robust estimation for tax rates on distilled spirits is not feasible.4Rork (2003)relies on least squares dummy variable (LSDV)estimates of the cross-sectional Kelejian and Prucha (1998)estimator.P .Egger et al./Economics Letters 88(2005)329–335332is due to the adjustment to the new Nash equilibrium based on the positively sloped reaction functions (the feedback effect;expressed in both absolute and relative terms).Third,we weight all associated changes by a state’s labor force to derive the group-specific and the overall US average changes in tax rates.Table 2provides the following insights.The Middle Atlantic (gasoline and beer)and Midwestern states (cigarettes and wine)have undertaken the strongest tax reductions in this period.However,the US average is dominated by the large Midwest.On average,the spatial feedback effect of an exogenous tax reduction is strongest in the Midwest and the Middle Atlantic states.In relative terms,spatial tax competition is lowest for beer.The extremely large feedback effect for wine taxes should be interpreted with care given the poor data coverage.For cigarettes,an exogenous change in tax rates leads to a more than 40%higher change than it would without spatial tax competition.Table 2Direct and indirect effects on tax rates after an exogenous one j decline of a typical US state’s tax rate in each group of states in percent (based on random effects models in Table 1)Tax change ln(1+t V )Àln(1+t )Spatial feedback effectOverall effectSpatial feedback in %of overallTax change ln(1+t V )Àln(1+t)Spatial feedback effectOverall effectSpatial feedback in %of overallGasolineCigarettes Middle Atlantic States À0.061À0.009À0.07013.2À0.063À0.093À0.15659.8Midwestern States À0.032À0.006À0.03815.7À0.117À0.098À0.21545.5New England States À0.048À0.007À0.05512.1À0.037À0.020À0.05634.6Pacific Coast States À0.033À0.005À0.03913.6À0.046À0.029À0.07538.9Rocky Mountain States À0.045À0.008À0.05314.3À0.081À0.051À0.13238.8Southern States À0.039À0.007À0.04715.3À0.056À0.041À0.09742.2Southwestern States À0.040À0.006À0.04612.1À0.040À0.031À0.07243.9AverageÀ0.041À0.007À0.04714.1À0.068À0.056À0.12445.4BeerWine Middle Atlantic States À0.040À0.010À0.05019.8À0.001À0.002À0.00463.1Midwestern States À0.036À0.005À0.04111.3À0.096À0.821À0.91789.5New England States À0.0030.000À0.0037.4À0.029À0.129À0.15881.4Pacific Coast States À0.025À0.002À0.0288.7À0.126À0.658À0.78483.9Rocky Mountain States À0.033À0.003À0.0368.5À0.019À0.069À0.08877.9Southern States À0.023À0.002À0.0258.9À0.027À0.098À0.12578.1Southwestern States À0.0040.000À0.0059.3À0.019À0.085À0.10481.4AverageÀ0.027À0.004À0.03111.7À0.061À0.383À0.44586.2The figures refer to the labor force weighted averages of the direct effect of a tax reduction amounting to 1S.D.in a particular state on this state.The above groups consist of the following US states (Alaska and Hawaii are excluded throughout).Middle Atlantic States :New Jersey (NJ),New York (NY),Pennsylvania (PA).Midwestern States :Illinois (IL),Indiana (IN),Iowa (IA),Kansas (KS),Michigan (MI),Minnesota (MN),Missouri (MO),Nebraska (NE),North Dakota (ND),Ohio (OH),South Dakota (SD),Wisconsin (WI).New England States :Connecticut (CT),Maine (ME),Massachusetts (MA),New Hampshire (NH),Rhode Island (RI),Vermont (VT).Pacific Coast States :California (CA),Oregon (OR),Washington (WA).Rocky Mountain States :Colorado (CO),Idaho (ID),Montana (MT),Nevada (NV),Utah (UT),Wyoming (WY).Southern States :Alabama (AL),Arkansas (AR),Delaware (DE),Florida (FL),Georgia (GA),Kentucky (KY),Louisiana (LA),Maryland (MD),Mississippi (MS),North Carolina (NC),South Carolina (SC),Tennessee (TN),Virginia (V A),West Virginia (WV).Southwestern States :Arizona (AZ),New Mexico (NM),Oklahoma (OK),Texas (TX).P .Egger et al./Economics Letters 88(2005)329–335334P.Egger et al./Economics Letters88(2005)329–335335 AcknowledgementThe authors gratefully acknowledge comments from an anonymous referee and financial support from the Austrian Fonds zur Foerderung der wissenschaftlichen Forschung through grant P17028-G05. Appendix A.Data sourcesTax rates on beer,wine,gasoline,and cigarettes;Top income tax rate;Public expenditure:Office for Tax Policy Research,World Tax Database(/index.html).Labor force:US Department of Labor,Bureau of Labor Studies,2002,Historical state labor force data,Washington,DC.Dependency ratio:Own calculations based on US Census Bureau,2002,Demographic trends in the 20th century,Washington,DC.Government ideological orientation:Berry,W.D.,Ringquist,E.J.,Fording,R.C.,Hanson,R.L.,1998, Measuring citizen and government ideology in the American states,1960–93,American Journal of Political Science42,327–348(updated1999version)(this index ranges from0to100,with100 indicating the most liberal policy orientation and it comprises several components,such as the ideology of the governor and the major legislative chambers).ReferencesBaltagi,B.H.,2001.The Econometrics of Panel Data,2nd ed.John Wiley&Sons,Chichester.Baltagi,B.H.,Egger,P.,Pfaffermayr,M.,2005.Estimating Models of Complex FDI:Are There Third-Country Effects?Texas A&M University,unpublished manuscript.Devereux,M.P.,Lockwood,B.,Redoano,M.,2004.Horizontal and vertical indirect tax competition:theory and some evidence from the USA.CEPR Discussion Papers vol.4470.Kanbur,R.,Keen,M.,1993.Jeux sans frontier:tax competition and tax coordination when countries differ in size.American Economic Review83,877–892.Kapoor,M.,Kelejian,H.H.,Prucha,I.R.,in press.Panel data models with spatially correlated error components,Journal of Econometrics.Kelejian,H.H.,Prucha,I.R.,1998.A generalized spatial two-stage least squares procedures for estimating a spatial autoregressive model with autoregressive disturbances.Journal of Real Estate Finance and Economics17,99–121. 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