*** THE APPENDICES ARE NOT FOR PUBLICATION ***

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1 *** THE APPENDICES ARE NOT FOR PUBLICATION *** Appendix A: The Tax Reaction Function: An Explicit Derivation This appendix contains a detailed development o our model o strategic competition and extracts implications or the tax reaction unction the equilibrium response o tax policy in a home (in-state) jurisdiction to tax policy in a oreign (out-o-state) jurisdiction. It is complementary to the discussion in Section II and Figure 5. We show that the slope o the reaction unction can be positive ( racing to the bottom ) or negative ( riding on a seesaw ) and that the sign o this slope depends on the sign o one key parameter the income elasticity o private goods relative to public goods. The sign o this elasticity is related to whether private goods as a whole are a necessary or luxury goods, a condition closely related to the validity o Wagner s Law. 1 The model developed in this section is useul or identiying the determinants o the slope o the reaction unction, suggesting hypotheses, and interpreting the empirical results. A. A Model O Tax Competition Our model o tax competition is based on six relations that describe the constraints aced by a government choosing business capital tax policy to maximize the utility o the representative domestic household. First, production in the home state is determined by a Cobb- Douglas unction that depends on a mobile capital stock and a ixed actor o production, such as land or inrastructure (the Cobb-Douglas assumption is adopted or analytic convenience). The capital stock available or home production (K) is the sum o the capital stocks owned by home residents ( k ) and, given the mobility o capital, the capital stock owned by oreign residents but located in the home state ( k ). 2 We write the production unction ( F[K] ) in the ollowing intensive orm relative to the ixed actor o production (note that brackets are used in this paper to identiy arguments in unctional relations), y F[K], (A-1) K k k, F'[K] 0, F"[K] 0. 1 Wagner s Law states that the share o government spending (as a percentage o GDP) increases with aggregate income. It is named ater the 19 th century German economist, Adolph Wagner. 2 I the state is a net capital exporter, k < 0. Without loss in generality, we analyze a capital importing state.

2 Second, as a result o capital mobility, the capital stock in a given state is sensitive to capital income tax rates prevailing in home and oreign states. Consequently, the capital stock in the home state depends negatively on the home capital tax rate ( ) and positively on the oreign capital tax rate ( ), as well as on a set o controls relecting home and oreign demographic and 2 economic variables ( xk and x k, respectively), k k k K[ :,x,x ], (A-2) K [.] 0, K [.] 0. This capital mobility unction allows economic and demographic variables to aect home capital demand insoar as they impact production possibilities and the marginal product o capital. It proves convenient to assume that the derivatives with respect to the home and oreign capital tax rates are equal and opposite in sign ( K [.] K [.]), though the qualitative results do not require this assumption. 3 Equations (A-1) and (A-2) can be combined to generate a relation between production and the home and oreign tax rates, y F[K] FK[ :,x k,x k] G :,x k,x k, (A-3) G [.] 0, G [.] 0. The derivative, G [.] 0, represents the incremental home production rom a tax-induced low o capital rom the oreign state to the home state. Third, we link net income to expenditures by means o GDP accounting relations. Net income available or domestic expenditures is measured by gross income (production) less the return on capital assets ( r ) owned by oreign residents but located in the home state. Net income is set equal to domestic expenditures, deined as the sum o public goods (g) and private goods (c), yr g c. (A-4) Fourth, the government budget constraint (stated per unit o the ixed actor) equates public goods expenditure to two sources o tax revenue. For the purposes o this study, the most 3 While equation (A-2) and its partial derivatives are consistent with the implications rom the standard constraint equating net-o-tax returns across jurisdictions, our ormulation allows or the possibility that, owing to a variety o rictions (discussed in the literature on the Lucas Paradox (Lucas, American Economic Review, 1980), the net-o-tax returns on capital may dier. See Appendix B.1 or analytic details about the capital mobility unction.

3 important tax is an origin-based tax on capital income. This tax is deined as the product o the capital income tax rate ( ) and capital income, the latter deined as the marginal product o capital ( F'[K]) multiplied by the capital stock located in the home state. The second source o 3 revenue is a sales tax deined as the product o the sales tax rate (s) and income. This tax rate will be held constant in this analysis. The government budget constraint becomes, g F'[K] K sy y sy s y. 4 (A-5) Fith, capital imported rom abroad is paid a return equal to the marginal product o capital multiplied by the amount o oreign capital located in the home state. As a result o the Cobb- Douglas production unction, the return on imported capital is a ixed share ( ) o output, r F'[K]k y, (A-6). Equations (A-4), (A-5), and (A-6) can be combined to generate a relation between the mix o public and private goods ( g/ c ) and the capital tax rate. We multiply and divide the two terms on the right-side o equation (A-4) by g, use equations (A-5) and (A-6) to eliminate g and r, respectively, and rearrange the resulting equation to obtain the ollowing equation, s g/c S[ ], (A-7) 1 s S[.] 0. This condition shows that an increase in the share o output devoted to public goods requires an increase in the capital tax rate. Equation (A-7) is the supply curve presented in Figure 1 to. The sixth and inal equation is the utility unction that represents preerences or public and private goods. This unction and its implications or were discussed in Section II.B, and is repeated here or convenience, 4 A wage tax at rate wage could enter the model by adding ( wage (1- ) y) to the right side o equation (A-5).

4 ,y k k,y,y g/c p y(1 ) p G :,x,x (1 ) D :,, g g c c (A-8a) / 0, (A-8b) ( c g 1) ( 1) c g p p /p 0, (A-8c),y g c 0. (A-8d) where, in equation (A-8a), we have substituted or y with equation (A-3). Equation (A-8a) is the 4 demand curve presented in Figure 1 relating to,, and,y. The above model serves as a vehicle or studying the properties o the tax reaction unction. The model is summarized by equations (A-3), (A-7), and (A-8). Substituting the irst two equations into the third equation, we determine the optimal capital tax rate, τ *, and its relation to the oreign capital tax rate, g/c [y(1 ) : x ], (A-9) * * 0 G[ :,x k,x k] (1 ) : x S[ ], 0 [ :,x]. k k x {x,x,x,,,s} Appendix B.2 veriies the existence o τ *.

5 5 *** NOT FOR PUBLICATION *** Appendix B: Additional Analytic Results For The Strategic Tax Competition Model Appendix B.1; Properties O The Capital Mobility Function This appendix provides some analytic details concerning the properties o the capital mobility unction (equation (A-2)) used in this paper. This unction allows or the possibility that, owing to a variety o rictions, the net-o-tax returns on capital may dier across jurisdictions. This appendix demonstrates that the capital mobility unction and its partial derivatives are consistent with the implications rom the standard constraint equating net-o-tax returns across jurisdictions. Equation (A-2) is reproduced here as ollows, k K[ :,x k,x k], (B.1-1) K [.] 0, K [.] 0. where k is the capital stock owned by oreign residents but located in the home state. Without loss o generality, we assume that the home state is a capital importer. The purpose o this exercise is to derive the properties o this unction rom a generalized equation relating net-o-tax returns in the home and oreign jurisdictions, which is written as ollows, (1 ) F '[K] (1 ) '[K ], (B.1-2) where is a wedge that represents a variety o rictions preventing equalization o net-o-tax returns across jurisdictions, F'[K] and '[K ] are the marginal products o capital or the home and oreign jurisdictions, respectively. The production unctions or both jurisdictions are subject to the Inada conditions (which guarantee that equation (B.1-2) will hold or some capital allocation). We assume that there is a ixed amount o capital ( K ) that is allocated between the home and oreign jurisdictions, KK k, (B.1-3a) K K k, (B.1-3b) where K and K are the initial amounts o capital in the home and oreign states, respectively. Substituting equation (B.1-3) into (B.1-2), dierentiating the resulting expression by k,, and, noting that dk dk, and rearranging, we obtain the ollowing derivatives,

6 6 dk F'[.] K[.] 0, (B.1-4a) d (1 ) F"[.] (1 ) "[.] dk '[.] d (1 ) F"[.] (1 ) "[.] K [.] 0, (B.1-4b) where we have assumed that the production unctions exhibit diminishing marginal products ( F"[.] 0, "[.] 0 ). I the production unctions are identical across jurisdictions, then K [.] K [.].

7 *** NOT FOR PUBLICATION *** 7 Appendix B.2: The Existence O An Equilibrium Tax Rate And Its Relation To The Pre-Tax Capital Income Share This appendix provides some analytic details concerning the existence o an equilibrium tax rate ( * ) in the indirect utility model and its relation to the pre-tax capital income share and the rate o sales taxation. We analyze a symmetric equilibrium between home and oreign jurisdictions. We begin with the three relations that summarize the content o the theoretical model presented in Section II.A, y F[K] FK[ :,x k,x k] G :,x k,x k, (B.2-1) G [.] 0, G [.] 0. 1 s s g/c S[ ], (B.2-2) S[.] 0.,y g/c p y(1 ) y:,p, D, g g c c (B.2-3a) / 0, (B.2-3b) ( c g 1) ( 1) c g p p /p 0, (B.2-3c),y g c 0. (B.2-3d) where equation (B.2-1) is equation (A-3) representing the production unction and the mobile capital stock, equation (B.2-2) is equation (A-7) representing the aggregate and government budget constraints, and equation (B.2-3) is equation (A-9) representing optimized choices o public and private goods. Under the symmetry assumption, no capital lows between jurisdictions because the tax rates are equal. Thus, equation (B.2-1) implies that the level o output in each country is constant, y y. Substituting this constant into equation (B.2-3) and eliminating with equation (B.2-2), we obtain the ollowing solution or *

8 * s * 1 s (1 ) s (1 ) *, (1 ) y:,p,, 8 (B.2-4) Since representative estimates o, s, and are 0.270, 0.025, and 0.33, respectively, * 0 is ensured because the maximum value o is (the capital income share). Moreover, equation (B.2-4) establishes that there is a negative relation between * and the pre-tax capital income share ( ), as well as the rate o sales taxation (s ).

9 *** NOT FOR PUBLICATION *** 9 Appendix B.3: Comparing the CES Direct and Addilog Indirect Utility Functions The addilog indirect utility unction that is the basis or our theoretical model is used less requently than a CES direct utility unction. (Note that a Cobb-Douglas direct utility unction is a special case o the CES.) This appendix compares the implications o both utility unctions or the relative public goods ratio,, and shows that the CES direct utility unction is less general than the addilog indirect utility unction. The CES direct utility unction is written as ollows, (1/ ) U[c, g] g (1 ) c, (B.3-1a) (1 ) / (B.3-1b) where is the CES distribution parameter, the substitution parameter, and the elasticity o substitution between g and c. The addilog indirect utility unction was presented in Section II, and it is reproduced here, g c. (B.3-2) V[y] y / p y / p g g c c where c, g, c, and g are positive parameters representing preerences. (For notational simplicity and without loss in generality, we have set 0.) Each utility unction generates demand unctions or c and g based on optimizing behavior subject to the ollowing budget constraint, y p g p c, (B.3-3) g c where p g and p c are the prices or g and c, respectively. The demand unctions or g and c ollowing rom the CES direct utility unction are as ollows, (1 ) pg y g *, (B.3-4a) (1 ) (1 ) p (1 ) p p g c g (1 ) p y c *, (B.3-4b) (1 ) c (1 ) (1 ) p g (1 ) pc pc These two demand unctions imply the ollowing relation or the relative demand or public goods, g/c,

10 10 CES p c. (B.3-5) (1 ) p g As discussed in Section II, a key property o the addilog indirect utility unction is that the ratios between any two expenditures have a constant elasticity with respect to total expenditure (Houthakker, 1960, p. 253). Relying on Roy s identity to generate the demand unctions or c and g, we obtain ater some additional manipulation the ollowing equation or the relative demand or public goods (Houthakker, 1960, equation (30)), Addi log,y py, (B.3-6a) g g c c / 0, (B.3-6b) ( c g 1) ( 1) c g p p /p 0, (B.3-6c),y g c 0. (B.3-6d) A comparison o equations (B.3-5) and (B.3-6) reveals that the addilog indirect utility unction yields a more general model o the determinants o the relative demand or public goods. The ollowing restrictions on equation (B.3-6) yield equation (B.3-5) or any values o and, g c 1, (B.3-7a) g c / /(1 ). (B.3-7b) Apart rom these restrictions, the addilog model generates a model that is more general and, most importantly or the study o tax competition, allows or income to have a direct impact on the relative demand or public goods.

11 ** NOT FOR PUBLICATION *** 11 Appendix B.4: Tax Competition In A Direct Utility Model This appendix analyzes the tax competition model developed in Section II with the indirect utility unction (equation (8)) replaced by the ollowing direct utility unction deined in terms o c and g, Ug,c c g. It proves convenient to rewrite equation (B.4-1) in terms o the private/public goods mix variable, (B.4-1) U,c g. (B.4-2) The optimization problem acing policymakers is to choose in order to maximize equation (B.4-2) constrained by equations (A-3), (A-5), and (A-7) reproduced here in abbreviated orm or convenience, y F[K] FK[ :,x k,x k] G :,x k,x k, (B.4-3) G [.] 0, G [.] 0. g F'[K] K sy y sy s y. (B.4-4) 1 s s g/c S[ ], (B.4-5) S[.] 0. To simpliy the analysis, we have assumed that capital income taxation is the only sources o revenue in equation (B.4-4) (i.e., setting s = 0 in equation (A-5)). Substituting equation (B.4-3) into equation (B.4-4) to eliminate y, and restating and c in equation (B.4-2) in terms o with equation (B.4-5) and the modiied (B.4-4), respectively, the optimization problem can stated solely in terms o, U S G (B.4-6) Dierentiating equation (B.4-6) with respect to and rearranging, we obtain the ollowing equation determining the optimal implicitly,

12 / (1 ) * 1. (B.4-7) (1 [ * : ]) where is the elasticity o output with respect to the capital tax rate (relecting both the sensitivity o capital lows to the capital tax rate and output to the capital stock; see equation (3b) or urther details). Assume that is constant. In this case, equation (B.4-7) has the reasonable properties that the optimal capital income tax rate depends (1) negatively on the relative utility weight on private goods ( / ), (2) negatively on the share o capital income (thus requiring a lower capital tax rate to collect a given amount o revenue), and (3) negatively on (relecting the amount o capital outlow or a given change in ). Dierentiating equation (B.4-7) with respect to and with the chain rule and rearranging yields the ollowing reaction unction, d * ', (B.4-8a) d 1 * ' 2 / (1 )/ 1 [.] 0, (B.4-8b) ' d /d. (B.4-8c) Relative to our preerred reaction unction derived rom an indirect utility unction, equation (B.4-8) is restrictive because its sign depends on the direction o change in an elasticity, a derivative that is unrelated to traditional economic mechanisms and intuition. Note that, i the production and capital low unctions constituting have constant elasticities, then ' 0 and d /d 0. Most importantly, the direct utility model does not allow or the possibility that the public/private good mix is sensitive to income. Such a restriction is relaxed in the indirect utility model and proves very important in understanding the slope o the reaction unction. 12

13 13 ** NOT FOR PUBLICATION *** Appendix C: Variable Deinitions and Data Sources 5 study: This appendix describes the construction o and data sources or the variables used in this 1. ACT: Average Corporate Tax Rate 2. CAW: Capital Apportionment Weight 3. CIT: Corporate Income Tax Rate 4. EXPS: State government expenditures share o state GDP 5. GDP (and GDPGROWTH): State Gross Domestic Product (and its growth rate) 6. ITC: Investment Tax Credit Rate 7. MFGSHR: Manuacturing share o state GDP 8. PERS: Personal Income Tax Rate 9. PREFERENCES: Voter Preerences 10. POPULATION (and POP20-64): Total Population (and population years old) 11. TAXREV: Corporate tax revenue share o state GDP 12. TD: Tax Depreciation 13. TWC: Tax wedge on capital 14. i,j : Spatial Lag Weights 15. Legend The series are or the 48 contiguous states (indexed by subscript s) or the period 1963 to 2006 (indexed by subscript t), unless otherwise noted. 6 Each o the above series is described in a separate section. The general organizing principle or each section is to irst deine each o the series mentioned above and then discuss its components. For each component, general issues concerning the construction o the series (i pertinent) and then data sources are discussed. Section 11 contains a Legend with abbreviations and sources. 5 In describing the raw data, we have taken some o the text in this data appendix directly rom government publications. 6 The most notable exception is that the Annual Survey o Manuacturers was not conducted rom 1979 to 1981.

14 1. ACT: Average Corporate Tax Rate The average corporate tax rate is measured as ollows, 14 ACT CIT i,t REV i,t GOS i,t, where GOS is state private gross operating surplus and REV i,t CIT i,t is state government revenues rom the corporate income tax. Gross operating surplus data come rom REA, and state tax revenues data comes rom STC. 2. CAW: Capital Apportionment Weight The capital apportionment weight (CAW) is the weight that the state assigns to capital (property) in its ormula apportioning income among the multiple states in which irms generate taxable income. The apportionment ormula is always a weighted average o the company s sales, payroll, and property (with zero weights allowed). However, the weights vary by state. In practice, the payroll and property weights are always equal, at least or the states and years in our sample, so that knowing one o the three weights or a state reveals the other two. We construct data rom on the actor apportionment weights or each o the 48 contiguous states. We use a number o dierent sources. OMER provides inormation on the year in which each state irst deviated rom the traditional three-actor, equal weighting ormula. Kelly Edmiston kindly provided data on apportionment weights or years 1997 and 2001 used in CESW. John Deskins kindly provided data panel data or used in BDF. Lastly, we were able to obtain weights or various years rom STH.

15 3. CIT: Corporate Income Tax Rate The eective corporate income tax rate at the state level ( i,t E,S ) is lower than the 15 legislated (or statutory) corporate income tax rate ( L,S t ) due to the deductibility (in some states) against state taxable income o taxes paid to the ederal government. 7 Some states allow ull deductibility o ederal corporate income taxes rom state taxable income; Iowa and Missouri allow only 50% deductibility; and some states allow no deductibility at all. The deductibility provision in state tax codes is represented by i,t {1.0,0.5,0.0}, and the provisional eective corporate income tax rate at the state level ( i,t #,E,S ) is as ollows, i,t #,E,S L,S t 1i,t i,t #,E,F. The eect o ederal income tax deductibility is represented by the provisional eective corporate income tax rate at the ederal level ( i,t #,E,F, deined below). The L,S i,t and series are obtained rom several sources. For recent years, data are i,t obtained primarily rom various issues o BOTS and STH, as well as actual state tax orms. Data or earlier years are obtained rom various issues o BOTS and SFFF. Additional inormation has been provided by TAXFDN. Many states have multiple legislated tax rates that increase stepwise with taxable income; we measure L,S i,t with the marginal legislated tax rate or the highest income bracket. The eective corporate income tax rate at the ederal level is lower than the legislated corporate income tax rate ( L,F t ) due to the deductibility against ederal taxable income o taxes paid to the state. The provisional eective corporate income tax rate at the ederal level is as ollows, i,t #,E,F L,F t 1 i,t #,E,S 7 In corporate income taxes we also include Texas ranchise tax, which has a very similar tax base as the traditional corporate income tax base.

16 The eect o state income tax deductibility is represented by the eective corporate income tax rate at the state level. The L,F t series is obtained rom GRAVELLE, Table 2.1. Our database L,F presents t in percentage points. It has not generally been recognized that, owing to deductibility o taxes paid to another level o government, the eective corporate income tax rates at the state and ederal levels are unctionally related to each other. As shown in the above equations, these interrelationships yield two equations in two unknowns, and thus can be solved or the eective corporate income tax rates at the state and ederal levels, respectively, as ollows, 16 E,S L,S L,F L,S L,F i,t i,t 1 i,t t 1 i,ti,t t, E,F L,F L,S L,S L,F i,t t 1 i,t 1 i,ti,t t. The overall corporate income tax rate is the sum o E,S E,F i,t and i,t. In the limiting case where ederal corporate income taxes are not deductible against state taxable income ( i,t 0 ), this L,S L,S L,F t. sum reduces to the more requently used ormula, i,t 1 i,t 4. EXPS: State Government Expenditures As A Share O State GDP The numerator comes rom SGF and the denominator comes rom REA. Both are measured in nominal dollars. 5. GDP: State Gross Domestic Product Data on real state gross domestic product (GDP) and its growth rate (GDPGROWTH) come rom REA.

17 6. ITC: Investment Tax Credit Rate The state investment tax credit is a credit against state corporate income tax liabilities. We ocus on investment tax credits that are permanent. In general, the eective amount o the L,S investment tax credit is simply the legislated investment tax credit rate ( ITC i,t ) multiplied by the value o capital expenditures put into place within the state in a tax year. The eective rate is lower than the legislated rate in a handul o states or two reasons. First, ive states (Connecticut, Idaho, Maine, North Carolina, and Ohio) permit the state investment tax credit to be applied only to equipment. Since equipment investment is approximately 85% o ASM total national investment, we multiply L,S ITC i,t by 0.85 or these ive states. Second, states generally require basis adjustments deducting the amount o the credit rom the asset basis or depreciation purposes; this adjustment is considered in the subsection on the Present Value o Tax Depreciation Allowances. We extend the state panel data on L,S ITC i,t rom Chirinko and Wilson (2008) through The original and extended data are obtained directly rom states online corporate tax orms and instructions. For most states with an investment tax credit, both current and historical credit rates are provided in the current year instructions (since companies applying or a credit based on some past year s investment apply that year s credit rate rather than the current rate). In those ew cases where some or all historical rates were missing rom the online orms and instructions, the missing rates are obtained via direct communication with the state s department o taxation. In some states, the legislated investment tax credit rate varies by the level o capital expenditures; we use the legislated credit rate or the highest tier o capital expenditures MFGSHR: Manuacturing State GDP As A Share O Total State GDP The numerator and denominator come rom REA. Both are measured in nominal dollars. 8. PERS: Personal Income Tax Rate The personal income tax rate is measured by the marginal tax rate or the median household computed rom the NBER TaxSim simulator. TaxSim generates the marginal state tax rate or each stateyear or a hypothetical taxpayer who iles jointly, has no dependents, and has household income equal to the 50 th percentile nationally or that year.

18 9. PREFERENCES: Voter Preerences Voter preerences are measured by political outcomes. Speciically, we measure the ollowing two political outcomes as indicator variables: 18 (a) the governor is Republican (R). (The complementary class o politicians is Democrat (D) or Independent (I). An inormal examination o the political landscape suggests that Independents tend to be more closely aligned with the Democratic Party. We thus treat D or I politicians as belonging to the same class, DI); (b) the majority o both houses o the legislature are R; The PREFERENCES variable takes on one o three values: 0 i the governor and the majority o both houses o the legislature are not R; 1/2 i the governor is R but the majority o both houses o the legislature are not R or i the governor is not R but the majority o both houses o the legislature are R; 1 i the governor and the majority o both houses o the legislature are R. Data or these political variables come rom the Statistical Abstract o the United States (U.S. Census Bureau (Various Years)). 10. POPULATION (And POP20-64): Total Population (And Population Years Old) Data on total population and population aged years old are obtained rom CENSUS. 11. TAXREV: Corporate Tax Revenue As A Share O State GDP The numerator comes rom SGF and the denominator comes rom REA. Both are measured in nominal dollars. 12. TD: Tax Depreciation Tax depreciation allowances accrue over the useul lie o the asset. We have assumed that the present value o tax depreciation allowances, TD i,t, is 0.70 or all s and t. We assume a slightly lower value than the average across asset types and years reported in GRAVELLE to adjust or the basis reduction by the amount o investment tax credits taken.

19 TWC: Tax Wedge on Capital The price o capital (tax-adjusted) is deined as the product o three objects relecting the purchase price o the capital good, the opportunity costs o holding depreciating capital, and taxes. This latter term comprises tax credits, tax deductions, and the tax rate on income, and we reer to these tax terms (less 1.0) as the tax wedge on capital, 1.0 ITCi,t CIT i,t *TD TWCi,t CIT i,t. In this paper, we deine TWC i,t only in terms o state tax variables. Note that the user cost o capital, which was introduced by JORGENSON-1 in 1963 and extended by, among others, HALL-JORGENSON, GRAVELLE, JORGENSON-YUN, and KING-FULLERTON, equals the price o capital divided by the price o output. 14. i,j : Spatial Lag Weights The spatial lag weights in our baseline speciications are measured by the inverse o the distance between state population centroids (data are rom CENSUS). In supplemental speciications, we also use spatial weights based oncommodity trade lows (data are rom TRANSPORT) and spatial weights based on population divided by distance. The population data are or the year 2000 and come rom CENSUS. All spatial weighting matrices are rownormalized.

20 Legend ASM: CENSUS, Annual Survey o Manuactures, Complete Volume (Various Years). ASM-GAS: CENSUS, Annual Survey o Manuacturers, Geographic Area Statistics (Various Years). Publications or the years 1994 to 2004 (except 1997 and 2002) are available online. These data are published on an establishment basis. The data are obtained rom electronic or paper documents depending on the time period: 2004 (Census website); 2003 to 1972 (CD's purchased rom Census); 1971 to 1963 (paper copies). URL: ASM-SIGI: CENSUS, Annual Survey o Manuacturers, Statistics or Industry Groups and Industries (1996). URL: BDF: Bruce, Donald, Deskins, John, and Fox, William F., On The Extent, Growth, and Eiciency Consequences o State Business Tax Planning, mimeo, University o Tennessee, BOTS: The Council o State Governments, The Book o the States (The Council o State Governments : Lexington, Kentucky, Various Issues). CBP: CENSUS, County Business Patterns. URL: CENSUS: Bureau o the Census, U.S. Department o Commerce. URL: CESW: Cornia, Gary; Edmiston, Kelly; Sjoquist, David L.; and Wallace, Sally, The Disappearing State Corporate Income Tax, National Tax Journal 58 (March 2005), FIXED: BEA, Standard Fixed Asset Tables. URL:

21 21 FRAUMENI: Fraumeni, Barbara M., "The Measurement o Depreciation in the U.S. National Income and Product Accounts," Survey o Current Business 77 (July 1997), GRAVELLE: HALL- JORGENSON: JORGENSON-1: JORGENSON-2: Gravelle, Jane G., The Economic Eects o Taxing Capital Income (Cambridge: MIT Press, 1994) plus updates kindly provided by Jane Gravelle. Hall, Robert E., and Jorgenson, Dale W., "Application o the Theory o Optimum Capital Accumulation," in Gary Fromm (ed.), Tax Incentives and Capital Spending (Washington: Brookings Institution, 1971), Jorgenson, Dale W., "Capital Theory and Investment Behavior," American Economic Review 53 (May 1963), ; reprinted in Investment, Volume 1: Capital Theory and Investment Behavior (Cambridge: MIT Press, 1996), Jorgenson, Dale W., "The Economic Theory o Replacement and Depreciation," in Willi Sellakaerts (ed.), Econometrics and Economic Theory: Essays in Honour o Jan Tinbergen (London: MacMillan, 1974), JORGENSON- Jorgenson, Dale W., and Yun, Kun-Young, Investment Volume 3: YUN: Liting the Burden: Tax Reorm, the Cost o Capital, and U.S. Economic Growth (Cambridge: MIT Press, 2001). KING- FULLERTON: King, Mervyn A., and Fullerton, Don (eds.), The Taxation o Income rom Capital (Chicago: University o Chicago Press (or the NBER), 1984). OMER: Omer, Thomas C., and Shelley, Marjorie K., Competitive, Political, and Economic Factors Inluencing State Tax Policy Changes, Journal o the American Tax Association, 26 (2004), REA: Bureau o Economic Analysis, Regional Economic Accounts URL: SGF: CENSUS, Survey o State Government Finances (SGF), various years.

22 22 SFFF: American Council on Intergovernmental Aairs, Signiicant Features o Fiscal Federalism (Washington, DC: American Council on Intergovernmental Aairs, Various Issues). URL (e.g., 1987): STC CENSUS, State Government Tax Collections report, various years. URL: STH: Commerce Clearing House, State Tax Handbook (Chicago: Commerce Clearing House, Various Issues). TAXFDN: Tax Foundation web site. URL: TRANSPORT: The U.S. Bureau o Transportation Statistics, 1997 Survey o Commodity Flows.

23 *** NOT FOR PUBLICATION *** 23 Appendix D: A Distributed Lag Reaction Function This appendix combines a static tax reaction unction with a partial adjustment model to derive the distributed lag reaction unction that generates the benchmark results in this paper. The low o capital among states may occur gradually over several years, and hence the observed t will dier rom the desired home state capital income tax rate, gradual response o t, we adopt the ollowing partial adjustment model, # t t t1 t1 vt # t. To allow or the, (D-1) where is a parameter determining how much o the discrepancy between the long-run and lagged 's will be eliminated in period t, and v t is a stochastic shock. The i subscripts have been omitted or convenience. Lagging equation (D-1) one period and successively substituting the lagged equations into equation (D-1) yields the ollowing equation, J J j # j (J1) t (1 ) tj (1 ) v tj (1 ) tj1 j0 j0. (D-2) As J, the last term vanishes. We use the static relation (equation (7)) to deine # t, # t t xt ut. (D-3) Substituting equation (D-3) into (D-2) and rearranging, we obtain the ollowing distributed lag model, t j tj jxtj wt j0 j0, (D-4) j (1 ), j, j (1 ) j j t tj tj j0 w (1 ) v u, (1 ). j j0 j0 j As shown on the last line o Equation (D-4), the estimated coeicients on the s sum to, t j

24 24 the slope o the reaction unction that is the prime ocus o this paper. Equation (D-4) is the basis or our estimation, which relies on a less general orm o this equation in three dimensions. First, the distributed lags are truncated at no more than our periods. Lagged dependent variables allow us to capture the eects o lags urther back in time, and this model is discussed in Appendix F. Second, in order to conserve degrees o reedom, we lag the x variables only one period. An implication o equation (D-4) is that the composite error term will be correlated with all o the t j 's, not just t. We explore the impact o this potential correlation on the coeicients o interest by instrumenting the lagged oreign tax rate variables with lags o our preerred instrument set (i.e., or a given n, i,tn is instrumented by * z,i,t n or n=1,4). (We estimate the time ixed eects model because estimation o the CCE model would be computationally demanding with this expanded number o instruments.) Standard errors increase sharply and do not permit us to make any meaningul inerences. This result is traceable to a small amount o incremental inormation in * z,i,t n relative to * z,i,t. The eigenvalue or assessing instrument relevance is less than one or each model (i.e., n=1, 2, 3, and 4), ar below the conventional critical value o (see Section IV.C). Our instruments do not have suicient variation to accurately discriminate among lagged t j 's. Third, we do not impose the parametric restrictions on the j 's and j 's in equation (D-4). While eiciency would be enhanced, a less restricted speciication continues to generate unbiased and consistent estimates. We preer a less restricted orm to acilitate computation o the CCE estimator and our instrument search algorithm.

25 *** NOT FOR PUBLICATION *** 25 Appendix E: The Three-Step Procedure For Estimating The Non-Linear CCE Model This appendix presents a more concise and ormal statement o our three-step procedure or obtaining consistent estimates with the non-linear CCE estimator described in Sections IV.B and IV.D. We begin by reproducing equation (10) as equation (E-1), N i,t 0ˆ i,t n i,tn xi,t i i,t n1 _ N _ i t 0 t n tn n1 ˆ x t, and rewriting it in the ollowing concise notation, m n o i,t =Q,, m all i 's and rom the irst line in equation (E-1) n all i 's and rom the second line in equation (E-1) o all i 's where the m, n, and o superscripts index iterations. Step 1 estimates the and parameters pre-setting to 1.0, (E-1) (E-2) 1 1 o i,t =Q,, 1. (E-3) Step 2 estimates the and parameters pre-setting the parameters to the estimates obtained in Step 1, i,t =Q,,, (E-4) and then iterates as ollows, i,t =Q,,, i,t =Q,,, (E-5)... until converge is achieved or each individual h th parameter h and the ollowing convergence criteria at the p th iteration, p p h according to h h (E-6)

26 Step 3 estimates the and parameters pre-setting the parameters to the consistent estimates obtained at the conclusion o Step 2, p1 p1 p i,t =Q,,. (E-7) Equation (E-7) is linear in the parameters and is the basis or the CCE estimates presented in the paper. 26

27 *** NOT FOR PUBLICATION *** 27 Appendix F: Notes on the Speciication o Dynamic Models This appendix provides the details supporting our discussion in Section V.D that A) the standard lagged dependent variable (LDV) model is nested within a more general dynamic model that includes no LDV but an ininite number o time lags o the independent variables and B) a restricted version o this latter model can be estimated by including N lags o the independent variables and the N+1 st lag o the LDV. An expanded speciication o our preerred model includes lags o all independent variables and is written as ollows, N t t n n t n0 x (F-1) where one o the variables in the x vector is the spatial lag o τ and N can go to ininity. (Note state subscripts have been omitted or expositional convenience.) Equation (F-1) is more general than our preerred speciication in equation (10) because it contains additional lags. Equation (10) can be obtained rom equation (F-1) by setting n 0 or n 1 in equation (F-1) and i i,t i 0 in equation (10). Now consider the lagged dependent variable (LDV) model: t t1x t t, (F-2) where t is an error term. The LDV can be eliminated by lagging this equation one period and substituting it into equation (F-2). The resulting equation contains the regressors x, t x t 1, and t2. The latter variable is eliminated by repeating the above procedure by lagging this transormed equation one period. I the procedure is repeated up to the N+1 st period, we obtain the ollowing equation, N N1 t tn1 tn n t n0 n n x, (F-3a), (F-3b) t N n tn. (F-3c) n0 The only important dierence between our preerred model (equation (F-1)) and the LDV model

28 N1 (equation (F-3)) is the LDV term t N. (The less important dierences involve redeining the coeicient vector on the x variables (equation (F-3b)) and the serial correlation in the error term (equation (F-3c).) The central point is that what we are omitting rom our model is NOT last year s tax policy ( t1 ), since the eects o this term are captured by the one-year lags o the x variables (and lagged error terms), but rather a term capturing the determinants o tax policy lagged more than N periods in the past. (The serial correlation in the error term does not pose any bias problems as long as the x variables are exogenous or instrumented.) As N goes to ininity, N1 goes to zero, and the LDV term vanishes. It is in this sense that the LDV model is nested within a more general model with an ininite number o lags o xt n. In practice, the question o whether our omission o the LDV term rom our estimating equation poses any problem depends on how ar back lags o xt n could reasonably be expected to aect tax policy. The results presented in the paper or models without an LDV are based on a maximum lag o N=4. However, we also have estimated a model in which we set N=3 and then 28 include the dependent variable lagged our periods (i.e., the term discussed briely in Section V.D. 31 t 3 1. These results are