»Learning Center
Location of State Enterprise Zones
Effective Tax Rates and Firm Valuation
The Incentive Effects of State Income Tax Laws
Book Store
  
» Modeling The Incentive Effects Of State Corporate Income Tax Laws

This study models the optimal location choice decisions of a firm in response to differential state corporate hiring and equipment tax credits, income apportionment rules, and other incentives, while controlling for different tax structures and tax rates. Results are that while hiring and equipment credits (e.g., enterprise zone credits) attract resources to a state, relatively low tax rates are more effective, especially in states using so-called unitary tax structures. While hiring and equipment tax credits are not individually very effective, together they are. The absence of sales “throwback” rules is an effective incentive, but results in a negative externality to other states. Placing extra weight on sales apportionment factors is effective only if used in a non-throwback state. These findings have important implications since virtually all states utilize these laws in an attempt to attract additional investment. The results also provide some theoretical support for very recent empirical findings (Gupta and Hofmann, 2003).

  
 
 

Introduction
A major policy utilized by states to attract new business is tax incentives. Four major tax incentives are hiring credits and equipment credits, absence of a sales “throwback” rule, and placing heavy emphasis on sales in apportionment rules. As discussed later in the paper, there are no theoretical and scant empirical analyses of the incentive effects of such tax laws. The purpose of this paper is to analytically examine these incentives using a multistate firm. The paper finds that while hiring and equipment credits affect location choice, their effectiveness is muted by the presence of unitary tax rules. Conversely, tax rate cuts are most effective in unitary tax states. Additionally, hiring and equipment credits individually are not particularly effective incentives, but together they are. The absence of so called “sales throwback” rules are effective incentives, but result in externality effects to the other states. Placing extra weight on sales apportionment factors are effective only in states without sales throwback, and have a collateral effect on other states. The results have significant policy implications, because lawmakers apparently rely on all of these rules in an attempt to attract new business investment into their states. The results also provide some theoretical support for very recent empirical findings (Gupta and Hofmann, 2003).

 

Tax Incentives and Business Location

 Numerous empirical studies (Carlton, 1983; cites in Sampson, 2001) find that state/local taxes appear to be secondary in location choice; labor force, quality and importance of transportation, quality of life, and business climate issues are consistently more important. Taxes often count heavily at the margin , i.e., if competing locations weigh in equally, taxes may sway the decision. While certain large projects may warrant special tax concessions by local governments, most expansions are of a size that the firm faces fixed/exogenous tax structures. Given the prevalence of state tax incentives, these empirical findings seem surprising.

This paper models a firm which can avail itself of state tax hiring credits, state tax equipment credits, favorable sales “throwback” rules, or favorable sales apportionment rules, in locating/expanding to a new state. Because the firm’s decision is also affected by state tax rates and structures, the model also allows for varying tax rates and both unitary and separate accounting tax structures. The firm faces two common scenarios. The first scenario is where the firm has narrowed down its location choice to one state due to compelling non-tax considerations. Resources are then allocated to this state in response to varying tax rates, tax credits, sales rules, and overall tax structures (unitary versus separate accounting). The setting is general enough that tax credits are either fixed/exogenous, or that they vary as a result of the firm’s negotiation with tax authorities. The second scenario assumes that the firm faces a choice between two states, each having varying tax rates and tax credits, sales rules, and unitary versus separate accounting tax structures. As with the first setting, tax credits can be considered either endogenous or exogenous. Although unitary/non-unitary tax structures are fixed (states have not changed in the last 40 years, and appear unlikely to do so in the near future), the model does allow the firm to chose between locating in unitary versus non-unitary states.

Because resource allocation/re-allocation effects are strongly altered by formula apportionment and unitary tax structures, these are discussed in the next section.

 

State Tax Rates and Structures

Income Tax Rules
All but four states impose a state corporate income tax. Rates range from 12%(Iowa) to 3.4%(Indiana). Although rates do not typically have large annual swings, rate changes of 1% are not uncommon for any particular state, in order to meet policy objectives or balance budgets. Equally as important as rates are the rules which determine the tax base, such as apportionment and whether the state follows unitary or separate accounting rules. All states require that income of a corporation be apportioned to the taxing state based on a factor formula; for most states, it is the three factor formula of the ratio of sales, payroll, and property within the taxing state to the corporation’s total sales, payroll, and property. Thus, if a corporation has operations in more than one state, income taxable in each apportioning state will be the firm’s total income (both within and outside the state) multiplied by the apportionment formula. Since the majority of states double weight the sales factor in the apportionment formula, I represent income apportioned to a state as :

Federal Taxable Income .(1)

Federal taxable Income either includes income solely from a single corporation (separate accounting), or from a combined group of entities which are part of the same “unitary group” (unitary taxation). For “unitary” states (primarily, those west of the Mississippi River) the unitary method is applied to determine the extent to which a corporation’s branches and affiliates are included in apportionable income and in a three-factor apportionment formula. The so-called “unitary tax” defines apportionable income and includes in the apportionment formula income from operations considered to be part of a unitary business of the corporation operating in its state. The basic characteristics of a unitary business are that the corporation’s operations are dependent upon or contribute to the business conducted by the group, and that there is at least a 50 percent common ownership or control between the corporation and the corporate group. Unitary states require filing of a combined (consolidated) corporate income tax return , where all affiliates considered to be part of the unitary business are included.

Instead of the unitary method, some states use the separate accounting method, whereby only the income of the entity conducting business in the state is included on the corporate income tax return. Because of this entity-level restriction, multi-state corporations can potentially engineer their tax liabilities by shifting more (less) income to the state if it has a relatively lower (higher) tax rate than that of affiliates located in other states. Intercompany transactions, e.g., transfer pricing, can be used to shift income in some limited circumstance. In contrast, taxes in unitary states can be manipulated by altering property, payroll, or sales. Since these are real economic choices, tax minimization may result in decreased pre-tax economic performance, both vis-a-vis a no-tax situation, and vis-a-vis the non-unitary setting. Manipualtion of payroll and/or property in a state (in response to differential tax rates across states) can have an effect on hiring and equipment credits received by that state. Accordingly it is important to understand not just the incentive effects of credits, but of factor apportionment effects on the tax base and tax rates as well. Accordingly, the next section discusses such incentive effects.


Incentive Effects of Tax Rates
Because of unitary structures (which require the combining of corporations for tax purposes), the effect of tax rates on location choice is not obvious. The only clear-cut case is where the corporation is located in a separate accounting (non-unitary) state, and is considering expansion solely into another non-unitary states. Here, assuming non-tax factors are the same, the firm would locate in the lowest tax-rate state.

On the other hand, if either (or both) the firm and its potential location-choice states use unitary accounting, because of formula apportionment, an obvious way for firms to allocate income from high tax states to low tax states is to shift sales, property, and/or payroll from high to low tax states. However, if firms are already in a profit-maximizing equilibrium, changing such allocations would result in a drop in pre-tax income. Accordingly, it is not immediately obvious, absent a more rigorous analysis, whether firms would find such tax planning profitable. When I include the possibility that one of the states uses non-unitary taxation (and the corporation is a separate corporation), the analysis becomes even more complex. If the two states have different rates, does it still make sense to move sales, capital, or labor, even though this has no direct impact on the non-unitary state’s tax base? And, if so, is it still profitable in light of the possible drop in pre-tax income? Again, some formalized thinking is necessary to answer this question.


Incentive Effects of Tax Credits
Tax credits result in a dollar-for-dollar reduction in a company’s taxes. This is contrast to deductions, which where the tax savings is the deduction times the firm’s tax rate. Virtually all states offer hiring credits for increased employment and/or equipment purchases. Many states offer such credits if a firm if located in a so-called “enterprise zone.” These are areas targeted by the state for economic growth. Additionally, a number of other states provide general hiring and equipment credits, regardless of location within the state, so long as a minimum threshold of business expansion is achieved. The general and enterprise zone credits for hiring and machinery and equipment are shown in Table 1 of the Appendix. As discussed later, there is no empirical evidence on the effectiveness of such credits in the context of unitary versus separate accounting structures.


Incentive Effects of No sales Throwback, and Extra Sales Weighting
Absence of sales throwback and extra sales weighting are favorable tax treatments. Between 1980 and 2000, five states repealed their throwback rules, and the number of states which placed more than equal weight on the sales factor went from 8 (17%) to 28 (62%).

Absence of sales throwback essentially converts a state into a territorial tax, i.e., no tax on out-of-state sales. To see this, assume a firm manufacturers in State A, and sells its output to States A and B. Assume the firm has no “nexus” (physical presence) in B. The firm will be taxed on State A sales. Since it has no nexus in B, it cannot be taxed by B. If State A is a non-throwback state, sales in B are not taxed by State A either. It is widely believed that absence of a throwback rule encourages firms to locate in that State, if they have direct sales to out-of-state customers.

A similar effect occurs with placing extra apportionment weights on sales. As discussed in the next section, a firm’s multistate income is apportioned into a state based on the ratios of property, payroll, and sales in that state to property, payroll, and sales in all states. The higher the weight a state places on the sales factor, the lower the weights placed on the property and payroll factors (because the three weights must sum to 100%). Because apportionment is essentially a separate tax on each of the three factors (as illustrated in the model), lower weights on property and payroll are essentially lower taxes on facilities located in the state.

 

Previous Research

Tax Rates and Unitary Structures
Numerous theoretical studies (cited in Wilson, 1999) have examined state tax rates from a macro, welfare-implications perspective. None of these studies considered the effects of tax credits. However, there have been a few theoretical studies which have focused on the effects of the unitary tax on the firm. McClure (1981) found that formula apportionment is similar to a separate tax on payroll, property, and sales. Focusing on incidence, McClure found that formula-based state corporate income taxes were likely to be borne by residents of the taxing state (consumers, owners of land, and immobile capital). Following up on the McClure(1981) idea that the unitary tax is three separate taxes, Gordon and Wilson (1986) separately analyzed the effects of the factors. Their model found that when states had different tax rates, the sales factor encouraged cross-hauling of output (selling in another state), the property factor provided incentives not to concentrate operations in one state, and the payroll factor induced firms to consolidate operations into one state. Williams and Swenson (2001) modeled the interaction of unitary/separate accounting structures and changing tax rates on interstate resource allocation, assuming the firm already had existing operations in both states (i.e., there was not a new choice location decision per se). They found that when the firm faced unitary structures in both states, rate changes encouraged the firm to move resources from the higher tax rate state to the lower tax rate state. In contrast, when the firm’s operations were only in separate accounting states, tax rate differentials between states had no affect on resource allocation. When the firm operated in both a unitary and separate accounting state, only rate changes affecting the unitary state resulted in resource allocation, and even then the resource reallocation was less than in the case of where the firm operated exclusively in unitary states.

Empirical evidence on the unitary tax is provided by Moore, et al. (1989) who applied the Carlton (1983) location choice model to foreign investment. Foreign firms were used because the literature suggested that they should respond much more to regional incentives (given favorable tax incentives) than should domestic firms. The tax variable was bifurcated into overall effective tax rates (calculated using the models in Vines, et al. 1994), and dummy variables were used to indicate the presence of unitary tax structures. Results indicated that foreign firms’ location choices were unresponsive to overall tax rates, but negatively influenced by the presence of unitary tax structures. The findings of Moore, et al. (1989) were essentially replicated and corroborated by Coughlin, et al.(1991). More recently, Gupta and Hofmann (2003) applied a panel data analysis across all states, using a location choice model similar to Moore et al. Regression results found that new capital spending was negatively influenced by unitary tax structures. The study also found that lower tax rates and incentives for assets (in that order) increased capital spending.

The reasons for expecting the disincentive effects of unitary tax structures were not guided by formal theory i.e., (modeling,) in the above empirical studies. Similarly, these studies were not guided by formal theory with respect to the interaction of tax rates and differences in structures (unitary versus non-unitary taxation). These studies also implicitly assumed that lower tax rates and/or an absence of unitary accounting methods would automatically provide an incentive to invest in a state. This is not necessarily the case, since location choice affects factor and point-of-sale locations, which in turn affect income allocations between states. Thus, it may be possible for lower tax rate states to have little or no comparative advantage.


State Hiring and Machinery Credits
No studies have theoretically examined the general impact of state hiring or equipment credits. However, a number of empirical studies (cited in Engberg and Greenbaum, 1999) have empirically examined the impact of enterprise zone tax credits. These studies have found conflicting evidence. A single empirical study (Faulk, 2002) examined the effects of general state hiring credits; this study found that Georgia hiring credits had a small increase on employment. This paper adds to the hiring and equipment/machinery credit literature by examining such credits in a model which incorporates the important effects of unitary /separate accounting structures and tax rates.


Absence of Throwback, and Extra Weighting on Sales
No theoretical and only three empirical study exist on these two effects. Empirically, Klassen and Shakelford (1999) found that while manufacturers shipments from throwback states were decreasing in corporate tax states, such shipments were not sensitive to sales weighting factors. By their own admission (p. 387), results should be cautioned because of lack of a rich theory, and because of the aggregate nature of the data (state totals, instead of firm data, were used).

Two studies have focused on the sales factor. Using aggregate data, Lopez and Martinez-Vazquez (1998) found that industries varied significantly in having their incomes either under- or over-apportioned by various states. Lightner (2000) empirically found that state tax rates, more so than formula apportionment, affect state employment growth.

 

General Model

 This study extends the only existing models of the unitary tax, those of Gordon and Wilson (1986) and Williams and Swenson (2001), by examining the effects of the most prevalent incentives: hiring and machinery credits, absence of sales throwback, and extra-weighting of the sales factor. In doing so, it considers the effects of all three factors simultaneously (sales, labor, and capital) as in Williams and Swenson (2001); Gordon and Wilson considered each of these factors independently. This three-factor setting allows for a more realistic study, providing for substitution of factors of production and sales both within and across states. Additionally, as in Williams and Swenson (2001), I examine control for the case of a multistate firm operating in both a unitary and non-unitary state. The setting is important because over half of the states follow non-unitary accounting, and it is thus likely that many multistate companies encounter both types of states, simultaneously, in their operations. Finally, since tax rate differentials can encourage firms to alter resource allocation, I control for differential tax rates in the model as well.

I model a stylized manufacturing firm with customers in State 1 and potential customers in State 2. The firm is considering expanding operations into State 2 due to favorable demand conditions. Thus, the firm does not face a location choice decision per se. This serves as a useful starting point to the pure location choice model, discussed later in the paper. To simplify the analysis, I assume that transactions costs of moving resources to any State 2 are equal and exceed return on investment requirements. Thus location costs can be ignored without generality. The firm is a “classic” example of a unitary business in that its multistate operations are functionally dependent on each other, with its headquarters in one state, and operations in another state, and clearly has taxable “nexus” (or business connection) in each of the states. The manufacturing process begins at the firm's headquarters in State 1, and the firm maintains production facilities in State 1 as well. The firm completes production and services customers from the respective local facility. I model the manufacturing process as potentially divisible at any stage. That is, at any point in the manufacturing process, the firm could ship the intermediate (or partially completed) product from the manufacturing center at the headquarters to the local facilities for completion and sale. The firm incurs a shipping charge for sending the product from the headquarters to the local facility in State 2 based on the number of units shipped. I assume that the local facility that completes the product and sells to customers in State 1 is adjacent to the headquarters, and thus no shipping charge is incurred on those units. I denote the quantities sold to customers in States 1 and 2 as, respectively, Q1 and Q2.

I begin by ignoring state income taxes. Management's objective is to maximize the firm's pretax profit. Based on the firm's revenue function and the costs it faces, management chooses the level of capital (K) and labor (L) to employ at each of the firm's three facilities (the manufacturing center and the local facilities in each state) so as to maximize the excess of revenue over cost. In making these decisions, management is constrained by exogenously determined production functions. Management must also choose the point in the manufacturing process at which production will shift from headquarters to the local production facilities (the degree of centralization). Denote this as the choice of ???the fraction of the manufacturing process performed at the headquarters, with (1 - f) being the percentage performed at the local production facilities, which is between zero and one. More formally, management chooses Ki, Li, and f (i Π{m, 1, 2}) so as to

(1a) 

subject to the production functions for the manufacturing facilities.

Assume the firm operates in an imperfectly competitive market and faces a downward-sloping demand curve in each state. Specifically, assume the inverse demand function is P = aj - bQj, where j Î {1, 2}. This leads to the firm's revenue function:

(1b) 

Assume the cost of production consists of the rental rate (or, in the alternative, the rate of return) on capital (r), the wage rate paid for labor (w), and the cost (s) of shipping a unit from the manufacturing center to the local production facilities in State 2. Assuming a single rental rate on capital for all facilities; however, allows wage rates to differ between the states. Formally, model the cost of production as:

(1c) 

Assume that production follows a generalized Cobb-Douglas production function where Yi = Lia Kib, with i Î {m, 1, 2}, a and b > 0, and a + b < 1. For the headquarters, Ym = f(Q1 + Q2). For the local production facilities, Yj = Qj(1-f) with j Î {1, 2}. Assume that the productivity of capital does not depend on its location; accordingly, b is the same for all three production facilities. I expect that a realistic setting should allow for differences in labor between workers in different states. For example, the average skill level is likely to be different as is the average level and quality of education. I choose however, to reflect these differences in the wage rates, w rather than in a. One way of viewing this is to assume that workers with the requisite skill and educational levels are available in each state, but that local differences in the supply and demand for those workers will potentially result in different prices for their labor.

The model is shown graphically in Figure 1.

[Figure 1 about here]

Combining equations (1a) and (1b) and specifying the production function constraints, the pretax model is shown symbolically in (2):

 
subject to: 
(2) 
When pretax profits are maximized,(with ). Therefore, ,
which is rearranged as (adding the appropriate subscripts).(3)

To solve this problem, the first step is to substitute (3) into each constraint for (2) and solve for the respective L in terms of the Q’s, f and exogenous variables. This result is then substituted into (2). The next step is to hold the Q’s constant and solve for f by differentiating the resultant equations with respect to the exogenous variables to obtain the first order conditions (FOC). Unfortunately, the resultant equations involve high degree polynomials for which a continuous form solution cannot be found for the entire system simultaneously. However, some partial findings can be derived as shown in the following pages.

 

Model Where Firm Has Selected One State

Both States Use Separate Accounting
Before examining the effects of tax incentives, it is useful to first examine the effects of non-unitary taxation on resource allocation. Here, I look separately at the effects on each state. First, note that non-unitary taxation of a subsidiary with only single-state operations, does not involve the use of factor apportionment. Hence, taxation of the firm is similar to a tax on pure profits, which is non-distortionary. With multi-state taxation and a transfer price set equal to average unit cost, I can separate total profits into two pieces, corresponding to the tax code as follows:

(4)

Note that the manufacturing center costs are included implicitly, since
pt(Q1 + Q2) = w1Lm + rKm. The transfer prices designate how much of the manufacturing center cost is deductible in each state. Technically, all those costs are deductible in State 1, but the State 1 firm must also recognize revenue from sales to State 2 of the unfinished product equal to ptQ2.

If the transfer price is treated as fixed, then the two states’ production and sales decisions can be made independently. In that case, the taxes are proportionate to economic profits. It is a well-known result in public economics (e.g., Atkinson and Stiglitz, 1980, p. 132) that a tax on pure profits does not distort factor inputs or sales decisions. Hence, any effect of a non-unitary tax on resource allocation must be due to an effect on the transfer price itself, which would be second order in nature.

As noted, the transfer price is the average unit cost of the manufacturing center. Since the production function exhibits decreasing returns to scale, the transfer price is increasing in total sales. This means that each state imposes an externality on the other state. By increasing sales in one state, costs increase for the other state. Given this externality, in the global optimum solution, it is desirable to underproduce in each state such that the marginal after-tax profit in each state of an additional unit exactly equals the externality imposed on the other state. If the tax rate increases, the marginal pre-tax profit must increase to maintain this balance. Therefore, I expect sales to decline slightly in response to a tax rate increase due to this indirect effect. Analytically, given (4) and with pS1p defined as State 1 pretax profit:

(5)

The left hand side of (5) is a function of Q1. Define it as

Given that the transfer price is convex (since production is concave) and pre-tax profits are concave in output, h is monotone increasing, which implies that its inverse is also monotone increasing. Define that inverse as H = h-1. Then H’ > 0. From (5),

(6)

It can be readily demonstrated that since a decrease in Q1 decreases the transfer price, providing an incentive to increase Q2 (this effect will partially offset the change in pt, so that on net the impact of the tax rate on the transfer price will be small). The effect of the tax rate on f is unclear; it is possible for the sign to be either positive or negative. As a consequence, the effect of the tax rate on labor and capital is also unclear, although labor and capital in each state are likely to move in the same direction as sales.

The analysis of t2 is identical to the analysis of t1. The effects of tax rates in this setting are summarized as follows. First, higher rates in State 1 will decrease that state’s sales and increase the State 2 sales (from 6). Conversely lower rates in State 1 will increase that state’s sales, and decrease sales in the State 2. Second, tax rates have an ambiguous effect on other decision variables in the firm. Finally, all effects of tax rates are second order in nature.

Next, examine effects of hiring credits. To control for pretax differences in wage levels, assume w1=w2=w. Define X2as the credit rate in State 2 . Holding tax rates constant and substituting X2w for w in (3), and rearranging we get:

(3a)


(3b)

To remain at the profit maximizing output, the firm then substitutes labor for capital. There is also an income effect: cheaper factors allow the State 2 operations to profitably move to a higher isoquant. A similar effect can be shown for a capital tax credit,

(3c)


(3d)

Therefore, when both states have separate accounting:

  • A hiring (capital) credit in State 2 causes an increase (decrease) in State 2 labor (capital). Similarly, a State 2 capital credit causes an increase (decrease) in State 2 capital (labor). Because production becomes cheaper in State 2 than in the primary manufacturing plant, production is shifted away from the primary manufacturer and into State 2.
  • A hiring or capital credit in State 2 causes a shift of production out of State 1, the primary manufacturer, and into State 2 as a fait accompli, since production by the primary manufacturer decreases, and the State 1 secondary manufacturer must move to a lower isoquant to remain profitable.
  • A hiring credit or capital in State 2 causes an overall drop in production, labor, and capital in State 1, i.e., a negative externality.

To examine the effects of different weighting schemes and throwback, add a new, nearby State 3, into which the firm sells (from its State 2 operations), but has no nexus (labor or capital). We must first make an assumption about sales made into State 3 which have been partly manufactured in State 2. Assume that goods made in State 2 can be sold both in State 2 and nearby State 3. Θ is the fraction of State 2 production sold to State 2 customers, and 1-Θ is the proportion sold to State 3 customers. Since States 2 and 3 are contiguous, assume that demand functions are similar between the two states. Rewrite the third equation in (4) where there is throwback of State 3 sales (Q3) into State 2 (i.e., State 3 sales are taxed by State 2) as:

(4a)

Since taxes are the identical on sales into either state, they are non-distortionary on interstate sales decisions. The rate of substitution between state sales is:

(4b)

The tax rates cancel out, and Θ is unaffected by taxes. Where State 2 has no throwback, State 3 sales escape taxation, and (4) is rewritten:

(4c)

The rate of substitution of sales between states is:

(4d)

Comparing (4b) to (4d), we see that the firm will shift sales from State 2 to State 3. It can also be shown that Q2 increases due to increased marginal profit (due to non-taxability of State 3 sales). As with the analysis in (6), ; conversely, a drop in the effective t2 results in an increase in Q2 and a drop in Q1. As with the analysis in (6), the effect on f is ambiguous, and the transfer price increases in both states, causing higher costs (a negative externality) in State 1.

The forgoing analysis ignores the effects of apportionment weights. To examine the impact of apportionment weights, define the weights for sales, property, and payroll as Sw, Kw, and Lw, respectively. Since each is defined as a per cent, the sum of the three weights must equal one. Rewrite the profit equation for the throwback state as:

(4e)

Differentiating (4e) sequentially for increases in Sw2, decreases in Kw2 and Lw2, and factoring out t2 (an exogenous constant here), we get:

(4f)

Thus, increased weights on sales have no incentive effect. The intuition is as follows. Increased sales weights are effectively a tax on sales; the marginal revenue product curve for the firm shifts down (in) at every level of Q2 sold in State 3. Similarly, lower weights on labor and capital are tax benefits at every level of factor inputs, shifting the marginal cost cure down/in. Thus, the net effect (depending on the shape of both curves) is little or no change in Q2, with no resultant effect on other decision variables.

Both States Use Unitary Accounting
Before examining the effects of tax incentives, it useful to first examine the effects of unitary tax structures. To examine the effects of a unitary tax structure in both states, the profit equation (2) is multiplied by tax rates, resulting in:

subject to:

Note that the apportioned unitary tax, tu, is the standard apportionment formula, equation (1) shown in the beginning of the paper, adapted to the property, payroll, and sales parameters of the model. Sales are doubled-weighted in the apportionment formula.

In examining (1) and (7), we see that the unitary tax is, as noted by McClure (1981) and Gordon and Wilson (1986), similar to a separate tax on each of sales, capital, and labor. As with the non-tax model above, it is too complex to solve analytically as an entire system. However, by making some simplifying assumptions, we derive some comparative statics. Essentially, an increase (decrease) in the tax rate in one state results in a movement of production and sales out of (into) that state and into (out of) the other state.

The effects of tax rate changes are much more complex in the unitary tax setting because of the apportionment factor. In order to analytically determine the effect of changes in tax rates on the decision variables, it is necessary to separately consider the effects on the sales quantities (Q1 and Q2) and on f. The labor and capital variables are solely determined by the sales quantities and f, through the standard Cobb-Douglas relationships, given w1, w2, and r. Unfortunately, the interaction between the Q’s and f is too complex to facilitate analysis without simplifying assumptions. When analyzing the effect of tax rates on Q1 and Q2, assume that f does not change. Similarly, when analyzing the effect of tax rates on f, assume that Q1 and Q2 do not change. The indirect effects ignored are likely to be of very low order, so the simplifying assumptions should not be problematic, although this is not known with any certainty.

First consider the effect of changes in tax rates on f (holding the Q’s constant). Consider the first order condition for the optimal choice of f:

(8)

where pp is pre-tax profit. Define

Also define F = f--1. It can easily be shown that for all i.
Thus, f'(f) > 0 The inverse of every monotone function is also monotone; hence, F’ > 0. Rearranging (8),

(9)

Holding the Q’s constant, f‘s only effect on tu is through a shift in property and payroll between the manufacturing center and the State 2 final production center. Increasing f increases the weight given to State 1 for those two components:

Both partial derivatives in the brackets are positive, thus Given (9),

(10)

Note that in the above differentiation, I ignore the minor effect that the tax rate differential can have on . That is a necessary simplification that I do not expect will affect the results.

Now consider the effect of changes in tax rates on sales quantities, holding f constant. The first order condition is

(11)

Define

Also define Gi = gi-1. Due to decreasing returns to scale, the second derivatives of capital and labor usage with respect to Qi are all positive. The second derivative of Q2 with respect to Qi is 0. Therefore, gi' > 0 and Gi' > 0. Rearranging (11) yields

(12)

Holding f constant, increasing Qi increases state i's weight on all three factors.

The partial derivatives are all positive for i = 1 and negative for i = 2. Thus,

Given that Gi' > 0, (12) implies that

(13)

The effect of tax rates on the labor and capital inputs can be derived from the effects on the Q’s and f. Unfortunately, these effects rarely all work in the same direction, so comparative statics are clear in only two cases, those involving L2 and K2. Both of those are increasing in Q2, decreasing in f, and unaffected by Q1. Therefore,

(14)

The effect of tax rates on L1 and K1 is unclear since they are positively affected by Q1 and negatively affected by f, leading to a conflicting effect with an ambiguous net result. LM and KM are also ambiguous since they are positively affected by f, Q1, and Q2. The effects of Q1 and Q2 are roughly offsetting, so it is likely that the f effect dominates, in which case

(15)

In summary, the effects of tax rates in the pure unitary tax setting are as follows. First, higher rates in State 1 (or lower rates in State 2) result in decreases in f(from 10) decreased Q1 and increased Q2 (from 13), increased L2 and K2 (from 14), and decreased Lm and Km (from 15). Second, higher rates in State 2 (or lower rates in State 1) result in increased f (from 10), decreased Q2 and increased Q1 (from 13), decreased L2 and K2 (from 14), and increased Lm and Km (from 15). Finally, there is no prediction on the effects of taxes on L1 and K1.

The intuition is clear. The firm will simply move factors of production from the high tax rate state to the low tax rate state, in order to decrease (increase) the amount of income allocated to the high (low) tax rate state. Of course, these are ceteris paribus conditions. Because of decreasing returns, additional capital and additional labor are more expensive per unit as the firm demands more of them in the low tax state. Similarly, the price of the firm’s output, per unit, declines as the firm produces and sells more in the low tax rate state, due to price elasticity in the output market. In contrast, per unit factor costs decline, and per unit sales prices increase, in the high tax state as the firm scales back operations there. These two effects should actually reduce pretax profits. The question then becomes to what degree the firm moves factors of production (or substitutes between them) and sales in order to maximize after-tax profits.

To examine the effects of tax credits in State 2, again assume w1 = w2 = w. Again, let be the wage tax credit rate (as a percent), and the capital tax credit (as a per cent). The primary effects of increases in and are the same as the separate accounting setting; production (including labor and capital) moves out of State 1 (at both the primary and secondary manufacturer levels) and into State 2. The countervailing effect is that, because relatively more factors of production flow to State 2, taxes are increased in State 2 (due to the use of apportionment). Conversely, there are less taxes in State 1. Whether this tax rate effect is less the tax credit effect is analytically too complex, and will instead be examined in a simulation, discussed later.

The effects of (no) sales throwback are as follows. With throwback, the previous results are unchanged, since it is as if State 3 is part of state 2 for tax purposes. When there is no sales throwback, and sales are double-weighted, rewrite the last term in (7) as:

With no adjustments to the decision variables, (7a)<(7). Since the numerator of the sales term in State 2 does not include State 3 sales, there is both an income and a substitution effect for the firm in State 2. State 2 sales are shifted to State 3; both Q2 and Q3 increase as well. This latter effect actually has a positive externality to State 1: the denominator of the sales factor increases resulting in a decrease in t1. But there is also a negative externality to State 1; increased production at the main plant increases the transfer price.

The effects of increased weighting of the sales factor in State 2 is as follows. Rewrite (7) to include apportionment weights for sales, property, and payroll as follows, assuming throwback:

What happens when the tax regime in State 2 places increased weight on sales? There is essentially no change in resource allocation. Intuitively this occurs because, while the firm’s marginal cost curve shifts downward (due to decreased weight, and thus tax, on property and payroll), the marginal revenue curve shifts downward as well (due to increased weight, and thus tax, on sales). Since there are no effects to States 2 and 3 the firm makes no adjustment which could result in an externality to State 1.

Assuming throwback, rewrite (7) with apportionment weights:

There is no effect on the second term, following the arguments above related to (7b). Nor is there any change in State 3 sales (the last term), since these sales are not taxed anyway. Thus, we can conclude: When both states are unitary, relatively higher weights on State 2 sales causes no effect on resource allocation.

One State Unitary, One State Uses Separate Accounting
Finally, a mixed tax structure is analyzed, in which one of the states is unitary, and the other has a non-unitary tax structure. Before examining the impact of tax credits, I examine the impact of the unitary/separate accounting structures. Under this specification and assuming that State 2 is the non-unitary state and that the firm separately incorporates its operations in each state , (4) is rewritten:

(1)

If State 1 is the non-unitary state, a similar transformation of (4) applies:

(1)

Here, pt is the transfer price charged by the manufacturing plant at the headquarters for the intermediate goods transferred to the facilities in State 2. The transfer price is the average unit cost of the manufacturing center. Note that the transfer price is not a decision variable in the optimization, although it does depend on total sales and f, with pt increasing in both. Upon examination of (16), it is clear that the two taxes enter the objective function in very different ways, leading to very different implications of changing either rate. First, if there are relatively higher (lower) rates in the state subject to the unitary tax (state 1 in the above example), the firm has the incentive to move property, payroll, and sales out of (into) the state to reduce the fraction of profits apportioned to the state. As with the case of two unitary states, the amount of shifting of resources out of (into) the unitary state is a matter of degree, limited by the downward slopes of demand in the two states as well as the decreasing returns nature of production at each site.

Second, if tax rates are higher (lower) in the non-unitary state, this causes a roughly proportionate decrease (increase) in after-tax profits from that state regardless of production and sales decisions. Hence, we would expect a minimal shift in resource allocation. The direction of that shift, however, is unclear as a number of conflicting forces exist. The main consideration is the nature of the externality that the non-unitary state imposes on the other state by increasing its sales and production. There are multiple externalities. The net effect of these externalities could be positive or negative but is more likely to be positive if the non-unitary state is state 1 since one externality is an increase in factor weights for the manufacturing center which is favorable for the unitary state if the unitary state does not contain the manufacturing center and unfavorable if it does. The existence of an externality induces the firm to deviate from the non-unitary state’s decentralized profit-maximizing sales (i.e., the optimum ignoring the externality imposed on the other state). Specifically, the firm will tradeoff efficiency losses in the non-unitary state with externality benefits for the unitary state. The higher the non-unitary state’s tax rate, the lower the after-tax cost of deviating from the decentralized optimum (since the government shares in any reduction in pre-tax profits in that state). Therefore, whatever distortion is induced by the externality will be exacerbated by an increase in the non-unitary state’s tax rate. The tax rate in the unitary state has an equivalent effect to the tax rates in the previous model where both states are unitary. All comparative statics follow.

The non-unitary tax rate, however, is more complicated. Recall that when both states are non-unitary, tax rates have an effect on resource allocation only because an externality exists (due to decreasing returns to scale at the manufacturing center) that induces overproduction in each state relative to the decentralized optimum. At higher tax rates even greater underproduction is warranted to balance the externality. In the case where the other state is unitary, three externalities exist for sales in the non-unitary state. Specifically, increased sales in the non-unitary state result in: higher unit cost at the manufacturing center, increasing costs for the other state (negative externality), higher factor weights for the non-unitary state, reducing taxes in the other state (positive externality), and higher factor weights for the manufacturing center state, increasing or reducing taxes in the other state depending on whether that state contains the manufacturing center (positive externality if State 1 and negative externality if State 2).

The overall incentive to under- or over-produce in the non-unitary state (relative to the decentralized optimum) depends on the net effect of these externalities. If the negative externalities dominate, the state will underproduce and higher tax rates will lead to a reduction in sales. If the positive externalities dominate, the state will overproduce and a higher tax rate will lead to an increase in sales. It is impossible to definitively sign the net externality effect; however, given the nature of the third externality, the effect of the non-unitary tax rate on in-state sales should be much more positive if State 1 is the non-unitary state than if State 2 is the non-unitary state.

As in the case with both states non-unitary, the effect of the non-unitary tax rate on f is ambiguous. The effects on labor and capital are likewise ambiguous, but are likely to correspond to the change in sales. In summary, the effect of tax rates in the case where one state has unitary taxation and the other state does not are as follows. First, when the tax rate is higher in the unitary state, resources flow out of it, and into the non-unitary state (except for K1 and L1, for which there are no prediction). Second, when the tax rates are higher in the non-unitary state, the effects on resource allocation are ambiguous. However, if the non-unitary state is State 1, the effect on that state’s sales will be more favorable than if the non-unitary state is State 2. Thus, higher (lower) tax rates in the unitary state should result in a decrease (increase) in resources and sales in that state, and an increase (decrease) in the non-unitary state’s resource usage and sales. Conversely, any change in the relative tax rate of the non-unitary state should result in a slight (perhaps insignificant) change in resources and sales in both states, with ambiguous signs. The only clear prediction is that if State 1 is the non-unitary state, then higher (lower) levels in its tax rate will have a more favorable (unfavorable) impact on its sales and production than if State 2 is the non-unitary state.

In terms of the effects of a State 2 hiring credit, , and State 2 the capital credit, ,the effects depend on the tax structure of State 2. If State 2 uses separate accounting, the effects are clearly a movement of resources from State 1 into State 2. Although State 1 is unitary, the reduction in factors employed in that state cause (via apportionment) less taxes in State 2; thus there is no countervailing effect. However, there is some ambiguity in the case of State 2 being unitary. Here, increased factors in State 2 lead to (via apportionment) potentially higher income taxes. Wherever this income tax effect dominates the credit incentive will be addressed through the simulation results.

With regard to throwback, as in all other settings, absence of throwback does not alter any resource allocations. Absence of sales throwback in State 2 encourages additional sales into State 3. Where State 2 is the separate accounting state, rewrite the tax constraints in (16) as:

The additional State 3 sales of Q2 causes two externalities in State 1. Because of concave production, the increase in Q3 results in a higher transfer price from the primary manufacturer for both states. Taxes actually decrease in State 1 since the denominator of all terms in tui increase due to increases in L2, K2, and Q3.

When State 2 is the unitary state, rewrite the tax constraints in (17) as:

Again, the absence of throwback encourages the firm to increase Q3. This increased production increases K2, L2, and Pt. Increased Pt results in a negative externality to State 1. State 1 tax actually decreases to the extent that the sales factor denominator increases (due to an overall increase in Q2 + Q3). State 2 taxes increase, since the numerator of all components of tu2 increase faster than the denominators.

What of the effects of increased weights on sales for State 2? If State 2 has separate accounting, rewrite State 2 tax constraints in (16) as:

(16c)

if no throwback, and

(16d)

with sales throwback.

As in (16b), it is intuitive that because the absence of taxes on State 3 sales increase the marginal revenue product of State 3, so K2, L2, and Pt all increase beyond the levels caused by the absence of throwback. A negative externality to State 1 results from the increased transfer price. A positive externality for State 1 results from the increase in the denominator of tu2 . The same effects, albeit less pronounced, occur when State 2 has throwback.

If State 2 has unitary taxation, rewrite the State 2 tax constraint from (17) as:

(17b)

where the weight are explained previously. As with the analysis relating to (7b) and (7c), there is no impact on resource allocation here.

Overall Predictions
Predictions of the impacts of tax incentives in State 2, for all four combinations of unitary and separate accounting settings, are reported in Table 1. Tax rate reductions are effective in unitary states, but only if the original state is also unitary. Tax credits result in some production increase, but mostly result in factor substitutions. Absence of a sales throwback rule results in increased production, although the primary effect is a shifting of interstate sales (from State 2 and into State 3). Increased weighting of sales is a stimulant only if the state does not have a sales throwback rule. In most cases, there are externalities to State 1 operations as a result of State 2 incentives. Where State 1 is unitary, tax credits in State 2 actually reduce State 1 taxes. In all cases where incentives increase State 2 production, State 1 profits fall due to an increase in the transfer price from the primary manufacturer.

[ Table 1 Here ]

 

Validating The Model: Simulated Data
As noted previously, some aspects of the model are too complex (without making some substantial assumptions) to solve. Accordingly, I use simulations to solve the equations. The simulations also serve to test the veracity of the model. The simulations were written in Mathematica, and run off of a UNIX server. The simulation first generates a range of observations for the exogenous variables, s, w2, r, and all tax –related variables (rates, unitary structures, credits, throwback or its absence, and weighting of the sales factor), Next, optimization algorithms determine firm-wide maximum profits by substituting numerous values of the choice variables, Lm, L1, L2, K1, K2, , and Θ. To add some realism, all parameters take on values from the computable general equilibrium (CGE) literature. These values are discussed in Table 1 of the Appendix; they represent an average firm, and are derived from empirical observations. I then regress the solved for values of sales, capital , labor, Θ, and f on the corresponding manipulated values of t1, t2, , , r, s, and indicator variables for throwback, 100% sales weighting, and the interaction of throwback and 100% sales weighting. The solved-for regression parameters show the average effects of changes in exogenous variables on endogenous variables, across the wide array of simulation data. Before running these regressions, I take the natural log of all continuous-form variables; this allows an interpretation of regression parameters as per cents. The next three sections report the results of these regression results on the simulated firm data.

Both States Use Separate Accounting
Regression results are reported in Table 2. Results for non-tax variables are consistent with expectations and will not be discussed further. Effects of tax variables are reported in the shaded rows of the Table. All results are consistent with expectations, specifically:

  • Tax rate reductions in State 2 have no impact on resource allocations.
  • A State 2 hiring credit causes a substitution of labor for capital in State 2, an increase in state production/sales, a decrease in work done by the primary manufacturer, and as a result of this last effect, a negative externality to State 1 (sales decreases and cost increases).
  • A State 2 capital credit causes a substitution of capital for labor, plus all of the other effects reported above for a State 2 hiring credit. Due to the simulation parameters, the effects of the capital credit are stronger than that of a hiring credit.
  • Absence of sales throwback in State 2 increases production/sales in State 2, and has the opposite effect on State 1, i.e. a negative externality to State 1.
  • 100% weighting of the sales factor has no effect, unless accompanied by absence of a throwback rule. When there is such a combination, the shifting of resources out of State 1 and into State 2 is more dramatic.

[ Table 2 Here ]

Both states Use Unitary Accounting
Regression results, where both states are unitary, are reported in Table 3. Results for non-tax variables are consistent with predictions, where predictions were possible.

[ Table 3 Here ]

Regression results for tax variables are reported in the shaded rows of the table. Results support predictions, as follows:

  • Tax rate reductions in State 2 cause an increase in sales, capital, and labor in State 2, and a decrease in production, capital, and labor at the main manufacturer (negative externality).
  • State 2 wage (capital) credits result in a substitution of labor (capital) for capital (labor) and a slight increase in output in State 2. There is also a decrease in State 1 and primary manufacturers labor, capital, and output (negative externality).
  • Absence of sales throwback, especially when accompanied by 100% sales weighting, increases State 2 output (as well as labor and capital) and decreases output (and labor, capital) at the primary manufacturer.

One State uses Separate Accounting, the Other Uses Unitary Accounting
Regression results for the case of where State 1 is unitary and State 2 uses separate accounting are shown in Table 4. Results for State 1 is non-unitary, and State 2 is unitary as shown in Table 5.

[ Table 4 and 5 About Here]

In general, all results are consistent with theory as follows:

  • State 2 tax rate cuts have no effect if State 2 uses separate accounting. If State 2 is unitary, tax rate cuts result in labor, capital, and sales increases for the State 2 operations. However, externalities occur; primary manufacturer operations decline, and overall State 1 sales drop.
  • State 2 tax credits have an impact regardless of whether State 2 is unitary, or uses separate accounting. Wage credits increase State 2 labor and decrease State 2 capital; capital credits increase State 2 capital and decrease State 2 labor. Both credits have State 1 externalities; primary manufacturer activity decreases and State 1 secondary manufacturer activity increases to make up the shortfall.
  • As in other settings, absence of a throwback rule in State 2 increases State 2 production (where most of the increase is sold to State 3). However, externalties result: primary manufacturer activity drops, while State 1 secondary manufacturer activity.
  • Extra weighting of State 2 sales, when combined with absence of a throwback rule, results in a significantly greater impact on all factors.

 

Firm Can Choose Between Two States
Under very restrictive conditions, the firm’s location choice is a simple corner solution. For example, holding all other effects constant, the firm would locate in the state having the most generous tax credits. However, such situations are likely rare; typically, the firm must consider trading off higher tax benefits of one type for lower benefits of another type, when choosing between states. The model and simulation in the previous section lays much of the groundwork for the two-state choice model. The following examines the situations of the parent company is located in a separate accounting state, or is located in a unitary state, in that order.

Parent Company Located in Separate Accounting State
When the parent is choosing between two non-unitary states, it will select the one with the lowest rate. In such a pure non-unitary setting, taxes have no pretax distortionary effect; hence, the firm will locate where the after tax rate of return is higher. The same is true of credits; ceteris paribus, the firm will locate in the state having the higher credit rate. In that state, the firm can profitably substitute labor for capital (or visa-versa). The less obvious case is where one state has a higher tax credit, but the other state has a lower tax rate.

Here, each 1% lower tax rate results in a 1% increase in after-tax profits, due to the non-distortionary nature of the tax. In contrast, since (under most reasonable circumstances) w << p each 1% decline in w (i.e., 1% increase in the credit rate) must have a lower affect on profits than a 1% decline in tax rates. Accordingly, unless the wage credit is fairly high, the firm would locate in the state with the lower tax rate. The same reasoning applies to capital credits.

When the parent firm faces a choice between two unitary states, again, the lower tax rate state is favored. Although (as demonstrated in the previous section) the firm can partly mitigate taxes in a unitary state, there is still a loss in after-tax income due to distortions induced. Thus, lower tax rates are always preferred. The effects of a credit are less straight forward. The tax credit, itself, allows this substitution of cheaper labor for capital (or visa-versa) and increased profits. On the other hand, the increased profits (and to a lesser extent, the increase in total factors employed which slightly increases income apportioned into the state) result in increased income taxes. Empirically, using the hiring credit as an example, we see in Table 5 (Column 1) that a 1% increase in x2 (the State 2 tax credit) results in net increase of .13% in pretax profit; thus the credit effect dominates.

Finally, consider the case of where the firm can chose between locating its new business in a unitary versus non-unitary state. As pointed out in the previous section, the complexity of the analytics suggest an appeal to the simulation results. As shown in Rows 3 and 4 of Table 2 (and as modeled) tax rate changes in State 2 have no effect on resource allocation or firm-wide profitability. On the other hand, Table 5 reveals that (due to the transfer-price related externality discussed in the previous section) lower rates (higher rates) in unitary State 2 actually reduce (attract) resources to the state, albeit small in magnitude (less than a .01% change for each 1% change in tax rates). Thus, the firm will be indifferent between unitary and non-unitary locations, based on tax rates alone.

For credits, the non-unitary state has a clear advantage, however. As shown in Column 1 of Table 2 (Table 5), a 1% increase in hiring credits result in a .09% increase (.13% increase) in profits by locating in a separate (unitary) accounting state. The same logic applies to capital credits.

If (and only if) the firm plans to use the new state as a production platform for sales into a third state, then absence of a throwback rule (especially if coupled with 100% weighting of sales) is a strong incentive. Since this is invariant across unitary/non-unitary regimes, any state having no throwback will be chosen over a state which does have throwback, ceteris paribus. In fact, examining coefficients in the tables absence of throwback (combined with 100% weighting of sales) has a stronger incentive effect than either a tax credit or lowered tax rates. Of course, this conclusion is sensitive to the parameters chosen.

Parent Company Located in Unitary State
When the firm must locate in one of two unitary states, the one with the lowest tax rate (holding credits constant) or highest credit (holding tax rates constant) will be chosen. Similarly, when the firm must locate in one of two separate accounting states, the one with the lowest rate (holding credits constant) or highest credit (holding rates constant) will be chosen. The logic is similar to that the case where the parent is located in a non-unitary state, and is corroborated by simulation results reported in Tables 3 and 4. However (in contrast to the separate accounting parent setting), credits have virtually identical effects. Thus, holding tax rates constant, whichever state has better credits (regardless of tax structure) will attract the investment.

The incentive effects of no throwback/100% weighting of sales are identical to the discussion in the previous section.

 

Conclusion
This study examines the resource allocation choice decisions of a firm planning to expand into another state, in response to differential tax rates, tax structures, and tax credits between states. Because the firm can engineer its tax liability by calibrating the between-state location of sales, property, and payroll, differences in relative state tax rates should result in the firm making such resource decisions. Results of a firm model (corroborated by simulation results) find that the firm would make such resource allocation changes to minimize company-wide state taxes. However, the impact of these tax effects is far from straightforward, and in some cases, contrary to popular belief. For example, tax credits are less effective in unitary states, or when they are given solely for labor or capital, but not both. Tax rate cuts are not very effective in non-unitary states. Placing extra weighting on the sales factor is not effective when the firm has a sales throwback rule as well. The implications for lawmakers include that many tax laws which are believed to be effective may not be, and that changing of the incentives, or alternative incentives, should be used instead. Of course, such policy implications should be tempered by one severe limitation on the model’s external validity—not allowing for the potential manipulation of transfer pricing. Additionally, the use of general equilibrium model is needed to examine the total effects on both a state’s economy and its overall tax base.

The results provide some theoretical underpinning for the very recent empirical findings of Gupta and Hofmann (2003). Using aggregate (statewide) data on levels of manufacturing assets, they observe that the following have, in descending order, the strongest incentive effects on plant expansion and new plant location: absence of a unitary tax structure; absence of sales throwback; extra weighting on the sales factor; lower rates; and tax credits. Here, while I did not compare unitary versus separate accounting directly, I did find that in unitary accounting states, tax credits were less effective than in separate accounting states. On the other hand, lower tax rates were more effective in unitary states. Similar to Gupta and Hofmann, I found that absence of throwback is an effective incentive. However, extra weighting on the sales factor is not effective unless combined with absence of throwback. When these two are combined, they provide incentives stronger that either lower rates or tax credits. Similar to Gupta and Hofmann. I found that credits are not very effective. This especially true in unitary states; however, they can be effective if both labor and capital credits are combined. Even if these two are combined, they are less of an incentive that lower rates, and much less effective than absence of throwback.

 

References
All-State Tax Guide, 2003. Commerce Clearing House.

Atkinson, A., and J. Stiglitz.1980. Lectures on Public Economics. Princeton University Press.

Anand, B. and R. Sansing. 2000. The weighting game: Formula apportionment as an instrument of public policy. National Tax Journal 53 (2): 183-1999.

Bartik, T. 1994. Jobs, productivity, and local economic development: What implications does economic research have for the role of government? National Tax Journal 47 (4): 847-861.

Berck, P., Golan, E., and B. Smith .1996. Dynamic Revenue Analysis for California. Sacramento: California Department of Finance.

Brunori, D. 1997. Principles of tax policy and targeted tax incentives. State Tax Notes (June 9): 111-127.

Burstein, M. and A. Rolnick. 1996. Congress should end the economic war among the states. State Tax Notes (June 24): 125-44.

Carlton, D. 1983. The location and employment choices of new firms: an econometric model with discrete and continuous endogenous variables. The Review of Economics and Statistics 65 (Aug.): 440-449.

Carroll, R. and M. Wasylenko. 1994. Do state business climates still matter? Evidence of a structural change. National Tax Journal 47 (1): 19-37.

Cooley, T., ed.1996. Frontiers of Business Cycle Research. Princeton: Princeton University Press.

Coopers & Lybrand .1997. International Tax Summaries. New York: Wiley.

Coughlin, C., Terza, J., and V. Arromalee.1991. State characteristics and the location of foreign direct investment within the united states. The Review of Economics and Statistics 73 (Nov.): 675-683.

Edmiston, K. 2002. Strategic apportionment of the state corporate income tax. National Tax Journal 55 (2): 239-262.

Edmiston, K., and F. Arze. 2002. Firm-level effects of apportionment formula changes. Working paper, Georgia State University, Atlanta, GA.

Engberg, J. and R. Greenbaum. 1999, The impact of State Enterprise Zones on Urban Housing Markets. Working Paper, Heinz School of Public Policy and Management, Carnegie Mellon University.

Goolsbee, A. and E. Maydew. 2000. Coveting thy neighbor’s manufacturing: The dilemma of state income and apportionment. Journal of Public Economics 75 (1): 125-143.

Gordon, R., and J. Wilson .1986. An examination of multijurisdictional corporate income taxation under formula apportionment. Econometrica (Nov.): 1357-1373.

Faulk, D. 2002. Do state economic incentives create jobs? An analysis of state employment tax credits. National Tax Journal (June): 263-280.

Gupta, S. and M.A. Hofmannn. 2003. The Effect of State Income Tax Apportionment and Tax Incentives on New Capital Expeditures. Journal of the American Taxation Association (Supplement):1-26.

Gupta, S. and L. Mills. 2002. Multistate tax planning: Benefits of multiple jurisdictions. Journal of Accounting and Economics 33 (1): 117-139.

Hellerstein, J. and W. Hellerstein. 1992. State Taxation. Warren, Gorham, and Lamont, New York.

Helms, L. 1985. The effect of state and local taxes on economic growth: A time series-cross section approach. The Review of Economics and Statistics 67 (4): 574-582.

Hines, J. 1996. Altered states: Taxes and location of foreign direct investment in America. American Economic Review 86 (5): 1076-1094.

Hofmann, M. Forthcoming. The state corporate income tax: A synthesis of recent research. Journal of Accounting Literature.

Klassen, K. and D. Shackelford. 1998. State and provincial corporate tax planning: income shifting and sales apportionment factor management. Journal of Accounting and Economics 25 (3): 385-406.

Knight, B. 2001. State capital taxes and the location of investment: Empirical lessons from the tax competition models. Working paper, Federal Reserve Board, Washington, D.C.

Lightner, T. 2000. The effect of the formulary apportionment system on state-level economic development and multijurisdictional tax planning.” Journal of the American Taxation Association (Supplement)

Lopez, S., and J. Martinez-Vazquez. 1998. State corporate income taxation: an evaluation of the formula apportionment system. National Tax Journal (Supplement): 155-161.

Martin, S. 1998. Industrial Economics. MacMillan, New York.

McLure, C. 1980. The state corporate income tax: lambs in wolves’ clothing. In Aaron, H. & Boskin, M. (Ed.), The Economics of Taxation. Washington, D.C.: Brookings Institution.

McClure, C. 1981. The illusive incidence of the corporate income tax: the state case. Public Finance Quarterly (Oct.): 395-413.

Mofidi, A. and J. Stone. 1990. Do state and local taxes affect economic growth? The Review of Economics and Statistics 72 (4): 686-691.

Moore, M., Steece, B., and C. Swenson .1987. An economic analysis of the impact of state tax rates and bases on foreign investment in the United States. The Accounting Review (October): 671 – 685.

Omer, T., and M. Shelley. 2002. Competitive, political and economic factors influencing state tax policy changes. Working paper, University of Illinois at Urbana-Champaign.

Papke, L. 1991. Interstate business tax differentials and new firm location: Evidence from panel data. Journal of Public Economics 45 (1): 47-68.

Sampson, G. 2001. A Preliminary Examination of North Carolina Tax Incentives. State Tax Notes (Oct 22): 277-298.

Wasylenko, M. 1997. Taxation and economic development: The state of the economic literature. New England Economic Review (March/April): 37-52.

Weiner, J. 1996. Estimates of How the Unitary Tax Affects Business Investment. Paper presented at the Allied Social Science Meetings, San Francisco, California.

Wetzler, J. 1995. Should the U.S. adopt formula apportionment? National Tax Journal (Sept): 357-362.

Williams, M. and C. Swenson . 2001. Effects of unitary versus non-unitary state income taxes on interstate resource allocation: some analytical and simulation results. Journal of the American Taxation Association (Spring): 39-60.

Wilson, J. 1999. Theories of tax competition. National Tax Journal 52 (June): 269-304.

 

Appendix

Table 1 - General Business Expansion and Enterprise Zone Tax Credits by State

 General (Expansion):Enterprise Zone: General (Expansion)Enterprise Zone:
StatePayroll/PropertyPayroll/PropertyStatePayroll/PropertyPayroll/Property
AlaskaNo/noNo/noMissouriYes/yesYes/no
AlabamaNo/yesYes/noMontanaYes/noNo/no
ArizonaYes/noYes/noNebraskaYes/yesYes/yes
ArkansasNo/noYes/noNevadaN/a-no taxN/a-no tax
CaliforniaNo/yesYes/noNew HampshireYes/noNo/no
ColoradoNo/noYes/yesNew JerseyYes/yesYes/no
ConnecticutNo/yesNo-profits creditNew MexicoNo/noYes/no
DelawareNo/yesYes/yesNew YorkNo/yesYes/yes
FloridaNo/yesYes/noNorth CarolinaYes/yesYes/no
GeorgiaNo/yesYes/noNorth DakotaYes/noNo/no
HawaiiNo/yesNo-profits creditOhioNo/yesYes/no
IdahoNo/yesYes/noOklahomaYes/yesYes/yes
IllinoisNo/yesYes/yesOregonNo/noYes/no
IndianaNo/noYes/noPennsylvaniaYes/noYes/no
IowaYes/yesYes/noRhode IslandNo/yesYes/no
KansasYes/yesYes/noSouth CarolinaYes/noYes/no
KentuckyNo/noYes/noSouth DakotaN/a-no taxN/a-no tax
LouisianaYes/noYes/noTennesseeYes/yesNo/no
MaineYes/noNo/noTexasYes/yesYes/yes
MarylandYes/noYes/noUtahNo/noYes/no
MassachusettsNo/yesNo/yesVermontNo/noNo/no
MichiganNo/yesNo-profits creditWashingtonN/a-no inc. taxN/a-no inc. tax
MinnesotaYes/noYes/noWest VirginiaNo/yesNo/yes
MississippiYes/noNo/noWisconsinNo/noYes/no
   WyomingN/a-no taxN/a-no tax

Source: Commerce Clearing House Multistate Tax Guide, 2003.

 

Table 2 - Factor Apportionment, and Sales Throwback, by State

StateSales, Property, and Payroll Weights:Sales Throwback:StateSales, Property, and Payroll WeightsSales Throwback:
   Missouri1/3 eachYes
Alabama1/3 eachYesMontana1/3 eachYes
Arizona.5,.25,.25NoNebraska1.0,0,0No
Arkansas.5,.25,.25YesNevadaN/a-no taxN/a-no tax
California.5,.25,.25YesNew Hampshire.43,.285,.285Yes
Colorado1/3 eachYesNew Jersey.5,.25,.25No
Connecticut.5,.25,.25NoNew Mexico1/3 eachYes
Delaware1/3 eachNoNew York.5,.25,.25No
Florida.5,.25,.25NoNorth Carolina.5,.25,.25No
Georgia.5,.25,.25NoNorth Dakota1/3 eachYes
Hawaii1/3 eachYesOhio.5,.25,.25No
Idaho.5,.25,.25YesOklahoma1/3 eachNo
Illinois1.0,0,0YesOregon.5,.25,.25Yes
Indiana.5,.25,.25YesPennsylvania.5,.25,.25No
Iowa1.0,0,0NoRhode Island1/3 eachNo
Kansas1/3 eachYesSouth Carolina1/3 eachNo
Kentucky.5,.25,.25NoSouth DakotaN/a-no taxN/a-no tax
Louisiana.5,.25,.25NoTennessee.5,.25,.25No
Maine.5,.25,.25YesTexas**1.0,0,0 
Maryland.5,.25,.25NoUtah1/3 eachYes
Massachusetts1.0,0,0YesVermont1/3 eachYes
Michigan*.9,.05,.05YesVirginia1/3 eachNo
Minnesota.7,.15,.15NoWashingtonN/a-no income taxN/a-no income tax
Mississippi1/3 eachYesWest Virginia.5,.25,.25No
Wisconsin.5,.25,.25YesWyomingN/a-no taxN/a-no tax

*Single Business Tax(SBT), using value added (but starting point is net income)
** Franchise tax, one part of which based on net income

 

Table 3 - Simulation Parameters

“Real World”* Simulation
 REVENUE 
Downward-sloping demand function; Price elasticities range from -.38 to –5.00 For all states, P=1-.1Q; Demand elasticities vary, with mean of –3.26, and range of –4.73 to –2.59. Elasticities varied such that States 1, 2, 3 and demand functions always unique
 OUTPUT 
Cobb-Douglas; approximate ratio of capital to output (K:Q)=3:1; approximate ratio of capital:labor=.60:.40 f ( Q1 + Q2 ) = Ym = Q (Lma . Kmb) for main plant,

and f Qi = Yi = Q (Lma . Kmb)

for secondary plants. Q = 3, which is chosen so that K:Q is approximately 3. In fact, K:Q varies somewhat for each of three plants, with mean = 3.05, and range of 2.11 to 4.53 across all observations. f is solved for, with mean=.33 and range of .15 to .55 across all observations. a and b set at .48 and .32, respectively (ie, .60:.40 relative ratio). L and K are solved for, for all three plants.
 COSTS 
Statewide per capita personal income varies from 71 (Mississippi) to 142 (Connecticut) percent of the national average. w is a numeraire.
The cost of capital is the interest rate adjusted for risk. Risk-free interest rates (one year Treasuries) have varied between 3.18 and 7.14 percent since 1990. Values of model have no risk so r takes on the conservative value of the highest risk rate of 7 percent.
Shipping cost (s) is unknown and likely to vary widely by industry. s takes on the values of 0, 5, 10, 15, or 20 percent of the maximum possible sales price.
 TAXES 
State tax rates range from 0 to 14% When both states are unitary, ?1 - ?2 takes on the values of -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8 when at least one state is non-unitary, ?1 and ?2 each takes on the values 0, 2, 4, 6, 8, 10, 12, or 14 percent
Hiring Credits c2 takes on values of 20, 40, 50, 60, 70 per cent
Machinery and equipment credits amounts vary widely by state  y2 takes on values of 10%, 30% and 50%
Apportionment factors; see Table 2 in Appendix Sales weight 50% or 100%; capital labor weights 25% or 0% each.
Throwback-varies by state; see Table 2 in Appendix Set to 0 or 1

*See Berck et al. (1996) and Cooley (1996) for non-tax parameters

 

Table 1

Summary of Comparative Statics

Impacts of Incentives on Resource Allocation

 

New State Incentive

Both States Separate Accounting

Both States Unitary

Original State Separate Accounting, New State Unitary

Original State Unitary,

New State Separate Accounting

Decrease in Tax Rate (↓ τ2)

 

None

↓φ ↓Q1 ↑Q2   ↓Lm ↓Km ↑L2 ↑K2

Unknown

Slight ↑K2    Slight ↑K2     Slight ↑Q2

Tax Credit for Labor (↑ x2)

 

↑L2  ↓K2 ↓φ ↓L1  ↑K1

↑L2  ↓K2 ↓φ ↓L1  ↑K1

↑L2  ↓K2 ↓φ ↓L1  ↑K1

↑L2  ↓K2 ↓φ ↓L1  ↑K1

Tax Credit for Capital (↑ ψ2)

 

↑K2 ↓L2  ↓φ ↓L1  ↑K1

↑K2 ↓L2  ↓φ ↓L1  ↑K1

↑K2 ↓L2  ↓φ ↓L1  ↑K1

↑K2 ↓L2  ↓φ ↓L1  ↑K1

No Sales Throwback (τ2·s3=0)

 

↑Q2 ↑Θ ↑L1 ↑K1 ↓Q1

↑Q2 ↑Θ ↑L1 ↑K1 ↓Q1

↑Q2 ↑Θ ↑L1 ↑K1 ↓Q1

↑Q2 ↑Θ ↑L1 ↑K1 ↓Q1

Increased Weighting for Sales (Sw2=1.00) with throwback

None

None

None

None

 

 

 

 

 

Increased Weighting for Sales

     (Sw2=1.00) No throwback

↑Q2 ↑Θ ↑K2 ↑L2  ↓Q1

↑Q2 ↑Θ ↑K2 ↑L2  ↓Q1

↑Q2 ↑Θ ↑K2 ↑L2  ↓Q1

↑Q2 ↑Θ ↑K2 ↑L2  ↓Q1

 

 

Table 2

Regression Results For Simulated Data:  Both States Non-Unitary

(State Tax Incentive Effects in Shaded Areas)

Dependent Variable:

Independent

Variable:

Firm Pretax Profits

 

State

1

Sales

State

2

Sales

State

1

Labor

State

2

Labor

State

1

Capital

State

2

Capital

Primary MFG Capital

Primary MFG

Labor

% work done  by Primary MFG

% Sales

 to S3

Constant

1.46

1.45

1.61

-1.10

-.46

2.58

2.13

1.23

-2.45

.09

N.A.

(2026.62)

(1352.58)

(1410.42)

(-104.19)

(-67.84)

(619.65)

(337.24)

(110.45)

(-223.13)

(32.35)

 

 

 

 

 

 

 

 

 

 

 

 

 

↓t2

.00

.01

-.01

-.03

-.04

.00

-.05

.09

.08

.02

N.A.

(.05)

(1.24)

(-2.23)

(-.69)

(-1.35)

(.22)

(-1.60)

(1.68)

(1.68)

(1.28)

 

 

 

 

 

 

 

 

 

 

 

 

 

c2

.09**

-.02**

.13**

.28**

.95**

.44**

-.09**

-.75**

-.75**

-.20**

N.A.

(192.89)

(-31.02)

(184.26)

(41.41)

(221.16)

(166.60)

(-22.25)

(-105.27)

(-107.10)

(-112.56)

 

 

 

 

 

 

 

 

 

 

 

 

 

ψ2

.18**

-.03**

.20**

.19**

-.04**

.26**

.50**

-.81*

-.81**

-.21**

N.A.

(200.71)

(-20.52)

(202.51)

(32.11)

(-18.56)

(37.85)

(210.33)

(-121.33)

(-199.45)

(-122.38)

 

 

 

 

 

 

 

 

 

 

 

 

 

No Sales Throwback

.22**

-.0 4**

ψ.25**

-.10**

.22**

-.11**

.26**

.21*

(.17)**

.26**

.20**

(219.43)

(-31.73)

(220.33)

(-28.83)

(21.17)

(-31.32)

(107.55)

(31.54)

(22.76)

(130.42)

(191.39)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0, Throwback

.00

.00

ψ-.01

(.000)

-.02

.00

.00

.02

.00

.01

.02

(.04)

(.10)

(-.12)

(.20)

(-.87)

(.25)

(.00)

(.21)

(.00)

(.96)

(1.44)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0,

No Throwback

.19**

-.04**

.27**

-.01*

.25**

-.06**

.30**

-.42**

-.42**

-.13**

.35*

(225.77)

(-30.84)

(237.43)

(-19.97)

(24.41)

(-18.18)

(185.02)

(-66.57)

(-68.14)

(-104.04)

(180.76)

 

 

 

 

 

 

 

 

 

 

 

 

r

-3.69

-2.54

-2.56

3.13

4.13

-15.36

-16.87

-13.42

7.58

.59

N.A

(-410.04)

(-186.89)

(-175.46)

(23.33)

(47.82)

(-290.18)

(-209.84)

(-94.62)

(54.27)

(16.50)

 

 

 

 

 

 

 

 

 

 

 

 

 

s

-1.14

.03

-1.40

.07

-1.72

.04

-1.71

-.80

-.80

-.01

N.A.

(-636.08)

(9.62)

(-480.09)

(2.53)

(-99.79)

(4.20)

(-106.53)

(-28.26)

(-28.64)

(-1.42)

 

 

 

 

 

 

 

 

 

 

 

 

 

t1

-.00

-.01

.01

.07

.06

-.01

.05

-.12

-.10

-.02

N.A.

(-.24)

(-1.05)

(2.21)

(1.40)

(1.14)

(-.63)

(1.49)

(-2.22)

(-2.02)

(-1.66)

 

 

 

 

 

 

 

 

 

 

 

 

 

Model R2

1.00

.95

.99

.55

.97

.98

.97

.92

.89

.87

 

 

 **Indicates tax rate or credit coefficient significant at .01 level or better (t statistics in parentheses).  All data subject to logarithmic transformation.

  Ψ Sum of State 2 and State 3 Sales
Table 3

Regression Results For Simulated Data:  Both States Unitary

(State 2 Tax Incentive Effects in Shaded Areas)

 

Dependent Variable:

Independent

Variable:

Firm Pretax Profits

 

State

1

Sales

State

2

Sales

State

1

Labor

State

2

Labor

State

1

Capital

State

2

Capital

Primary MFG Capital

Primary MFG

Labor

% work done  by Primary MFG

% sales

to S3

Constant

1.29

 

1.04

 

           1.21

 

-1.10

 

-.46

 

2.58

 

2.13

 

1.24

 

-2.44

 

.09

 

N.A.

(1122.42)

(857.09)

(947.70)

(-94.63)

(-62.08)

(508.03)

(312.59)

(101.83)

(-204.60)

(30.68)

 

 

 

 

 

 

 

 

 

 

 

 

 

↓t2

.02**

-.13**

.22**

.72**

1.01**

.73**

1.39**

-1.65**

-1.52**

.45**

N.A.

(3.39)

(-23.36)

(37.73)

(13.42)

(29.63)

(31.09)

(44.09)

(-29.46)

(-27.55)

(31.83)

 

 

 

 

 

 

 

 

 

 

 

 

 

c2

.13**

-.02**

.13**

.29**

.96**

.44**

-.08**

-.75**

-.75**

-.20**

N.A.

(183.47)

(-26.81)

(169.36)

(38.85)

(202.63)

(131.52)

(-19.49)

(-97.69)

(-99.00)

(-103.92)

 

 

 

 

 

 

 

 

 

 

 

 

 

Ψ2

 

.18**

-.01**

.20**

.35**

-.12**

.36**

.95**

-.78*

-.78**

-.21**

N.A.

(199.58)

(-17.44)

(185.11)

(41.73)

(-21.49)

(92.71)

(198.46)

(-95.42)

(-96.13)

(-110.91)

 

 

 

 

 

 

 

 

 

 

 

 

 

No Sales Throwback

23.**

-.05**

Ψ.28**

-.12**

.23**

-.13**

.27**

.22**

.19**

.28**

.21**

(222.46)

(-33.18)

(243.37)

(-41.28)

(30.37)

(-48.81)

(111.88)

(36.06)

(25.54)

(144.14)

(201.81)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0, Throwback

.01**

-.01**

Ψ.10**

.01

.59**

.01

.62**

-.41**

-.41**

-.10**

.01

(1.95)

(-20.28)

(140.28)

(.18)

(109.19)

(.19)

(123.77)

(-49.72)

(-51.08)

(-32.10)

(.05)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0,

No Throwback

.21**

-.06*

Ψ.31

-.03**

.38**

-.07

.41**

-.52**

-.52**

-.25**

.40**

(240.04)

(-41.21)

(298.82)

(-28.18)

(39.77)

(-22.89)

(202.18)

(-81.28)

(-90.39)

(-110.96)

(195.29)

 

 

 

 

 

 

 

 

 

 

 

 

s

-1.23

.02

-1.40

.11

-1.72

.03

-1.71

-.81

-.81

-.01

N.A.

(-419.18)

              (10.98)

(-443.45)

(3.58)

(-90.59)

(2.57)

(-198.34)

(-26.32)

(-26.57)

(-1.78)

 

 

 

 

 

 

 

 

 

 

 

 

 

t1

-.03**

-.22**

.21**

.38**

.84**

.53**

1.19**

-1.89**

-1.69**

-.40**

N.A.

(-5.02)

(-38.37)

(37.48)

(7.06)

(24.31)

(22.42)

(37.66)

(-33.62)

(-30.51)

(-28.01)

 

 

 

 

 

 

 

 

 

 

 

 

 

Model R2

1.00

.95

.99

.55

.97

.98

.97

.92

.89

.87

 

 

 

 

 

 

 

 

 

 

 

 

 

ΨSum of State 2 plus State 3 sales.

 **Indicates tax rate or credit coefficient significant at .01 level or better (t statistics in parentheses).  All data subject to logarithmic transformation.

Table 4

Regression Results For Simulated Data:  State 1 is Unitary; State 2 is Non-Unitary

(State 2 Tax Incentive Effects in Shaded Areas)

Dependent Variable:

Independent

Variable:

Firm Pretax Profits

 

State

1

Sales

State

2

Sales

State

1

Labor

State

2

Labor

State

1

Capital

State

2

Capital

Primary MFG Capital

Primary MFG

Labor

% work done  by Primary MFG

% Sales

to S3

Constant

1.30

1.04

1.20

-1.11

-.48

2.56

2.12

1.13

-2.54

.09

 

   (2301.74)

   (1881.57)

(2147.16)

(-259.59)

(-162.76)

(1239.43)

(716.83)

(200.70)

(-453.55)

(74.10)

N.A.

 

 

 

 

 

 

 

 

 

 

 

 

 ât2

.00

-.00

-.01**

.00

.00

-.03**

-.03

-.03**

.03

.01

 

(.10)

(-2.20)

(-4.90)

(.30)

(.21)

(-3.58)

(-1.23)

(-2.79)

(1.49)

(.42)

N.A.

 

 

 

 

 

 

 

 

 

 

 

 

c2

.14**

-.03**

.14**

.21**

.98**

.38**

-.14**

-.73**

-.73**

-18**

 

(389.37)

(-86.54)

(392.38)

(79.20)

(492.40)

(269.59)

(-77.74)

(-210.78)

(-211.89)

(-238.94)

N.A.

 

 

 

 

 

 

 

 

 

 

 

 

Ψ2

 

.19**

-.03**

.18**

.19**

-.20**

.41**

.98**

-.79**

-.79**

-.19**

N.A.

(395.95)

(-75.82)

(414.78)

(65.58)

(-80.18)

(288.60)

(300.55)

(-231.47)

(-234.18)

(-301.26)

 

 

 

 

 

 

 

 

 

 

 

 

 

No Sales Throwback

.22**

-.03**

Ψ.25**

-.11**

.21**

-.11**

.25**

.21**

.16**

.26**

.20**

(202.55)

(-28.82)

(219.19)

-31.09)

(20.00)

(-30.98)

(100.48)

(31.40)

(20.08)

(129.09)

(193.35)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0, Throwback

.01

-.01

Ψ.01

.00

.01

-.01

.01

-.01

-.01

.00

.03

(1.22)

(-.22)

(1.29)

(.01)

(.55)

(-.35)

(.65)

(1.35)

(-1.22)

(.05)

(1.52)

 

 

 

 

 

 

 

 

 

 

 

 

Sw2=1.0,

No Throwback

.21**

-.05**

Ψ.30**

-.01**

.27**

-.07**

.31**

-.45**

-.45**

-.14**

.37**

(241.87)

(-35.88)

(245.10)

(-20.38)

(28.80)

(-20.29)

(200.82)

(-70.70)

(-71.81)

(-120.21)

(202.709)

 

 

 

 

 

 

 

 

 

 

 

 

r

-5.91

-2.66

-2.53

2.01

3.50

-15.94

-17.74

-11.27

9.54

1.03

N.A.

(-848.20)

(-389.52)

(-364.77)

(37.95)

(95.44)

(-624.50)

(-484.82)

(-161.61)

(137.55)

(69.04)

 

 

 

 

 

 

 

 

 

 

 

 

 

s

-1.23

.01

-1.36

.13

-1.72

-.05

-1.71

-.69

-.70

.01

N.A.

(-881.78)

(41.87)

(-979.6