Tax competition leading to strict environmental policy

We study tax competition when pollution matters. Most notably we present a dynamic setting, where the supply of capital is endogenous. It is shown that tax competition may involve stricter environmental policy than the cooperative outcome..


Introduction
The theoretical and empirical literature on a race to the bottom in terms of environmental standards in case of mobile capital is vast. On the empirical side Wilson (1997) argues that the fear of a race to the bottom has induced a shift of control of environmental policy from the States to the Federal government (see also Vig and Kraft (1994)). List and Gerking (2000) however, do not …nd any evidence of a race to the bottom in environmental standards when US environmental policy was delegated to the States during the Reagan administration. The survey by Levinson (1997a) is inconclusive. The theoretical paper by Oates and Schwab (1988) is a classic. It shows that a race to the bottom does not occur if governments behave competitively, meaning that in determining the optimal source-based capital tax and the optimal environmental tax, they take the net rate of return on capital in all other jurisdictions as given. However, if the capital tax is exogenously …xed, the environmental tax will be set too low: a …rst-best optimum across all jurisdictions commands a higher environmental tax. A recent contribution was made by Ogawa and Wildasin (2009) who extend the Oates and Schwab framework by allowing for transboundary pollution, caused by the use of capital. They show that decentralized decision making results in a …rst-best optimum if jurisdictions recognize that capital

The model
The objective of the present paper is to add dynamics to the conventional framework. In the model we analyse an economy consisting of two countries, home and foreign, with activities extending over two periods of time. We aim at showing that in the cooperative equilibrium the pollution tax can be lower than in the non-cooperative equilibrium. We restrict ourselves to the case of identical countries and we take speci…c functional forms for the preferences, the damage functions and the production functions. Consumers are homogeneous and derive utility from consumption in the …rst and second period, and disutility from second period pollution resulting from investments made in the …rst period, as well as utility from a public good that is provided in the second period only.
We describe the home economy. The foreign economy's variables are denoted by hats. The welfare function of the representative consumer reads Here c 1 ; c 2 ; g; x and b x denote …rst period consumption, second period consumption, consumption of the public good, pollution generated in the home country and pollution generated in the foreign country, respectively. The damage function is linear, with marginal damage from pollution generated at home equal to ! and marginal damage attributable to transboundary pollution equal to . In the instantaneous utility functions for consumption the parameter is the negative of the elasticity of marginal utility. In the welfare function is the discount factor. The parameter " denotes the relative weight attached to public consumption.
At the outset of the …rst period, the individual holds lump-sum wealth w, which may be used for three purposes: period-1 consumption c 1 , domestic investment k h , and investment abroad k f . Therefore In the second period the individual may choose to relocate capital across borders, but at a cost. This process results in k h and k f ; the actual inputs of home owned capital in home production and foreign production, respectively. Hence, total capital used in domestic production is given by Of course it must hold that respect, among others, Hoel (1997), Krumm and Wellisch (1995), Markusen et al. (1995), Motta and Thisse (1994), Rauscher (1995), Ulph (1994)), Venables (1999), Wellisch (1995)) abstracts from the issue of endogenous savings.
Production takes place in the second period according to a Cobb-Douglas technology employing capital k and the polluting input x.
The representative …rm hires capital at the rental rate r, and pays a pollution tax t: It then follows from pro…t maximization that Pro…ts made by the …rm are The second period budget constraint of the representative individual reads Here h is the capital tax imposed on revenues on home owned capital, and b f the foreign tax on home owned capital revenues. The relocation costs are quadratic, with parameter > 0: The corporate pro…t tax is ; which is given for the time being. After the two governments have set their taxes the representative individual in the home country maximizes consumption, i.e., maximizes (8) by optimally moving capital across borders, taking into account that k h + k f = k h + k f : She ignores the potential e¤ect of her decision on pro…ts : Given the governments'decisions this yields the individual's optimal allocation of capital. The agent, confronted with tax di¤erentials, minimizes her cost given her initial allocation, yielding Here^ f is the foreign tax on home owned capital revenues. Similarly, for the foreign representative capital owner Here f is the home tax on foreign owned capital revenues. Then, as a …nal step in this procedure we will consider relocation at in…nitely small cost, i.e., for ! 0: The governments know this reallocation behavior, which is henceforth internalized by them when taking their actions. The government's budget constraint reads

Equilibrium
We consider two types of equilibria. In the non-cooperative equilibrium four stages can be distinguished. 1. At the outset of period 1 the representative individual decides on savings and investment allocations. The home consumer determines (k h ; k f ) whereas the foreign consumer sets ( b k h b ; k f ): These decisions are made based on rational predictions of future governments'policies.
2. At the outset of period 2 the home government chooses h ; f and t (taking as given b h ; b f and b t) so as to maximize the welfare of the resident representative individual. Similarly, the foreign government chooses b h ; b f and b t (taking h ; f and t as given). For the time being we assume an a priory …xed corporate tax.
3. Individuals observing the governments' decisions may then choose to relocate capital.
4. Taxation, public spending, production and hence pollution as well as consumption take place.
The cooperative equilibrium di¤ers from the non-cooperative equilibrium only in that at the outset of period 2 both governments choose h ; f ; t, b h ; b f ; and b t so as to maximize the sum of utilities of both representative individuals.
The timing of the policy game captures the feature that the initial allocation of capital is …xed when the government sets the capital tax, and that individuals' savings depend on the anticipated capital tax. Hence, individuals make their savings decision at the outset of period 1, and the government makes the tax decision at the beginning of period 2.

Second-period equilibrium
The cooperative second-period equilibrium is easy to calculate. Given that the countries are identical, the capital taxes are all the same as well as the capital stocks at the outset of the second period. Moreover, there is no need for reallocation. Hence the problem is just to maximize where we have omitted the index for the period of time. It readily follows that the Samuelson condition holds from which the tax rate can be determined. Moreover, the pollution tax is Pigovian and therefore equals marginal damage, normalized by the marginal utility of consumption So, for every initial second period capital stock we can determine the optimal pollution tax as well as the rate of pollution. Note that the capital tax is independent of the initial capital stock. Moreover, foreign investments are not needed at all. It is also straightforward to see that if the corporate tax is a policy instrument as well, we have an additional degree of freedom. Any combination of capital taxes and corporate taxes satisfying (14) is optimal. It is considerably more complicated to determine the second-period noncooperative equilibrium. The technical details are given in the appendix. Here we restrict ourselves to giving the results and providing the economic intuition. The home government chooses h ; f and t (taking b h ; b f and b t as given) so as to maximize period-2 utility of the resident individual subject to the constraints: (1)- (2), (5) and (6) and the foreign counterpart (7)-(13). The initial investment allocations k and b k are given to the governments. Given the fact that countries are symmetric the equilibrium is characterized by equal tax rates and allocations across the two countries. Consequently, no reallocation of capital from one country to another will take place. This can in a convenient way be captured by assuming that the reallocation cost parameter converges to zero. The most remarkable feature of the solution is that given k and b k there are unique positive optimal allocations of capital to home and foreign: k h ; k f ; b k h and b k f : To see why this is the case let us …rst assume that the corporate tax is a policy instrument and is not subject to any restrictions. In that case the Samuelson condition will hold since the marginal utilities of private and public consumption are equal (as a consequence of maximization of the Lagrangian of the problem with respect to the corporate tax (see the appendix)). Then the countries enter into a race to the bottom when it comes to capital taxation in order to attract capital. One reason is to bene…t from the pro…ts of higher production. Another reason is that, given the other country's pollution tax, higher capital input in the other country will also increase its emissions, which are harmful. For the model at hand, it can be shown that the optimal non-cooperative capital tax satis…es Hence the tax is negative. It is the more negative the larger the marginal damage of pollution ‡owing in from the other country relative to the marginal damage of the country's own emissions. Moreover, the higher the production elasticity of emissions the more negative the capital tax is. It is also straightforward that in the equilibrium the pollution tax is Pigovian, but only taking local pollution into account.
Next we turn to the case of an a priori given corporate tax rate, thereby allowing for a deviation from the Samuelson rule. In an equilibrium we still have identical capital tax rates across countries, and countries will not discriminate between home owned and foreign owned capital. De…ne z( ) 1 " (1 ) + (1 ) 1 (1 ) (1 ) Then the second-period non-cooperative equilibrium (in the limit, for ! 0) can be characterized as follows.
The proof is given in the appendix. Several remarks are in order. First of all, if the corporate tax is close to the optimal one, we are back in the previous case of the endogenous corporate tax. Consequently, if the given corporate tax happens to be close to the optimal one, we can still have a negative capital tax. We also see that for a given initial capital endowment there is a unique equilibrium allocation between foreign and home. This is a consequence of the trade o¤ between the bene…ts of production at home, with the higher pro…ts and production abroad, yielding less pollution at home. We also see that the equilibrium pollution tax has the ‡avor of a Pigovian tax, but now the local marginal damage is normalized by a weighted sum of the marginal utilities of private and public consumption.
Comparing the cooperative and the noncooperative equilibrium we note that competition takes place by means of the capital tax. Indeed, regardless of the initial conditions, the noncooperative capital tax is smaller than the cooperative capital tax coop > noncoop : This holds regardless of the initial conditions. A comparison of the pollution taxes is less straightforward because the capital stocks di¤er between de di¤erent regimes. This is the subject of the next section.

Endogenous savings
For each regime (cooperation or non-cooperation) the individual agents anticipate the capital tax as well as the equilibrium interest rate in the second period. The individual chooses the amount of investment in order to maximize the utility from consumption

Written in terms of investment this is
Indeed, the agent knows that the net returns on capital don't di¤er across countries. Moreover, the agent rightly assumes there is no need for relocation of capital. As is standard we assume that each individual is "small"and cannot a¤ect the pro…ts of the …rm when making her savings decision. This implies that the pollution taxes don't play a direct role in the agent's decision problem. Maximization with respect to k yields Another way of writing this is

Strict environmental policy in the non-cooperative equilibrium
Given the second-period tax rates (giving x as a function of k) we can now determine the full cooperative and non-cooperative equilibrium. The main question we wish to address is whether in a cooperative equilibrium environmental policy is more stringent or more lenient than in the non-cooperative equilibrium.
We have seen before that the capital tax is higher in the cooperative equilibrium. This will trigger less investments in the cooperative equilibrium. Then it may be the case that the emission tax is low because emissions are low by themselves, whereas in the non-cooperative regime the producers, having more capital at their disposal, should be more discouraged to emit. Obviously, it is insurmountable to provide a full analytical answer. For that reason we rely on some numerical exercises. We take = 0:2; = 0; " = 2:186; = 0:9; = 0:319202; ! = 0:3; w = 3: Furthermore we take the production elasticity of capital, pro…ts after taxation , and the transboundary pollution as a pivotal parameters. Figure 1, gives the di¤erence between environmental taxation under the cooperative and the noncooperative equilibrium (hence a positive number implies that environmental taxation is higher in the cooperative equilibrium).
As can be observed from the …gure environmental taxes may be lower under cooperation compared to non-cooperation. Which regime leads to higher taxation depends on the production technology. A higher production elasticiy of capital (an increase in ), as well as a reduction in pollution from abroad and a reduction in pro…t taxation result in a situation in which it is more likely that there is lower taxation under the cooperative equilibrium compared to the non-cooperative equilibrium. Table 1 Table 1: Levels of production input and corresponding tax rates in a competitive and in a cooperative setting for two di¤erent levels of production elasticity of capital As can be observed from the table pollution taxes are not necessarily higher under one regime compared to the other. Whether we have a race to the bottom will thus depend on the parameter values used. Furthermore, the results con…rm that in a competitive setting more capital is available. Due to a higher availability of capital the polluting good becomes more productive, leading to a higher demand, which might induce higher environmental taxes. However, if pollution is transboundary this e¤ect is mitigated. Which e¤ect dominates depends on the setting.
Besides the government taxing companies, returns on capital and pollution the government could also opt for subsidizing companies by applying a negative . For example the case where = 0:1; = 0:5 and = 0:1 would result in a strong increase in environmental taxation under the cooperative equilibrium while there are limited e¤ects on the non-cooperative equilibrium. Other implications are a reduction in taxes on returns on capital as well as an increase in government spending. This is the result of an increase in capital in the home country in the second period. Given the implications of a change in , this warrants a search for the optimal . Unfortunately this search is only possible for the cooperative equilibrium with the usage of the fact that c g has to equal 1. The optimal turns out to equal 1:67 when = 0:5 and = 0:1. This also yields a negative taxation on returns on capital.

Conclusion
The paper provides a dynamic model of tax competition in a world with transboundary pollution. Most notably due to introducing dynamics the supply of capital is no longer …xed nor is the return on capital. Agents determine their saving decision and thereby available capital in the next period based on future expected tax regimes.Without dynamics and with a …xed return on capital and with optimal non-distortionary taxes the resulting equilibrium equals the autarky situation. With distortionary taxes emission taxes are higher in cooperation compared to the Nash equilibrium. Introduction of dynamics will yield the same results if non-distortionary taxes are available. If these taxes are not available results are no longer unambiguous. Whether the competitive case or the cooperative case has the more stringent policy depends on the parameter values. The ambiguity originates from opposing factors. In a competitive case there is a higher demand for the polluting good due to a higher availability of capital while the transboundary characteristic of the pollution reduces the need for a higher pollution tax. Thus with one production technology we might experience a race to the bottom while with another technology this might not be the case.