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Applied Economics
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Inconsistent preferences in environmental protection
investment and the central government's optimal
policy
Ming-Chung Chang a & Jin-Li Hu b a
Department of Risk Management , Kainan University , Taiwan b
Institute of Business and Management, National Chiao Tung University , Taiwan Published online: 18 Jun 2009.
To cite this article: Ming-Chung Chang & Jin-Li Hu (2011) Inconsistent preferences in environmental protection investment
and the central government's optimal policy, Applied Economics, 43:6, 767-772, DOI: 10.1080/00036840802599891
To link to this article: http://dx.doi.org/10.1080/00036840802599891
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Inconsistent preferences in
environmental protection
investment and the central
government’s optimal policy
Ming-Chung Chang
a,* and Jin-Li Hu
b aDepartment of Risk Management, Kainan University, Taiwan
b
Institute of Business and Management, National Chiao Tung University, Taiwan
Environmental protection plans cannot succeed without full cooperation among related units. However, inconsistent investment preferences toward environmental protection increase the damage to the environment. This article employs the contract mechanism to analyse environmental protection effects when the central government directly subsidizes the local governments. The results reveal that subsidies from the central government are not only unable to solve the problem of the inconsistent investment preferences among the central and local governments but also induce the free-riding behaviour of local governments. Because of the free-riding behaviour of the local governments, there is no such equilibrium in which the central government prefers the sequential investment mode while the local governments prefer the simultaneous investment mode.
I. Introduction
Many studies suggest that the government should subsidize environmental protection activities. Hence, governments all over the world expend sizable budgets to subsidize the natural resource sectors such as agriculture, energy, water, forestry and fisheries (OECD, 1998, 1999; van Beers and de Moor, 2001). However, many environmental protection activities cannot succeed without the full cooperation among different countries’ governments. Many real examples can illustrate the importance of collaboration in environmental protection. For instance, the Dead Sea is a well-known tourist spot, but it is also disappearing. The main reason for the Dead Sea to be literally on the verge of death is an interception in the upstream of the Jordan River by
the bordering countries of Israel, Jordan and Palestine for agricultural irrigation purposes. However, the countries bordering the Dead Sea are planning to save the Dead Sea (DWNEWS, 2006). Besides, the lakes Ohrid and Prespa are the largest natural reservoirs in Europe. However, they are being damaged by the pollution from agricultural waste-water that is passing through them. Macedonia and Albania have thus signed a contract to protect them (Environment News Service, 2003).
The Tamsui River in Taiwan is a boundary river between Taipei county and Taipei city, and the renovation of the Tamsui River requires a joint collaboration on the part of the Taipei county government, the Taipei city government and the central government in Taiwan. In this case, the cooperation in relation to environmental protection
*Corresponding author. E-mail: changmc@mail.knu.edu.tw
Applied EconomicsISSN 0003–6846 print/ISSN 1466–4283 onlineß 2011 Taylor & Francis 767 http://www.informaworld.com
DOI: 10.1080/00036840802599891
is formed by two local governments and a central government. Because of the inconsistent investment preferences in environmental protection among the central and local governments, subsidies from the central government may induce social welfare losses. This article applies the game-theoretic approach to analyse the environmental protection effects when the central government directly subsidizes the local governments. We also examine how direct subsidies from the central government affect the local govern-ments’ environmental protection behaviour. Our direct subsidy method is different from those in standard public economics: the traditional public economics theories often analyse the subsidy as a negative tax (Atkinson and Stiglitz, 1980). The subsidy by way of the negative tax can be seen as an indirect subsidy. Hence the central government can use a direct subsidy to affect the environmental protection investment outcomes of the local governments.
The previous literature regarding environmental protection subsidies consists of general and partial equilibrium analyses. The general equilibrium modelling requires many assumptions regarding the behaviour of consumers and sectors, as well as many
parameters that need to be estimated (see
also Burniaux et al., 1992). Although the partial equilibrium analysis is restricted to a single sector, the single-sector effects of specific subsidies in a partial equilibrium framework can also provide good intui-tion and insight in environmental economics (Larsen and Shah, 1992; Ostbye, 1998; Giosa et al., 1999; International Energy Agency, 1999; van Beers et al., 2007). The previous studies, however, do not use the contract mechanism to analyse the effect of environ-mental protection. By contrast, this article employs the contract mechanism to analyse the environmental protection effects when the central government directly subsidizes the local governments in a partial equilibrium framework.
There arises the problem of the inconsistent investment preferences of contracting parties when an investor cannot obtain the investment gain (Hart and Moore, 1988) or when the investment contract is incomplete (Grout, 1984; Grossman and Hart, 1986; Hart and Moore, 1988). The problem of inconsistent investment preference can be solved by formal fixed-wage contracts (MacLeod and Malcomson, 1993), renegotiation on contract content (Aghion et al., 1994), simple option contracts (No¨ldeke and Schmidt, 1995), or increasing collateral over time (Neher, 1999). We employ the models of Smirnov and
Wait (2004a, b) to discuss the central and local governments’ environmental investment preferences and the optimal policy to maximize the social welfare. We find that the environmental protection subsidy from the central government is unable to achieve the socially optimal point because of free-riding beha-viour among local governments. It is possible that the investment preference in environmental protection is inconsistent between the central and local govern-ments. The penalty for violating the environmental protection contract induces the consistent investment
preference between the central and local
governments.
The remainder of this article is organized as follows: Section II consists of the model setup and the process for calculating the sub-game perfect Nash equilibrium. Section III discusses investment prefer-ence inconsistency among the central government and local governments. Section IV resolves the problems caused by inconsistent investment preferences. Section V concludes the article.
II. Model Setup
We employ a two-period, three-stage model with two local governments (GOV A and GOV B) and one central government. In the first stage, the central government chooses a subsidy to optimize the environmental protection effect. In the second stage, two local governments decide either to adopt the simultaneous mode or the sequential investment mode. In the third stage, two local governments decide the optimal environmental protection invest-ment quantities. We characterize the sub-game perfect Nash equilibrium and adopt backward induction to calculate the solution to this game.
Two local governments’ investment quantities are defined as mA and mB. Following the formulation
of Smirnov and Wait (2004a), we define the environ-mental protection effect function as E ¼ m1=2A þ m1=2B , where 40, mi0 and i ¼ A, B.1
This functional form indicates that there is a positive relationship between the environmental protection investment quantity and the environmen-tal protection effect. Moreover, the marginal effect of investment is negative, i.e. @E/@mi40, @2E=@m2i 5 0.
This functional form also indicates that there are independent relationships among the environmental protection investors. Furthermore, if all investors are engaged in the environmental protection’s 1
Smirnov and Wait (2004a) used a similar function to analyse the optimal collaborative investment-timing and the influence of the hold-up problem on the social welfare. The setup for their function was E ¼Riln mi, where i ¼ A or B.
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M.-C. Chang and J.-L. Hu
investment, then there will be a significant environ-mental protection effect. The parameter is the coefficient of the environmental protection effect.
Because the central government pursues the optimal environmental protection effect, it plays a role of subsidizing the local governments’ environ-mental protection investment. Assume that the central government only subsidizes the local govern-ments in the first period and then does not provide any subsidy in the second period. Under the subsidy case, if the central government subsidizes local government i, then local government i’s total invest-ment quantity is miþs, where s is the subsidy from
the central government and s 0. We also assume that GOV A invests in two periods and GOV B starts to invest either in the first period or in the second period. If both local governments start to invest in the first period, then this is defined as the simultaneous investment mode; if both local governments start to invest in different periods, i.e. GOV A starts to invest in the first period and GOV B starts to invest in the second period, then this is defined as the sequential investment mode.
Regardless of whether the simultaneous investment mode or the sequential investment mode is adopted, the coefficient of the environmental protection effect in the first period is . In the second period the coefficient of the environmental protection effect is SI (¼ þ "SI) in the simultaneous mode, and the coefficient of the environmental protection effect is SE (¼ þ "SE) in the sequential investment mode, where "SI4"SE40. The parameter "jis an externality in the environmental protection investment, where j ¼SI or SE. Furthermore, "SI4"SE40 indicates that the externality in the simultaneous investment mode is larger than that in the sequential investment mode. Many political economists have proposed that the central government should establish a reward system to encourage the local government to achieve a good performance. Hence we assume that if the environ-mental protection effect is more significant, then the local government can obtain a bigger reward. Besides, the reward is also a function of the proportion of the population. Define the parameter u as the proportion of the population in the area of GOV A and the proportion of population 1 u in the area of GOV B, where u 2 [0, 1]. Following the idea of Grossman and Helpman (1994), we assume that the local govern-ment maximizes the revenue function.
Solution in the third stage
In this stage, the local government decides the optimal environmental protection investment quantity.
Simultaneous investment mode. According to the model setup, in the first period the revenue functions of GOV A and GOV B are RSI
A1¼u[(mA1þsSI)1/2þ
(mB1þsSI)1/2] mA1, and RSIB1¼(1 u)[(mA1þsSI)1/2þ
(mB1þsSI)1/2] mB1, where sSIis a subsidy from the
central government in the case of the simultaneous investment mode. In the second period, the revenue
functions of GOV A and GOV B are RSI
A2¼ u½SIm1=2 A2 þSIm 1=2 B2 mA2, and RSIB2¼(1 u) ½SIm1=2 A2 þSIm 1=2
B2 mB2. We obtain the two local
governments’ optimal investment quantities in the first period as mSI
A1¼(u/2) 2
sSI and mSI B1¼
((1 u)/2)2sSI. The optimal investment quantities in the second period are mSI
A2¼(u SI /2)2 and mSI B2¼((1 u) SI
/2)2. Hence the reduced forms of GOV A’s and GOV B’s revenue functions for the two periods, i.e. RSI i ¼RSIi1 þrRSIi2, are: RSIA ¼2u u 2 4 ½ 2þrðSIÞ2 þsSI ð1Þ RSIB ¼1 u 2 4 ½ 2þrðBSIÞ2 þ sSI ð2Þ
where r is the discount factor, and r 2 [0, 1].
Sequential investment mode. In the first period, the revenue functions of GOV A and GOV B are RSE
A1¼
u[(mA1þsSE)1/2þ(sSE)1/2] mA1, and RSEB1¼
(1 u)[(mA1þsSE)1/2þ(sSE)1/2], where sSE is
a subsidy from the central government in the case of the sequential investment mode. In the second period, the revenue functions of GOV A and GOV B are RSEA2¼u½SEm1=2A2 þSEm1=2B2 mA2, and RSEB2¼
(1 u)½SEm1=2A2 þSEm1=2B2 mB2. The optimal
invest-ment quantities that we obtain in the first period are mSEA1¼(u/2)2sSEand mSE
B1¼0. The optimal
invest-ment quantities in the second period are mSE A2¼
(uSE/2)2and mSE
B2¼[(1 u) SE
/2]2. Hence the reduced forms of GOV A’s and GOV B’s revenue functions for the two periods, i.e. RSE
i ¼RSEi1 þrRSEi2 , are: RSEA ¼upffiffiffiffiffiffiffisSEþsSEþu22þrð2u u2ÞðSEÞ 2 4 ð3Þ RSEB ¼ ð1 uÞ pffiffiffiffiffiffiffisSEþu 2 2 þrð1 þ uÞ SE 2 2 " # ð4Þ We find that in the first stage the environmental protection investment quantity of the local ment is a decreasing function of the central govern-ment’s subsidy. The more subsidies there are from the central government, the less that a local government will invest. Subsidies for the environmental protec-tion investment from the central government cause
the local governments to adopt free-riding behaviour. Hence we obtain the following proposition:
Proposition 1: Subsidies for the environmental protection investment from the central government cause the local governments to exhibit free-riding behaviour.
Solution in the second stage
In this stage we attempt to find the optimal investment mode, which is either the simultaneous investment mode or the sequential investment mode. Because GOV A invests in the first period, GOV B is the key decider of the investment mode. If RSI
B4(5)RSEB , then the optimal investment
mode is simultaneous (sequential). By letting RSI
B RSEB 40, the condition must be satisfied as
follows: ð1 uÞ2þrð1 þ uÞ ð SIÞ2 ðSEÞ2 þ4 s SI 1 ub ffiffiffiffiffiffiffi sSE p 4 0 ð5Þ
The first item and the second item on the left-hand side of Equation 5 are positive. If the third item on the left-hand side of Equation 5 is positive, then sSI4(1 u)pffiffiffiffiffiffiffisSE. This implies that if the subsidy
in the simultaneous investment mode is large, then the local governments prefer the simultaneous investment mode. On the contrary, if the subsidy in the sequential investment mode is large enough to cover the first term and the second term, then the local governments prefer the sequential investment mode. Hence the local governments’ investment preference is affected by the magnitude of the investment subsidy from the central government and the magnitude of the investment externality.
Solution in the first stage
In this stage, the central government decides the optimal investment subsidy.
Simultaneous investment mode. In this stage the central government chooses the optimal subsidy to maximize the environmental protection effect, i.e. ESI¼E1SIþrESI2 , where ESI1 ¼ðmSIA1þsSIÞ1=2þ
ðmSIB1þsSIÞ1=2, and ESI2 ¼SIðmSIA2Þ1=2þSIðmSIB2Þ1=2. The optimal subsidy for the central government is sSI*¼0. The reduced form of the environmental protection effect for the two periods is:
ESI¼2=2 þ ðr=2ÞðSIÞ2 ð6Þ
Sequential investment mode. In this mode, the function of the environmental effect for the two periods is ESE¼ESE1 þrESE2 , where ESE1 ¼ðmSEA1þ sSEÞ1=2þðmSE B1þsSEÞ 1=2, and ESE 2 ¼SEðmSEA2Þ 1=2þ SEðmSE
B2Þ1=2. The optimal subsidy for the central
government is sSE*¼(u/2)2. The reduced form of the environmental protection effect for the two periods is: ESE¼u2þ ðr=2ÞðSEÞ2 ð7Þ From Equations 6 and 7, if ESI4ESE, then the central government prefers the simultaneous investment mode. On the contrary, if ESI5ESE, then the central government prefers the sequential investment mode. The condition that the central government prefers the simultaneous mode is:
ESIESE¼ ½ð1=2Þ u2þ ðr=2ÞðSIþSEÞðSISEÞ ¼ ½ð1=2Þ u2þ ðr=2Þð2 þ "SIþ"SEÞ
ð"SI"SEÞ4 0 ð8Þ
Substituting sSI*¼0 and sSE*¼(u/2)2 into Equation 5 and rearranging it, we obtain the condition that the local government prefers the simultaneous investment mode as follows:
RSIB RSEB ¼ ð1 3uÞ2þrð1 þ uÞðSIþSEÞðSISEÞ ¼ ð1 3uÞ2þrð1 þ uÞð2 þ "SIþ"SEÞ
ð"SI"SEÞ4 0 ð9Þ
III. Inconsistent Preferences in the Environmental Protection Investment In this section, we examine the problem of an inconsistent investment preference in environmental protection.
It can be easily checked from Equations 8 and 9 that if "SI"SE¼0 then the intercept terms of the curves ESIESE¼0 and RSI
B RSEB ¼0 are 1/2 and
1/3, respectively. Furthermore the slope of the curve ESIESE¼0 is always larger than the slope of the curve RSI
B RSEB ¼0. In other words, there is no
intersection between the curve ESIESE¼0 and the curve RSI
B RSEB ¼0. The relationship between
the two curves in the geometric figure can be shown in Fig. 1.
In Fig. 1, regimes I and III are areas in which the central government and the local governments have the same investment preference. In regime I (III), both of them prefer the simultaneous (sequential) investment mode. However, regime II is a preference inconsistent area. In this area, the central government prefers the simultaneous investment mode and the
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M.-C. Chang and J.-L. Hu
local governments prefer the sequential investment mode. Hence we have the following proposition: Proposition 2: It is possible to have inconsistent preferences in the environmental protection investment between the central government and the local govern-ments; besides, the equilibrium where the central government prefers the sequential investment mode and the local governments prefer the simultaneous mode does not exist because of the free-riding behaviour of the local governments.
In Fig. 1, we also find that when the externality of the simultaneous investment mode is large, the central government prefers the simultaneous investment mode. If the proportion of the reward that the local government B obtains (i.e. 1 u) is small, then the local governments prefer the sequential investment mode. Hence if the externality of the simultaneous investment mode is large and the proportion of the reward that the local government B obtains is small, then both of them have an inconsistent investment preference. We then have the following proposition:
Proposition 3: The investment preference
inconsistency is the cause of a small proportion of the reward that the critical local government obtains and the greater externality in the simultaneous invest-ment mode.
IV. Solution of the Inconsistent Preferences in the Environmental Protection Investment
In a contract mechanism, the penalty can punish the player that violates the contract in order to ensure that the contract can work. In Fig. 1, regime II is an
area of inconsistent preferences in environmental protection investment. In regime II, GOV B selects the sequential investment mode. However GOV B’s preference violates the central government’s prefer-ence. Hence the central government should set a penalty to make GOV B invest in the first period.
In regime II, the payoff for GOV B in the sequential investment mode is higher than that in the simultaneous investment mode, i.e. RSEB 4 RSIB. If two local governments agree on a simultaneous investment contract and the penalty that violates the contract is Z RSE
2 RSI2 , then GOV B will abide
by the simultaneous investment contract. Hence the central government can encourage the local govern-ments to negotiate a simultaneous investment contract and to set a penalty for solving the problem regarding the inconsistent investment preference.
V. Conclusion
This study uses a two-period, three-stage game to discuss the issue of the inconsistent preference in environmental protection investment. We find that if the central government increases its subsidy in relation to environmental protection investment, then the local government will decrease its investment in environ-mental protection. In other words, the local govern-ments exhibit free-riding behaviour in their environmental protection investment, and the central government’s investment preference is affected by the externality of the investment mode. If the externality of the simultaneous investment mode is large, then the central government will prefer the simultaneous investment mode. Hence, it is possible to have an inconsistent investment preference between the central government and the local governments. The reasons that give rise to the inconsistent invest-ment preference between the central governinvest-ment and the local governments are the large externality that arises from the simultaneous investment mode and the small proportion of the reward that the critical local government obtains. However there is no such equilibrium in which the central government prefers the sequential investment mode and the local govern-ments prefer the simultaneous investment mode.
Acknowledgements
The first author gratefully acknowledges the financial support provided by Taiwan’s National Science Council (NSC 95-2415-H-424-001). 1 0 u 1/2 1/3 ESI– ESE= 0 RBSI– RBSE= 0 εSI−εSE
Fig. 1. Investment preference in environmental protection
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