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Siting noxious facilities: A siting lottery with victim compensation
IOURNAL
OF URBAN
ECONOMICS
31, 360-374 (1992)
Siting Noxious Facilities: A Siting Lottery with Victim Compensation ARTHUR M. SULLIVAN Graduate School of Management, and Department of Economics, University of California, Davis, California 95616
Received June 14, 1990; revised October 15, 1990 This paper proposes a scheme to facilitate the siting of noxious facilities. A regional government announces that it will (a) use a lottery to choose a site for a noxious facility and (b) transfer income from tenants to host-city landowners to at least partly offset the effects of the noxious facility on local property values. The government will hold the lottery only if all citizens agree, in advance, to abide by the resulting siting decision. The lottery approach is superior to the conventional approach to siting (advance notification) in the sense that the lottery approach achieves unanimous support for the siting decision with less compensation. The compensation scheme can be financed with a regionwide tenant tax or a tax on residents in the nonhost city. For “small” compensation programs, the nonhost tax k SUperiOr t0 the regional tax. 0 1992 Academic Press, Inc.
1. INTRODUCTION This paper proposes a scheme to solve the problem of siting noxious facilities. The siting problem occurs when a facility that would generate positive net benefits for a region is opposed by people who own land near the noxious facility. Although the local losses (decreases in property value) are dominated by the regional benefits of the facility, landowners in the host city often exercise veto power and prevent the siting of the efficient facility. One approach to facilitate siting is to transfer some of the regional benefits of the facility to host-city landowners. Economists and policymakers have proposed a number of schemes to facilitate the siting of noxious facilities. Under the conventional approach, the regional government picks a site and then negotiates a compensation package for host-city landowners. For a discussion of the various compensation schemes designed to support this conventional approach, see [l-4]. Under the siting scheme proposed in this paper, the regional government offers its citizens the following siting game. The government will use a lottery to pick a site for the noxious facility, and then transfer income from tenants to host-city landowners to at least partly offset the losses in property value caused by the noxious facility. The government will run the game only if all citizens in the region agree in advance to abide by the siting decision. The trick is to develop a compensation program that 360 0094-1190/92 $5.00 Copyright All rights
0 1992 by Academic Press, Inc. of reproduction in any form reserved.
SITING NOXIOUS FACILITIES
361
generates unanimous support for the siting lottery. The task is complicated by the fact that most types of victim compensation distort location choices and thus cause inefficiency (see [5, 41). The objective of the regional government is to choose the compensation scheme that achieves unanimous support in the most efficient manner. The paper produces three basic results. First, the lottery approach is superior to the conventional approach (advance notification) because the lottery approach achieves unanimous support for the facility with less compensation-and thus less distortion of location decisions. Second, the welfare effects of the siting game depend on how the compensation program is financed. Two financing schemes are considered: a tax on tenants throughout the region, and a tax on tenants outside the host city. Although the nonhost tax distorts location choices, it is a more powerful redistributional tool, so it may be more efficient than the nondistortionary regionwide tax. I use a simple computational model of a two-city regional economy to show the third result of the paper: for “small” compensation schemes (those involving relatively small transfers to host-city landowners), the tax on nonhost tenants is superior to the regional tax. 2. THE MODEL AND THE MARKET EFFECTS OF THE SITING DECISION This section outlines a simple model of open cities in a closed region. The population of the region is exogenous, but the population of each city is endogenous. Households in the region can move between cities within the region at zero cost, but cannot leave the region. In Section 6, I explain how the results of the paper change when the assumption of perfect intercity mobility is dropped. The closed-region model has been used by Sullivan [6] to consider the intercity effects of the industrial property tax, by Scotchmer [7] to consider the intercity effects of the provision of local public goods, and by Sullivan [4] to consider the spatial effects of conventional victim ccqpensation schemes. Consider a two-city region with a fixed number of identical households. Each household maximizes a utility function of the form
(1) where Pd is the price of housing, P, is the price of the good produced by the noxious facility, P, is the price of a numeraire good, Y is net income (the sum of exogenous labor income and governmental transfers), and E is exposure per household to pollution. Each household chooses quantities of housing, the noxious good, and the numeraire good. In addition, each
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household chooses a city. For locational equilibrium, each household must be indifferent among all cities in the region, so in equilibrium, the two cities generate the same utility level: V” = Vh (“/z” for host city and “n” for nonhost city). In the initial equilibrium, the two cities are identical. I assume that each city has the same exogenous land area. Before the noxious facility appears in the region, X is imported to the region at a relatively high price, and there is no pollution: E” = Eh = 0. The prices of X and Z are the same in both cities, and there are no governmental transfers, so Y” = Yh. For locational equilibrium (V” = Vh), the two cities must have the same price of housing. Housing is produced with the same technology and the same input prices throughout the region, so the fact that the two cities have the same price of housing means that they also have the same price of land (land is the residual claimant). Therefore, the two cities have the same population density, meaning that the region’s fixed population is divided equally between the two cities: N = H. The noxious facility produces X, a good consumed throughout the region. Suppose that the siting of the noxious facility decreases the price of X: instead of importing X at a relatively high price, the residents of the region purchase X from the regional facility at a lower price. The market price of X equals the marginal social cost of production within the region, which equals the sum of the exogenous marginal private cost of production (p’) and the marginal external cost of production (the Pigouvian externality tax): P,=MSC=p’+e’.P;H,
(2)
where P, is the monetized value of the marginal disutility of pollution and e’ is the exposure to pollution per household per unit of output. The revenue from the externality tax is redistributed, in lump-sum fashion, to all residents of the region. The siting of the noxious facility affects tenant-consumers in two ways. First, it decreases P,, so it increases utility throughout the region. Second, it decreases the environmental quality in the host city: exposure per household rises from zero to Eh = e’ * X,
(3)
where X is the output of the noxious facility. Therefore, the utility level of the host city decreases relative to the utility level in the other city, causing
SITING
NOXIOUS
363
FACILITIES
Utility Level
-.----.-v n’ &
.-.-
.-.-. --.-
.-.-
---.
-
.-.-.-“’
-_-_-.-_
,_
V*
Vh’
““!
\
j
Vh H'
Populnmn
-
Population
of Nonhost City
FIG. 1. Distribution
H*
of population
of Host City
before and after siting.
migration from the host city. The intercity migration decreases the prices of housing and land in the host city and increases prices elsewhere. Figure 1 shows the effects of the siting decision on the distribution of population between the two cities. The horizontal axis measures the number of households (tenants) in the individual cities, and the vertical axis measures the utility level. The utility curves are negatively sloped because an increase in the population of a particular city increases the prices of housing and land, decreasing utility. In the presiting equilibrium, the two utility curves (Vh(H) and V”(N)) are identical, and equilibrium (equal utility) occurs when the two cities have the same population. The siting decision shifts both utility curves upward, to Vhf and I/“‘, with a larger shift in the nonhost city. Locational equilibrium is restored with a higher regionwide utility level (V’ instead of V*) and a shift in population to the nonhost city: the population of the nonhost city increases from N* to N’, and the population of the host city drops from H* to H’. Although the environmental quality is lower in the host city, the prices of housing and land are low enough to make households indifferent between the two cities. The utility level of landowners depends on their net income, defined as rental income plus any transfer payments from the regional government. Figure 2 shows the landowners’ utility function. The utility function is concave from below, reflecting the assumption of diminishing marginal utility of income. The siting of the noxious facility increases land rent in
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Income FIG. 2. Income and utility of landowners.
the nonhost city (from I* to ZJ and decreases rent in the host city (from I* to ZJ. As pointed out by Sullivan [4], the changes in land rent sum to zero if the utility function of tenants is separable, so the income losses of host-city landowners equal the gains of nonhost landowners. In the absence of compensation, the utility of landowners in the nonhost city would increase from U” to U,,, and the utility of host-city landowners would decrease from U” to U,,. If the site for the noxious facility is to be determined by a lottery, the expected utility of landowners depends on rental income in both cities. Expected utility is defined as
EU= +U(Z,) + +U(Z,) = ;(Z,J' + +(I,)',
(4)
where the degree of risk aversion is (j3 - 1): if p = 1, risk aversion is zero. In the absence of compensation, the siting decision decreases expected utility from U* to U" (the utility level at the midpoint of the straight line connecting points a and e). Although the siting decision does not change the average rental income, it decreases expected utility because landowners are risk-averse. Figure 2 illustrates the siting problem. In a certain world in which the regional government simply announces its siting decision, the choice will
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be opposed by host-city landowners because their rental income drops from Z* to I,, decreasing their utility level from U* to U,,. If the government proposes a siting lottery without compensation, landowners oppose the siting game because it decreases their expected utility from CJ* to U”. 3. THE EFFECTS OF LANDOWNER
COMPENSATION
Landowner compensation can be used to persuade landowners to accept a siting decision or play the siting lottery. In a certain world in which the regional government simply announces its siting decision, there is unanimous support for the siting decision if host-city landowners are fully compensated for the losses in property value caused by the siting decision. In Fig. 2, the compensation payment must be at least (I* - Z,>. The lottery approach requires a smaller compensation payment to generate unanimous support for the siting process. Landowners support the siting lottery if it generates an expected utility of at least U" (the original utility level). In Fig. 2, this occurs if host-city landowners receive compensation of at least
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M. SULLIVAN
rental income rises from Z* to I”. The compensation program transforms a zero-sum change in landowner income (a decrease in expected utility) into a positive-sum change in income (an increase in expected utility). 4. THE EFFECTS OF THE TENANT TAXES This paper considers two means of financing the compensation program for host-city landowners: a tax on all tenants in the region, and a tax on tenants outside the host city. The two taxes differ in their redistributive power and their effects on location choices and the marginal social cost of the good produced by the noxious facility. Consider first the effects of the regional tax. The tax does not affect the relative attractiveness of the two cities, so it does not affect location choices. In Fig. 1, the regional tax would shift the two tenant utility functions down by the same amount, so the tax would not affect the distribution of population between the two cities. Therefore, it would not affect the price (marginal social cost) of the noxious good. The regional tax simply redistributes income from tenants to host-city landowners. The region’s tenants supporting the siting lottery if the benefit (the increase in utility from the decrease in the price of the noxious good) exceeds the cost (the decrease in utility from the income lost through the tax). Note that because the revenue from the Pigouvian tax is redistributed, in lump-sum fashion, to the region’s residents, the regionwide tenant tax is equivalent to a scheme under which the government uses the revenue from the Pigouvian tax to finance its compensation program. Consider next the effects of the tax on tenants outside the host city. The nonhost tax increases the relative attractiveness of the host city, causing migration that increases the price of land in the host city and thus at least partly offsets the losses in property value resulting from the siting of the facility. Because of these locational effects, the nonhost tax differs from the regional tax in two ways. First, the nonhost tax has greater redistributive power. Second, the nonhost tax causes locational inefficiency. Figure 2 shows that the nonhost tax has more redistributive power than the regional tax. Consider a regional tax that restores the presiting utility level U*, i.e., a tax that allows a transfer of
SITING
NOXIOUS
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FACILITIES
income (I”) is achieved with a smaller intercity difference in rental income. If one assumes that the switch from the regional tax to the nonhost tax does not affect the utility level of tenants, the nonhost tax is superior to the regional tax. The switch to the nonhost tax decreases tenants’ utility because it distorts location choices. The migration to the host city causes two types of locational inefficiency. First, migration increases the number of people exposed to the pollution generated by the noxious facility, increasing the price (marginal social cost) of the noxious good (see (2)). The increase in P, decreases consumer surplus for consumers throughout the region. Second, the migration causes a divergence between the equilibrium and optimum intercity distributions of population. Figure 3 shows that the second type of locational inefficiency increases with the size of the compensation program. The nonhost tax shifts the utility curve of the nonhost city down from V”’ to Vnu’,causing a new equilibrium with utility level V” and a transfer of population from the nonhost city to the host city of (N” - N’). One measure of the locational inefficiency of the tax is the gap between points b and c (the difference between V”’ and Vnw at N”): the gap equals the utility gain that could be realized if one tenant were transferred from the host city to the nonhost city. The larger the nonhost tax (the larger the compensation program), the larger the gap between b and c, so the larger the locational inefficiency of the nonhost tax.
Utility Level
““,~~..~..-‘::‘r-:“h, :: “Ii’ :::: :::: N’ H’ H”
N”
Population of Nonhost City
FIG. 3.
Locational
Popularion of Hosr City
inefficiency
of nonhost tax.
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ARTHUR
M. SULLIVAN
5. NUMERICAL RESULTS The numerical features of the computational model are as follows. The utility function of tenant-consumers is a Cobb-Douglas function with budget shares of 25% for housing, 10% for the good produced by the noxious facility, and 65% for the numeraire good. Housing is produced with capital and land with Cobb-Douglas production technology. The exponent of the expected utility function of landowners (B) is 0.75. Table 1 provides a summary of the numerical results. The siting decision decreases the population of the host city from 1000 to 432 and causes zero-sum changes in land rent in favor of nonhost landowners. The decrease in the price of the noxious good (from $10 to $5) increases the utility level of the region’s tenant-consumers, with a compensating variation of $17.39 per week (compared to an initial income of $400 per week). Landowners experience a loss in utility (measured as a compensating variation) of $23.99 per week (compared to an initial income of $400 per week). Columns 3 and 4 of Table 1 show the superiority of the lottery approach to the conventional approach. The two compensation schemes finance compensation with the nonhost tax, but one scheme uses a lottery and the other uses the conventional approach of advance notification. In both
TABLE 1 Numerical Results Unanimous support for siting
Variable Population Host city Nonhost city Price of noxious good Compensating variation Tenants Landowners Landowner income Host city Nonhost city Nonhost tax Price of land Host city Nonhost city
Initial equilibrium
Siting equilibrium
Nonhost tax: Lottery
Nonhost tax: Advance notification
1000 1000 10.0
432 1568 5.0
452 1548 5.03
554 1446 5.16
16.15 1.0
10.31 97.51
183 654 1.68
401 598 9.89
10.14 45.72
13.33 41.89
0 0 400 400 27.98 27.98
17.39 - 23.99 136 664 9.54 46.47
SITING
NOXIOUS
1
14
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FACILITIES
Frontter for
15
16
17
CompensatingVariation of Tenants FIG. 4.
Utility
possibility frontiers for regional tax and nonhost tax.
cases, the nonhost tax is just high enough to generate unanimous support for the siting process: under the lottery approach, the expected utility of landowners increases by a small amount (CV = $1); under the conventional approach, the net income of host-city landowners increases by a small amount relative to the initial equilibrium (Net income = $401). The lottery approach achieves unanimity with a lower tax ($1.68 per household instead of $9.89), a smaller population in the nonhost city (452 instead of 5541, and a lower price of the noxious good ($5.03 instead of $5.16). Figure 4 shows the utility possibility frontiers for the lottery approach under the two alternative taxes (the regional tax and the nonhost tax). The horizontal axis measures the weekly compensating variation for tenants (relative to the presiting equilibrium). The vertical axis measures the weekly compensating variation for landowners. For the relatively small compensation programs shown in Fig. 4, the utility possibility frontier of the nonhost tax lies above that of the regional tax. For the threshold compensation programs (which make landowners indifferent about the siting lottery), the nonhost tax is superior to the regional tax (points f and g). Although it’s not apparent from Fig. 4, the utility possibility frontier for the nonhost tax is concave from below. This occurs because the marginal distortionary cost of the tax increases with the size of the compensation program. The utility possibility frontiers of the two compensation schemes intersect at a combination of CWtenants) = 10.64 and CWlandowners) = 92.77; for larger compensation programs, the regional tax is superior to the nonhost tax.
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ARTHUR
M. SULLIVAN
Compensating Variation of Tenants
FIG. 5. Utility possibility frontiers for nonhost tax under different degrees of risk aversion.
Figure 4 also shows the utility possibility frontier for a compensation plan based on a system of land subsidies (for host-city landowners) and taxes (for nonhost landowners). Such a plan would increase the utility of landowners (by decreasing risk) without affecting tenants. The land tax/subsidy scheme is not among the many compensation schemes proposed by policy analysts (see [3]). The shapes and the positions of the utility possibility frontiers depend on the risk aversion of landowners. Figure 5 shows the utility possibility frontiers for the nonhost tax with three different values of l3: 0.50, 0.75, and 0.90. As S increases (as the degree of risk aversion decreases), the siting decision has a smaller negative effect on the expected utility of landowners, so a smaller compensation program is required to offset the negative effects of the facility. Less compensation is required to achieve given level of expected utility, so tenants will be better off (lower tax liability and less distortion of location decisions). In the limit (risk-neutrality among landowners), the zero-sum changes in rental income caused by the siting decision would not affect the expected utility of landowners, so a trivial compensation payment would be enough to generate unanimous support for the siting lottery. Therefore, the compensation variation of tenants would be just less than the amount associated with the siting decision ($17.39). 6. RELAXING THE ASSUMPTIONS The results of this paper depend on a number of assumptions. In this section, I discuss the implications of dropping four of the key assumptions: 1. The region is closed (no interregional migration). 2. Intercity moving costs are zero.
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3. Only the residents of the region benefit from the facility. 4. The pollution from the noxious facility does not vary within the host city. Consider first the assumption of a closed region. The model assumes that households move from the host city to another city in the region (a city that participates in the siting lottery). Suppose instead that some households leave the region, moving to a city outside the control of the government holding the lottery. This “leakage” from the regional economy means that the siting decision causes negative-sum changes in land rent in the lottery region: the decrease in land rent in the host city exceeds the increase in land rent in the nonhost city. In the model of the closed region, the lottery is effective (i.e., it requires less compensation) because it exploits the increases in land rent outside the host city and redistributes income, in a probabilistic sense, from the winners (landowners outside the host city) to the losers (landowners in the nonhost city). In the open region, the lottery is less effective because the leakages from the regional economy decrease the opportunities for this type of income redistribution. The efficacy of the lottery approach depends on its geographical scope. The larger the jurisdiction running the lottery, the smaller the leakages and the greater the opportunities to exploit the increases in property values outside the host city. One of the principles of public economics is that a political jurisdiction should be large enough to contain all the people who are affected by public policy. This principle applies to siting decisions and the lottery approach to the siting problem. The local approach to siting noxious facilities (trying to site a facility in a city without involving people outside the host city) usually fails because the local costs dominate the local benefits. The prospects for siting a noxious facility increase as more of the beneficiaries (people outside the host city) are involved in the process. Similarly, the efficacy of the lottery approach increases as the lottery is extended to include landowners outside the host city who benefit from the siting decision. In an open region, the taxes used to support the compensation program would distort location decisions. An increase in either the regionwide tax or the nonhost tax would cause migration to cities outside the region. The locational distortions would decrease the efficiency of any type of compensation program that is financed with taxes on households: these distortions would decrease the efficiency of both the traditional approach (advance notification and full compensation) and the lottery approach. The locational distortions from taxes in the open region will not affect the relative efficiencies of the two approaches. Consider next the assumption of zero moving costs. Suppose instead that moving costs are so high that the siting decision does not cause any
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migration from the host city to the nonhost city. In the immobile situation, there is no change in housing prices or land rent, meaning that (a) landowners are not affected by the siting decision and (b) the utility level in the nonhost city exceeds the utility level in the host city. Although it is possible for the siting to increase utility in the host city (if the decrease in the price of the noxious good is large relative to the pollution generated by the facility), suppose that the siting decision decreases utility in the host city. Under the assumption of zero moving costs (the original model), only landowners are affected by the siting decision. Under the assumption of perfect immobility, it is residents-not landowners-who are affected by the siting decision. In the case of perfect immobility, the lottery applies to residents, not landowners. If the facility is efficient from the regional perspective, the siting decision increases the average utility in the region. If residents are neutral with respect to risk, the expected utility from the lottery is positive, and residents require no compensation to play the siting game. If residents are averse to risk, they require some compensation, but less compensation than under the traditional approach (advance notification). In the intermediate case of moderate moving costs, the siting decision affects both residents and landowners. The utility of host-city residents decreases relative to the utility of other residents; rent in the host city decreases; rent in the nonhost city increases. If the utility of host-city residents increases in absolute terms, unanimous support for the facility could be achieved without involving residents in the lottery: as in the case described earlier, the lottery could be used to get host-city landowners to agree to play the siting game. If the siting decision decreases the utility of host-city residents in absolute terms, residents must be involved in the lottery. Consider next the assumption that the benefits of the noxious facility (the decrease in the price of the noxious good) are confined to residents of the region. In this paper, landowner compensation is financed with taxes on the region’s residents. Residents play the siting game if the benefits associated with a lower price for the noxious good dominate the costs associated with the taxes used for landowner compensation. To the extent that households outside the region benefit at the expense of households within the region, residents are less willing to pay taxes to support any type of compensation program. The leakage of benefits from the facility decreases the feasibility of both the traditional approach and the lottery approach. The leakage does not affect the relative advantage of the lottery approach: for a given benefit for the region’s residents, the lottery approach requires less compensation. Consider finally the assumption that the pollution generated by the facility does not vary spatially within the host city. A more reasonable
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NOXIOUS
FACILITIES
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assumption is that the exposure to pollution varies with distance from the facility, so that landowners closer to the facility experience larger decreases in property values. In principle, compensation could be tied to the losses in property values associated with the siting decision. Such a modification of the compensation scheme would not change the basic logic of the lottery approach. 7. CONCLUSIONS AND EXTENSIONS This paper suggests a new approach to the siting of noxious facilities. The lottery approach is superior to the conventional approach because it requires less compensation of host-city landowners. It requires less compensation because it exploits the fact that the siting decision increases land rent in the nonhost city and redistributes income, in a probabilistic sense, from the winners (landowners outside the host city) to the losers (host-city landowners). The paper considers two means of financing the compensation of host-city landowners: a regional tenant tax, and a tax on tenants outside the host city. The nonhost tax is a more powerful redistributional tool because it causes zero-sum changes in land rent. The nonhost tax also causes locational inefficiency. The nonhost tax will be superior to the regional tax if the locational inefficiency is relatively small. The numerical examples in the paper suggest that the nonhost tax may be superior to the regional tax for small compensation programs. How could the analysis be extended? First, one could relax the assumption that the price of the noxious good is independent of the siting decision. If there were spatial variation in the production costs for the noxious good and the regional government would normally pick the least-cost site, the lottery approach, which might pick an inefficient site for the facility, may be inferior to the conventional approach. As a second extension, one could consider alternative financing instruments. For example, the regional government could finance the compensation program with property taxes. Since part of the property tax would be a nondistortionary land tax, the property tax might be superior to the lump-sum nonhost tax. REFERENCES 1. R. Mitchell and R. Carson, Property rights, protest, and the siting of hazardous waste facilities, American Economic Reuiew, 76 (1986). 2. H. Kunreuther, P. Kleindorfer, P. J. Knez, and R. Yaksick, A compensation mechanism for siting noxious facilities: Theory and experimental design, Journal of Enuironmental Economics and Management, 14, 371-383 (1987). 3. U.S. Environmental Protection Agency, “Using Compensation and Incentives When Siting Hazardous Waste Management Facilities” (EPA 530,S.W 942, 1982).
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4. A. M. Sullivan, Victim compensation revisited: Efficiency versus equity in the siting of noxious facilities, Journal of Public Economics 41, 211-225. (1990). 5. W. J. Baumol and W. E. Oates, The Theory of Environmental Policy, 2nd ed., Cambridge Univ. Press, Cambridge (1988). 6. A. M. Sullivan, The general equilibrium effects of the industrial property tax, Regional Science and Urban Economics, 14,547-563 (1984). 7. S. Scotchmer, Local public goods in an equilibrium, Regional Science and Urban Economics, 16 463-482 (1986).
OF URBAN
ECONOMICS
31, 360-374 (1992)
Siting Noxious Facilities: A Siting Lottery with Victim Compensation ARTHUR M. SULLIVAN Graduate School of Management, and Department of Economics, University of California, Davis, California 95616
Received June 14, 1990; revised October 15, 1990 This paper proposes a scheme to facilitate the siting of noxious facilities. A regional government announces that it will (a) use a lottery to choose a site for a noxious facility and (b) transfer income from tenants to host-city landowners to at least partly offset the effects of the noxious facility on local property values. The government will hold the lottery only if all citizens agree, in advance, to abide by the resulting siting decision. The lottery approach is superior to the conventional approach to siting (advance notification) in the sense that the lottery approach achieves unanimous support for the siting decision with less compensation. The compensation scheme can be financed with a regionwide tenant tax or a tax on residents in the nonhost city. For “small” compensation programs, the nonhost tax k SUperiOr t0 the regional tax. 0 1992 Academic Press, Inc.
1. INTRODUCTION This paper proposes a scheme to solve the problem of siting noxious facilities. The siting problem occurs when a facility that would generate positive net benefits for a region is opposed by people who own land near the noxious facility. Although the local losses (decreases in property value) are dominated by the regional benefits of the facility, landowners in the host city often exercise veto power and prevent the siting of the efficient facility. One approach to facilitate siting is to transfer some of the regional benefits of the facility to host-city landowners. Economists and policymakers have proposed a number of schemes to facilitate the siting of noxious facilities. Under the conventional approach, the regional government picks a site and then negotiates a compensation package for host-city landowners. For a discussion of the various compensation schemes designed to support this conventional approach, see [l-4]. Under the siting scheme proposed in this paper, the regional government offers its citizens the following siting game. The government will use a lottery to pick a site for the noxious facility, and then transfer income from tenants to host-city landowners to at least partly offset the losses in property value caused by the noxious facility. The government will run the game only if all citizens in the region agree in advance to abide by the siting decision. The trick is to develop a compensation program that 360 0094-1190/92 $5.00 Copyright All rights
0 1992 by Academic Press, Inc. of reproduction in any form reserved.
SITING NOXIOUS FACILITIES
361
generates unanimous support for the siting lottery. The task is complicated by the fact that most types of victim compensation distort location choices and thus cause inefficiency (see [5, 41). The objective of the regional government is to choose the compensation scheme that achieves unanimous support in the most efficient manner. The paper produces three basic results. First, the lottery approach is superior to the conventional approach (advance notification) because the lottery approach achieves unanimous support for the facility with less compensation-and thus less distortion of location decisions. Second, the welfare effects of the siting game depend on how the compensation program is financed. Two financing schemes are considered: a tax on tenants throughout the region, and a tax on tenants outside the host city. Although the nonhost tax distorts location choices, it is a more powerful redistributional tool, so it may be more efficient than the nondistortionary regionwide tax. I use a simple computational model of a two-city regional economy to show the third result of the paper: for “small” compensation schemes (those involving relatively small transfers to host-city landowners), the tax on nonhost tenants is superior to the regional tax. 2. THE MODEL AND THE MARKET EFFECTS OF THE SITING DECISION This section outlines a simple model of open cities in a closed region. The population of the region is exogenous, but the population of each city is endogenous. Households in the region can move between cities within the region at zero cost, but cannot leave the region. In Section 6, I explain how the results of the paper change when the assumption of perfect intercity mobility is dropped. The closed-region model has been used by Sullivan [6] to consider the intercity effects of the industrial property tax, by Scotchmer [7] to consider the intercity effects of the provision of local public goods, and by Sullivan [4] to consider the spatial effects of conventional victim ccqpensation schemes. Consider a two-city region with a fixed number of identical households. Each household maximizes a utility function of the form
(1) where Pd is the price of housing, P, is the price of the good produced by the noxious facility, P, is the price of a numeraire good, Y is net income (the sum of exogenous labor income and governmental transfers), and E is exposure per household to pollution. Each household chooses quantities of housing, the noxious good, and the numeraire good. In addition, each
362
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household chooses a city. For locational equilibrium, each household must be indifferent among all cities in the region, so in equilibrium, the two cities generate the same utility level: V” = Vh (“/z” for host city and “n” for nonhost city). In the initial equilibrium, the two cities are identical. I assume that each city has the same exogenous land area. Before the noxious facility appears in the region, X is imported to the region at a relatively high price, and there is no pollution: E” = Eh = 0. The prices of X and Z are the same in both cities, and there are no governmental transfers, so Y” = Yh. For locational equilibrium (V” = Vh), the two cities must have the same price of housing. Housing is produced with the same technology and the same input prices throughout the region, so the fact that the two cities have the same price of housing means that they also have the same price of land (land is the residual claimant). Therefore, the two cities have the same population density, meaning that the region’s fixed population is divided equally between the two cities: N = H. The noxious facility produces X, a good consumed throughout the region. Suppose that the siting of the noxious facility decreases the price of X: instead of importing X at a relatively high price, the residents of the region purchase X from the regional facility at a lower price. The market price of X equals the marginal social cost of production within the region, which equals the sum of the exogenous marginal private cost of production (p’) and the marginal external cost of production (the Pigouvian externality tax): P,=MSC=p’+e’.P;H,
(2)
where P, is the monetized value of the marginal disutility of pollution and e’ is the exposure to pollution per household per unit of output. The revenue from the externality tax is redistributed, in lump-sum fashion, to all residents of the region. The siting of the noxious facility affects tenant-consumers in two ways. First, it decreases P,, so it increases utility throughout the region. Second, it decreases the environmental quality in the host city: exposure per household rises from zero to Eh = e’ * X,
(3)
where X is the output of the noxious facility. Therefore, the utility level of the host city decreases relative to the utility level in the other city, causing
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FACILITIES
Utility Level
-.----.-v n’ &
.-.-
.-.-. --.-
.-.-
---.
-
.-.-.-“’
-_-_-.-_
,_
V*
Vh’
““!
\
j
Vh H'
Populnmn
-
Population
of Nonhost City
FIG. 1. Distribution
H*
of population
of Host City
before and after siting.
migration from the host city. The intercity migration decreases the prices of housing and land in the host city and increases prices elsewhere. Figure 1 shows the effects of the siting decision on the distribution of population between the two cities. The horizontal axis measures the number of households (tenants) in the individual cities, and the vertical axis measures the utility level. The utility curves are negatively sloped because an increase in the population of a particular city increases the prices of housing and land, decreasing utility. In the presiting equilibrium, the two utility curves (Vh(H) and V”(N)) are identical, and equilibrium (equal utility) occurs when the two cities have the same population. The siting decision shifts both utility curves upward, to Vhf and I/“‘, with a larger shift in the nonhost city. Locational equilibrium is restored with a higher regionwide utility level (V’ instead of V*) and a shift in population to the nonhost city: the population of the nonhost city increases from N* to N’, and the population of the host city drops from H* to H’. Although the environmental quality is lower in the host city, the prices of housing and land are low enough to make households indifferent between the two cities. The utility level of landowners depends on their net income, defined as rental income plus any transfer payments from the regional government. Figure 2 shows the landowners’ utility function. The utility function is concave from below, reflecting the assumption of diminishing marginal utility of income. The siting of the noxious facility increases land rent in
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Income FIG. 2. Income and utility of landowners.
the nonhost city (from I* to ZJ and decreases rent in the host city (from I* to ZJ. As pointed out by Sullivan [4], the changes in land rent sum to zero if the utility function of tenants is separable, so the income losses of host-city landowners equal the gains of nonhost landowners. In the absence of compensation, the utility of landowners in the nonhost city would increase from U” to U,,, and the utility of host-city landowners would decrease from U” to U,,. If the site for the noxious facility is to be determined by a lottery, the expected utility of landowners depends on rental income in both cities. Expected utility is defined as
EU= +U(Z,) + +U(Z,) = ;(Z,J' + +(I,)',
(4)
where the degree of risk aversion is (j3 - 1): if p = 1, risk aversion is zero. In the absence of compensation, the siting decision decreases expected utility from U* to U" (the utility level at the midpoint of the straight line connecting points a and e). Although the siting decision does not change the average rental income, it decreases expected utility because landowners are risk-averse. Figure 2 illustrates the siting problem. In a certain world in which the regional government simply announces its siting decision, the choice will
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be opposed by host-city landowners because their rental income drops from Z* to I,, decreasing their utility level from U* to U,,. If the government proposes a siting lottery without compensation, landowners oppose the siting game because it decreases their expected utility from CJ* to U”. 3. THE EFFECTS OF LANDOWNER
COMPENSATION
Landowner compensation can be used to persuade landowners to accept a siting decision or play the siting lottery. In a certain world in which the regional government simply announces its siting decision, there is unanimous support for the siting decision if host-city landowners are fully compensated for the losses in property value caused by the siting decision. In Fig. 2, the compensation payment must be at least (I* - Z,>. The lottery approach requires a smaller compensation payment to generate unanimous support for the siting process. Landowners support the siting lottery if it generates an expected utility of at least U" (the original utility level). In Fig. 2, this occurs if host-city landowners receive compensation of at least
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rental income rises from Z* to I”. The compensation program transforms a zero-sum change in landowner income (a decrease in expected utility) into a positive-sum change in income (an increase in expected utility). 4. THE EFFECTS OF THE TENANT TAXES This paper considers two means of financing the compensation program for host-city landowners: a tax on all tenants in the region, and a tax on tenants outside the host city. The two taxes differ in their redistributive power and their effects on location choices and the marginal social cost of the good produced by the noxious facility. Consider first the effects of the regional tax. The tax does not affect the relative attractiveness of the two cities, so it does not affect location choices. In Fig. 1, the regional tax would shift the two tenant utility functions down by the same amount, so the tax would not affect the distribution of population between the two cities. Therefore, it would not affect the price (marginal social cost) of the noxious good. The regional tax simply redistributes income from tenants to host-city landowners. The region’s tenants supporting the siting lottery if the benefit (the increase in utility from the decrease in the price of the noxious good) exceeds the cost (the decrease in utility from the income lost through the tax). Note that because the revenue from the Pigouvian tax is redistributed, in lump-sum fashion, to the region’s residents, the regionwide tenant tax is equivalent to a scheme under which the government uses the revenue from the Pigouvian tax to finance its compensation program. Consider next the effects of the tax on tenants outside the host city. The nonhost tax increases the relative attractiveness of the host city, causing migration that increases the price of land in the host city and thus at least partly offsets the losses in property value resulting from the siting of the facility. Because of these locational effects, the nonhost tax differs from the regional tax in two ways. First, the nonhost tax has greater redistributive power. Second, the nonhost tax causes locational inefficiency. Figure 2 shows that the nonhost tax has more redistributive power than the regional tax. Consider a regional tax that restores the presiting utility level U*, i.e., a tax that allows a transfer of
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FACILITIES
income (I”) is achieved with a smaller intercity difference in rental income. If one assumes that the switch from the regional tax to the nonhost tax does not affect the utility level of tenants, the nonhost tax is superior to the regional tax. The switch to the nonhost tax decreases tenants’ utility because it distorts location choices. The migration to the host city causes two types of locational inefficiency. First, migration increases the number of people exposed to the pollution generated by the noxious facility, increasing the price (marginal social cost) of the noxious good (see (2)). The increase in P, decreases consumer surplus for consumers throughout the region. Second, the migration causes a divergence between the equilibrium and optimum intercity distributions of population. Figure 3 shows that the second type of locational inefficiency increases with the size of the compensation program. The nonhost tax shifts the utility curve of the nonhost city down from V”’ to Vnu’,causing a new equilibrium with utility level V” and a transfer of population from the nonhost city to the host city of (N” - N’). One measure of the locational inefficiency of the tax is the gap between points b and c (the difference between V”’ and Vnw at N”): the gap equals the utility gain that could be realized if one tenant were transferred from the host city to the nonhost city. The larger the nonhost tax (the larger the compensation program), the larger the gap between b and c, so the larger the locational inefficiency of the nonhost tax.
Utility Level
““,~~..~..-‘::‘r-:“h, :: “Ii’ :::: :::: N’ H’ H”
N”
Population of Nonhost City
FIG. 3.
Locational
Popularion of Hosr City
inefficiency
of nonhost tax.
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5. NUMERICAL RESULTS The numerical features of the computational model are as follows. The utility function of tenant-consumers is a Cobb-Douglas function with budget shares of 25% for housing, 10% for the good produced by the noxious facility, and 65% for the numeraire good. Housing is produced with capital and land with Cobb-Douglas production technology. The exponent of the expected utility function of landowners (B) is 0.75. Table 1 provides a summary of the numerical results. The siting decision decreases the population of the host city from 1000 to 432 and causes zero-sum changes in land rent in favor of nonhost landowners. The decrease in the price of the noxious good (from $10 to $5) increases the utility level of the region’s tenant-consumers, with a compensating variation of $17.39 per week (compared to an initial income of $400 per week). Landowners experience a loss in utility (measured as a compensating variation) of $23.99 per week (compared to an initial income of $400 per week). Columns 3 and 4 of Table 1 show the superiority of the lottery approach to the conventional approach. The two compensation schemes finance compensation with the nonhost tax, but one scheme uses a lottery and the other uses the conventional approach of advance notification. In both
TABLE 1 Numerical Results Unanimous support for siting
Variable Population Host city Nonhost city Price of noxious good Compensating variation Tenants Landowners Landowner income Host city Nonhost city Nonhost tax Price of land Host city Nonhost city
Initial equilibrium
Siting equilibrium
Nonhost tax: Lottery
Nonhost tax: Advance notification
1000 1000 10.0
432 1568 5.0
452 1548 5.03
554 1446 5.16
16.15 1.0
10.31 97.51
183 654 1.68
401 598 9.89
10.14 45.72
13.33 41.89
0 0 400 400 27.98 27.98
17.39 - 23.99 136 664 9.54 46.47
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1
14
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Frontter for
15
16
17
CompensatingVariation of Tenants FIG. 4.
Utility
possibility frontiers for regional tax and nonhost tax.
cases, the nonhost tax is just high enough to generate unanimous support for the siting process: under the lottery approach, the expected utility of landowners increases by a small amount (CV = $1); under the conventional approach, the net income of host-city landowners increases by a small amount relative to the initial equilibrium (Net income = $401). The lottery approach achieves unanimity with a lower tax ($1.68 per household instead of $9.89), a smaller population in the nonhost city (452 instead of 5541, and a lower price of the noxious good ($5.03 instead of $5.16). Figure 4 shows the utility possibility frontiers for the lottery approach under the two alternative taxes (the regional tax and the nonhost tax). The horizontal axis measures the weekly compensating variation for tenants (relative to the presiting equilibrium). The vertical axis measures the weekly compensating variation for landowners. For the relatively small compensation programs shown in Fig. 4, the utility possibility frontier of the nonhost tax lies above that of the regional tax. For the threshold compensation programs (which make landowners indifferent about the siting lottery), the nonhost tax is superior to the regional tax (points f and g). Although it’s not apparent from Fig. 4, the utility possibility frontier for the nonhost tax is concave from below. This occurs because the marginal distortionary cost of the tax increases with the size of the compensation program. The utility possibility frontiers of the two compensation schemes intersect at a combination of CWtenants) = 10.64 and CWlandowners) = 92.77; for larger compensation programs, the regional tax is superior to the nonhost tax.
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Compensating Variation of Tenants
FIG. 5. Utility possibility frontiers for nonhost tax under different degrees of risk aversion.
Figure 4 also shows the utility possibility frontier for a compensation plan based on a system of land subsidies (for host-city landowners) and taxes (for nonhost landowners). Such a plan would increase the utility of landowners (by decreasing risk) without affecting tenants. The land tax/subsidy scheme is not among the many compensation schemes proposed by policy analysts (see [3]). The shapes and the positions of the utility possibility frontiers depend on the risk aversion of landowners. Figure 5 shows the utility possibility frontiers for the nonhost tax with three different values of l3: 0.50, 0.75, and 0.90. As S increases (as the degree of risk aversion decreases), the siting decision has a smaller negative effect on the expected utility of landowners, so a smaller compensation program is required to offset the negative effects of the facility. Less compensation is required to achieve given level of expected utility, so tenants will be better off (lower tax liability and less distortion of location decisions). In the limit (risk-neutrality among landowners), the zero-sum changes in rental income caused by the siting decision would not affect the expected utility of landowners, so a trivial compensation payment would be enough to generate unanimous support for the siting lottery. Therefore, the compensation variation of tenants would be just less than the amount associated with the siting decision ($17.39). 6. RELAXING THE ASSUMPTIONS The results of this paper depend on a number of assumptions. In this section, I discuss the implications of dropping four of the key assumptions: 1. The region is closed (no interregional migration). 2. Intercity moving costs are zero.
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3. Only the residents of the region benefit from the facility. 4. The pollution from the noxious facility does not vary within the host city. Consider first the assumption of a closed region. The model assumes that households move from the host city to another city in the region (a city that participates in the siting lottery). Suppose instead that some households leave the region, moving to a city outside the control of the government holding the lottery. This “leakage” from the regional economy means that the siting decision causes negative-sum changes in land rent in the lottery region: the decrease in land rent in the host city exceeds the increase in land rent in the nonhost city. In the model of the closed region, the lottery is effective (i.e., it requires less compensation) because it exploits the increases in land rent outside the host city and redistributes income, in a probabilistic sense, from the winners (landowners outside the host city) to the losers (landowners in the nonhost city). In the open region, the lottery is less effective because the leakages from the regional economy decrease the opportunities for this type of income redistribution. The efficacy of the lottery approach depends on its geographical scope. The larger the jurisdiction running the lottery, the smaller the leakages and the greater the opportunities to exploit the increases in property values outside the host city. One of the principles of public economics is that a political jurisdiction should be large enough to contain all the people who are affected by public policy. This principle applies to siting decisions and the lottery approach to the siting problem. The local approach to siting noxious facilities (trying to site a facility in a city without involving people outside the host city) usually fails because the local costs dominate the local benefits. The prospects for siting a noxious facility increase as more of the beneficiaries (people outside the host city) are involved in the process. Similarly, the efficacy of the lottery approach increases as the lottery is extended to include landowners outside the host city who benefit from the siting decision. In an open region, the taxes used to support the compensation program would distort location decisions. An increase in either the regionwide tax or the nonhost tax would cause migration to cities outside the region. The locational distortions would decrease the efficiency of any type of compensation program that is financed with taxes on households: these distortions would decrease the efficiency of both the traditional approach (advance notification and full compensation) and the lottery approach. The locational distortions from taxes in the open region will not affect the relative efficiencies of the two approaches. Consider next the assumption of zero moving costs. Suppose instead that moving costs are so high that the siting decision does not cause any
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migration from the host city to the nonhost city. In the immobile situation, there is no change in housing prices or land rent, meaning that (a) landowners are not affected by the siting decision and (b) the utility level in the nonhost city exceeds the utility level in the host city. Although it is possible for the siting to increase utility in the host city (if the decrease in the price of the noxious good is large relative to the pollution generated by the facility), suppose that the siting decision decreases utility in the host city. Under the assumption of zero moving costs (the original model), only landowners are affected by the siting decision. Under the assumption of perfect immobility, it is residents-not landowners-who are affected by the siting decision. In the case of perfect immobility, the lottery applies to residents, not landowners. If the facility is efficient from the regional perspective, the siting decision increases the average utility in the region. If residents are neutral with respect to risk, the expected utility from the lottery is positive, and residents require no compensation to play the siting game. If residents are averse to risk, they require some compensation, but less compensation than under the traditional approach (advance notification). In the intermediate case of moderate moving costs, the siting decision affects both residents and landowners. The utility of host-city residents decreases relative to the utility of other residents; rent in the host city decreases; rent in the nonhost city increases. If the utility of host-city residents increases in absolute terms, unanimous support for the facility could be achieved without involving residents in the lottery: as in the case described earlier, the lottery could be used to get host-city landowners to agree to play the siting game. If the siting decision decreases the utility of host-city residents in absolute terms, residents must be involved in the lottery. Consider next the assumption that the benefits of the noxious facility (the decrease in the price of the noxious good) are confined to residents of the region. In this paper, landowner compensation is financed with taxes on the region’s residents. Residents play the siting game if the benefits associated with a lower price for the noxious good dominate the costs associated with the taxes used for landowner compensation. To the extent that households outside the region benefit at the expense of households within the region, residents are less willing to pay taxes to support any type of compensation program. The leakage of benefits from the facility decreases the feasibility of both the traditional approach and the lottery approach. The leakage does not affect the relative advantage of the lottery approach: for a given benefit for the region’s residents, the lottery approach requires less compensation. Consider finally the assumption that the pollution generated by the facility does not vary spatially within the host city. A more reasonable
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assumption is that the exposure to pollution varies with distance from the facility, so that landowners closer to the facility experience larger decreases in property values. In principle, compensation could be tied to the losses in property values associated with the siting decision. Such a modification of the compensation scheme would not change the basic logic of the lottery approach. 7. CONCLUSIONS AND EXTENSIONS This paper suggests a new approach to the siting of noxious facilities. The lottery approach is superior to the conventional approach because it requires less compensation of host-city landowners. It requires less compensation because it exploits the fact that the siting decision increases land rent in the nonhost city and redistributes income, in a probabilistic sense, from the winners (landowners outside the host city) to the losers (host-city landowners). The paper considers two means of financing the compensation of host-city landowners: a regional tenant tax, and a tax on tenants outside the host city. The nonhost tax is a more powerful redistributional tool because it causes zero-sum changes in land rent. The nonhost tax also causes locational inefficiency. The nonhost tax will be superior to the regional tax if the locational inefficiency is relatively small. The numerical examples in the paper suggest that the nonhost tax may be superior to the regional tax for small compensation programs. How could the analysis be extended? First, one could relax the assumption that the price of the noxious good is independent of the siting decision. If there were spatial variation in the production costs for the noxious good and the regional government would normally pick the least-cost site, the lottery approach, which might pick an inefficient site for the facility, may be inferior to the conventional approach. As a second extension, one could consider alternative financing instruments. For example, the regional government could finance the compensation program with property taxes. Since part of the property tax would be a nondistortionary land tax, the property tax might be superior to the lump-sum nonhost tax. REFERENCES 1. R. Mitchell and R. Carson, Property rights, protest, and the siting of hazardous waste facilities, American Economic Reuiew, 76 (1986). 2. H. Kunreuther, P. Kleindorfer, P. J. Knez, and R. Yaksick, A compensation mechanism for siting noxious facilities: Theory and experimental design, Journal of Enuironmental Economics and Management, 14, 371-383 (1987). 3. U.S. Environmental Protection Agency, “Using Compensation and Incentives When Siting Hazardous Waste Management Facilities” (EPA 530,S.W 942, 1982).
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4. A. M. Sullivan, Victim compensation revisited: Efficiency versus equity in the siting of noxious facilities, Journal of Public Economics 41, 211-225. (1990). 5. W. J. Baumol and W. E. Oates, The Theory of Environmental Policy, 2nd ed., Cambridge Univ. Press, Cambridge (1988). 6. A. M. Sullivan, The general equilibrium effects of the industrial property tax, Regional Science and Urban Economics, 14,547-563 (1984). 7. S. Scotchmer, Local public goods in an equilibrium, Regional Science and Urban Economics, 16 463-482 (1986).