Optimal and Second-Best Timing of Environmental Cleanups Jacob LaRivierea, Matthew McMahonb, and Justin Roushc August 2016

Abstract Yearly allocations to EPA Superfund cleanups are relatively fixed, but like other federal agencies, the EPA is given significant flexibility over where to clean sites that do not pose an immediate threat to human health. Given that Superfund cleanups are associated with local economic benefits, such as increased housing values, we show in a theoretical model that spatially heterogeneous economic conditions can influence the optimal and second-best timing of environmental cleanups. When a localized environmental problem is identified, there may be an incentive for the regulator to wait to clean it up in order to use cleanup funds at sites where immediate productivity gains from remediation are more valuable. Using carefully calibrated Monte Carlo simulations, we find that expected welfare costlessly increases by .05%-.25% at site locations (i.e., a 0.2%-1.0% increase in consumption) if the EPA were to account for economic criteria in ordering their cleanup decisions.

JEL Codes: Q52, Q58, H4 Keywords: Environmental Policy, Superfund, Government Spending, Countercyclical Policy

a

Senior Researcher, Office of the Chief Economist, Microsoft; Adjunct Assistant Professor, University of Tennessee; Affiliate Professor, University of Washington. Corresponding Author: Office of the Chief Economist, Building 99, Office 4623, Seattle, WA 98052. Phone: (425) 703-3085. Email: [email protected] b Assistant Professor, Department of Economics and Finance, University of Arkansas at Little Rock c Assistant Professor, Department of Economics and Finance, Georgia College & State University

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Introduction

Increased federal government spending will often increase economic activity in the location where it occurs. There are generally two effects of such government spending. One is a longrun effect if the government spending is associated with a durable fixed cost investment. The second is a short-run effect which temporarily increases economic activity. To this end, the federal government sometimes waits to spend discretionary funds on “shovel ready” projects like infrastructure improvements until a negative economic shock occurs. This can create a tension between making investments with large long-run net benefits immediately versus waiting to allow such projects to provide countercyclical spending. In the United States, for example, environmental remediation funded by the Environmental Protection Agency (EPA) can have stimulating effects on local economies. Recent research shows that cleaning a Superfund site causes a statistically significant increase in nearby house values of between 5%-25% (Gamper-Rabindran, Mastromonaco, and Timmins (2011) and GamperRabindran and Timmins (2013)).1 To this end, the EPA requires that plans for economic redevelopment be considered prior to remediation at each Superfund site.2 One (sometimes overlooked) feature of EPA remediation expenditures is that administrators have significant spatial flexibility in deciding where the money is spent. Removal actions for sites that pose an immediate threat to human health must be implemented upon discovery. Remaining sites are placed on the National Priorities List (NPL) for later remediation. However, there are significantly more cleanup sites than can be cleaned given available funds in any given year. As a result, the geographical distribution of spending on environmental remediation within and across years is subject to significant regulatory leeway. It is somewhat surprising, then, that there is no clear policy in place for allocating funds to Superfund and Brownfield sites which are eligible for

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These studies improve on the results of Greenstone and Gallagher (2008), who find that site cleanup has negligible increases on housing values, by utilizing the full distribution of housing values within a housing tract instead of the median housing value only. 2 The EPA set this requirement in the Superfund Amendments and Reauthorization Acts (SARA) of 1986 and strengthened its importance in the Land Use Directive of 1995 and the 2010 memorandum entitled, “Considering Reasonably Anticipated Future Land Use and Reducing Barriers to Reuse at EPA-lead Superfund Remedial Site.” All policy guiding reuse can be found at http://www.epa.gov/superfund/programs/recycle/policy/reuse.html.

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funds but pose no immediate risk to human health.3 This paper develops criteria for how the EPA can increase welfare by accounting for spatially heterogeneous economic impacts of their mandated, federally funded cleanups. We develop a simple Ramsey model based on Heutel (2012) to represent localized economies which are both eligible to receive remediation funds and are directly affected by waste.4 For these site-proximate communities, we model both a long-run and short-run effect of cleaning a site. In the long run, cleaning up a site acts to increase the productivity and wealth of the local economy. This dynamic reflects the well-documented empirical finding that remediation increases local wealth through two channels: site redevelopment and the removal of an environmental disamenity. The joint impact of these two channels can be observed through changes of local housing prices (Gamper-Rabindran and Timmins (2013) and Mastromonaco (2013)). Importantly, redevelopment planning for sites is an integral component of any environmental remediation. Remediation also has a short-run effect. Exogenous federal dollars enter the local economy through contracting with local firms. Very importantly, as occurs in practice, federal dollars are not repaid by the receiving area. Cleanup spending can be large relative to the 3 kilometer ball for which housing prices are affected (Gamper-Rabindran and Timmins (2013)) as opposed to the larger MSA in which the site is located. For example, if there is a Superfund site in Houston, we don’t claim that Houston’s economy is impacted overall; rather, we claim there is evidence for economic impacts within 3 kilometers of the site. We discuss evidence for this short-run modeling assumption at length below. The social planner’s problem in the model is to maximize expected welfare by optimally allocating funds across economically heterogeneous areas. We allow heterogeneity over three different economic variables, which are all easily observable to a regulator and display significant

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Similar lack of structure exists for other types of government spending which can have stimulating economic effects. Examples include Department of Education expenditures on new schools and educational programs and Department of Transportation spending on roads and infrastructure. For example, Leduc and Wilson (2012) conclude that transportation spending is associated with larger economic benefits than other types of government spending, but no structure is in place dictating the spatial allocation of spending on these projects. 4 Specifically, the scale of our model is within the 3 kilometer radius of a site, the distance identified by Gamper-Rabindran and Timmins (2013) as realizing increased housing prices after Superfund site cleanup.

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variation in the data: local economic volatility, the relative size of remediation funds to the local economy, and local discount rates (proxied by municipal bond yields). We study the impact of these three characteristics for multiple levels of the long-run effect of waste on local economies. We assume that each area is subject to an idiosyncratic chance of recession. Since yearly funds are limited, the opportunity cost of using a cleanup as a countercyclical policy is cleaning the site which would receive the largest economic benefit when in steady state. As a result, the regulator faces both temporal and spatial choices. Temporally, the regulator must decide for each site whether to clean now or to wait for a negative economic shock to hit the local economy; spatially, the regulator must decide across sites whether to prioritize sites based on short-run or long-run gains. Both of these choices depend on the site-specific variables mentioned above. We focus on this (joint) problem because it is the exact policy issue regarding fiscal federalism that is faced by regional EPA offices and many other US governmental agencies (e.g., the Department of Transportation) who are allocated a given amount of funding in a fiscal year. The problem of the optimal allocation of funding used for cleanups in general is a different but related problem we do not address in this paper.5 We first numerically solve for expected welfare as a function of different cleanup policies over a large range of parameter values, as calibrated based on empirics. Three policy relevant findings emerge from our model. First, and unsurprisingly, it is never optimal to wait to clean a site if funds are unlimited, even as a countercyclical stimulus. This is due to the long-run effect of cleanup on productivity. Second, in our model the most important economic criterion in ordering sites for cleanup is often the long-run opportunity cost of not cleaning. Specifically, areas in which waste is most harming long-run economic activity (e.g., most significantly lowering property values) should always be cleaned first. This second finding is our main contribution: even though we allow for extremely large (based on actual data) short-run economic stimulus effects, the long-run effects always dominate. Third, insofar as there is any countercyclical benefit to cleanup, when all areas are in steady state it is best to clean sites with low economic volatility,

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To this end, Hamilton and Viscusi (1999) finds that it may be optimal to simply fence off certain sites rather than pay the cost of cleanup when accounting for the opportunity cost of funds used to clean sites.

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high discount rates, and major long run-impacts of cleanup.6 Put another way, it is best to wait to clean areas with high volatility until they are in recession because the expected time to recession is low and thus the net present value (NPV) of the countercyclical effects of cleanup are relatively large, all else equal. Similary, high discount rates act to increase the net present value of cleaning now versus waiting. Importantly, though, these countercyclical effects are an order of magnitude lower than long-run economic effects. We then use carefully calibrated Monte Carlo simulations to calculate the magnitude of the expected welfare increase due to prioritizing site cleanups as suggested by our model. We initially calculate the first-best welfare from cleaning all sites immediately given no funding constraints. As a baseline for our policy relevant and financially constrained simulation, we assume that the government only has funds to cleanup roughly 5% of sites in any given year and does not account for economic criteria when cleaning.7 We choose 5% because remediation begins for roughly 5% of sites on the NPL in any given year. We then implement a second-best cleaning policy which maximizes expected welfare accounting for the previously discussed economic criteria. We find that ordering sites using our second-best policy yields an increase in the net present value of welfare by 18%-36% of the welfare gain that would result from the first-best policy of cleaning all sites immediately. Using the current policy as a counterfactual, we find that ordering sites using our second-best policy yields an increase in the NPV of expected welfare by .05% to .25% relative to ordering sites randomly with respect to the identified economic criteria; this is equivalent to roughly a 0.2%-1.0% increase in consumption. Importantly, these welfare gains are entirely free in that they only require strategic re-ordering of existing sites as a function of easily observable economic data. The majority of the difference in welfare between the first- and second-best cleanup strategies is due to the timing: in the first-best strategy, all cleanup occurs immediately (due to the lack of funding constraints), while in the

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We are not aware of any empirical work studying the short-run local economic impacts of EPA expenditures. However, the EPA claims there are such short-run economic benefits: http://www.epa.gov/region4/superfund/ sites/npl/featuredsite/gulfstatesalfeature.html (last retrieved June 15, 2014). Presumably, short-run benefits of cleanup are increasing in the size of cleanup cost since federal expenditures act as benefits to the local economy. 7 While the EPA does have criteria for ranking sites, none of them are economic in nature. We discuss these criteria in more detail in the next section.

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second-best case cleanup occurs over a number of years. In our sensitivity analysis, we find that gains from ordering sites are the greatest when long-run economic damages from environmental waste are the largest since welfare gains from cleanup are magnified in that scenario. Lastly, we find that at least 80% of the gains in welfare from accounting for economic criteria are due to the long-run effects of cleanup rather than any short-run countercyclical effects. While there is a literature on optimal timing of enacting environmental policy, such as pollution taxes as a function of economic activity or dynamic characteristics of the damage function, we are not aware of any research which examines the optimal timing of environmental cleanups or any other similarly mandated spending (Pindyck (2002), Fischer and Springborn (2011), Heutel (2012), and Sims and Finnoff (2012)). As a result, our paper adds to the economics literature in three ways. First, we link a literature on local economic benefits from government spending on Superfund sites to a literature on optimal timing of environmental policy. Second, we extend the Heutel (2012) model to allow for local economic heterogeneity and a long-run form of environmental damage associated with Superfund sites. Third, we find several easily implementable policy-relevant tools regulators can use to improve social welfare. Finally, we are careful to build our model conditioning on both insufficient funding to clean all sites immediately and the legal mandate in place that all sites must be cleaned. The larger economic question of whether it is optimal to clean a site, as is the current legal mandate, we leave to future work. Our results inform policy in several ways. First, it is costly for policy makers to ignore the longrun stimulus associated with environmental remediation. Strategically ordering Superfund and Brownfield sites using economic criteria would allow the EPA to increase welfare. Furthermore, these welfare increases are costless in that they only require reorganizing existing protocol according to the economic criteria we identify, all of which are widely available.8 In the face of non-economic criteria already used for site ordering, adding economic criteria (even if second-order in the decision-making process) will necessarily weakly increase welfare. To the extent that any changes to the status quo policy incur any fixed costs, our calibrated simulations provide a benefit estimate with which those fixed costs can be compared.

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This feature is similar to increasing educational attainment by accounting for peer effects in assigning students to classrooms (Duflo, Dupas, and Kremer (2011)).

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The economic criteria we identify could also be used in other areas with similarly structured federal spending. In areas ranging from transportation to education, there are funds which are temporally constrained but given significant spatial flexibility. Even if regulators have other conerns for any other projects, such as equality or distributional concerns, implementing secondary prioritization based on these criteria will always be weakly welfare-enhancing. Last, future work in applying these results to similarly structured federal spending should be careful to account for our result that long-run economic gains are more important than any possible short-run countercyclical effects. The remainder of this paper is organized as follows: Section 2 gives background information on our motivating example, environmental cleanups in the US, providing some summary statistics and placing the current paper in context with previous literature. Section 3 introduces the model. Section 4 presents the model’s findings and offers some illustrative calibrated simulations. Section 5 briefly concludes and offers suggestions for future research.

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Background

This section discusses the key features of environmental cleanup funds. Critically, these funds are both temporally rigid and spatially flexible, and they have also been shown to improve local economic conditions by increasing land values. However, the EPA does not use any economic criteria when ordering sites for remediation. Superfund was established in 1980 by the Comprehensive Environmental Response, Compensation and Liability Act (CERCLA). It provides the EPA with the federal authority and the financial resources to clean and secure both releases and threatened releases of substances from abandoned waste sites. In order to improve the quality of Superfund cleanups, the Superfund Amendments and Reauthorization Act (SARA) was passed in 1986, which called for the planning of commercial and public-use site redevelopment prior to remediation, thereby ensuring Superfund cleanups have lasting positive economic impacts (Hamilton and Viscusi (1999)). There is a well-defined process to list and remediate a waste site under CERCLA. The EPA uses the Hazardous Ranking System (HRS) to assign a score between 0 and 100 to each site. This ranking is based on five explicit criteria (extent of risk to the exposed human population, 7

contaminant stability, contaminant characteristics, threat to a significant environment, and program management considerations) with four possible pathways of contamination (groundwater, surface water, soil, and air). Sites with scores above a lower threshold are placed on the National Priorities List (NPL) to be cleaned. Sites that pose an immediate threat to human health, however, bypass this and receive immediate cleanup funding. Hence, sites on the NPL do not pose an immediate health hazard to humans. The results of this paper do not suggest altering decisions regarding sites that pose immediate harm to humans. Rather, the results are meant to guide prioritization of sites on the NPL. The EPA oversees 10 regional offices and delegates cleanup mobilization decisions to these regions. The EPA regional offices receive annual appropriations from the EPA headquarters to distribute among the sites on the NPL in their region. For new construction activities, funding priorities are established via a panel that selects sites based on the same five criteria used for HRS scoring and a “feasibility study” which predominantly involves assessing costs. There are nine final criteria the EPA uses in deciding which site is selected for remediation off the NPL list: overall protection of human health and the environment; local laws; long-term cleanup effectiveness and permanence; reduction of toxicity, mobility, or volume; short-term effectiveness; implementability; cost; state acceptance; and community acceptance. According to the EPA’s own criteria, then, the EPA does not prioritize site cleanups based upon local economic conditions nor the magnitude of long-run economic impact from cleanup even though there is no law preventing it.9 Further, it is not evident that short-run or long-run benefits to cleanup are correlated in any way with any of the nine final criteria associated with remediation. To that end, cleanup is likely to be random with respect to both local economic

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If this is indeed already taking place, then it should be evident empirically. Burda and Harding (2014) found that while there were initially biases against black, urban, and lower educated neighborhoods on the external margin (selection of NPL sites to begin cleaning), these biases seem to disappear over time, especially following a 1994 executive order that officially recognized Environmental Justice as an active policy concern. Gupta, van Houtven, and Cropper (1996) look at several factors that potentially affect allocation decisions on the internal margin (quality/permanence of cleanup). They find no evidence that the EPA discriminates on the internal margin against sites due to nearby racial composition or to either average or median income level. They do find evidence, however, that the EPA discriminates against higher cleanup costs. As previously disscussed, we assume that the EPA allocates funds orthogonally to cleanup costs and local economic criteria. However, if the EPA does discriminate against higher cleanup costs, then our estimates of the short-run impact of cleanup offer lower bound inference on what the true impact of considering all sites would be.

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Figure 1: Yearly federal appropriation to site remediation in the US from 2001-2011. conditions and the magnitude of long-run economic impact from cleanup. The flexibility present in NPL cleanup guidelines allows for the possibility that the EPA may also incorporate other variables into the allocation process since there is no immeditate threat to human health. In sum, regional offices have significant flexibility over where to spend their yearly budgets within the region. Yearly Superfund expenditures are large, relatively constant over time, and insufficient to meet all site cleanup needs in the United States. Figure 1 shows the level of obligations on site cleanup since 2001.10 Average yearly allocations are roughly $2 billion over the last ten years, spread over roughly 300 sites per year. Still, the NPL is long; as of October 12, 2012, there were 1313 sites remaining on the NPL with another 54 proposed for listing.11 When the EPA decides to clean a site, each aspect of the remediation process is contracted out to private companies. This creates an immediate one-time transfer payment from the federal level directly to the contractor. There is significant heterogeneity in individual contracts within

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According to http://www.usaspending.gov, a website that catalogues all government contracts, the total government obligation for Hazardous Waste, Clean-up & Disposal Services & Operational Support (contract code F108) was $1.7 billion in 2011, which is around $225,000 per contract. These figures do not include funds secured through private party commitments, which were estimated to total $1.6 billion from in FY2013 (EPA National Accomplishments Summary). Additionally, each site attracts numerous contracts throughout remedial action. The EPA lists 61 sites that began remedial action in 2011. These values are before any deobligations. 11 A full list of final and proposed sites by region can be found at http://www.epa.gov/superfund. A summary of historical activity is here: http://www.epa.gov/superfund/accomp/17yrrept/report2.htm.

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and across Superfund sites. Figure 2 demonstrates a large right tail in the distribution of contract sizes awarded over the last ten years. The sum of all contracts for any individual site is also large. Although the EPA looks for alternative programs and agencies as well as individual state programs for primary cleanup efforts, it is required to remediate the site even if no responsible party can be identified. In all cases, they maintain control of the program throughout the cleanup process.12 The location of these contractors, especially for smaller contracts, is near cleanup sites. For larger contracts, however, contractors are often located hours away from the remediation site.13 Still, as Figure 1 demonstrates, there are a significant number of large contracts, providing evidence that individual subcontracts to local firms can be large. If the contract (or subcontract) is awarded to a local firm, this transfer acts as a short-run benefit to the local economy through many channels (firms hire local workers, buy capital, etc.). Importantly, the locality does not repay these cleanup funds to the federal government. Thus, a federal government expenditure arrives at the local level as a benefit. It is legally mandated that this expenditure must occur, and thus it is viewed within the model of the local economy exclusively as a short-run benefit. There is a large literature that finds positive long-run localized economic impacts from Superfund site cleanup. It is commonplace to use housing values to proxy for the economic and wealth impacts of waste site remediation (Boyle and Kiel (2001)). Gamper-Rabindran, Mastromonaco, and Timmins (2011) find that the median house values increase by 15.4%. Both Gamper-Rabindran, Mastromonaco, and Timmins (2011) and Mastromonaco (2013) find that proximity of the household to the site accounts for significant heterogeneity in housing price increases across the distribution of home prices. In a case study, Kiel and Zabel (2001) estimate localized economic benefits from remediation ranging between $72-122 million. A meta-analysis

12 Moreover, the EPA may allocate funds to clean a site before seeking reimbursement from responsible parties. The EPA secured $292 million in reimbursements in FY2013. For a historical account of Superfund costs see Beider (1994). 13 We are not aware of any study which carefully documents the spatial distribution of Superfund remediation contractors. However, a simple search of EPA awards in the USA contracts database for remediation contracts (code F108) shows variation in contractor site proximity by contract size: http://www.usaspending.gov. For example, one large contract (∼ $30 million) to clean up the Calumet River system between Gary, Indiana and Chicago, Illinois was awarded to a conglomeration of three companies based in Wisconsin, Missouri and a proximate based in both Chicago and Indiana. In every case, though, contracts specify a “principal place of performance” where the contracted work must be performed (i.e., the remediation site).

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Figure 2: Distribution of obligation amounts for site remediation in the US from 2001-2011. These include only federal dollars spent at sites before any deobligations. The figure shows the distribution of individual contracts, not the sum of expenditures at given sites; there are generally multiple contracts per site. also found significant heterogeneity in long-run effects on price impacts (Kiel and Williams (2007)). Other research suggests a similar impact on industrial properties as well. Ihlanfeldt and Taylor (2004) show that industrial property values across Fulton County, Georgia depreciated by $56 million total in response to waste site discoveries. In sum, waste cleanup appears to increase the value of land capital in the immediate proximity of the cleanup site.

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Theoretical Model

In order to examine the variables that affect the optimal timing or ranking of cleanups, we construct a model in which the social planner chooses between cleaning when a local economy is in steady state or waiting for a recession to clean as a de facto stimulus. The model utilizes a similar approach to Heutel (2012), in which a central planner chooses consumption (c), as well as the cleanup timing, in order to maximize expected social welfare. We introduce the model’s

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steady state, then the mechanism for cleanup and recession dynamics, followed by the social planner’s timing problem. We model local economies using a continuous-time Ramsey framework and assume that each local economy is initially in steady state. A local economy can be thought of as the area immediately surrounding the Superfund site, such as the 3 kilometer ball around a Superfund site identified by Gamper-Rabindran and Timmins (2013). For example, if there is a Superfund site in Houston, we don’t claim that Houston’s economy is impacted overall; rather, we claim there is evidence for economic impacts within 3 kilometers of the site. We abstract from technical progress and population growth to simplify the analysis in our model:

Z max ct

∞

U (ct )e−θt dt

(1)

0

s.t. k˙ t = A(w)f (kt ) − ct

(2)

Equations (1) and (2) represent a simple Ramsey model augmented with a multiplicative productivity modifier, A(w). A(w) represents the productivity dampening effects of being near a waste site, where waste is represented by w. As a result, A(w) ∈ (0, 1]. A(w) is decreasing in w, where A(0) = 1 indicates the complete absence of waste. For any given level of A(w), there is a resultant steady state level of consumption, c∗ , and capital, k ∗ .

3.1

Cleanup Dynamics

Following Heutel (2012), an increase in environmental quality, in our case achieved via cleanup, acts to increase the productivity and equilibrium wealth in the local economy. We model a cleanup as having one short-run component and one long-run component. In the short run, when a site is remediated, the federal EPA dollars enter into the local economy as a temporary capital ¯ We model the short-run benefits as a capital injection as opposed to a government injection, k. transfer to the local economy in order to capture the fact that all federal cleanup funds must be spent on cleanup. That is, the local economy is not free to allocate cleanup funds between

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consumption and capital; they all must be dedicated to cleanup. As described above, it is possible that some of the capital injection for remediation could accrue to firms from outside the affected community. As a result, our measure k¯ represents only that spending which occurs in the local economy. While we are not aware of any empirical work studying the short-run local economic impacts of EPA expenditures, the EPA claims there are such short-run economic benefits. Federal spending projects (e.g., transportation projects), though, are generally thought to have have similar local stimulating effects as what we model here. In the model, while k¯ is a short-run effect, it has no long-run impact. We make a few simplifying assumptions to keep focus on the regulator’s opportunity to increase welfare by ordering sites along economic criteria. First, we assume that k and A(w) are orthogonal throughout this section. As we show in the simulations, however, the magnitude of k is second-order. Second, we abstract from the more general problem of the regulator splitting k across multiple sites to only partially clean a site. This assumption accords well with EPA remediation policy since a site is deleted from the NPL once it is fully cleaned. We assume the temporary capital injection is exogenous to reflect the reality that local economies do not have to repay federal cleanup funds. Third, in the theoretical exposition, we assume A(w) is constant across sites. In the simulation we perform sensitivity analysis over heterogeneity in A(w). Upon cleanup, waste in the local economy is eliminated. More formally, assume that precleanup waste is w0 > 0 and post cleanup waste levels are w1 = 0. This means that cleanup increases the productivity multiplier to unity, from A(w0 ) < 1 to A(w1 ) = A(0) = 1. In the long run, the higher level of productivity after cleanup implies that the economy will converge to a new higher steady state level of consumption, c∗1 , and capital, k1∗ . This modeling approach is motivated by the empirical finding that there is a documented increase in land values around cleanup sites implying that such land creates more wealth (Gamper-Rabindran, Mastromonaco, and Timmins (2011) and Gamper-Rabindran and Timmins (2013)). Insofar as land is a form of capital, its value should reflect its marginal productivity in equilibrium. As a result, in order for the value of land capital to increase (whether for residential

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or commercial use) the productivity of the resource must increase.14 Further, in the case of the EPA, superfund cleanup requires redevelopment plans that are specifically designed to facilitate increased economic productivity post cleanup.15 The short-run boost in capital may or may not outweigh the magnitude of the long-run increase in the steady state level of capital. There are potentially many factors that determine which increase is larger for a given project, like site location characteristics, the nature of site use post-remediation, the characteristics of the local economy, etc.16 When the short-run boost dominates, this is called overshooting; the initial capital increase overshoots the new equilibrium level, causing a subsequent decrease of the capital stock over time as it approaches its new equilibrium. The opposite situation is known as undershooting. For such a cleanup, the initial jump does not boost capital as high as the new equilibrium value. The capital stock subsequently increases over time as it approaches the new equilibrium level. Both overshooting and undershooting are shown in the top and bottom panels of Figure 3, respectively. Figure 3 plots consumption levels as a function of time for cleanup occurring upon discovery.17 Note that consumption’s time path follows a qualitatively similar time path to that followed by capital.18

14 We are not aware of any theoretical model which explains the increase in housing prices upon Superfund cleanup. More work along this dimension is needed in the literature. Our modeling strategy reflects the empirical findings of increased property values following cleanups. In our simple Ramsey model, higher steady state income and consumption can only be achieved by an increase in the total factor productivity parameter A(w), since increases to the prevailing capital stock would only increase consumption in the short run. By increasing the productivity parameter, the marginal rate of return of capital is higher. In the absence of the obvious capital injection from Superfund cleanup, economies substitute away from short-run consumption in favor of capital formation, resulting in increased long-run wealth and consumption. The additional capital injection serves to increase consumption and wealth in the short run as well. 15 By modeling individual local economies separately, there is an implicit assumption that capital is not mobile across economies. If capital were mobile, then an increase in productivity in an economy (via the elimination of waste) would draw in capital from elsewhere. This influx of capital would enter the model as another (or a series of future) exogenous capital increase(s). We abstract away from this second-order effect in our model. 16 These factors are all exogenous to the planner and are treated as such in the model. 17 For some sites, there is a considerable lag between (true) discovery and NPL listing. In those cases, “discovery” here means the period in which the site is listed and ready to be cleaned. 18 Overshooting and undershooting refer to short-run dynamics of the theoretical Ramsey model only and have nothing to do with cleanup per se, except for being related to the relative magnitude of long-run versus short-run economic effects.

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Figure 3: Long run dynamics of consumption when cleanup occurs upon discovery (t=0). The top panel shows the case of overshooting. The bottom panel shows the case of undershooting. ¯ The initial increase in consumption is due to the direct effect of the short run capital increase k.

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3.2

Recession Dynamics

Turning to recession dynamics, at each moment there is a constant probability, ρ, that each local economy could enter a recession. An intuitive way to think about the recession’s process is as the expected value of the first order statistic of a Poisson distribution in which the recession has some instantaneous arrival rate λ. The stochastically determined time at which the recession hits is given by T . The goal of this modeling approach is to provide the simplest possible model for a social planner to trade off the long-run effects of cleanup against any possible short-run benefits due to countercyclical policy. Following Heutel (2012), a recession is modeled as a one-time decrease in the capital stock, kR . After the recession, the economy immediately begins converging back to its initial steady state. This one-time drop in capital is an alternative way of modeling a temporary negative productivity shock and greatly simplifies analysis. That is, consider a one-time negative multiplicative productivity shock πt , where 0 < πt < 1. Output in the event of a recession is then yt = πt A(w)f (kt ), with capital and consumption falling due to the negative productivity shock. We make some simplifying assumptions in modeling recessions. First, we define kR ≡ (1 − πt )(A(w)f (kt ) − ct ) to be the equilibrium capital level in a recession. This captures the full effects of the temporary productivity shock but greatly simplifies the analysis.19 For convenience, we assume only one recession can occur in a local economy.20 The recession is characterized by a one-time drop in the capital stock of size kR , which occurs at time T . After this one-time drop, capital stock begins to increase back to the original steady state level (if no cleanup occurs). This definition of a recession has a natural analog in our simulations, which we run as a discrete-time version of our continuous-time Ramsey model. In the (discrete) period in which the recession occurs, capital drops by kR . In the following period, capital begins to increase back toward the original steady state level, just as in the continuous-time model.

19 A local economy is a 3 kilometer ball around a site. A recession, though, could occur on a larger scale. We only model the portion of the recession which manifests in this smaller community. 20 Ignoring the possibility of more recessions further into the future should not impact results. We find that it is always optimal to clean now rather than wait for the first recession (given no funding constraints), so it naturally follows that it would be better to clean in the first recession than in any subsequent recessions.

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3.3

The Social Planner’s Decision

The social planner’s problem in the model is deciding whether they should clean a particular site in a particular local economy now or wait until a recession in that economy in order to use the government funds as a de facto stimulus. When deciding whether to clean now or wait for a recession, the planner must consider that the cleanup provides both short-run and long-run benefits to the local economy. Specifically, the short-run benefits in the form of federal ¯ provide a direct countercyclical benefit to a local economy. expenditures, k, Examining only such short-run effects, however, ignores many welfare gains to the local economy that have previously been identified and calculated within the relevant literature. Chiefly, as the housing market adjusts over time, there is an increase in home values for home-owners around the cleanup site (Gamper-Rabindran, Mastromonaco, and Timmins (2011)). Moreover, this home value increase is strongly positively correlated with proximity to the site. Unlike the short-run transfer benefits, however, these benefits are not seen immediately. The housing market adjustments reflect general equilibrium effects, and thus local home-owners’ subsequent wealth increases are realized gradually over the long run. For clarity, Figure 4 shows the expected long-run dynamics of the capital stock in one particular case we consider in the model: immediate cleanup upon discovery in a case of overshooting. We show capital stock as opposed to consumption or output to highlight the relative magnitudes of ¯ the recession’s effect on capital, kR , and the long run increase the short run capital injection, k, in the capital stock due to cleanup, k1∗ − k0∗ . In the case of immediate cleanup, upon discovery ¯ Since cleanup occurs, the there is an immediate exogenous increase in the capital stock, k. productivity of the local economy increases (i.e., A(w) < A(0) = 1) and capital approaches its new steady state level k1∗ . At some point in the future, a recession is expected to occur. At that point, there is a one-time negative shock to the economy, kR . After the recession the economy immediately starts to converge to its post-cleanup steady state, k1∗ . Alternatively, the planner can choose to wait to clean until the recession occurs (not pictured). In this scenario, capital remains in its original steady state until the recession and cleanup concurrently take place, at which point it simultaneously drops due to the recession and boosts back up due to the cleanup. It then begins its approach to the new steady state. 17

Figure 4: Time path of capital in case of overshooting when cleanup occurs immediately upon discovery (at t = 0) and a recession (at t = T ) occurring later. In sum, the model here exhibits the salient features of both a particular type of spatially flexible but temporally rigid government spending and a literature which finds long-run general equilibrium effects of the spending. Specifically, there is both an immediate short-run boost to the local economy via federal transfers being realized through local cleanup contracts and a gradual long-run boost to the economy through the channel of wealth increases to local home-owners. The short-run benefits are modeled as a reduced-form boost via a one-time increase in capital, while the long-run benefits are reflected as a new, higher steady state (for each variable) that the economy subsequently approaches. The next section addresses the social planner’s problem of how to allocate funds across sites as a function of three area specific economic variables: interest rates, funding needed to perform a cleanup, and economic volatility.

4

Methods and Results

There are two important aspects of the social planner’s problem of allocating limited funds to cleanup sites: the first is a spatial component and the second is a temporal component. The spatial question asks: if two sites are completely identical except that one is currently in a

18

recession and the other is not, to which site should a welfare maximizing social planner allocate funds? We call this the spatial aspect because it addresses how to allocate funds across space within a time period based upon different economic conditions. The temporal question asks: if two sites are both in long-run equilibrium but one site has a higher probability of going into a recession in the next period than the other, for example, which site should the regulator clean? Put another way, the temporal aspect regards which site the regulator should clean between two sites that are in the same economic condition (i.e., both in a steady state) but are characterized by different economic characteristics. We call this the temporal aspect because it is possible that different economic characteristics of a local economy can affect the optimal temporal ordering of sites whose economies are in steady state. We address these two questions in detail in the appendix. However, we summarize the most critical findings from these questions below. We solve the model presented above for equilibrium levels of capital, consumption, and output using the same method as when solving a typical Ramsey Model.21 Using the equilibrium results, we calculate the expected NPV of total utility resulting from different cleanup policies. While getting closed form solutions for the time paths of capital, consumption, and output using the Ramsey model is straightforward, getting analytical solutions for the NPV of utility over time is more challenging. Specifically, deriving analytical solutions for NPV of utility severely restricts the class of utility functions we can consider.22 We use a CES utility function, which is in line with the literature of policy comparisons. We then analytically solve for capital, consumption, and output and subsequently numerically calculate welfare for alternative policies.23 We use a carefully parameterized simulation to obtain all of the results in this paper. Table 1 shows the various functional forms and baseline parameter values used in all simulations below. When possible we take our values from the literature. We use an impact of waste on economic activity (A(w)) that implies cleanup will increase the equilibrium capital stock by roughly 12%, which is in line with the estimates in Gamper-Rabindran, Mastromonaco, and

21

See Chapter 2, pp 37-48, in Blanchard and Fischer (1989). Analytical welfare comparisons for a utility specification linear in consumption are available upon request. 23 Similarly, while the comparative statics over the parameters that drive welfare differences can be found analytically, in many cases it is impossible to order them by relative magnitudes, even when assuming a CES utility function. For this reason, we focus on our numerical results, which in turn provide some evidence as to the parameters’ relative magnitudinal order. 22

19

Table 1: Base case parameter values Parameter

Value

Description

Source

U (c) f (k) α

c1−γ −1

A(w)k α 0.36

Utility function Production function Curvature of production function

A(w)

0.93

Productivity dampening

θ γ ρ kR

0.0141 2 0.09 0.1 · k0∗

k k

0.5 · (k1∗ − k0∗ ) 1.5 · (k1∗ − k0∗ )

Discount rate Coefficient of relative risk aversion Probability of recession Recession is 10% of pre-cleanup steady state level of capital Size of cleanup: Undershooting Size of cleanup: Overshooting

Heutel (2012) Heutel (2012) Chang and Kim (2007), Kydland and Prescott (1982) Implied by Gamper-Rabindran, Mastromonaco, and Timmins (2011) and Gamper-Rabindran and Timmins (2013) Heutel (2012) Stern (2008), Weitzman (2007) BEA 2000-2007 MSA average

1−γ

Note: Probability of recession is constructed from quarterly BEA MSA-level data for changes in local economic activity. It represents the probability that an MSA experienced, in any given quarter, a decrease in economic output.

Timmins (2011) and Gamper-Rabindran and Timmins (2013) conditional on the other parameter values. As shown in Section 2, remediation expenditures are subject to significant variation. Given the magnitude of yearly remediation expenditures and the magnitude of estimated benefits to cleanups, there is considerable uncertainty with respect to these parameterizations. As a result, we perform extensive sensitivity analysis over these, and other parameter values, in our simulations.24

4.1

Optimal Cleanup Across Space

We constructed the theoretical model in Section 3 to analyze when accounting for economic conditions can increase welfare from site cleanup. Consider the relative benefits of cleaning a site in a recession versus a site in long-run equilibrium as a function of each local economy’s characteristics. Recall throughout that for simplicity and clarity we assume that an economy can only suffer from one recession. Also, recall that there is no evidence that a site’s location on the

24

We also note that there is likely imprecision introduced by using national level parameters from the literature to represent local communities that are affected by Superfund sites.

20

current NPL list is systematically correlated with local economic conditions or the magnitude of long-run economic impact of cleanup. As a result, this simulation assumes that all sites are identical from the perspective of the five criteria outlined above which EPA administrators currently consider for sites on the NPL. Consider the expected increase in welfare of cleaning a site that is in a recession relative to not cleaning it: ∞

Z VC|R =

−θt

U (ct )e 0

Z dt|k0 =k∗ −kR +k;A(w)=1 − 0

0

∞

U (ct )e−θt dt|k0 =k0∗ −kR ;A(w)<1

(3)

In equation (3), VC|R represents the increase in net present value (NPV) of welfare from cleanup to a representative agent in a local economy conditional on a recession occurring at time zero. We use as a baseline an economy being in recession and converging back to steady state without any other form of intervention. Similarly, consider the relative increase in expected NPV of welfare due to the cleanup of an economy not in a recession (i.e., in steady state) at time zero. The steady state economy could suffer a recession at any time T . The timing of T is dictated by a pdf g(T ). The counterfactual we consider is not cleaning the site in steady state in any time period, even if it does eventually suffer a recession at time T . As a result, the expression representing cleaning a site now that is in steady state is given by:

Z Z

T

VC|SS =

U (ct )e 0

Z Z − 0

T

−θt

Z dt|k0 =k∗ +k;A(w)=1 +

∞



dt|kT =kT −kR ;A(w)=1 g(T )dT  Z ∞ U (ct )e−θt dt|k0 =k0∗ ;A(w)<1 + U (ct )e−θ(t−T ) dt|kT =k0∗ −kR ;A(w)<1 g(T )dT 0

U (ct )e

−θ(t−T )

T

T

(4) The first line in equation (4) represents the expected welfare from cleaning a site that is initially in steady state given that a recession occurs at time T . The second line of equation (4) represents the expected welfare from not cleaning the same site. As a result, equation (4) is the net benefit of cleaning a site in steady state accounting for the opportunity cost of not cleaning it. Now consider the social planner’s problem of allocating cleanup funds across space to one of 21

two identical sites: one in a recession and one in steady state. The expected change in welfare from cleaning the site in recession relative to the site in steady state is VC|R − VC|SS . This difference represents the change in welfare from cleaning the site in recession relative to the steady state site assuming that there are only enough funds available to clean one site. More generally, this counterfactual represents one in which the social planner is resource constrained, a counterfactual that accords well with the data.25 We find that it always better to clean a site in a recession than an identical site in steady state. This is unsurprising given that the utility function demonstrates decreasing marginal returns to utility; the short-run boost to consumption is relatively more valuable since consumption is lower for the economy in a recession.26 This result is robust to various parameterizations of the model, as can be seen in the appendix.

4.2

Optimal Cleanup Across Time

Consider the social planner’s problem if there are no sites in recession and the social planner is deciding which sites they should clean first. Motivating this approach is that the social planner should clean sites in the order that gives the largest amount of expected social welfare. Further, building on the results above, we know that when comparing whether to clean a site in steady state versus one in recession, it is always better to clean the site in recession. As a result, in this subsection the social planner is comparing two scenarios: whether to clean a particular site now or wait until a recession affects the local economy of a site in order to clean it. The temporal aspect of cleaning evaluated in this subsection is shown graphically in Figure 5. We show the dynamics with respect to the capital stock as it makes precise transitions clear. Our findings show that it is never optimal to wait to clean. In the case of undershooting, capital is always higher when cleaning immediately than when waiting to clean, as illustrated in the

25 Our model assumes that site discovery is exogenous (i.e., the list of sites is predetermined). Boyd, Harrington, and Macauly (1996) illustrates that commercial property development can lead to site discovery, potentially making site discovery procyclical. However, it may be some time before a discovered site is listed on the NPL. This paper considers the optimal cleanup strategy of sites on the NPL conditional on the mandate that all sites have to be cleaned up. Not all discovered sites will be cleaned under Superfund. For simplicity, we treat discovery and listing as the same. 26 It may be the case that the EPA can seek funds from a private party when the site is not in a recession. In this case, it may be difficult to arrive at a settlement when the use of the funds will not be immediate (e.g., prices may change in the future). However, the EPA can begin remediation and seek reimbursement for recalcitrant responsible parties at a later date (Boyd, Harrington, and Macauly (1996)).

22

top panel of Figure 5. In the case of overshooting, it is possible for capital and consumption levels to be larger after the recession if the social planner waits to clean. Still, we show that it is always best to clean immediately if possible since the rate of convergence back to the new steady state level of capital (k1∗ ) is not sufficiently high to make up the difference in forgone utility from cleaning now. This situation is shown in the bottom panel of Figure 5. Consider the welfare resulting from an immediate cleaning of the site:

T

Z Z VN OW =

U (ct )e

−θt

Z dt|k0 =k∗ +k;A(w)=1 +

U (ct )e

0

0

∞

−θ(t−T )

T

 dt|kT =kT −kR ;A(w)=1 g(T )dT (5)

Equation (5) measures the expected discounted NPV of all future utility given that the site is cleaned up now, accounting for the probability distribution of the timing of a future recession. The inside of the brackets is the sum of two separate integrals: the first measures welfare from the cleanup at time 0 until the time of recession T , while the second measures welfare from the time of recession T onward toward an infinite horizon. The outside integral allows for the time of the recession T to vary according to its probability distribution, g(T ), which is a function of ρ. The welfare function illustrating the benefits from waiting until a recession to clean is similarly constructed as:

Z Z VW AIT =

T

−θt

U (ct )e 0

Z dt|k0 =k0∗ ;A(w)<1 +

∞

U (ct )e T

−θ(t−T )

 dt|kT =k∗ +k−kR ;A(w)=1 g(T )dT 0

(6) The first inside term represents welfare from time 0 until the time of recession T , and the second measures welfare from that time of recession and the simultaneous cleanup onward toward an infinite horizon. Notice that the first piece here is simply the NPV of utility from consumption at the original equilibrium over the specified time period, since no shock occurs to the system until T . The outside integral allows for the time of the recession T to vary according to its pdf, g(T ). Note that the only differences between equations (5) and (6) are the initial conditions on the state variable k at times 0 and T and the time in period in which A(w) < 1 becomes A(0) = 1.

23

Figure 5: Long run dynamics of capital when cleanup occurs upon discovery (t = 0) versus waiting until recession (t = T ). The top panel shows undershooting while the bottom panel shows overshooting.

24

The difference between the two welfare functions is:

VN ET = VN OW − VW AIT

(7)

If VN ET > 0, then it is optimal to clean the site immediately. If VN ET < 0, then it is optimal to wait until the expected time of a recession to clean the site. We find in all of our simulations over many different parameterizations that it is never optimal to wait to clean a site as a countercyclical policy. There are two main reasons which we carefully outline in the appendix, although they are both very straightforward and intuitive. First, discounting future payoffs gives a higher value to any benefits which accrue immediately, meaning that the relative welfare gains to countercyclical cleaning are reduced. This is important in a temporally constrained environment in which all sites cannot be cleaned in the current period. Second, there are immediate long-run gains to cleanup in the form of more wealth and output of local economic agents. This gives added incentive to the social planner to clean immediately. For example, we show in the previous section that it is always welfare enhancing to clean a site in a recession rather than an identical site which is not in a recession, ceteris paribus. Additionally, we find that it is never optimal to wait until a recession to clean a site.

4.3

Conditional Optimization of Cleanup Decisions

While it is never optimal to wait to clean a site relative to not waiting, it is still possible to order sites based upon second-best criteria. Put another way, the regulator can prioritize sites each year in the presence of limited yearly funding. To this end, this model provides criteria that advise site prioritization based on welfare gains from accounting for economic variables. To optimize welfare conditional on limited funding, the regulator should order sites by the largest gain in NPV of welfare from immediate cleanup, accounting for long-term productivity gains in addition to short-run countercyclical benefits. The conditionally optimal strategy is for the regulator to work down an ordered list of sites (conditioned on local economic characteristics)

25

until there are not enough funds left to clean any more sites.27 The optimal listing would be dynamically updated each year as the random recessionary shocks are realized. In order to understand the relative gains from conditionally optimizing cleanup decisions, we calibrate our model to reflect the change in welfare from accounting for economic criteria of simulated sites relative to when site rankings are orthogonal to economic characteristics. This baseline of (economically) random ordering implicitly assumes that the central planner is not maximizing welfare when ordering sites, which both contrasts with our model’s approach and better represents the observed status quo. We allow sites to vary by the three characteristics identified by our theoretical model: discount rate, cleanup cost, and probability of recession. One nice feature of our model is that these economic criteria are easily observable. The EPA has data on expected expenditures for each site on the NPL. Local economic stability is easily observable and varies to a large extent throughout the United States. Local discount rates can be proxied by local municipal bond ratings, which are also observable. The only variable not easily observable is the effect of waste on long-term steady state consumption by site. As a result, we assume all sites share identical long-term productivity dampening effects of waste (i.e., A(w) identical across sites) but solve for expected welfare gains at different levels of A(w). However, assuming A(w) is identical across sites does not mean that benefits from cleanup are identical across sites; different simulated sites have different ex ante and ex post cleanup equilibrium levels of output and consumption due to different simulated discount rates. That source of heterogeneity drives differences in the long-run effects of cleanup, which the empirical literature observes (Gamper-Rabindran and Timmins (2013) and Kiel and Williams (2007)), even if A(w) is constant across sites. Further, letting A(w) vary over sites would be somewhat ad hoc since the productivity dampening effects of waste are challenging to parameterize. As a result, we let variation in discount rates drive differences in long-run effects of cleanup. We calibrate the theoretical model to reflect observed economic circumstance whenever possible. For example, average annual cleanup cost per site in remediation was $3 million

27

While the broader question of how the level of government funds for cleanup should vary across years is interesting and important, we leave that question to future work.

26

throughout the 2000’s. However, that number understates the true cost of actively cleaning a site since it includes sites that had any work being done (i.e., were monitored in any way). As a result, actual cleanup phase for sites is often on the order of $10-20 million per year. We assume that cleanup costs are normally distributed around 75% of equilibrium capital before cleanup with a coefficient of variation of .33: k ∼ N (.75k0∗ , (.25k0∗ )2 ). The magnitude of these cleanup costs may seem large at first, but it is important to keep in mind the proximity to the site our model considers. Gamper-Rabindran and Timmins (2013) find that most increases in long-run housing values occur within 3 kilometers of the site. Given that capital in our model is meant to capture land values, the implication is that $10-20 million is equal to 75% of the value of the capital stock within 3 kilometers of the remediation site. As a result, even though the short-run impact to the larger MSA of this cleanup expenditure may be small if the site is in a more urban area, to the proximate community shown to be affected by cleanup, it is likely non-trivial. The previous section shows that adjusting the mean cleanup cost increases the short-run benefits (e.g., countercyclical benefits) from cleanup. We assume that annual discount rates are implicitly defined by 10 year municipal bond yields.28 Using Bloomberg data we get a range of quarterly discount rates that are normally distributed around .9772 with a standard error of .0058: r ∼ N (.9772, (.0058)2 ). This discount rate reflects an average yield to maturity for 10 year municipal bonds of 2.28%, which is what we observe in the 2012 Bloomberg data. The variance around this mean is similarly calibrated. Finally, we assume that in each quarter, a site has a probability of entering a recession of ρ ∼ N (.074, (.05)2 ). We calculated this using quarterly recession probabilities implied by year to year changes in real GDP per capita from the BEA for the 369 largest Metropolitan Statistical Areas in the US from 2000-2007.29 We drop years including the “great recession” to avoid biasing our recession probabilities. This construction represents the probability that an MSA experienced, in an given quarter, a decrease in economic output. We do not account for important issues like temporal correlation in this simulation, nor variation in the magnitude

28

To be clear, a discount rate is inversely proportional to the municipal bond yield: lower borrowing rates imply that future payoffs are worth more. 29 Using data for smaller 3 km balls, were it available, would likely just add noise from intra-city demographic trends that may not capture the general nature of a macroeconomic recession.

27

of recessions, in order to focus on the first-order effect of conditionally optimizing the timing of environmental cleanups. We also impose that the probability of recession must always be positive, which would occasionally be violated given our normality assumption for the probability of recession ρ. We carry forward the parameterizations for all other parameters in the model from the previous sections. For each run of the simulation, we simulate 500 sites characterized by a draw from each of the distributions (i.e., discount rates, recession probability, and cleanup costs) discussed above. We perform welfare calculations for cleanup in three scenarios. Scenario 1 cleans sites randomly. This corresponds to how the EPA currently cleans up sites because sites are cleaned randomly with respect to economic criteria. In Scenario 2, we order sites based on the economic criteria previously discussed. For each site, we find the expected NPV of welfare if the site is cleaned now. This accounts for that site’s probability of entering a recession in each future period. If a site is in a recession in a particular period, it moves that site up on the list, ceteris paribus. Sites are then cleaned in order until all funds for cleanup in that period are exhausted. This ordering accounts for both the temporal and spatial aspects of cleanup. As a result, Scenario 2 represents the second-best policy for cleanup accounting for economic variables. Scenario 3 is the first-best case in which all sites are cleaned immediately in the first period of each simulation. This third scenario is valuable because it gives us an upper bound for the maximum welfare achievable. We calculate welfare from each scenario for each run of the simulation. We perform 1000 Monte Carlo draws and construct two summary statistics which relate welfare for each scenario. The first statistic, called Case 1, is the welfare increase from the second-best policy (i.e., Scenario 2) relative to random cleanup as a percent of the welfare increase of the first best policy (i.e., Scenario 3) relative to random cleanup. Specifically, this statistic is

W2 −W1 W3 −W1

where Wi refers to

the NPV of welfare in scenario i and Scenarios 1, 2, and 3 are random, second-best, and first-best cleanup, respectively. The second summary statistic, called Case 2, shows the percentage increase in welfare from cleaning sites with the second-best policy relative to cleaning them randomly. This statistic is

W2 −W1 W1 .

We report mean, standard error, min, max, and coefficient of variation

for the first statistic (Case 1) and the second statistic (Case 2). We do this for three different values of A(w) for each site: .85, .93 and .97. We use an annual budget of 22.5 · k0∗ (plus the

28

Table 2: Monte Carlo Results Case

A(w)

Mean

Stan. Dev.

Min

Max

Coef. Var.

(1) (1) (1)

.85 .93 .97

.268 .272 .291

.052 .055 .062

0 0 .021

.622 .556 .589

.198 .202 .212

(2) (2) (2)

.85 .93 .97

.0025 .0010 .0005

.0006 .0002 .0001

0 0 0

.0074 .0027 .0013

.224 .225 .226

Note: Each row summarizes the results of 1000 runs of the Monte Carlo simulation. Units are percents. Case 1 is the welfare increase from the second-best policy (i.e., Scenario 2) relative to random cleanup as a percent of 2 −W1 the welfare increase of the first-best policy (i.e., Scenario 3) relative to random cleanup: W . Case 2 is the W3 −W1 percentage increase in welfare from cleaning sites with the second-best policy relative to cleaning them randomly: W2 −W1 . W1

small amount leftover from the previous period), which allows for roughly 30 sites to be cleaned each year. These numbers are in line with the average number of sites cleaned per year (30).30 We run the simulation under the assumption that the regulator uses one quarter of her yearly funds in each quarter.31 We run each simulation out 15 years, or 60 quarters. Results from 1000 Monte Carlo runs are shown in Table 2. All units for both summary statistics are shown in percent changes in welfare. The most important feature of Table 2 is the “mean” summary statistic for each (A(w), case) pair. Recalling that A(w) = .93 corresponds to equilibrium capital increases from cleanup of roughly 12% (near the median increase in housing prices found in Gamper-Rabindran and Timmins (2013)),32 our calibrated simulation implies that by strategically ordering cleanups along economic dimensions, the EPA yields an increase in the net present value of welfare that is 27.2% of the welfare gain that would result from the first-best policy (relative to randomly cleaning). Our simulated results show that this percentage increase

30

Average funding per year comes from 75% of the value of the local housing stock, as shown by GamperRabindran and Timmins (2013), and an average of k0∗ based on the parameters sourced in Table 1. An average of 30 sites cleaned per year is based on roughly 300 sites monitored per year with an average of roughly 10 years from beginning of monitoring until completion (Sigman (2001)). 31 We use quarters because our parameters are calculated using quarterly data. In a sense, the size of each period is irrelevant since it is simply a matter of scaling. The larger question of how to optimally bank funds across time we leave to future work. 32 Specifically, Gamper-Rabindran, Mastromonaco, and Timmins (2011) find that housing values increase between 18.2% for houses lowest in the housing value distribution and 11.4% for houses highest in the value distribution. We chose 12% as a conservative lower bound for the impact of cleanup on housing value appreciation. Total impact over the entire housing value distribution may be larger. Note that we use the numbered term “Case” simply as a means of easing references, since each Case presents a statistic determined using alternative counterfactuals.

29

is subject to significant variation across runs. Simulated 95% confidence intervals put increases from strategic ordering at roughly 18%-36% of the increase from cleaning sites immediately. The statistics from Case 1 also show that the relative benefit of ordering is increasing slightly as damages from waste decrease (i.e., A(w) increases), but that increase is very small. This makes sense given that the statistic normalizes welfare increases by the increase in welfare from cleaning all sites immediately, and the welfare from cleaning all sites immediately necessarily decreases as the productivity gain from cleaning up sites gets smaller. The second summary statistic, Case 2, shows the percentage increase in welfare from ordering sites relative to cleaning randomly. Ordering sites offers an average increase in welfare of between .05%-.25% depending on the size of damages from waste. Importantly, this increase in welfare would be costless in that it would only require the administrative costs of ordering the sites along the lines described in this paper and implementing the ordering. Given our parameterizations in the simulation, a .25% increase in welfare represents an increase in consumption of nearly 1.0% meaning that ordering sites using this criteria is equivalent to increasing consumption in these communities by 0.2%-1.0%, depending on the magnitude of the damages from waste. Intuitively, the percentage increase in welfare from ordering is increasing in the damages from waste. If damages are higher (e.g., A(w) = .85), then any benefits of cleaning more valuable sites are larger than if damages were lower (e.g., A(w) = .93). As noted above, then, there are two sources for how ordering sites increases welfare. The first is the temporal aspect of cleanup (i.e., cleaning the same site when it is in a recession rather than when it is not) and the second is the spatial aspect of cleanup (i.e., cleaning sites which will lead to larger welfare increases, ceteris paribus, based on the three economic criteria previously noted). The simulation results reinforce comparative statics shown in the appendix. Consider, for example, the relationship between the discount rate and the productivity dampening effect of waste. For simplicity, suppose there are two sites, H and L, that are identical in every way except that site H has a higher discount factor (lower discount rate, θ). Even though the two sites have have an identical dampening effect of waste, site H has more welfare than site L both pre- and post-cleanup. The discount factor acts as a scalar to each sites’ welfare. Hence, if cleanup occurred simultaneously at each site, then the difference in post-cleanup welfare

30

levels across sites would be scaled up. Thus this post-cleanup welfare difference would be larger than the pre-cleanup difference. Correspondingly, this implies that the welfare gain from cleanup for site H is larger than that for site L because site H’s pre- and post-cleanup welfare levels are both scaled by a larger discount factor. Now consider the how the productivity dampening effect of waste relates to the size of the gap between site H’s welfare gains from cleanup and site L’s (smaller) welfare gains. Recall that the two sites initially have an identical level of waste dampening. Suppose this dampening level were to decrease (that is, A(w) were to increase) at an equal pace for each site. In limit, as the dampening approaches the fully clean level (A(w) = 1), each site’s pre-cleanup welfare level would approach its respective post-cleanup level. Although the two sites’ dampening coefficients are closing over the same distance, site H’s pre- and post-welfare gap must be closing faster than site L’s gap because site H’s gap is larger (as just discussed). Thus, a decrease in the dampening effect (an increase in A(w)) decreases the welfare gain from cleanup at a faster rate for sites with higher discount factors (lower discount rates). This breeds an important policy implication. As previously discussed, it is better to clean a site with a low discount rate, ceteris paribus. However, this result shows that the gain from doing so is increasing as A(w) decreases. The productivity dampening effect from waste, even when constant across two sites, scales up the relative welfare gains from cleaning a site with a low discount rate over its high rate counterfactual. Thus, ordering sites based on the long-run gains realized by eliminating the dampening effect of waste leads to a larger increase in welfare than simply using cleanup as a countercyclical stimulus. Critically, the simulation results also support this finding. Consider the Case 2 statistic, as shown in Table 2. In the simulation, the largest possible welfare gains from using cleanup as a de facto stimulus are just 20% of the those from ordering based on long-run cleanup impact ( .0005 .025 = 20%). Simply put, the simulation reinforces the notion that cleaning sites which will have a larger economic gain from cleanup under normal economic conditions is more welfare enhancing than simply using cleanup as a countercyclical policy. That said, as the short-run benefits of cleanup get larger, the countercyclical benefits of cleanup are relatively larger. It follows then, that accounting for variability in damages caused by waste across sites, as found in

31

Kiel and Williams (2007), is vitally important. This section illustrates that the EPA can take multiple economic criteria into consideration in order to minimize welfare losses that arise from spatially flexible but temporally binding budgets for site cleanup. While we find it is never optimal to wait to clean up a site, we also find that conditional on having to wait to clean a site, sites with larger cleanup costs, more stable economies, and higher discount rates should be given a priority during normal economic conditions. Similarly, insofar as there are countercyclical benefits from cleanup and spatial heterogeneity in economic conditions within EPA regions, the EPA can costlessly increase welfare by strategically using cleanups as a de facto stimulus in areas suffering from negative local economic shocks, in addition to ordering sites based on easily observable economic characteristics to leverage the long run gains from cleanup. This result is intuitive: we find that accounting for opportunity costs in government decision making increases welfare.

5

Conclusion

This article finds that government agencies with flexibility in how to allocate yearly expenditures across locations can costlessly increase welfare by strategically ordering how funds are used as a function of local economic characteristics. We find that a social planner increases welfare by accounting for local economic conditions in two ways. First there is a spatial element of how to distribute funds across two identical sites: it is welfare enhancing to clean in areas when there is a localized negative economic shock so that federal monies can act as a de facto local economic stimulus. Second, there is a temporal element: it is always optimal to clean any particular site sooner rather than later. Further, areas where waste is most harming productivity should be cleaned first. We find that if the EPA were to allocate Superfund cleanup funding across sites (that do not pose an immediate threat to human health) based upon local economic criteria, welfare would increase on the order of .05%-.25% in these communities. This welfare increase is equivalent to a 0.2%-1.0% increase in consumption. The importance of this welfare increase has distributional implications as individuals affected by Superfund sites are often lower income households (Gamper-Rabindran and Timmins (2013)). We do not argue that the EPA should adapt policy to consider only these economic criteria. Rather, by not considering any of these 32

economic criteria in addition to the current nine non-economic criteria in site prioritization, the EPA (and other government agencies with similar funding characteristics) are leaving welfare on the table. Even if there are other dimensions determining regulators’ allocation decisions, such as inequality aversion, incorporating the findings here will always weakly increase welfare. The findings in this article lead to several avenues for future research. Parsing out the precise conditions when the temporal versus spatial aspects of cleanup are relatively more or less important could be an important guide to policy makers. There are also important distributional concerns which this article has ignored. While studies have shown that environmental cleanups increase surrounding housing values, the temporal diffusion of those increases is unclear. Further, there could be heterogeneity in these diffusion processes as a function of both cleanup and local economic characteristics. That is, the approach path to new equilibrium after cleanup could be endogenous to system characteristics. This is especially important when the findings of this article are applied to government expenditures with characteristics similar to spending on environmental cleanups, such as federal education or health expenditures. Also, it is unclear which characteristics of an EPA Superfund site lead to relatively larger or smaller long-run improvements in local economic activity. Lastly, we address the fiscal federalism problem of how to maximize welfare conditional on a given level of federal funding. As a result, cleanup costs act as local benefits even though the magnitude of those local benefits are small compared to the long-run economic gains of cleanup. A more general welfare function, in which the regional social planner problem considered here is nested within a global social planner’s problem that accounts for the opportunity cost of cleanup funds, is a straightforward and important theoretical extension. For example, Hamilton and Viscusi (1999) find that it may be optimal to simply fence off certain sites rather than pay the cost of cleanup when accounting for the opportunity cost of cleaning sites. Nesting our model within the more general model, though, would not affect our findings. Rather, it would simply bound the set of sites which should be cleaned since it would be optimal to not clean sites with an insufficiently high benefit-cost ratio. We leave these interesting topics to future research.

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References Beider, P. (1994): The Total Costs of cleaning Up Nonfederal Superfund Sites, vol. 74. Congressional Budget Office. Blanchard, O., and S. Fischer (1989): Lectures on macroeconomics. The MIT press. Boyd, J., W. Harrington, and M. Macauly (1996): “The Effects of Environmental Liability on Industrial Real Estate Development,” Journal of Real Estate Economics and Finance, 12, 37–58. Boyle, M., and K. Kiel (2001): “A Survey of House Price Hedonic Studies of the impact of Environmental Externalities,” Journal of Real Estate Literature, 9(2). Burda, M., and M. Harding (2014): “Environmental Justice: Evidence from Superfund Cleanup Durations,” Journal of Economic Behavior and Organization, forthcoming. Chang, Y., and S.-B. Kim (2007): “Heterogeneity and Aggregation: Implications for LaborMarket Fluctuations,” American Economic Review, 97, 1939–1956. Duflo, E., P. Dupas, and M. Kremer (2011): “Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya,” American Economic Review, 101(5), 1739–1774. Fischer, C., and M. Springborn (2011): “Emissions Targets and the Real Business Cycle: Intensity Targets Versus Caps or Taxes,” Journal of Environmental Economics and Management, 62, 352–366. Gamper-Rabindran, S., R. Mastromonaco, and C. Timmins (2011): “Valuing the Benefits of Superfund Site Remediation: Three Approaches to Measuring Localized Externalities,” National Bureau of Economic Research Working Paper #16655. Gamper-Rabindran, S., and C. Timmins (2013): “Does Cleanup of Hazardous Waste Sites Raise Housing Values? Evidence of Spatially Localized Benefits,” Journal of Environmental Economics and Management, 65(3).

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Greenstone, M., and J. Gallagher (2008): “Does Hazardous Waste Matter? Evidence from the Housing Market and the Superfund Program,” Quarterly Journal of Economics, 123(3), 951–1003. Gupta, S., G. van Houtven, and M. Cropper (1996): “Paying for Permanence: An Economic Analysis of EPA’s Cleanup Decisions at Superfund Sites,” RAND Journal of Economics, 27, 563–582. Hamilton, J., and K. Viscusi (1999): “How Costly is Clean? An Analysis of the Costs of Superfund Site Remediations,” Journal of Public Analysis and Management, 18(1), 2–27. Heutel, G. (2012): “How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks,” Review of Economic Dynamics, 15(2), 244–264. Ihlanfeldt, K., and L. Taylor (2004): “Externality Effects of Small-scale Hazardous Waste Sites: Evidence from Urban Commercial Property Markets,” Journal of Environmental Economics and Management, 47, 117–139. Kiel, K., and M. Williams (2007): “The Impact of Superfund Sites on Local Property Values: Are All Sites the Same?,” Journal of Urban Economics, 61, 170–192. Kiel, K., and J. Zabel (2001): “Estimating the Economic Benefits of Cleaning up Superfund sites: The Case of Woburn, Massachusetts,” Journal of Real Estate Finance and Economics, 22, 163–184. Kydland, F., and E. Prescott (1982): “Time to Build and Aggregate Fluctuations,” Econometrica, 50, 1345–1370. Leduc, S., and D. Wilson (2012): “Should Transportation Spending be Included in a Stimulus Program? A Review of the Literature,” Federal Reserve Bank of San Francisco: Working Paper #2012-15. Mastromonaco, R. (2013): “Hazardous Waste Hits Hollywood: Superfund and Housing Prices in Los Angeles,” Environmental and Resource Economics, forthcoming.

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Pindyck, R. (2002): “Optimal Timing Problems in Environmental Economics,” Journal of Economic Dynamics and Control, 26, 1677–1697. Sigman, H. (2001): “The Pace of Progress at Superfund Sites: Policy Goals and Interest Group Influence,” Journal of Law and Economics, 44, 315–343. Sims, C., and D. Finnoff (2012): “The Role of Spatial Scale in the Timing of Uncertain Environmental Policy,” Journal of Economic Dynamics and Control, 36, 369–382. Stern, N. (2008): “The Economics of Climate Change,” American Economic Review, 98(2), 1–37. Weitzman, M. (2007): “A Review of the Stern Review of the Economics of Climate Change,” Journal of Economic Literature, 45(3), 703–724.

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6

Appendix: Simulated Comparative Statics

6.1

Optimal Cleanup Across Space

We consider the comparative statics for VC|R − VC|SS in percentage terms for two different levels of cleanup cost (k).33 As shown in Table 1, we allow for both overshooting and undershooting in our simulated comparative statics. We perform comparative statics for the percentage change in welfare from the spatial choice of cleaning a site in recession relative to an identical site in steady state equilibrium for four key parameters of interest. All panels are presented on similar vertical axes so relative magnitudes are clear. Figure 6 shows the percent difference in the increase in welfare from cleaning a site in recession relative to cleaning one in steady state for four model parameters. In this exercise it is helpful to separately consider how a change in a parameter effects both the welfare gained from cleaning a site in steady state relative to not cleaning it and the welfare gained from cleaning a site in recession relative to not cleaning it. If a parameter has a larger impact on the welfare gained from cleaning a site in steady state, then the percent difference in welfare gained from cleaning in a recession will be smaller. Notice that in all four panels the difference is in the positive domain, illustrating that it is always better to clean a site in recession. This is an expected result given the utility function exhibits decreasing marginal utility. Furthermore, undershooting (small cleanup cost) always provides a larger percentage increase in welfare when cleaning a site in recession relative to a site in steady state than overshooting (large cleanup cost). This is due to the change in local economic productivity upon cleanup (i.e., since A(w) = 1 after cleanup). Consider the extreme case where there is no local short term benefit from cleanup. All benefits manifest in converging to a higher steady state level of capital and consumption. As the short run benefits of cleanup increase, the site that was in steady state enjoys higher consumption for longer than the site which started in a recession. Therefore, an increase in the size of the short run benefit to cleanup makes the site starting in steady state relatively better off, even though it is still always welfare improving to clean the site in a recession.

33

Note that this is not the same as percentage points.

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Figure 6a also shows a monotonically increasing relationship between the benefit for cleaning a site in recession relative to one in steady state as a function of A(w) for two different cleanup costs. Recall that as A(w) approaches one there is no effect of waste on economic activity. As this occurs, the increasing relationship is attributable to all benefits being short run benefits. Put another way, as A(w) approaches one, the immediate countercyclical benefits of cleanup dominates all others. Thus, this increasing relationship seen in Figure 6a is expected. Figure 6b relates yearly discount rates to the relative benefits of cleaning a site in recession. The discount rate maps to

1 1+r

where r is the rate of interest.34 The relative benefits of cleaning

a site in recession initially decrease as the discount rate increases (i.e., the interest rate falls), but for values nearly equal to one, the relative benefits of cleaning a site in a recession increase again. There are two main drivers behind these dynamics. If the future is heavily discounted, only immediate benefits matter. As a result, the welfare increase from cleaning a site in recession is greatest when the future is discounted the most. However, there is a long run benefit to cleaning a site that is in steady state now. In the future, when a recession occurs, the consumption level does not drop to as low of a level as it would have were the site not cleaned. Therefore, the long run benefit of cleaning a site in steady state receives more weight when the future is not discounted as heavily. Figure 6c shows comparative statics over the probability of recession. The benefit of cleaning a site in recession relative to an identical site in steady state is decreasing as the chance of a recession occurring in the steady state site increases. If the steady state economy is very stable, then the chance it will suffer from a recession soon is low. Since we make the simplifying assumption of at most one recession per site, all dynamics in this panel are driven by changes in welfare in the economy which has not yet suffered a recession. The difference in welfare between cleaning and not cleaning for a stable economy is very small and almost entirely determined by the difference in steady state levels of consumption. As the probability of a recession increases, the economy in steady state looks more like the site that is in a recession. In the extreme case where the probability of recession equals one, they are identical. As a result, the difference

34

The interest rate here represents the interest rate earned on municipal bonds in a municipality. It proxies for the cost of working capital and therefore is used to discount future payoffs.

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between the cleaning strategy approaches zero as the probability of recession approaches one. Figure 6d shows comparative statics for different cleanup costs conditioned on various levels of productivity reduction brought by waste. As A(w) is small, the long run benefits of cleanup are large, whereas when k¯ increases, the short run benefit to a local economy from cleanup increases. As discussed above, the benefit of cleaning a site in recession relative to cleaning a site in steady state falls as the short run benefit increases (i.e., the cleanup cost k¯ increases). Similarly, the relative benefit of cleaning a site in recession falls as the long run benefit of cleanup increases (i.e., A(w) falls). If the long run benefit is large, then cleaning a site that is in steady state creates a large increase in welfare relative to not cleaning it. As a result, the percentage increase in welfare from cleaning a site in recession relative to one in steady state mechanically falls as the the long run benefit of cleanup increases. The preceeding result is consistent with a local rather than global welfare function since the opportunity costs of spending on cleanup is not accounted for in the social planner’s welfare function. However, this is the correct counterfactual since we study the fiscal federalism policy problem faced by regional EPA offices (and other subnational governmental agencies) who are allocated a given amount of funding from the federal government in a fiscal year. The problem of regional EPA offices, then, is to maximize welfare conditional on a given budget. As stated before, the problem of the optimal level of funding to allocate to regional EPA offices accounting for both the optimal cleanup rule studied here and the opportunity cost of funding is a different but related problem we do not address in this paper. In sum, Figure 6 shows that it is always welfare increasing to clean a site in a recession relative to an identical site in steady state. However, there are important comparative statics which increase or decrease the relative benefit of doing so. These distinctions become important when considering how to clean two sites which are not identical: sites with larger cleanup costs, more stable economies, and higher local discount rates should be prioritized conditional on all economies being in a recession. Additionally, there is always a larger increase for undershooting sites, measured as a percent difference between cleaning a given site in recession and in steady state. For example, the relative welfare increase from cleaning a small economy in a recession versus a large economy that is in steady state is not addressed in this section. However, this

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section does suggest that sites or local economies with different economic characteristics present tradeoffs to a social planner with limited resources.

6.2

Optimal Cleanup Across Time

Following the exposition above, we compare the relative benefit of cleaning a site in steady state immediately versus waiting until the same site is in a recession to clean for various parameterizations. Specifically, we evaluate the comparative statics for VN ET for different levels ¯ and long run benefit (A(w)) in order to show the relative benefits of of short run benefit (k) cleaning a particular site immediately or waiting until that site is in a recession to clean it. Figure 7 shows it is always optimal to clean a site immediately as opposed to waiting to use the short run benefit as a countercyclical policy (in an unconstrained world). The welfare gains from a more productive local economy outweigh those from preventing low levels of future consumption. Figure 7a shows the relationship between lost productivity due to waste and the relative benefits to cleaning now versus waiting for a recession for two different levels of cleanup cost. As the long run benefits of cleanup decrease (A(w) increases), the only difference between cleaning strategies is whether a temporary increase in consumption immediately is more valuable than a countercyclical benefit in the future. When the long run effect of waste is large (A(w) small), there is an additional benefit of cleanup now in the form of larger immediate consumption values at the new and higher equilibrium level of consumption, c∗1 . Figure 7b shows the relationship between discounting behavior and the relative benefits to cleaning now versus waiting for a recession for two different levels of cleanup cost. As an economy’s discount rate decreases, the benefit of cleaning now relative to waiting to clean increases. This is because the future benefits of cleaning now receive more weight (i.e., future benefits are discounted less). Although the countercyclical benefits of cleaning up in a future recession also have relatively greater present value when the discount rate falls, the relative increase in benefits from cleanup now are larger. Further, as in Figure 7a, the benefit of cleaning a site immediately is larger when the short run benefits of cleanup are larger. Put another way, overshooting makes cleaning a site immediately an even more appealing policy than it would be with undershooting since the increased consumption now takes longer to converge back to steady

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state. Figure 7d shows the same relationship explicitly. As the short run benefits of cleanup increase, the relative benefits of cleaning a site immediately increase as well. Figure 7c shows the relationship between the probability of recession and the relative benefits to cleaning now versus waiting for a recession. As the probability of recession increases, the expected time of recession moves closer to the present. As a result, the relative merits of waiting to use cleanup as a countercyclical benefit also increase due to intertemporal discounting. As before, though, it is still always better to clean a site immediately rather than to wait. In sum, Figure 7 shows that it is always better to clean a site now relative to waiting to clean a site. As in the comparison in Section 6.1, sites with larger cleanup costs, more stable economies, and higher discount rates should be prioritized. Unlike the previous comparison, though, the temporal comparison highlights the short run benefits of cleanup. This distinction is evident by the larger welfare gain from overshooting sites than from undershooting sites (when using the temporal counterfactual). However, the magnitude of the temporal difference is significantly smaller than the difference between cleaning a site in a recession relative to cleaning one in steady state from the previous subsection. As a result, the spatial decisions of which sites to clean in a given time period are likely to have more importance than the decisions of how to order cleanup of sites when no local economy is in a recession.

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(a) A(w)

(b) θ

(c) ρ

(d) k¯

Figure 6: Percentage increase in welfare gains from cleaning a site in a recession relative to cleaning one in steady state as a function of A(w), the yearly discount rate (θ), ρ, and k¯

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(a) A(w)

(b) θ

(c) ρ

(d) k¯

Figure 7: Percentage increase in welfare when cleanup occurs immediately versus waiting until recession to clean as a function of A(w), the yearly discount rate (θ), ρ, and k¯

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