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Ecosystem Services and Land Rental Markets: Producer Costs of Bat Population Crashes

Abstract

Nonmarket natural capital provides crucial inputs across the economy. We use land rental market data to calculate the welfare impacts of a change in an unpriced natural capital while accounting for spatial spillovers. We apply the welfare analysis to examine the cost of white-nose syndrome (WNS) in bats, which provide pest control services to agricultural producers. WNS, a disease that decimates bat populations, arrived in the United States in the mid-2000s. Leveraging the exogenous change in bat populations, we find that the loss of bats in a county causes land rental rates to fall by $2.84 per acre plus $1.50 per acre per neighboring county with WNS. Agricultural land falls by 1,102 acres plus 582 acres per neighboring county with WNS. As of 2017, agricultural losses from WNS were between $426 and $495 million per year. These estimates of ecosystem service values can inform public management of society’s natural capital.

Natural capital stocks provide valuable inputs into the creation of human well-being. In many cases, they support production of goods and services, while in others they directly enhance welfare (Freeman et al. 1973). Many valuable natural capital inputs, including ecosystems (Barbier 2016), lack market prices (Fenichel and Hashida 2019), which complicates their valuation and leads the market economy to underinvest in their maintenance. Therefore, economists can contribute to the efficient management of society’s natural resources by estimating the value generated by natural capital stocks.

In this paper, we estimate the cost to agriculture in the United States of losing healthy bat populations. Through bats, nature provides a free pest control service (Cleveland et al. 2006). In 2006, white-nose syndrome (WNS) arrived in the United States from Europe and subsequently spread across space and time, causing bat population crashes of 80% on average. Affected populations show little evidence of recovery (Frick et al. 2010). Because bats are beneficial to agriculture, bat declines may cause the derived demand curve for agricultural land to shift back, affecting both land price and quantity. We use the quasi-random spread of this disease over space and time to estimate the average effect of bat population crashes on county average agricultural cash rental rates and acres of land in agriculture. Impacts include the effects of WNS within a county (a “direct” impact) and on neighboring counties (a “spillover” impact), which may also lose some of the services provided by the infected bats. Leveraging the weak complementarity (Bockstael and McConnell 2007) between agricultural land and the ecosystem services provided by bats, we use our econometric estimates to calculate the lost surplus—or welfare change—in agricultural land markets caused by WNS.1

Valuing the lost ecosystem services from bats can inform public policies to manage bat populations, both generally2 and in response to the spread of WNS. WNS, caused by a fungus, spreads between bat populations as bats come into contact during active periods of the year. Infected bats bring the disease back to winter roosts (e.g., caves), where it spreads rapidly and causes sharp declines in bat populations. Humans can also transport WNS to winter roosts through transmission vectors like hiking boots.3 Dzal et al. (2011) show that the collapse in populations measured in winter roosts corresponds to substantial drops (78%) in the summer activity of bats, which includes pest control.

With many winter roosts located on public lands, information on the value of preventing disease spread can inform public expenditure on costly disease control measures that range from closing cave access to applying fungicide (Szymanski et al. 2009) or vaccinating bats. Existing estimates of the value of ecosystem services provided by bats suggest that they may contribute substantial value to US agriculture. Kunz et al. (2011) review previous studies of the range of services provided by bats, which include pollination and fertilizer services in addition to pest control. Cleveland et al. (2006) use avoided damage and replacement cost methods to find the benefit of pest control by bats in Texas cotton fields to be $741,000 per year. Boyles et al. (2011) extrapolate this estimate to all agricultural land in the United States and find that the loss of bats could result in agricultural losses of $22.9 billion per year, or $74 per cropland acre. This exercise shows the potential for large values of services provided by bats. However, those methods do not account for human responses to the loss of bats like reducing the acres of land farmed, and this previous work does not account for the considerable heterogeneity in the value of pest control from bats that likely exists across the country (Fisher and Naidoo 2011).

To account for human behavioral responses, we apply a revealed preference approach that uses the quasi-random spread of disease to identify and value the average effects of the loss of bats on agricultural outcomes. We build on Frank (2021), who uses the spread of WNS to estimate the impact of substitution to chemical pesticides on infant mortality. Using a difference-in-difference estimation, Frank (2021) confirms that the arrival of WNS coincides with an increase in the use of chemical pesticides and at least temporary decreases in crop yields. This suggests that farm profitability decreases when WNS decimates bat populations. Consistent with this, we find that the arrival of WNS in a county causes the quantity and price of land in agriculture to fall and thus directly decreases welfare in the land market by between $564,937 and $657,319 on average per county-year, depending on what price elasticity of demand for agricultural land prevails. These average values, equivalent to $3.95 to $4.60 per base acre, correspond to a change of 2.7% and 2.5% of base welfare in the land market, respectively.4

In addition to the direct effect of WNS within a county, we find that welfare falls in neighboring counties, defined as counties that share a border. For example, with one neighboring WNS outbreak (and no direct outbreak), annual welfare decreases by between $298,586 and $347,412. With four neighboring outbreaks, these spillover costs climb to $1,187,041 and $1,381,154 per year. These estimates imply that the total cost of WNS to crop producers as of 2017 was between $426 and $495 million per year. We also find evidence that the average effect is driven by decreases in corn, wheat, and soy yields. Further, input expenses per cropland acre increase as producers substitute market-supplied pesticides for the pest control provided by bats.

This paper advances several strands of research. First, we add to research that uses the arguably exogenous spread of disease, wildlife population crashes, and other natural shocks to identify causal effects. For example, Jones (2019) uses zebra-mussel population crashes to identify the impact of algal blooms on infant health, and economists have used natural shocks to quantify the impacts of climate change (Carleton and Hsiang 2016), temperature shocks (Dell et al. 2012), and natural disasters such as hurricanes (De Silva et al. 2010) and other extreme weather events (Gray and Mueller 2012). Others have used ecosystem shocks to estimate the cost of invasive species (Horsch and Lewis 2009) and plant diseases (Kovacs et al. 2011). Guignet et al. (2017) use variation in the presence of beneficial submerged aquatic vegetation in the Chesapeake Bay to estimate its capitalization into nearby home prices. We advance this area of research by proposing a theory-based approach to estimate direct and spillover welfare effects of such natural ecosystem shocks.

Through our valuation approach, we advance a second literature that uses weak complements in production to calculate welfare changes from environmental change (Huang and Smith 1998). To use weak complementarity in production for nonmarket valuation, two conditions must hold. The marginal product of a market good (in our case, land) must depend on the level of the environmental good (in our case, bats) (Bockstael and McConnell 2007) and the impact of the nonmarket environmental good on welfare must be zero when agents do not use the marketed good (Maler 2013).5 Pattanayak and Butry (2005) apply this concept to estimate the value of nonmarket forest ecosystem services based on weak complementarity with (market) farm labor in Indonesia. Other analyses have used output markets to value ecosystem services provided by mangroves (Barbier et al. 2002) and natural pest control (Letourneau et al. 2015) but, to our knowledge, no one has used agricultural land rental markets within a welfare economics framework to estimate the benefits of a local ecosystem service while allowing for spatial spillovers. The publicly available cash rent data from the US Department of Agriculture (USDA) make this a generalizable approach to estimate how variation in natural capital stocks across space and time influences welfare.

Our work is related to a third body of research that uses Ricardian estimates of the impact of climate (Mendelsohn et al. 1994; Schlenker et al. 2005; Fezzi and Bateman 2015) and other ecosystem services (Ma and Swinton 2011), including water (Mendelsohn and Dinar 2003), on land value. However, our estimates account for changes in both prices and quantities in the land market and use annual rental data to calculate the flow values of ecosystem services derived from a stock. Ortiz-Bobea (2020) discusses the advantages of using cash rental data when estimating the costs of climate change. Specifically, rental rates more accurately reflect agricultural profitability because they do not build in the potential for land use changes in the future. Since endogenous land quantities can change land quality on average, we control for time-varying cropland quality distributions at the county level.

We also quantify spatial spillovers in the impacts of WNS outbreaks. Dundas and Lewis (2020) highlight the importance of spatial spillovers when estimating the property price impacts of the ability to protect homes against erosion in Oregon. In the context of disease spread, a bat population crash could cause a loss of pest control services in both treated and neighboring counties, as bat populations cross county lines.6 Further, as WNS spreads across space, it is likely that a county is simultaneously treated directly and by WNS in neighboring counties. Therefore, we estimate the welfare cost of WNS in a given county simultaneously with the cost of WNS in neighbor counties. We adapt a method by Butts (2021) to estimate direct and spillover effects of WNS on rental prices and cropland acres, and develop a workable solution for estimating the welfare effects of both direct WNS effects and the effects driven by spatial spillovers across county lines.

Finally, land price data are used in a fourth body of research in agricultural economics that measures the capitalization of policy benefits into land values and rental rates (Roberts et al. 2003; Kirwan 2009; Latruffe and Le Mouël 2009). This literature finds incomplete pass-through of policy benefits to landowners, suggesting that land supply is not perfectly inelastic and that welfare impacts should consider changes in both land prices and quantities. Borchers et al. (2014) find that agricultural land values depend on both profitability and other factors that include access to amenities and population density. However, this strand of research has not yet worked directly to estimate the values of natural capital in US agricultural settings.

Overall, the valuation exercise in this paper makes two key contributions to applied economics and policy. First, we knit together research on the causal effects of environmental change, nonmarket valuation, and the determinants of agricultural land rents in a new approach to nonmarket valuation that exploits the weak complementary of agricultural land and natural capital to value ecosystem services using well-identified impacts of environmental changes on land markets. We demonstrate the utility of this method in the presence of spatial spillovers. Second, we provide a timely estimate for the agricultural value of the ecosystem services provided by bats. Importantly, our revealed preference approach refines previous research on the value of bats in agriculture by accounting for actual human behavioral and market responses to the loss of bats, so the findings have improved value in guiding management decisions for bat conservation.

This paper is laid out as follows. In section 1, we present a theoretical model that describes how the value of changes in natural capital can be inferred from agricultural land markets. Section 2 describes data and econometric specifications that allow us to parameterize that model for US agriculture. Section 3 presents econometric results and welfare estimates along with tests of robustness, spatial heterogeneity, and the mechanisms driving changes in the market. Finally, we discuss and conclude in section 4.

1.  Valuing Ecosystem Services in Land Rental Markets

To provide a theoretical basis for using land rental markets to estimate the value of ecosystem services, we model a representative producer at the county level. First, we assume that total agricultural production in a county depends on the amount of land used, L, and an exogenous stock of natural capital, N. Given this, production in the county, y, is equal to

(1)y=f(L,N).
We assume nonincreasing returns to scale in L and N and that total production increases in the amount of land planted, which is a choice variable. It also increases in the stock of natural capital. In other words, fi>0,i=L, N. We also assume decreasing marginal benefit of land, fLL<0, reflecting variable land quality within a county.

Next, we assume that fLN=fNL>0. This implies that increasing the stock of natural capital increases the marginal product of land (and vice versa). In this case, land and natural capital are complements in production. To infer welfare impacts from a change in nonmarket goods and services using the market for other inputs, the market and nonmarket inputs must be “weak complements” (Bockstael and McConnell 2007). This requires the further assumption that fN(0,N)=0. In other words, the marginal value of a change in natural capital stock is zero when no land is planted. This assumption is defensible when focusing on ecosystem services that principally support agricultural production. If other values exist (e.g., existence, bequest, health benefits), these cannot be inferred from the market for the (weakly) complementary input. Finally, we assume that the demand for land has a finite choke price.

In the context of pest control provided by bats, the assumption that fLN=fNL>0 implies that the value marginal product of land increases with the bat population. This occurs because bats provide a valuable service free of charge. Therefore, land is more productive when the bat population is healthy. As land becomes more productive, producers optimally adjust all priced inputs in response to the additional productivity. This likely includes a reduction in the use of chemical pesticides but can also include adjustments to labor and other inputs.

In the county, land is supplied with a marginal opportunity cost of S(L) with SL>0. This increasing marginal cost of land reflects heterogeneity in alternative uses for agricultural land. For example, land closer to an urban area may have a higher opportunity cost than land in more remote locations.

Given an exogenous agricultural output price equal to 1 and land price, r, the objective of the representative producer is to choose L to maximize

(2)f(L,N)rL.
Taking the first-order condition (FOC), the optimal quantity of agricultural land can be described by
(3)fL(L,N)r=0.
This FOC can be solved for a unique L(r; N) as long as fLL0, which is true by assumption. The slope of L(r; N) with respect to r is
(4)Lr=1fLL<0.
Inverting the derived demand curve for land, L(r; N) produces the value-marginal product of land, conditional on the level of natural capital. We call this downward sloping curve VMP(L; N). It represents the marginal willingness to pay (or inverse demand) for agricultural land.

We now consider a change in natural capital stock from N0 to N1<N0. This describes the loss of a natural capital, for example, from disease or other activity that destroys the stock. As N changes, the model assumes that all other inputs are optimally adjusted. For example, as bat populations decrease, crop yields could fall because of increased pests. At the same time, producers can offset yield losses from pests by increasing expenditure on chemical pesticides. Lower yields and higher input costs lower the net value marginal product of land.

To proceed, we assume that VMP(L; N) and S(L) are linear. Figure 1 shows the equilibrium land rental price and quantity for natural capital stock N0, equal to r0 and q0, respectively. Applying the implicit function theorem to equation (3),

(5)LN=fLNfLL>0.
This implies that a small increase in N increases the quantity of land demanded. Since fLL is always negative and fLN is always positive, this holds for a discrete increase in N.
Figure 1. 
Figure 1. 

Welfare impact of decline in natural capital. Area X+Y equals the welfare loss of a decline in natural capital stock from N0 to N1.

Equation (5) implies that as N0 falls to N1, VMP(L; N) shifts down. Assuming that fLN/fLL is constant, figure 1 shows the impact of this change in natural capital on land prices and quantities. Land rental price and quantity fall to r1 and q1, respectively.

To calculate welfare impacts in the land rental market, we build on Alston et al. (1995), who develop a method for estimating the welfare impact of a supply shift in an agricultural output market. While our approach is similar, we model a shift in the derived demand curve for land. Also, our model uses revealed information from well-identified impact estimates to calculate the welfare implications of changes in natural capital stocks. Therefore, we infer the impact of natural capital shocks on supply or demand curves from observed outcomes with minimal assumptions about how changes in natural capital affect demand or supply curve parameters.

Since land and natural capital are weak complements, the welfare loss in the agricultural land market from a change in natural capital input is equal to the area X+Y in figure 1. Given the linearity assumptions, this is equal to the difference in areas of two triangles. The small triangle, formed from the supply curve y-intercept, (0, c), to (q1, r1) to (0, aK), represents the equilibrium surplus after the shock. This area is subtracted from the area of the larger triangle (base surplus) formed by (0, c), (q0, r0), and (0, a). With a vertical shift in the y-intercept of VMP(L; N) equal to K, the welfare loss is equal to

(6)Loss=12(ac)q012(aKc)q1.

Assuming an elasticity of demand at the original equilibrium of ϵd, we can solve for a, given observed land market price and quantity.

(7)a=r0+q0r0q01ϵd,
where the slope of VMP(L; N) is r0/q01/ϵd. The term c can be calculated from the base and post-shock equilibrium prices and quantities in the land market (see app. A). Equation (6) holds for c greater than or less than 0.

1.1.  Parallel Shift in VMP of Land

Assuming a parallel shift in VMP(L; N), we can solve for K as a function of observed changes in prices and quantities as well as the elasticity of demand for land at the initial land rental price and quantity, defined as ϵd. Specifically,7

(8)K=r0r1econometric estimate+r0q0initial averages1ϵdspecify(q0q1)econometric estimate.

Changes in land rental prices or quantities from both direct and spillover losses of natural capital can be estimated econometrically. The base and new levels of price and quantity can be calculated using averages in the data and coefficient estimates. Finally, we use incidence estimates from the literature (Dinterman and Katchova 2019) to calculate an implied range for ϵd. This allows us to fully parameterize equations (6), (7), and (8) as a function of the direct impact of WNS and the number of neighbors with WNS.

1.2.  Nonparallel Shift in VMP

Equation (8) holds for a parallel shift in VMP(L; N). If the slope of VMP(L; N) is also affected by the shock to natural capital, we can define the shift in the y-intercept of VMP(L; N) as

(9)K=r0r1+r0q01ϵd(q0q1)+Δslopeq1,
where Δslope is the change in the slope of VMP(L; N).

For our main analysis, we assume a parallel shift in VMP(L; N) (Δslope=0), but to demonstrate the importance of this assumption for our numerical estimates, we explore how welfare estimates change if lower quality or higher quality land experiences larger drops in productivity, corresponding to a steeper or flatter post-shock VMP(L; N) curve, respectively. Appendix B presents the derivation of K and graphically shows the welfare measure for a nonparallel shift in VMP(L; N). As with a parallel shift, welfare is calculated as the difference between two triangle areas.

2.  Data and Econometric Specification

In this section, we describe the data and econometric methods used to calculate the economic loss to agriculture from bat population crashes in the United States.

2.1.  Data

This analysis uses data from several sources. First, information on the spread of WNS over space and time at the county level comes from the Wildlife Health Information Sharing Partnership (WHISPers), coordinated by the US Geological Survey.8 This data set reports incidents of wildlife disease for a wide variety of diseases. Each detected event is recorded as an observation and includes the disease name, the number of affected individuals, the species impacted, the start and end date over which measurements were taken, and the county in which the outbreak occurs. For this analysis, we include all outbreaks of WNS and observe if at least one outbreak is detected in each county and year starting in winter of 2007. Figure 2 shows a map of the study region and includes county boundaries for those included in the analysis. Since the disease spread has concentrated in the east and middle parts of the country, we omit mountain and western states from the analysis. Other counties are omitted due to lack of other data.

Figure 2. 
Figure 2. 

Counties affected by white-nose syndrome. Shaded counties indicate the year in which WNS was first detected. White counties are included in the analysis but do not have a detected outbreak. Counties with no border are excluded from the analysis because of missing land rental or control data, or because they are outside the area of study. Albany and Schoharie counties had WNS detected in 2007. Since 2007 precedes the period in which cash rent data are available, their outbreaks do not provide identifying variation.

The shaded counties have had WNS detected according to the WHISPers data set. Lighter shades indicate more recent arrival of the disease while missing boundaries indicate that a county is omitted from the analysis either because it is outside the region in which WNS has spread or because of missing agricultural data. The map demonstrates that WNS arrived first in New York and has spread from there in all directions. Along the path and over time, some counties experienced outbreaks while others did not. We use this plausibly exogenous spread to identify the average effect of WNS detection in bats on agricultural outcomes. While it is possible that producer behavior influences this spread through pesticide use, evidence suggests that this mechanism is unlikely. For example, Frank (2021) tests the exogeneity of WNS spread by showing that arrival of the fungus does not affect outcomes until it is detected in bat populations. WNS has continued to spread since 2017, but these data are not used in our analysis because of the temporal coverage of our dependent variables.

Variables describing agricultural outcomes come from the USDA National Agricultural Statistics Service (NASS). We use county-level cash rental data available from 2008 to 2017. Specifically, we use the rental rate from nonirrigated cropland. In the sample, many counties do not report irrigated rental rates because of the relatively small number of irrigated acres. To graphically explore the connection between land rental rates and WNS, figure 3 presents coefficients from a pooled ordinary least squares (OLS) regression of county rental rate on indicators for the number of years since WNS was first detected in bats in a county. This exercise explores the correlation between rental prices and WNS. The omitted year is the first year of WNS detection. In the years before WNS arrival, rental rates were similar to the first year of arrival. This holds true for the year following the first detected case of WNS in a county. Then, starting two years after, rental rates begin to fall, potentially reflecting lower productivity or higher input costs with the loss of bats.9 Due to data availability, this figure does not include a balanced sample across the years since WNS arrival and does not include controls. Therefore, we interpret this as suggestive evidence of a connection between WNS and county land rental rates.

Figure 3. 
Figure 3. 

Land rental values and white-nose syndrome. The figure presents coefficient estimates from an unbalanced OLS regression of land rental rate on years since WNS arrival. Omitted category is first year of WNS detection.

To examine impacts of WNS on the number of agricultural acres in a county, we use agricultural census data on the number of cropland acres in each county in the years 1997, 2002, 2007, 2012, and 2017. For consistency, we use only counties that report cash rental rates. For this analysis, we use total cropland acres and not rented cropland. We do this because producers who use their own land face an opportunity cost of not renting out the land. A consistent interpretation is that farmers using their own land rent it from themselves. This requires an assumption that changes in cash rental rates on rented land reflect changes in profitability on owner-operated land as well. While land tenure can affect the propensity to make long-term conservation investments (Soule et al. 2000), there is strong empirical support for the capitalization model that land values are the capitalized value of cash rents and other factors like direct subsidy payments (Schnitkey and Sherrick 2011). Therefore, the relevant quantity in the land rental market is total cropland acres, not only acres that are explicitly rented.

It is possible that conservation investments made by owner-operators alter the impact of WNS on farm profitability. For example, Liu et al. (2016) suggest that rotations may decrease the need for pesticides, which would lower the value of the pesticide services provided by bats. If this is true, then the derived demand for land may not experience a parallel shift in response to WNS. We explore the implications of this in section 3.3.4.

To explore mechanisms behind the impacts of WNS in land rental markets, we calculate yields for three key crops in the regions affected most by WNS: corn, wheat, and soy.10 To do this, we divide total production of each crop by the number of acres planted, both provided by NASS. We also obtain farm input expenses from the agricultural census data. We divide this by total cropland acres to obtain input costs per acre.

Since WNS spread could potentially be affected by human populations and weather, and both could affect land rental rates, we also include data to control for these potential confounders. We use county estimates of human population from the Surveillance, Epidemiology, and End Results Program11 and quarterly precipitation and average minimum temperature from PRISM.12 In our empirical specifications we include quarterly average minimum temperature and total precipitation realizations and annual population as controls.

Finally, since we model a change in equilibrium price and quantity in land markets, we control for the distribution of cropland quality in each county-year. Since lower-productivity land leaves production first, average cropland rents may increase because of the increase in average quality of remaining cropland. This could confound estimates of the impact of shocks on land productivity. To control for this, we overlay cropland data layer (CDL) files with the NRCS SSURGO data set13 for each county-year of our analysis. The CDL files provide reliable spatial data indicating which land is in crop production every year since 2008. While the SSURGO data are time invariant, the changing land in production leads to changing land quality distributions.

To measure land quality, we use the Land Capability Class (LCC) from SSURGO for cropland within a county. There are eight LCCs that range from the highest quality (1) to lowest quality (8) land. We create three variables for each county-year that include the proportion of cropland that is high quality (LCC=1), medium quality (LCC=2, 3, or 4), and low quality (LCC>4). The exact choice of LCC aggregation does not affect our results in a quantitatively meaningful way. Including these LCC variables as controls for land quality in a county-year avoids confounding the impacts of WNS with the impact of changing land quality.

All variables used in the analysis are summarized in table 1. Variables used in the cash rents analysis have 17,459 county-years, reflecting rent data that are available annually starting in 2008. Other variables from NASS are summarized for the county-years included in the analysis. Variables from the census have fewer observations because of lower temporal frequency. Crop yields are available for more county-years because they are available annually and prior to 2008. Weather variables, human population, and LCC proportions are summarized for county-years included in the land rent analysis.

Table 1. 

Summary Statistics

 Variable MeanSDN
Rent ($ per acre, nonirrigated)78.7662.3017,459
Agricultural land (acres)146,313.11137,585.2911,617
Corn yield (bushel per acre)92.2444.3059,109
Wheat yield (bushel per acre)34.9316.6852,420
Soy yield (bushel per acre)32.6011.3951,405
Input expense per acre ($)26.2530.5611,547
Q1 precipitation (mm)202.83120.8117,459
Q2 precipitation (mm)334.30123.0417,459
Q3 precipitation (mm)301.52124.4417,459
Q4 precipitation (mm)217.30114.7517,459
Q1 minimum temperature (°C)−3.196.0917,459
Q2 minimum temperature (°C)11.603.7217,459
Q3 minimum temperature (°C)16.873.1917,459
Q4 minimum temperature (°C) 1.514.4917,459
Human population (count)69,963.39174,048.4017,459
Cropland share high quality.05.0917,459
Cropland share medium quality.79.1817,459
Cropland share low quality.15.1717459
WNS.04.1917,459
WNS neighbor count.24.6917,459
WNS neighbor indicator.14.3417,459

2.2.  Econometric Specification

To estimate the average impact of WNS and the subsequent loss of bat populations on agricultural land rental markets, we model county outcomes as a function of an indicator, WNSct, which equals one if a WNS outbreak has occurred in county c in any year prior to or including year t. To allow for spatial spillovers, we also include a count of the number of border counties that have had a WNS outbreak in any year before or including year t(WNSctn). If spillovers exist, failing to control for neighboring outbreaks would violate the assumption of a stable unit treatment value (SUTVA). We estimate average impacts on cash rents, crop yields, and input expenses. The empirical specification for these outcomes is

(10)yct=β0WNSct+β1WNSctn+β2Xct+δst+αc+εct,
where yct is the dependent variable of interest in county c and year t.

The term Xct includes contemporaneous weather (quarterly minimum temperatures and precipitation), human population, and LCC distribution variables.14 Since the LCC variables sum to 1, we avoid perfect collinearity by excluding the cropland share that is low quality. The term αc is a county fixed effect that controls for time-invariant differences between counties, including climate and soil productivity. This also controls for the importance of bats for pest control within a given county. Our main specification includes a state-year fixed effect, δst. This controls for time-varying shocks common to all counties in a state such as commodity price changes or state policies. Finally, ϵct is a random error term, clustered at the county level to allow for within-county correlation over time.

First, we examine impacts on the average rental rate in county c and year t, rct. In this model, β0 tells us the average effect of WNS detection on the rental rate in a county, conditional on the number of neighbor counties with an outbreak. For β0 to be unbiased, the existence of a WNS outbreak in a county-year must be uncorrelated with the model’s error term. Since identification of WNS impacts comes from within-county variation over time, this requires that the timing of WNS arrival is exogenous to land rental prices. Given that WNS spread is largely determined by biology and is out of the control of producers, this is a reasonable assumption. Similarly, the timing of neighboring WNS outbreaks must be exogenous to county rental prices for β1 to be identified. As described in Butts (2021), including neighboring counties allows us to identify the direct effect and the spillover impact if the spillover impacts do not affect counties beyond neighboring counties. To examine the robustness of our estimates to specific modeling assumptions, we include robustness checks with alternative controls and specifications (see the online appendix).

Next, we explore how WNS affects the quantity of agricultural land by estimating

(11)qct=θ0WNSct+θ1WNSctn+θ2Xct+δstq+αcq+εctq,
where the number of cropland acres in county c and year t is the dependent variable. Treatment and control variables are the same as for land rent, but we exclude the LCC shares because we do not want to condition the change in cropland on a land quality distribution. County and state-year fixed effects are included and can differ from those in equation (10), indicated by superscript q.

Given our assumption of a fixed supply curve in the land market, shocks to the inverse demand for land must result in new prices and quantities that lie on the same supply curve. This introduces restrictions to the parameter values in equation (11). The land supply curve is r=c+dq, implying that a shock must lead to changes in land price and quantity that are consistent with a constant slope, d. Therefore, the ratio of direct price and quantity impacts must equal the ratio of spillover price and quantity impacts. This implies that d=Δr/Δq=β0/θ0=β1/θ1. This can be solved for θ1=β1θ0/β0, which can be substituted into equation (11) to produce the constrained regression,

(12)qct=θ0(WNSct+β^1β^0WNSctn)+θ2Xct+δstq+αcq+εctq,
where β^1/β^0 are the parameters estimated from equation (10). The variable WNSct+(β^1/β^0)WNSctn can be calculated after estimating equation (10). After estimating the constrained model, the coefficient on the transformed variable, WNSct+(β^1/β^0)WNSctn is equal to θ^0 and the estimate of θ1 can be recovered as θ^1=β^1θ^0/β^0. The standard errors for θ^0 and θ^1 are estimating using clustered bootstrapping (with 200 samples) to account for the variability in the estimated parameters used to generate the reduced form independent variable in equation (12).

The coefficients β0, β1, θ0, and θ1 from equations (10) and (11) are used to parameterize equations (6) and (8). The total vertical shift and welfare loss from spillovers depend on the presence of an outbreak in a county and on how many neighboring counties experience an outbreak. Therefore, the shift and welfare loss are calculated separately for counties with and without a WNS outbreak and with one, two, three, four, and five neighbors with WNS (for a total of 10 possible combinations). The maximum number of neighbor counties with WNS in our data set is five. In our sample, as of 2017, 1,695 counties have zero neighbors with WNS, 337 have one, 177 have two, 79 have three, 29 have four, and 10 have five. The spillover effects are generated by WNS in just 178 counties. This illustrates that the spillover effects impact many more counties than those that directly experience WNS outbreaks. To obtain total costs, we first calculate the vertical shift in the inverse demand curve for a county with n neighboring outbreaks as

(13)Kcn=r0r1cn+r0q01ϵd(q0q1cn),
where r1cn=r0+β0WNSc+β1WNScn, with WNSc as an indicator for whether a county has a WNS outbreak and WNScn is the number of neighbor counties with a WNS outbreak. Similarly, the new quantity of agricultural land is calculated as q1cn=q0+θ0WNSc+θ1WNScn. This leads to a total cost that depends on the vertical shift and changes in price and quantity, which in turn depend on a WNS outbreak in a county and how many neighboring counties have a WNS outbreak. The total cost of WNS for a county becomes
(14)Losscn=12(ac)q0+12(aKcnc)q1cn.
To calculate a total cost of WNS, we use average r0 and q0 and estimate q1cn, r1cn, Kcn, and Losscn for all counties in our analysis using the location of WNS outbreaks as of 2017 and sum the costs across all counties.15

Finally, we test the mechanisms driving the changes seen in the land rental market and explore regional heterogeneity. First, we model yields of corn, wheat, and soy as the dependent variable in equation (10). Following Schlenker and Roberts (2009), we use the natural log of crop yields as dependent variables. Then, we examine WNS impacts on logged input expenses per crop acre in a county-year. To explore regional heterogeneity, we estimate the model separately for regions within the eastern and central parts of the United States. We also examine alternative specifications to determine the robustness of our main econometric results.

3.  Results

In this section, we report coefficient estimates from econometric models estimating the effects of WNS in county land rental markets. Then, we describe the parameterization and calculation of direct and spillover annual welfare losses that result from WNS and the loss of bat populations. The section concludes by exploring the mechanisms for the impacts we see in the land market and demonstrating sensitivity to the definition of neighboring WNS outbreaks and a changing slope of the land demand curve.

3.1.  Main Econometric Estimates

Table 2 demonstrates the impact of WNS on county cropland rental rates. Column 1 is our preferred specification, using county and state-year fixed effects, and demonstrates an average effect of WNS on rental rates of −$2.84 per acre per year for an outbreak within a county. This represents 3.5% of the 2008 average rental value in included counties. For every neighboring county with WNS, rental rates fall by $1.50 per acre (or 1.9% of base rent levels). This suggests an economically significant impact of WNS on agricultural producers and net value.

Table 2. 

Impact of White-Nose Syndrome on Nonirrigated Land Rental Values

VariablesRent
(1)
Rent
(2)
Rent
(3)
ln(Rent)
(4)
Rent
(5)
WNS−2.839**−3.715***−2.839**−.0237*−4.214***
 (1.242)(1.236)(1.247)(.0141)(1.236)
Neighbors with WNS−1.497***−1.656**−1.457***−.0138*** 
 (.413)(.731)(.414)(.00454) 
Constant96.86***96.61***89.92***4.167***95.46***
 (7.171)(7.176)(.297)(.101)(7.194)
SpecificationMainBinary neighbor variableNo controlsLogged dependent variableExcluding neighbor
Observations17,45917,45917,45917,45917,459
R-squared.682.681.680.495.681
Number of counties2,3272,3272,3272,3272,327

Note. Standard errors clustered at the county. All models include county fixed effects, human population, quarterly temperature, LCC distribution, and precipitation controls, unless otherwise indicated. Column 1 is the main specification, with rent included in levels and a count of neighbor counties with WNS. Column 2 includes an indicator for whether a neighbor county has a WNS outbreak. Column 3 excludes controls. Column 4 uses the natural log of rent. Column 6 omits a control for neighboring outbreaks.

*p < .1.

**p < .05.

***p < .01.

View Table Image

The results in column 1 of table 2 are used to calculate welfare impacts, but point estimates do not vary substantially with alternative specifications. Column 2 tests for spillover effects using an indicator for whether any neighbor county has a WNS outbreak. The point estimates of both direct and spillover effects become larger in magnitude, but results remain qualitatively similar. Column 3 confirms that results do not change quantitatively with the exclusion of population, weather, and land quality controls. Column 4 presents results using the natural log of rent as the dependent variable. Estimates suggest that a WNS outbreak decreases land rents within a county by 2.4%. Spillover effects lead to a decrease in land rent of 1.4% per neighbor with WNS.

Finally, column 5 presents estimates for the direct impact of WNS without considering spatial spillovers. The significant impact of neighboring counties on land rents in columns 1–4 suggests that this model in column 5 does not identify the effect of WNS because neighboring counties are also impacted. In this case, the estimated direct impact is larger than the estimate when controlling for spatial spillovers. This occurs because the estimated effect captures both the direct impact of WNS and the spillover effects into the county with WNS. Using this model to estimate welfare impacts would overstate the direct impact of WNS while ignoring the spillover effects that impact significantly more counties. Therefore, in all welfare calculations, we use the coefficients presented in column 1.

Next, table 3 presents the impact of WNS on the number of cropland acres in a county. Column 1, our main specification, shows model coefficients that are constrained to imply a constant land supply curve slope. Results suggest a direct impact of −1,102 acres, or 0.8% of the 2007 average of cropland acres. The number of cropland acres decreased by 581.6 per neighboring county with a WNS outbreak. Column 2 presents the same coefficients but without including controls. Coefficients remain quantitatively similar. In column 3, we present the results of an unconstrained model. While point estimates are noisier, they are quantitatively close to the constrained estimates. This suggests that the estimated impacts are approximately consistent with a constant supply curve slope. The constrained regression increases model precision without greatly altering coefficient estimates.

Table 3. 

Impact of White-Nose Syndrome on Cropland Acres

VariablesAcres
(1)
Acres
(2)
Acres
(3)
ln(Acres)
(4)
Acres
(5)
WNS−1,102**−1,046**−1,196−.0462***−1,783*
 (436.5)(437.4)(998.3)(.0155)(942.9)
Neighbors with WNS−581.6**−551.6**−557.8−.0165*** 
 (230.3)(230.7)(349.5)(.00491) 
Constant178,495.6***141,363.9***178,504***11.92***177,999***
 (14649.01)(14649.01)(13,015)(.111)(13,002)
SpecificationConstrainedConstrained, no controlsUnconstrainedLogged dependent variableExcluding neighbor
Observations11,61711,61711,61711,61711,617
R-squared.353.346.353.537.353
Number of counties2,3272,3272,3272,3272,327

Note. Standard errors clustered at the county level in parentheses. Boostrapped standard errors with 200 draws shown for constrained models. Columns 1 and 2 present the result of constrained models with and without controls. Column 3 presents results of the unconstrained model while column 4 presents the unconstrained model with a logged dependent variable. Column 5 presents the unconstrained model with no spatial spillover control. All models include controls for human population and weather.

*p < .1.

**p < .05.

***p < .01.

View Table Image

To test robustness to functional form, column 4 of table 3 presents results with the natural log of acres as the dependent variable. Results suggest that WNS directly decreases acres by 4.6% and spillovers cause the number of acres to fall by 1.7% per neighbor county with a WNS outbreak. Finally, column 5 presents results without a control for neighboring WNS outbreaks. Consistent with the rental model, excluding neighboring WNS outbreaks leads to a larger point estimate of the impact of WNS but ignores the larger number of counties indirectly impacted by WNS. As before, we use coefficient estimates shown in column 1 for welfare analyses.

3.2.  Welfare Estimates

We use our econometric estimates to calculate welfare losses in each county in our data set based on WNS outbreaks as of 2017. This allows us to quantify the total annual losses to US agriculture from WNS. First, we use our estimated impacts to calculate Kcn (the vertical shift in the y-intercept of the derived demand for agricultural land) from the theoretical model as a function of direct WNS presence within a county and the number of neighboring counties with WNS outbreaks. Using this, we calculate the dollar value of annual surplus losses in each county as a function of the price elasticity of the derived demand for agricultural land. For our base results, we assume that the derived demand for land experiences a parallel shift as a result of WNS. By bootstrapping using 200 draws, we include standard errors on our estimates of Kcn and welfare losses. Estimates of Kcn and welfare losses for direct and indirect (only) impacts are presented in table C1 where we also present direct and indirect costs per county as a proportion of base acres and base welfare (see app. D for calculation of baseline welfare).

To calculate Kcn, we use the average base rental rate of $80.97 (r0) and base number of acres (q0) equal to 142,996. Both averages are from the year in the data closest to 2007, when WNS was first detected. Therefore, they reflect outcomes with bat populations that existed prior to outbreaks of WNS. To calculate the welfare loss, we also need an estimate of the new level of acres, q1 which we obtain using the estimated coefficients reported in table 3 along with q0. Specifically, q1cn=q0+θ0WNSc+θ1WNScn.16

Combined with parameter estimates from column 1 of tables 2 and 3 and a demand elasticity, we can calculate Kcn that includes both direct and spillover impacts. We assume a range of possible demand elasticities that are consistent with our data and the tax incidence estimates in Dinterman and Katchova (2019). Specifically, they find that a one dollar increase in land tax increases land prices by between $0.31 and $0.40; those values imply demand elasticities of 0.54 and 0.36, respectively.17

Figure 4 presents the total welfare costs of WNS, broken up by direct and spillover effects. Total costs are calculated using Kcn and new land prices and quantities that result from both direct and spillover effects. The direct cost calculates the loss considering only Kcn and the change in prices and quantities predicted when WNScn=0 for all counties.

Figure 4. 
Figure 4. 

Welfare impacts of white-nose syndrome, 2017. The figure presents the welfare cost of WNS in counties with an outbreak and on neighboring counties, as of 2017. Detailed information is available in table C1.

Each column of figure 4 presents results for a different land demand elasticity, equal to 0.35, 0.45, or 0.55. Results suggest that the total cost of WNS in 2017 was between $426 and $495 million. Importantly, while the coefficient estimate is largest for counties that experience WNS outbreaks, the spillover effects lead to larger total costs because many more counties are impacted. Given all three land demand elasticities, spillover costs account for 76.4% of the total costs of WNS. Ignoring the impact of neighboring WNS outbreaks (using econometric estimates that exclude this variable as in column 5 of tables 2 and 3) leads to an estimated total welfare cost of between $153 and $180 million (results not shown in the figure). Therefore, failing to account for spillover effects leads to a significant underestimation of the welfare costs of WNS.

The welfare costs presented in figure 4 demonstrate that WNS is an economically important shock to agricultural value. The direct impact in counties with WNS is between $564,937 and $657,319 per county per year. For context, the agricultural sector had an average net farm income of $30.8 million per county, according to the USDA.18 The direct cost per county represents a shock of between 2.5% and 2.7% of baseline welfare. As the demand elasticity at the initial point increases, the implied vertical shift decreases and leads to smaller surplus losses because of the shock to natural capital (losses increase as a percentage of baseline surplus). With base acres, q0=142,996, this range of surplus losses implies a loss of $3.95 to $4.60 per base acre in the county. Results also suggest that the total cost per acre could be as high as $15.13 per acre for a county with a WNS outbreak and five neighbor counties that also have outbreaks (the total loss with a direct impact and five neighbors is $2,163,523).

These estimated losses are economically significant at the county level but remain small compared to central per-acre estimates of $74 used in Boyles et al. (2011). Our estimates are likely smaller because of the range of responses available to producers that may exceed those considered in the simulation presented in Boyles et al. (2011). For example, producers may switch crops, change the number of acres operated, or adjust the timing of input use in ways that are not captured in the modeling exercise described in Boyles et al. (2011). Also, in practice, while WNS significantly decreases bat population counts, it may not drive the population to zero. In this case, the service provided by nature does not cease completely.

3.3.  Mechanisms, Spatial Heterogeneity, and Robustness

Our estimates of WNS impacts in land rental markets suggest that the loss of bats has economically significant implications for agricultural production. In this section, we explore the drivers of these impacts by testing for impacts on crop yields and input expenses. We also examine spatial heterogeneity in impacts and demonstrate the impacts of alternative ways to measure neighboring WNS outbreaks. Finally, we show the impact of our assumed parallel shift in the derived inverse demand curve for land.

3.3.1.  Mechanisms

Table 4 presents the estimated impacts of WNS on corn, wheat, and soy yields including (cols. 1–3) and excluding (cols. 4–6) neighboring WNS outbreaks.19 For years prior to 2008, we assume constant LCC distributions because we do not have them prior to 2008. This means that LCC distributions are measured with error prior to 2008. Nevertheless, the 2008 LLC distributions likely provide a reasonable proxy control for two reasons. First, the land quantity changes over time are small relative to the total stock of cropland. Therefore, changes in the land quality distribution are small. Next, our point estimates in table 2 do not change when we exclude the LCC controls (see col. 3), suggesting that in this context, controlling for LCC distribution has a minimal impact on our estimates. On the other hand, excluding years with no LCC information greatly reduces the number of years prior to the WNS outbreak, which reduces the ability to identify impacts based on within-county changes over time (see the online appendix for results when excluding years prior to 2008).

Table 4. 

White-Nose Syndrome and Crop Yields

 Including Neighbor WNS OutbreaksExcluding Neighbor WNS Outbreaks
Variablesln(cornyield)
(1)
ln(wheatyield)
(2)
ln(soyyield)
(3)
ln(cornyield)
(4)
ln(wheatyield)
(5)
ln(soyyield)
(6)
WNS−.0304−.0116−.0120−.0547**−.0315−.0275**
 (.0261)(.0272)(.0122)(.0240)(.0262)(.0117)
Neighbors with WNS−.0212**−.0171**−.0135***   
 (.00955)(.00861)(.00339)   
Constant6.118***5.042***4.171***6.110***5.035***4.164***
 (.157)(.214)(.0862)(.156)(.214)(.0862)
SpecificationRegion-year FERegion-year FERegion-year FERegion-year FERegion-year FERegion-year FE
Observations59,10952,42051,40559,10952,42051,405
R-squared.442.260.525.442.260.525
Number of counties2,1752,1592,0232,1752,1592,023

Note. Standard errors clustered at the county. All models include county fixed effects (FE), human population, quarterly temperature, Land Capability Class (LCC) distribution, and precipitation controls. Columns 1–3 include outbreaks within a county and the number of neighbors with an outbreak. Columns 4–6 exclude the count of neighbors with outbreaks.

*p < .1.

**p < .05.

***p < .01.

View Table Image

Notably, WNS causes yields to fall for corn, wheat, and soy. The point estimates are negative for all three crops for both direct and spillover effects of WNS. While the spillover effects are estimated more precisely, they do not differ statistically from the noisier direct effects. When excluding the neighboring WNS outbreaks (cols. 4–6), the direct impacts appear statistically significant. This suggests that a high degree of multicollinearity between WNS outbreaks within a county and its neighbors likely affects the precision of our estimated impacts in columns 1–3.

The estimated yield impacts range from 1.2% for wheat and soy to 2%–3% for corn. This is consistent with additional pests during the growing season for all three crops, and particularly for corn. Corn and soy are harvested in the fall, after the season during which both bats and pests are most active. While wheat is harvested earlier in the year, our results suggest that increased pest pressure from the loss of bats can also impact wheat yields.

Next, we test whether producer input costs are affected by WNS (see table 5). Again, we present results including (cols. 1–3) and excluding (cols. 4–6) neighboring WNS outbreaks. We again assume constant LCC prior to 2008 (results excluding years prior to 2008 are included in the online appendix).

Table 5. 

White-Nose Syndrome and Input Expenses

 Including Neighbor WNS OutbreaksExcluding Neighbor WNS Outbreaks
 (1)(2)(3)(4)(5)(6)
Variablesln(input exp per acre)
(1)
ln(input exp per acre)
(2)
ln(input exp per acre)
(3)
ln(input exp per acre)
(4)
ln(input exp per acre)
(5)
ln(input exp per acre)
(6)
WNS.0430.0493.0401.0667**.0838***.0613**
 (.0324)(.0334)(.0324)(.0293)(.0295)(.0292)
Neighbors with WNS.0226**.0271***.0198**   
 (.00948)(.00952)(.00942)   
Constant2.961***3.310***3.297***2.983***3.310***3.305***
 (.249)(.200)(.00646)(.248)(.200)(.00566)
SpecificationBaseRegion-year FENo vontrols FEBaseRegion-year FENo controls
Observations11,54711,54711,54711,54711,54711,547
R-squared.757.737.757.757.737.756
Number of counties2,3272,3272,3272,3272,3272,327

Note. Standard errors clustered at the county. All models include county fixed effects (FE), human population, quarterly temperature, LCC distribution, and precipitation controls. Columns 1–3 include outbreaks within a county and the number of neighbors with an outbreak. Columns 4–6 exclude the count of neighbors with outbreaks.

*p < .1.

**p < .05.

***p < .01.

View Table Image

Across all specifications, point estimates suggest that input costs per acre increase with a WNS outbreak within a county or neighboring counties. As with yield impacts, spillover effects are estimated more precisely, but when excluding neighboring WNS outbreaks, the direct effects become statistically significant. This again suggests that multicollinearity complicates the separate identification of direct and spillover effects in this context. While the direct effects are less precisely estimated, their magnitudes are larger, suggesting that a WNS outbreak within a county increases input costs per acre by 4%–5%. Each neighboring county with WNS increases costs per acre by 2%–3%.

Taken together, we find evidence that the decrease in agricultural land rents is driven by decreased yields of corn and soy and increased input costs. Both of these decrease agricultural profitability, lower the derived demand for land, and lead to measurable impacts in land rental markets.

3.3.2.  Spatial Heterogeneity

In this section, we consider the spatial heterogeneity in the impacts of WNS on outcomes in the land rental market. Agricultural production differs considerably across the region of our analysis, with larger farms in the central and western parts of the United States. Additionally, counties further west are larger on average. Therefore, we divide our data into three regions (East, East Central, and West Central) and estimate the impact of WNS on rental rates and the number of cropland acres.

Table 6 shows that the impact of WNS on average rental rates is qualitatively similar across the three subregions, with WNS decreasing rental rates. Here again, multicollinearity decreases the precision of estimates but all point estimates are negative, and in each region either the direct or spillover impact is statistically significant. These results suggest that WNS has negative impacts in counties in all three regions.

Table 6. 

Regional Impacts of WNS on Nonirrigated Land Rental Values

VariablesEast Central
(1)
East
(2)
West Central
(3)
WNS−3.898**−1.996−2.609
 (1.927)(1.385)(2.602)
Neighbors with WNS−.786−2.194***−2.318***
 (.619)(.685)(.827)
Constant158.7***88.68***67.99***
 (16.10)(31.57)(7.644)
Observations5,7233,9737,772
R-squared.690.383.729
Number of counties7385591,031

Note. All standard errors are clustered at the county. All models include county and state-year fixed effects, human population, quarterly temperature, and precipitation controls.

*p < .1.

**p < .05.

***p < .01.

View Table Image

Table 7 presents the results of constrained models of cropland acres for all three regions. The magnitude of impacts differs across the regions. Notably, only the East and West Central regions experience a statistically significant effect on the number of acres in agriculture. This could be the case if, for example, the East and West Central regions have more marginal cropland. Since the East Central region contains counties in the productive agricultural states in the US Corn Belt, land in that region may remain viable even after WNS outbreaks.

Table 7. 

Regional Impacts of WNS on Cropland Acres

VariablesEast Central
(1)
East
(2)
West Central
(3)
WNS244.60−537.3**−2,601**
 (1,049)(255.8)(1,008)
Neighbors with WNS49.3−590.8**−2,310**
 (211.5)(281.3)(896.3)
Constant119,415.3***31,028.0***286,725.5***
 (13,544.4)(11,048.4)(24,986.6)
Observations3,6903,7465,316
R-squared.367.374.346
Number of counties7387561,070

Note. All standard errors are clustered at the county. All models are constrained and include county and state-year fixed effects, human population, quarterly temperature, and precipitation controls. Model coefficients are constrained to imply a constant supply curve slope.

*p < .1.

**p < .05.

***p < .01.

View Table Image

Also, the impacts in the West Central region are much larger in magnitude than the impacts in the East. This is intuitive because of variability in the mean number of acres across the regions. In the West Central region, counties average approximately 206,000 cropland acres while the East Central and East regions average 108,000 and 42,000 cropland acres, respectively. This suggests that a given percentage change would have a much larger level effect in the West Central region. Consistent with this, the impact of WNS on cropland acres (table 3) is more precisely estimated when using the natural log of the number of acres. Taken together, these regional estimates suggest that the average effects presented in section 3.1 are driven by rental rate effects in all regions and acreage effects that largely occur in the counties in the western and eastern portions of the sample.20

3.3.3.  Robustness

In this section, we explore alternative measures of neighboring WNS outbreaks. Our base specification simply counts the number of counties that share a border with a specific county and have a WNS outbreak. Alternatively, we could consider all counties whose centroids are within a certain distance of the centroid of the specific county. This could allow for spillovers to occur across multiple county lines while excluding outbreaks in some neighbor counties if the county is particularly large.

Table 8 includes specifications that estimate the impact of WNS in a given county with alternative measures of neighboring outbreaks. Column 1 is our base specification while columns 2–5 count other counties with a WNS outbreak if the counties’ centroids are within 10–140 kilometers of a given county. Results from these models suggest that direct effects remain negative and significant across all measures of neighboring outbreaks. As we consider neighboring outbreaks that are further away, the estimated spillover effect becomes smaller, suggesting that further-away counties have smaller (or zero) spillover effects when compared to considering only neighboring counties. Further, when considering only counties within 10 kilometers, coefficient estimates increase in magnitude. This likely occurs because both the included neighbors and the direct effect are contaminated by spillovers from other neighboring counties.

Table 8. 

WNS Syndrome in Neighboring Counties, Alternative Spillover Measures

VariablesRent
(1)
Rent
(2)
Rent
(3)
Rent
(4)
Rent
(5)
WNS−2.839**−3.510***−3.360***−3.522***−4.222***
 (1.242)(1.266)(1.252)(1.243)(1.236)
Neighbors with WNS−1.497***    
 (.413)    
Neighbors with WNS (140 km) −.394***   
  (.122)   
Neighbors with WNS (50 km)  −.825***  
   (.310)  
Neighbors with WNS (25 km)   −1.052** 
    (.469) 
Neighbors with WNS (10 km)    −3.987
     (3.245)
Constant96.86***96.49***96.30***96.10***95.45***
 (7.171)(7.188)(7.175)(7.174)(7.196)
Observations17,45917,45917,45917,45917,459
R-squared.682.682.682.681.681
Number of counties2,3272,3272,3272,3272,327

Note. All standard errors are clustered at the county. All models include county fixed effects, human population, quarterly temperature, and precipitation controls, unless otherwise indicated. Neighbors with WNS (X km) is a count of the number of counties with WNS detected with centroids within X km of the centroid of a given county.

*p < .1.

**p < .05.

***p < .01.

View Table Image

The results in table 8 provide evidence that counting the neighboring counties with WNS is a useful way of capturing the spillover effects of WNS. Including only close neighbors excludes counties that influence the spillover effect. As counties can be further away, the estimated spillover effect decreases considerably, suggesting that the counties at larger distances do not contribute as significantly to the spillover effect. Therefore, including all neighboring counties balances these trade-offs by including relevant counties and ensuring that nontreated counties are not experiencing spillovers and therefore serve as appropriate controls in our main specification.

Ferraro and Miranda (2017) find that common fixed effects modeling approaches such as that applied in this paper do not always produce unbiased estimates in observational settings. They suggest that combining matching methods with panel fixed effects produces more reliable estimates. In the online appendix, we demonstrate that the counties that experienced a WNS outbreak differ from those with no outbreak. Therefore, we combine matching methods with our fixed effects specifications to explore model robustness. While matching reduces sample sizes, the analyses do not contradict the results from our main specifications that use all observations.

3.3.4.  Changing Demand Slope

For our base welfare calculations in figure 4, we assume a parallel shift in the derived demand for land. This implies that land of all quality experiences an equivalent drop in profitability. In reality, it is likely that land of higher or lower quality may be more impacted by the loss of pest control. For example, higher quality land likely has higher baseline yields. A proportionate shock may therefore have a larger level effect on profitability on high quality land. On the other hand, crop growth on high quality land may be more resilient to shocks, resulting in smaller losses in productivity. This could occur, for example, if inframarginal owner-operated land uses more conservation practices such as crop rotations that slow the spread of some pests. Given this uncertainty in the impact of ecosystem service shocks on the slope of the derived demand for land, we calculate welfare impacts under alternative assumptions about the change in slope of the derived inverse-demand curve for land.

Figure 6 presents aggregate welfare impacts as of 2017, including direct and spillover effects under the assumptions of a parallel shift (col. 1), a pivot around the y-intercept (col. 2), and a doubling of the Kcn implied by the parallel shift (col. 3). See figure 5 for a graphical illustration of each of these assumed changes in the slope of derived demand for land. After a change in natural capital (N) from N0 to N1, the new derived demand always passes through the same observed post-shock land quantity and price. The expression VMP(L; N1)parallel shows the parallel shift while VMP(L; N1)pivot illustrates the pivot around a and VMP(L; N1)double presents the curve if the y-intercept shifts by twice the level of Kcn implied by a parallel shift.

Figure 5. 
Figure 5. 

Alternative changes in inverse demand curve slope. The figure shows the implications of assuming that the demand curve pivots around a (VMP(L; N1)pivot), shifts parallel (VMP(L; N1)parallel), and that the intercept changes by twice the amount implied by a parallel shift (VMP(L; N1)double).

All three scenarios in figure 6 assume a demand elasticity of 0.45. Assuming linearity, welfare impacts theoretically increase in Kcn, and this exercise is meant to reveal the magnitude of the change. We choose the alternative slope changes to bound our estimates between a pivot around the y-intercept and a change in y-intercept that is twice as large as would occur with a parallel shift.

Figure 6. 
Figure 6. 

Welfare impacts of white-nose syndrome, 2017, alternative slope scenarios. The figure presents the welfare cost of WNS in counties with an outbreak and on neighboring counties, as of 2017. Parallel shift replicates the base assumption. Pivot around the y-intercept assumes that the demand for land pivots around the base y-intercept. Double baseline K assumes that the y-intercept of the demand for land shifts by twice as much as in the parallel shift. The demand elasticity for land is 0.45 in all three scenarios. Detailed information available in table C2.

Table C2 presents the county-level results of this sensitivity analysis and demonstrates that direct welfare costs from WNS range from $2.11 to $6.29 per base acre as Kcn ranges from 0 to twice the baseline level. Pivoting around the y-intercept implies an increase in b of 0.00003. Since the slope of the VMP of land is −b, this implies a steeper downward slope. With the larger Kcn, the slope decreases by the same amount. For spillover impacts, the resulting change in slope differs for the two scenarios. If the y-intercept is fixed, the change in slope increases as the number of neighboring WNS outbreaks increases. When Kcn doubles from its base level, the implied change in slope becomes larger with more neighboring outbreaks.

Overall, this exercise suggests that the assumed change in inverse demand curve slope can numerically affect welfare estimates, with total losses per year falling between $228 and $678 million as the change in y-intercept goes to zero or doubles in size relative to the case of a parallel shift. Continuing to increase the change in slope (through a larger change in Kcn) further increases the estimated welfare loss. In all cases, the spillover costs significantly exceed the direct costs of WNS within a county.

4.  Discussion and Conclusion

In this paper, we theoretically describe a method to use land rental market data to infer the welfare impacts of changes to a natural capital stock that supports agricultural production. The method can be applied when impacts of changing natural capital stocks flow across the boundaries of the units of observation (e.g., county lines). We operationalize this method using widely available data on cash rents from the USDA, so our approach can serve as a useful bridge between causal impact identification prevalent in natural resource economics settings (Ferraro et al. 2019) and a welfare-theoretic framework for nonmarket valuation. The method and land rental market data described in this paper provide a path to valuing other ecosystem services that contribute to agricultural value.

The method described here can complement structural demand approaches such as those employed in Fezzi and Bateman (2011), Fezzi et al. (2014), and Laukkanen and Nauges (2014). While our approach requires data to estimate impacts to land prices and quantities, structural approaches require detailed data on many output and input quantities and prices in the study region over enough years for a meaningful econometric analysis and can require plausible instrumental variables when land share allocations are endogenous. Therefore, in contexts with plausibly exogenous shocks to natural capital stocks, the land rental approach can estimate the benefits and costs of environmental change with information on relatively few variables. Importantly, since cash rent values reflect land profitability assuming optimal adjustments, we do not need separate information on all inputs, outputs, and their costs. Instead, the net impact of these adjustments is reflected in changing land rents.

We find that WNS, which destroys bat populations, decreases farm welfare by reducing corn, wheat, and soy yields while increasing input expenses per acre. Welfare costs of between $426 and $495 million per year demonstrate the economic significance of the ecosystem services provided to agriculture from unpriced natural capital stocks such as bat populations. These estimates likely represent lower bounds of social values because they do not include other impacts such as those to human health (Frank 2021). Of course, the final cost to society of WNS depends on how long it takes for bat populations to recover. If they recover quickly (e.g., because of adaptation; Frank et al. 2019), costs may be low compared to a scenario in which populations remain low for many years.

Our results also highlight the potential economic importance of the spillover effects from losses in natural capital. The existence of spatial spillovers means that each shock affects multiple counties. Ignoring this effect can bias econometric estimates and in the case of WNS would lead to significant underestimates of the costs of natural capital losses.

The economically significant value of the ecosystem services provided by bats can justify the use of public resources to prevent the spread of WNS and other threats to bat populations. In addition to implementing existing management strategies (e.g., closing caves), research that could improve management effectiveness may also be cost effective and justified by the large agricultural benefits of healthy bat populations.

To more precisely compare our estimated benefits to program costs, we perform a back-of-the envelope cost estimate for two strategies currently under consideration by the US Fish and Wildlife Service. These include vaccinating individual bats or using fungicide in locations where bats hibernate. Vaccination protects individual bats while fungicide controls spread in a given location. According to communications with US Fish and Wildlife Service officials, the expected cost per bat of the vaccination program, excluding research and development, is estimated to be $1.75 per bat plus a 20% markup to cover overhead. For bat population numbers, we use estimates from Cheng et al. (2021), focusing on little brown bat populations with at least 50 individual bats. These data suggest that there are an average of 2,250 brown bats per colony (though the distribution is skewed, with a median of approximately 400 bats per colony; Russell et al. 2014). For this exercise, we assume an average of two sites per county and examine the costs of preventing future WNS outbreaks after bat populations recover in counties that already experienced bat population crashes due to WNS.

This calculation suggests an average vaccination program cost of $9,450 per county for a total of $22 million across the 2,327 counties in our analysis. Similarly, the expected cost per site (excluding research and development) for area fungicide is assumed to be $7,500 plus a 20% overhead cost. Across the two sites per county, the cost of this program is $18,000 per county or nearly $42 million.21 At least initially, both treatments would be applied annually, making them comparable to our estimated annual costs of WNS.

Comparing our estimated agricultural benefits of $426–$495 million per year to the program costs of $22 and $42 million suggests that current initiatives to slow WNS spread could produce substantial benefits that exceed their cost if they effectively control the spread. Since this net benefit excludes research and development costs, it represents a maximum willingness to pay per county for research and development assuming perfect efficacy of the implemented control effort. Even with imperfect efficacy, a net benefit remains. For example, if treatment avoids future WNS outbreaks with just 9.86% efficacy, our lower bound benefit estimate suggests that the net benefits of the fungicide treatment for little brown bats go to zero ($4260.0986=$42).

The analysis points to the value of scientific efforts such as NABat22 to compile and standardize data on ecosystems and other natural capital stocks that provide value to society. Similar efforts could contribute to the valuation and management of other ecosystem components that support the market economy. With consistent data on important ecosystem stocks (including species presence/absence) over space and time, economists can use revealed preference methods to enhance our understanding of the contribution of natural capital stocks to a wide range of economic activities and health outcomes. This also suggests that citizen science efforts (Aceves-Bueno et al. 2017) could be leveraged to estimate the economic value provided by a wide range of species and habitat.

The importance of systematic data on natural capital stocks over space and time points to the shortcoming of this paper. While we use WNS presence as a proxy for the crash of bat populations, we do not observe the number of bats at any point in time. This limits the valuation exercise to the average effects of a detected WNS outbreak of any size on US agricultural value. To the extent that treatment effects vary over time or counties, our estimated average effects are likely subject to attenuation bias (Goodman-Bacon 2018).23

With data on bat populations and abundance, we could model how the intensity of changes in bat stocks affects agricultural welfare. It would also allow for a better understanding of the heterogeneity of impacts across counties and facilitate the scaling of average effects to estimate the costs of future outbreaks. For example, certain bat species may be more susceptible to WNS (O’Keefe et al. 2019), and their prevalence may vary across counties and states (Cheng et al. 2021). With currently available data, we do not know whether counties impacted by WNS have similar bat populations to those that have not yet detected the disease. We also cannot tease out the bat populations whose losses drive agricultural impacts.

A final caveat to our welfare estimates is that they consider only value to agricultural producers and under the assumption of exogenous output prices. If WNS affects a wide enough area, supply shocks could lead to higher prices and consumer impacts, which we do not consider. Additionally, bats provide society with other services not measured here. These include the health benefits of reduced pesticide use (Frank 2021) and slower transmission of mosquito-borne illnesses (Puig-Montserrat et al. 2020), existence value (some bat species are endangered),24 and the potential to study antiviral immune responses (Baker et al. 2013). Of course, bats may also impose unpriced costs on society that should be accounted for as well, including the transmission of diseases such as rabies (Turmelle et al. 2010) and coronaviruses (Poon et al. 2005), though this is rare in the United States.25

These caveats suggest two avenues for future research. First, biologists and economists would benefit from collaborations that create and integrate standardized biological and economic data sets over space and time. Second, future work could extend this welfare analysis to account for additional values from bats while allowing for general equilibrium changes as natural capital stocks are impacted over large spatial scales. Overall, combining land market data with consistent biological data provides a useful avenue for valuing a wide range of ecosystem services that support agricultural production.

Appendix A.  Supply Curve Parameters

Assume a land supply curve equal to r=c+dq where c and d are parameters. Given two equilibrium points, we can solve for the land supply slope as

(A1)d=r1r0q1q0.
Given the slope and observed market equilibrium the intercept becomes
(A2)c=r0dq0.
Finally, the elasticity of supply at the initial market equilibrium, ηs, can be calculated as
(A3)ηs=r0q0q1q0r1r0.

Appendix B.  Derivation of Vertical Shift in VMP(L;N)

This derivation is related to the model developed in Alston et al. (1995, 211) to evaluate the welfare impacts of a shift in the supply curve in an agricultural output market. In contrast to their derivation in the output market, the shock in land markets affects the derived demand instead of supply. Also, we use information on price and quantity before and after a shock while Alston et al. (1995) use only initial price and quantity. This perfectly identifies supply curve parameters (see app. A) and allows us to calculate welfare changes given only an assumption on the elasticity of derived demand for land.

Assuming linear demand in the land market, let initial inverse demand be r=abq where a and b are positive parameters and r and q are the price and quantity of land in the rental market, respectively.

If r0 and q0 are equilibrium price and quantity, then we know that r0=abq0.

Assume a vertical shift in the y-intercept of the derived (inverse) demand for land equal to K and new equilibrium price and quantity of r1 and q1. If the slope of derived demand changes by Δb, this means that r1=aKbq1Δbq1.

Using the new inverse demand equation,

(B1)K=ar1bq1Δbq1.
Also, the initial inverse demand curve can be solved for a,
(B2)a=r0+bq0.
Substituting a in equation (B1),
(B3)K=r0+bq0r1bq1Δbq1(B4)=r0r1+b(q0q1)Δbq1.

The demand curve for land is q=a/br/b. Therefore, the elasticity of demand at the initial point is

(B5)ϵd=qrr0q0=r0q0b.
Solving for b,
(B6)b=1ϵdr0q0.
Plugging equation (B6) into equation (B4) produces
(B7)K=r0r1+1ϵdr0q0(q0q1)Δbq1,
which is equivalent to equation (8) in the text when Δb=0. When Δb0, then this is equivalent to equation (9) (see fig. B1).

Figure B1. 
Figure B1. 

Welfare impact of decline in natural capital. Area W+X+Y+Z equals the welfare loss of a decline in natural capital stock from N0 to N1.

Appendix C.  Detailed Simulation Output

This appendix presents the detailed results of welfare impact simulations used to generate total costs presented in figures 4 and 6. Table C1 shows the results considering alternative demand elasticities for land, and table C2 presents results for alternative shifts in the demand curve slope. The tables include the same information, including the estimated vertical shift in the demand curve for land, surplus losses per county per year for direct and spillover (only) effects, the costs per base number of acres, and the cost as a proportion of base welfare as estimated in the land market. The spillover (only) effects represent impacts on counties that do not experience a direct WNS outbreak. To obtain total effects in counties with WNS and neighboring outbreaks (results not shown), Kcn, r1cn, and q1cn are all calculated and used as an input into calculation of the total loss. Due to the nonlinearity of the loss in q1cn (see eq. [6]), these losses do not equal the sum of the direct and spillover impacts.

Table C1. 

Direct and Spillover Welfare Cost of WNS, Agricultural Land Market

 Elasticity of Derived Demand for Land
 .35.45.55
Vertical shift (K) ($):   
 WNS within the county4.61**4.22**3.97**
 (2.02)(1.83)(1.71)
 One neighbor with WNS2.43***2.23***2.09***
 (.68)(.61)(.57)
 Two neighbors with WNS4.87***4.45***4.18***
 (1.36)(1.22)(1.14)
 Three neighbors with WNS7.3***6.68***6.28***
 (2.05)(1.84)(1.71)
 Four neighbors with WNS9.74***8.9***8.37***
 (2.73)(2.45)(2.28)
 Five neighbors with WNS12.17***11.13***10.46***
 (3.41)(3.06)(2.85)
Surplus loss per county year ($):   
 WNS within the county657,319.1***600,863.4***564,937.1***
 (144,722.4)(130,665.1)(121,989.3)
 One neighbor with WNS347,412.1***317,573.7***298,585.6***
 (48,770.1)(43,754.2)(40,754.9)
 Two neighbors with WNS693,408.4***633,853.1***595,954.3***
 (97,050.7)(87,089.4)(81,138.2)
 Three neighbors with WNS1,037,989***948,838.3***892,106.1***
 (144,843.7)(130,008.1)(121,152.6)
 Four neighbors with WNS1,381,154***1,262,529***1,187,041***
 (192,151.2)(172,512.4)(160,800.4)
 Five neighbors with WNS1,722,902***1,574,926***1,480,759***
 (238,975.1)(214,604.7)(200,084.1)
Average cost per base acre per year:   
 WNS within the county4.604.203.95
 One neighbor with WNS2.432.222.09
 Two neighbors with WNS4.854.434.17
 Three neighbors with WNS7.266.646.24
 Four neighbors with WNS9.668.838.30
 Five neighbors with WNS12.0511.0110.36
Cost per base welfare:   
 WNS within the county.025.026.027
 One neighbor with WNS.013.014.014
 Two neighbors with WNS.026.027.029
 Three neighbors with WNS.039.041.043
 Four neighbors with WNS.052.054.057
 Five neighbors with WNS.064.068.071

Note. q0=142,996; p0=80.97. WNS = white-nose syndrome.

*p < .1.

**p < .05.

***p < .01.

View Table Image: 1 | 2
Table C2. 

Direct and Spillover Welfare Cost of WNS, Alternative Inverse Demand Slope Changes

 Change in Slope Scenario
 Parallel Shifty-Intercept PivotDouble Baseline K
Vertical shift (K) ($):   
 WNS within the county4.22**08.44**
 (1.83)(.)(3.53)
 One neighbor with WNS2.23***04.45***
 (.61)(.)(1.16)
 Two neighbors with WNS4.45***08.9***
 (1.22)(.)(2.31)
 Three neighbors with WNS6.68***013.35***
 (1.84)(.)(3.47)
 Four neighbors with WNS8.9***017.8***
 (2.45)(.)(4.62)
 Five neighbors with WNS11.13***022.25***
 (3.06)(.)(5.78)
Surplus loss per county year ($):   
 WNS within the county600,863.4***301,594.2***900,132.6***
 (130,665.1)(126,144.0)(124,356.6)
 One neighbor with WNS317,573.7***159,110.4***476,036.9***
 (43,754.2)(41,151.6)(41,187.1)
 Two neighbors with WNS633,853.1***318,220.8***949,485.4***
 (87,089.4)(82,303.3)(81,658.6)
 Three neighbors with WNS948,838.3***477,331.2***1,420,345***
 (130,008.1)(1,23,454.9)(121,423.5)
 Four neighbors with WNS1,262,529***636,441.6***1,888,617***
 (172,512.4)(164,606.5)(160,491.1)
 Five neighbors with WNS1,574,926***795,552***2,354,300***
 (214,604.7)(205,758.2)(198,870.9)
Average cost per base acre per year:   
 WNS within the county4.202.116.29
 One neighbor with WNS2.221.113.33
 Two neighbors with WNS4.432.236.64
 Three neighbors with WNS6.643.349.93
 Four neighbors with WNS8.834.4513.21
 Five neighbors with WNS11.015.5616.46
Cost per base welfare:   
 WNS within the county.026.013.039
 One neighbor with WNS.014.007.021
 Two neighbors with WNS.027.014.041
 Three neighbors with WNS.041.021.061
 Four neighbors with WNS.054.027.081
 Five neighbors with WNS.068.034.101

Note. q0=142,996; p0=80.97. WNS = white-nose syndrome.

*p < .1.

**p < .05.

***p < .01.

View Table Image: 1 | 2

Appendix D.  Demand Elasticities and Base Surplus

Calculating base surplus in the land market requires information on supply and demand elasticities in the land market. Appendix A describes the derivation of supply curve parameters. Here, we describe how we estimate the elasticity of demand for agricultural land (see eq. [8]). To obtain this, we use incidence calculations from Dinterman and Katchova (2019) together with the supply slope implied by the observed land market response to WNS. Specifically, the initial equilibrium in the land market, which equates supply and inverse demand, is

(D1)q0=acb+d.
Using the inverse demand curve, this implies that
(D2)r0=ab(acb+d).
To parameterize the inverse demand for land, we calculate the slope parameter, b, implied by a unit tax on land. Specifically, with a tax of τ per unit of land, the new intercept of the supply curve becomes c+τ. Therefore, the equilibrium price with the land tax is
(D3)rτ=ab(a(c+τ)b+d).
Setting τ=1, the change in price can be written as26
(D4)rτr0=Δr=bb+d.
Solving for b,
(D5)b=Δrd1Δr.

The term Δr is obtained from Dinterman and Katchova (2019) and has a range of 0.31 to 0.40. The term d is (r1r0)/(q1q0)=(78.1480.97)/(141893142996)=0.0026, which implies an initial land supply elasticity of 0.22 (see eq. [A3]).

This implies that b is between 0.0012 and 0.0017, with associated initial elasticities of 0.48 and 0.33. Given this range of elasticities, we present welfare calculations for elasticities of 0.35, 0.45, and 0.55 in figure 4.

Given positive demand and supply parameters, base welfare is equal to the triangle

(D6)Welfare=12(ac)q0,
where a is the inverse demand curve intercept. Using equation (B2), equation (A2), and the relationship between slope parameters and elasticities,
(D7)Welfare=12((1+1ϵd)(11ηs))r0q0.

In the US agricultural context, we obtain a supply intercept that is less than 0 (c=−255). Therefore, we calculate baseline welfare as the area between the demand and supply curve and above the x-axis (see bolded region in fig. D1). This implies that agricultural acres below the x-intercept are assumed to have zero opportunity cost, which is consistent with the relatively low supply elasticities documented in the literature (Maligaya and White 1989; Gurgel et al. 2007). In this case, from equation (D7), we subtract the area (1/2)(c)q¯, where q¯ is the x-intercept of the supply curve, equal to 109,000. This adjusted area is used as the denominator when calculating percentage changes in welfare.

Figure D1. 
Figure D1. 

Baseline welfare in land market with negative supply intercept. Bolded region is baseline welfare used for calculating welfare changes as a percentage of baseline.

Notes

Dale T. Manning is an associate professor in Agricultural and Resource Economics, Colorado State University (). Amy Ando is a professor in Agricultural and Consumer Economics, University of Illinois Urbana-Champaign (). This paper is based in part on work funded by the USDA-NIFA W4133 Multistate Research Grant 1008843. We thank Brian Reichart, Winifred Frick, Eyal Frank, Jeremy Coleman, Jonathan Reichard, and Ellen Martin for their valuable contributions to this project. Reid Hensen helped prepare spatial data for calculating land quality distributions. Participants in the Colorado State Univerity DARE Environmental and Resource Economics Workshop and the W4133 annual meeting also provided useful feedback on this work. Thanks to Luanne Lohr for initial discussions about this research and to the editor and two anonymous reviewers for constructive feedback on this paper. All remaining errors are our own.

1. This lost surplus does not include changes in benefits to consumers or other ecosystem values provided by bats (e.g., existence values).

2. For example, there are efforts in the United States to protect bats from the coronavirus that causes Covid 19. There is also concern for the impact of windmills on bat populations (Boyles et al. 2011).

3. See https://www.nps.gov/articles/what-is-white-nose-syndrome.htm.

4. While the latter cost per acre is higher, the implied base welfare is also higher, leading to a smaller impact as a percentage of base welfare.

5. To obtain nonmarket values from a weak complement, the market good must also be nonessential. A finite choke price is sufficient for this condition to be met.

6. Davis and Hitchcock (1965) find that bats can travel 140 kilometers. Tuttle (1976) provides evidence of travel distances exceeding 500 km. A more recent study by Roby et al. (2019) finds a mean travel distance of 165 km, though many bat species travel much shorter distances.

7. See app. B for derivation.

8. See whispers.usgs.gov.

9. Du et al. (2007) attribute discrepancies between the short- and long-run impacts of commodity prices on land rents to inertia in contract renegotiations. Delayed price impacts could also occur because of a lag between first detection of WNS and the collapse of bat populations.

10. We do not include cotton because production concentrates in southern counties while WNS outbreaks began in the northern United States. Therefore, there are very few counties with reported cotton data and WNS.

11. See https://seer.cancer.gov/popdata/download.html.

12. See http://www.prism.oregonstate.edu/.

13. See https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/survey/?cid=nrcs142p2_053627.

14. In the online appendix, we also consider specifications that include the annual lags of weather variables. Results do not significantly change.

15. We apply estimated average effects to average initial price and quantity. Therefore, we isolate heterogeneity in the number of neighboring WNS outbreaks conditional on initial land market conditions and impact coefficients.

16. We use WNS outbreak locations and apply estimated average effects to average base acres and rental price in all counties. Assuming county-specific base acres and rental price leads to qualitatively similar results.

17. Appendix D describes the calculation of these demand elasticities given incidence estimates and the supply slope implied by our price and quantity changes in the land market.

18. See https://www.ers.usda.gov/data-products/ag-and-food-statistics-charting-the-essentials/farming-and-farm-income/.

19. We use region-year fixed effects instead of state-year due to computation restrictions from the large number of state-years in the yield data.

20. We can use region-specific coefficients to calculate welfare impacts but did not report results here because of additional assumptions required (namely, region-specific elasticities for the derived demand for land).

21. While the vaccination program is less costly, determination of which program is preferred depends on effectiveness as well. This is an area of current research.

22. See https://www.nabatmonitoring.org/.

23. We implement the method proposed in Callaway and Sant’Anna (2021) while treating spillovers as a control and confirm that our estimated impacts are robust with an average treatment effect for land rent equal to −3.41 (SE=1.27). The 95% confidence interval includes the point estimate using our base (two-way fixed effects) model.

24. See https://www.whitenosesyndrome.org/static-page/bats-affected-by-wns.

25. For example, the United States averages only one to three rabies cases per year, though bats cause 70% of rabies deaths in the United States (https://www.cdc.gov/media/releases/2019/p0611-bats-rabies.html).

26. This is consistent with the well-known incidence formula, dr/dτ=ηs/(ηs+ϵd), where all elasticity parameters are positive.

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