Monetary compensation for changing forest management practices to increase water availability in Georgia, United States

Forests provide many ecological services, including carbon sequestration, biofuel provision, and recreation, yet the influence of forests on water resources is still often debated. While increased forest cover is generally associated with greater water quality, the value-added component of enhanced water services associated with reduced forest cover is less understood. At the same time, ensuring adequate water supplies remain a common goal of many natural resource managers due to growing concerns over freshwater security. This study derives a baseline of willingness-to-accept estimates to supply water flows by investigating the behavior of tree farm owners in Georgia, United States. Little is known about landowner preferences among incentives related to the adoption of different silvicultural practices to increase downstream water yields. A discrete choice experiment was designed to ascertain monetary compensation amounts required to alter established planting densities and thinning intensities likely to result in increased water yields. Results show that landowners may adopt such forest management strategies if appropriately compensated. Specifically, landowners on average, desired approximately $0.06 to $0.19 more per acre per year for every unit decrease in planting density. These are significant findings given that existing relevant stakeholders on the ‘consumer’ side may be ready and willing to fund such practices. We hope our study can contribute towards establishing market-based incentives for private forest landowners to encourage the conservation and improvement of forested watersheds in Georgia and beyond.


Introduction
The total forest cover in the Southern United States is about 245 million acres, or roughly 46% of all land across the region (Oswalt et al 2019). The nation's forest products industry, a major contributor to economic development in rural America, is concentrated in southern states (Abt et al 2002, Dahal et al 2015. This region is commonly termed the 'wood basket of the world' , thereby providing a range of ecosystem services, from carbon sequestration to biodiversity, as well as several recreational opportunities such as hunting, hiking, biking, and general sightseeing. In this context, this study specifically aims to value the supply of water flows, a critical forest-based ecosystem service, by investigating the behavior of Georgia landowners whose forests support a multitude of critical ecological services. For any payments for ecosystem services (PES) design to actually work, the buyer covers the cost of provision, which must be (i) lower than any alternative method by which the buyer might secure the same service and (ii) sufficient to ensure that the alternatives are economically inferior (Fripp 2014). PES designs must be based on relatively accurate levels and transparent metrics. This is vital to build an attractive business case for buyers. Payments will emerge only if buyers believe the recommended land management practices will result in the necessary water yields downstream.
Payments could be made one of two ways (Smith et al 2013). First, performance-based payments driven by enhanced water yields and measured by observed increases in water quantity. Second, input-based payments driven by certain resource management practices. This study considers the measurement of input-based payments. Practical financing structures could come in various forms, for example, municipalities downstream making a direct payment to foresters, the government levying a certain tax (e.g. direct transfer payment) on downstream users/households, or perhaps a water utility paying upstream foresters on behalf of its customers.
Indeed, fully functioning water markets may act to allocate water-based ecosystem services derived from forestlands more efficiently but remain in the early stages of governance. This contributes to a lack of explicit values concerning respective water rights that may otherwise better inform society. More broadly, established markets for (other) ecosystem services in the United States take many forms and are themselves still evolving. Current federal cost-share schemes include the Conservation Stewardship Program and Environmental Quality Incentives Program (EQIP), both of which encourage forestry producers to adopt sustainable management practices and target overall improved forest health. At the state level, in return for enhancing wildlife habitat through conservation actions, Safe Harbor Programs guarantee participating landowners will not incur any new restrictions on their land should endangered species take up residence. The Southern Pine Beetle Prevention Program, another cost-sharing partnership between private landowners and the government, is active in several southern states. With respect to water-based services, Florida's Lake Okeechobee Protection Act of 2000 (and amended in 2007) established a restoration program for the lake (Northern Everglades and Estuaries Protection Program 2021). As part of the protection program, projects comprised cooperative agreements with landowners on private lands in which state agencies (Florida Department of Environmental Protection, South Florida Water Management District) funded participating landowners in exchange for the provision of water storage efforts. Other recent examples of payments for water services include a fee ($0.04/1000 gallons) charged by the Beaver Water District in Fayetteville, Arkansas, in support of a Source Water Protection Fund and a watershed protection fee ($0.1122/100 ft 3 ) in Raleigh, North Carolina that supports restoration projects under the Upper Neuse Clean Water Initiative.
Assuming a forest landowner has the right to pursue planting as many trees as they see fit, they will have to be compensated to curtail operations. Accordingly, our study assumes downstream water users may pay upstream forest landowners to promote water yields (through adopting certain silvicultural practices). We investigate two silvicultural practices likely to promote water flow and ease water shortages on existing loblolly pine stands in the state of Georgia, increased forest thinning and lower planting density, to ascertain trade-offs between changes in private landowner profits and associated fluctuations in water yield. Derived values estimate the minimum compensation levels required to entice a typical private forest landowner to alter forest management practices. The resulting willingness-to-accept (WTA) represents the compensation necessary for a crop quantity decline, a measure of compensating surplus with an implied right to the initial situation or status quo (a condition where current planting density and thinning intensity is sufficient and need not be decreased and/or increased respectively) 4 .
We have two objectives. First, to elicit amounts of compensation deemed sufficient (by the landowner) to promote enhanced water yield downstream, and relatedly, how WTA bid amounts may change when personal attributes concerning risk tolerance and experience participating in cost-share programs with government entities are included. Second, to ascertain whether the probability of success in meeting a projected increase in water yields has any effect on choices by the landowner. We reason higher preferences for this attribute would reflect sentiment for wanting any proposed practices to succeed. Our study focuses on the producer's (i.e. the landowner's) perspective. The analysis is comparable in that it also considers a reduction in utility, although not in water services, but in the form of the cost and effort incurred in adopting newly proposed land management practices. However, the interpretation again reverts to a measure of compensating surplus, in this case, the WTA an adverse decline.
The paper continues with a brief literature review. Next, we describe the theoretical framework, our collected dataset, survey design, and subsequent econometric analysis as part of our methods section. The results and discussion that follow offer an analysis of the costs and benefits involved with making appropriate decisions for the efficient management of water stock derived from forestlands.

Literature review
Effects of silvicultural treatments (e.g. clear-cutting) and different harvesting techniques on water yield, defined as the combined volume (minus transmission loss) of surface runoff, groundwater flow, and tile flow for a specific period, have been investigated throughout the United States (Rothacher 4 Conversely, forest landowners may compensate downstream users for reduced water flow if downstream water users have implied rights to a minimum level of water. To a certain extent, these rights may be undefined and murky as to which party should compensate the other. Irrespective, by the Coase Theorem (and assuming minimum transaction costs), bargaining will guarantee a socially optimal outcome when an externality transpires between private parties (Baumol et al 1988). 1970, Patrick 1980, Keppeler and Ziemer 1990, Lynch and Corbett 1990, Stednick 1996, 2008, Keppeler et al 2008. Studies consistently conclude an inverse relationship between the amount of forest cover and water yield (Harr 1983, Erskine 2001, Vose 2019. Nonetheless, as Ellison et al (2012) note, a secondary viewpoint argues that planting additional forests should raise downstream water availability and intensify the hydrologic cycle.
The current study is predicated on the former, that is, less forest cover is linked to greater water yields. Here we assume the greater water yields, computed based off projected reductions in trees to a single loblolly pine stand, occur downstream. Comparatively, the work that has documented a positive relationship between forest cover and water yield occurs over larger spatial scales. Results in these instances are derived from measurements of water vapor and condensation nuclei (from added trees) that contribute to rainfall outside the immediate study region. Regardless of the forest cover-water yield relationship, the consumer (i.e. the downstream user) may view any deviation from the average level as an imposed 'quantity' change, whereby the derived compensating surplus is interpreted as a willingness to pay (WTP) to obtain an increase in general water services (Shultz and Soliz 2007, Bogale and Urgessa 2012, Doherty et al 2014, Dias and Belcher 2015, Aguilar et al 2018, Hynes et al 2021, Tadesse et al 2022. In their meta-analysis of household WTP for improved drinking water services, Van Houtven et al (2017) found WTP was sensitive to the magnitude of improvement, household income, and stated-preference elicitation method. Further studies consider an imposed water quantity (or quality) decrease for which the corresponding equivalent compensation measure is interpreted as the WTP to prevent such an adverse decline (Amponin et al 2007, Cerda 2013, Kreye et al 2014, Chaikaew et al 2017. In the specific case of water services, compensation will be required to incentivize the adoption of certain silvicultural practices likely to generate water benefits downstream (see Cristan et al 2016 for a review of recent studies; alternatively, see Xu et al 2015, Chu et al 2020 for applications on consumer WTA for water security). The compensation amounts required by forest landowners to provide enhanced water services equate to opportunity costs related to adopting targeted practices. For example, Vedel et al (2015) investigated the link between forest landowners' current management and their WTA payments for providing various ecosystem services by surveying landowners on their current practices prior to a choice experiment on contracts. A more recent study investigated WTA amounts for managing a hypothetical tract of loblolly pine for multiple ecosystem services (Mutandwa et al 2019). In terms of water quality, perhaps more well-known is work exploring farmer preferences for implementing certain best management practices as measured by both WTA (Cooper and Kleim 1996) and willingness to participate (Zhong et al 2016); as it relates specifically to water quantity, Wang et al (2019) estimated farmer WTA amounts for afforestation efforts aimed at water loss reduction which came at the expense of reduced accounting profit.
Just over a decade ago, a National Research Council report (National Research Council 2008) revealed reduced forest cover may increase water yield, albeit as generally short-lived enhancements. More recently, however, for the first time, researchers (Roche et al 2018) were successful in producing robust estimates of changes in evapotranspiration from different forest treatments using Landsat-derived imagery. A natural extension of this work lies in the valuation realm. Although the link between increased forest cover and enhanced water quality has been well established, the value-added component related to enhanced water quantity associated with a reduction in trees per unit area (the trade-off) has yet to be investigated. On this point, while advocating for the sustainable development of water resources, Garrick et al (2017) explicitly call for innovation in the WTA space to address concerns regarding incomplete water valuation estimates. Still, it becomes apparent from a literature review that prior studies have not considered compensation values attached to reduced crops for the sole purpose of increasing water yields downstream. Given Georgia's recent water disputes with surrounding states, the location makes for a compelling case study to fill this research gap.
A general deficiency of this study is that it only considers benefits associated with enhanced water yield instead of a more comprehensive measure incorporating 'stacked' ecosystem services, that is, a complete tally of the ecosystem services and disservices that would accompany the proposed changes in forest management practices. Our application still presents an interesting case since, to estimate a total economic value; one first requires reliable estimates of the individual components. And for our study area, it is plausible that enhanced water yields would make up a significant and noteworthy ecosystem service. Moreover, while our choice experiment is organized, displayed, and explained in a manner conveying increases in water yield as the sole benefit of the proposed management practices, the choice set also depicts associated probabilities of success that the practices proposed are efficient enough at producing stated increases in water yield. By including the probability of change in ecosystem service and the change itself (the amount of increased water yield to be realized downstream) as explicit attributes, an element of risk (as it relates to water provisioning) is incorporated in our survey design.

Geographic location
Growing populations and unfavorable changes in climate contribute to water supply stress in the region (Sun et al 2008), with expensive 'water wars' between Georgia and its bordering states, Florida and Alabama, having persisted for decades. Georgia has long justified water withdrawals as necessary to fuel its urban growth centers. Florida consequently has expressed concern over destructive ecological conditions to critical downstream waterways. Such interstate disputes underscore the need for innovative solutions to increase existing area water supplies.
A recent report supporting the 2020 Resources Planning Act assessment (Oswalt et al 2019) estimates close to 67% of all land in the state as forested. Thus aside from Atlanta and its larger emerging megalopolis corridor, as well as the several midsized cities dotting the central and lower half of the state, forest cover dominates. While wildfires are certainly a threat to the region, the relatively humid climate (e.g. compared to the western U.S.) supports the integration of woody wetlands, rather than dryer vegetation (i.e. scrub biomes), which are generally less conducive to fire danger. A 2021 estimate of the hardwood-softwood breakdown throughout the state approximates the split fairly evenly at 54% and 46% respectively (USDA Forest Service 2021). Some 3.6 million acres of these pine stands (and moreover, 60% of all Georgia forestlands) are owned by family forest landowners (Brandeis 2015). Figure 1 depicts combined loblolly pine (Pinus taeda L.) and shortleaf pine (Pinus echinate) dispersion throughout the state. The Georgia Forestry Commission estimates that 65% of the state's 52 watersheds flow through forests, with an approximate 57% of the state's population depending on water from forested watersheds (Liu et al 2020). Since 91% of the forestlands in Georgia are privately owned (Harper 2012), individual landowner forest management practices play a significant role in determining overall water quality and surface flow and/or aquifer recharge. In the case of silvicultural operations aimed at reducing biomass cover, it becomes imperative that forest landowners seeking to maximize timber profits are appropriately incentivized to compensate for any losses incurred (as a result of switching established practices).

Data collection of sample population
Adjustments were made to the initial survey format based on feedback from relevant field experts in academia and industry (Georgia Forestry Commission as well as private forest landowners). The final survey packet consisted of three main sections. The first section, the introduction, provided a brief overview describing in detail the two silvicultural practices considered in our study, relative changes in thinning intensity, and planting density. The main choice set experiment followed. The last section elicited socio-demographic information from the participants. Introductory eligibility questions confirmed survey takers were actual landowners (i.e. not agents), 18 years and above, and owned more than ten acres in Georgia.
Our sample constitutes forest landowners belonging to the Georgia Tree Farm Program (GTFP). Descriptive statistics are presented in table 1. An overwhelming majority of those surveyed were male, college educated, and white; the mean age was approximately 65 with a mean woodland holding of 1464 acres. The GTFP is part of the larger network of the American Tree Farm System, the largest and oldest sustainable woodland system in the United States. Landowners partnering with the GTFP were selected in part since participants hold a shared vision of sustainable management of forestland for wood, wildlife, recreation, and, most notably, water. This subgroup then makes for an especially interesting case study in the context of valuing competing ecosystem services, e.g. changes in extraction versus changes in water yields.
The preliminary mailing list of potential survey participants contained 1115 entries. Instances of duplicate agents associated with the same address were identified, dropping 122 observations in the process, and reducing the number of names to 993. Postcards containing a brief introduction regarding the survey were mailed during the first week of September 2020, with actual survey packets administered ten days following. Reminder postcards were mailed the first week of the next month, with reminder survey packets being mailed later that same month.
After accounting for duplicate response packets (three), we counted a total of 409 initial responses. From these, 19 of the forms contained incomplete responses, 15 were deemed non-applicable (e.g. owner not growing loblolly on land), and 31 indicated they did not voluntarily agree to participate in our survey. A further 105 forms were dropped due to null replies and answers expressing explicit noncompliance in the pre-survey questions. The response rate was calculated at 24.07% (n = 239).
The presence of unit non-response in our data was tested by investigating the relationship for ten socioeconomic variables between the first 10% and last 10% (in the context of the response order) of landowners in our sample. Here, the first 10% of landowners were representative of responders, while the last 10% of landowners surveyed served as a proxy for non-responders (see Nybakk et al 2009, Mutandwa et al 2019. The continuum of resistance model (Lin and Schaeffer 1995) assumes those who respond only after considerable time and effort (i.e. late respondents) resemble non-respondents in the behaviors of interest (Zhao et al 2009). The basic premise is that these late respondents are more similar to non-respondents than early respondents are; presumably, individuals who required (more) reminders before participating would have otherwise been non-respondents had data collection finished before they had a chance to respond. Accordingly, late respondents, most resemble non-respondents and are thus exploited as proxies for non-respondents in estimating non-response bias (Lahaut et al 2003).
Researchers have routinely applied this model in attempts to evaluate non-response bias in survey data (Clarsen et al 2020). For our study, t-tests for all examined characteristics indicated no presence of non-response bias (p > 0.10).
Collected data were ultimately verified and entered in a created codebook with variable names specified for each survey question. Frequency tables ensured final response values fell within the appropriate range for each question. Survey IDs entered in the dataset were compared with information in actual questionnaires to check for further errors in the data.

Choice experiment
The non-market value of enhanced water yields is estimated using a stated preference approach. Here, observations (responses to questions) on intended behavior are elicited in an experimental setting where money and commodities do not change hands. For our survey, a choice experiment was created, designed to extract individual preferences regarding alternative policy proposals. Each choice set consists of a status quo assumed current management (ACM) scenario and two alternative options, Scenario A and Scenario B (figure 2). Levels associated with each attribute appear in table 2. Six attributes define each choice scenario: (1) thinning intensity; (2) planting density; (3) stated net increases in water yield (made available to downstream users); (4) probability of meeting the stated net increase; (5) compensation or bid amount; and (6) payment vehicle for receiving this compensation amount (i.e. annual tax or monthly electric bill credit). The last column describes the characteristics of the ACM scenario.
Downstream users, in this case, were presumed to be any community residing within a watershed that would be affected by the proposed forestry management practices due to their geographic and topographic proximity as well as hydrological connectivity to the affected forestlands-in this case, the collective of households in the state of Georgia. The term net increase (in water yield) refers to the excess water generated downstream due to switching from the current management scenario to one of the proposed scenarios, A or B. The ACM scenario trivially assumes the probability of meeting the stated increases in water yield is 0%, thus implying an increase of 0 gallons acre −1 made available to downstream users. The ACM scenario is further defined by the following silvicultural practices: 726 seedlings acre −1 and 39% thinning (at the 18th year after planting). It is acknowledged that conditions under the ACM may not precisely mirror landowners' current silvicultural practices. Yet, while landowners can be considered heterogeneous at many levels, in our survey, participants were told that, for purposes of the experiment, to assume they faced the ACM scenario as described. Preliminary focus groups with landowners and academics were conducted to pre-test the ACM scenario along with the survey at large. Feedback from field experts regarding the survey instrument was generally positive, and upon revisions, the introductory section containing the description of the ACM scenario with the help of visual aids was deemed appropriate in presenting a realistic default scenario for loblolly pine landowners in the region (the handful of returned surveys that expressed in writing such a scenario could not be assumed were dropped from the analysis) 5 .
The range of compensation amounts included in the experimental design was based on estimates of economic rent faced by the landowner because of changes in thinning intensity and planting density for simulated loblolly stands in the Lower Coastal Plain (see Bawa and Dwivedi 2021); similarly, reported water yields were also computed as a function of thinning and planting density. Participants were randomly assigned to treatments where the payment vehicle took the form of an annual tax credit or equivalent monthly compensation credited to their electric bill. Options offered as a payment vehicle should be described as very real and credible (Lewis et al 2017). While an income tax credit is commonly employed in environmental valuation, we reasoned a monthly electric bill credit met these criteria. Moreover, because a utility bill tends to be somewhat more unpredictable compared to an annual tax, it provides for a diverse alternative, yet realistic choice for landowners. 5 An alternative strategy for the design of the ACM would have been to elicit from each individual landowner their current management strategy and employ a pivot design for the choice experiment. Based upon our focus groups and pre-tests of the survey instrument, a common ACM was employed to avoid potential confusion and challenges for respondents completing a mail survey who may employ different management strategies on different parcels.
In addition to socio-demographic data elicited basic information on participant's age, gender, race, education, and income, presented was a straightforward yes or no question asking whether the landowner in the past five years had received any financial assistance from the government to undertake a conservation practice on their property. The individual was also asked to rate their willingness to take risks in general on a scale from 1 (completely unwilling) to 10 (completely willing). This general risk question relies on an individual's self-reported propensity for risk, the format for which does not take up much time for the user, with the added advantage of being relatively simple to understand. Dohmen et al (2011) found strong support for the external validity of this approach in that it did well at predicting risk-taking behavior in a field experiment with real monetary states.
Based on the presented number of attributes and associated levels, a main effects fractional factorial design was generated in Ngene software (ChoiceMetrics 2018). The block design consisted of six blocks for which each respondent faced eight choice sets. A review of the choice sets among the six blocks confirmed that no choice strictly dominated our design. Such a layout was deemed a good fit given managing trade-offs between changes in D-efficiency score, and the number of choice sets the participant was being asked to complete based on feedback from landowners during survey pre-tests.

Derivation of WTA estimates 4.2.1. Theoretical framework
Forestlands jointly produce timber, a private good, along with other ecosystem services, deemed as public goods. Typically, the more timber or aboveground biomass, the greater the environmental benefits 6 . However, the increase in downstream water yields considered in this study stem from lessening in aboveground biomass. By assuming some increased rate of thinning, downstream users, it can be argued, will enjoy some level of increased water yields relative to a typical status quo (thinning) scenario. Accordingly, for any marginal increase in thinning and/or 6 At the same time, it must be noted that greater amounts of aboveground biomass would seemingly strengthen the chance of wildfire, a serious risk to many forests throughout western North America and to a lesser extent, the U.S. south. comparable decrease in planting density, landowners would incur an opportunity cost to supply additional amounts of water stock. Comparatively, other enhanced ecosystem services such as biodiversity and recreational services may benefit the landowner in the form of the increased land value, and therefore, the landowner would be willing to provide these services up to a certain point. Users would have to pay for additional quantities of the environmental service past this point as a further supply of the ecosystem service would be considered economically suboptimal by the landowner. Zhang (2016) notes the increase in water yield is not an ordinary private service that can be supplied when the price is zero. Because positive externalities (associated with the ecosystem service) are usually not internalized by the private landowner, the true worth of forests to society may be undervalued.
The WTA amount can be defined as the amount of money received which would leave the landowner just as well off after an imposed quantity change as it was before the quantity change. Consider the landowner who faces a loss in forest stock from its present stock level, F 0 , to F 1 . The WTA amount needed to leave the firm (i.e. the landowner) as well off as they were before the quantity change is calculated as the change in the non-market component of the forest (i.e. downstream water yields) as well as the income loss realized because of undertaking the proposed forest practices. We can define this formally in terms of the landowner's indirect utility function, V(): where P is the price of goods, Q (·) measures nonmarket benefits, and M (·) captures market benefits, namely through timber production. Here, M (·) is conditioned on the initial forest stock, F 0 , because it is assumed the landowner has rights to the status quo state of the world. Implicit in our setup is that market-generated income from timber is strictly less in the subsequent scenario, i.e. M ( The compensating surplus or change in the nonmarket component of the forest depends on how forest landowners view amenity values before and after the change in forest stock.

Econometric modeling
The choice experiment methodology is rooted in random utility theory. While equation (1) is meant to highlight the trade-offs involved when adopting certain forestry practices from the perspective of a landowner (that is, defining the amount of money required for an environmental improvement as a function of the landowner's indirect utility function) 7 , after rearranging terms, landowner WTA can be defined as a function of additional variables. Based on this universe of variables, corresponding mixed logit models were estimated using the package mlogit in RStudio (RStudio Team 2020).
For a decision-maker i, the utility of alternative j in choice scenario t is a function of the attributes of the alternative. Faced with a series of alternatives, the option providing the highest utility will be the preferred choice (McFadden 1974, Louviere et al 2000. Utility for a good, denoted U ijt , is allocated between a systematic component, V ijt , and a random component, ε ijt , which is assumed independently, identically type I extreme value distributed. The coefficient βs are unknown to the researcher and vary over individuals with a given density, g (·), which we assume to be normally distributed.
The systematic utility derived from the chosen option takes a panel specification and is described as a function of seven attributes: where variables, BID, PD, TI, WY, and PWY refer to respective attributes bid amount, planting density, thinning intensity, water yield, and the probability of meeting water yield (see table 3 for a full list of variable descriptions). Two indicator variables are also included in equation (2). TC captures the effect of receiving compensation via annual tax credit vs. a monthly electric bill credit; similarly, ACM was included to describe the utility associated with a landowner selecting the ACM scenario. The βs designate regression coefficients of the attributes. Because the researcher does not observe the βs, the unconditional choice probability is expressed as the integral of the probability conditional on the β vector of coefficients over all possible βs, The selected mixed logit form relaxes the Independence from Irrelevant Alternatives hypothesis by allowing the random components of the alternatives to be correlated while maintaining the assumption that they are identically distributed (Greene and Hensher 2003). 7 More precisely, in our case, equation (1)   In addition to any of the main effects, we are interested in exploring how landowner behavior may change based on two individual traits. We extend equation (2) by incorporating interaction terms related to the participant's general risk tolerance, RSK, and a dummy variable CFA, indicating whether the landowner had received financial assistance from the government in return for undertaking a conservation practice within the past five years. The following three models, equations (4)-(6) (as well as equation (2)), assume a fixed price parameter and random main effects and are estimated based on 10 000 Halton draws in a simulated maximum likelihood algorithm 8,9 .
The premiums for a unit change of a given attribute can be computed as the marginal rates of substitution between the quantity expressed by the attributes and the price (Louviere et al 2000). Since utilities are modeled as linear functions of the attributes of management schemes, the marginal rate of substitution between two attributes is the ratio between the coefficients. If we useβ l to represent a particular estimated attribute coefficient, the marginal WTA for the attribute can be expressed as: In equations (4)-(6), the cross products comprise two different coefficients. If we label the interaction effectβ m and (continuing with prior notation) the main effect asβ l , both terms are expressed as a function of WTA × . The subscript × is added to designate interaction WTA, which is evaluated at the mean of each individual's particular attribute, L:

Results
Likelihood ratio tests were performed for each relevant model comparison. Two versions of our nested design appear in table 4, for which model 2 is nested within model 3 and model 1 is nested within model 2.
We reject the null hypothesis that model 1 provides as good a fit as the more complex models 2A and 2B, and thus models 2A and 2B are both preferred at the 0.001 Table 4. Comparison of fit among the utility (in preference space) regressions. The matrix reports associated p-values based on likelihood ratio chi-squared tests.

Model 1 Model 2A Model 2B Model 3
Log-Likelihood −1,045.9 Model 1 0.0000 * * * 0.0000 * * * 0.0000 * * * −1,982.1 Model 2A 0.0000 * * * −1,519.3 Model 2B 0.0000 * * * −2,053.3 Model 3 * * * p< 0.001.  significance level. Similarly, we reject the null that the relatively smaller models 2A and 2B provide as good a fit as model 3 (p < 0.001). Based on these considerations, we reasoned model 3 provided the best model fit. Table 5 presents the basic results of landowner utility from all models. While a brief examination of the second half of the table is offered in the next section, we request the reader focus their attention on the top half or mean estimates. Here, we are interested in what variables may play a role in influencing landowner satisfaction. In the main effects model (Model 1), as the compensation amount increased, landowners had positive utility in undertaking a particular set of proposed practices (p < 0.001). Similarly, landowners, on average, experienced positive utility associated with compensation amounts paid out in the form of an annual tax credit versus a monthly electric bill credit (p < 0.001); and with increased rates of success in meeting stated water yield targets (p < 0.001). Lastly, landowners experienced negative utility associated with decreased planting density (p < 0.001) 10 . Dividing the preference coefficients by the price coefficient (see equations (7) and (8) yields corresponding WTA amounts presented in table 6. Subsequently, we are interested in how estimated WTA amounts within models compare to each other in the relative sense, i.e. the marginal WTA for a scenario. In model 1, landowners, on average, were willing to accept $5.685 less per acre per year if it meant increasing the probability of success in meeting stated water yields by one percentage point. Likewise, landowners were willing to accept $0.056 more per acre per year for every unit decrease in planting density. Required compensation dropped by $4.211 per acre per year, whereby payment is provided in the form of an annual tax credit compared to remuneration via monthly electric bill credit.
Models 2A, 2B, and 3 incorporate added interactions per each attribute: interactions with RSK (model 2A), interactions with CFA, (model 2B), and interactions with both RSK and CFA (model 3). As in the main model, the price had a significant and positive impact on participants' utility for management practice, as expected (p < 0.001). While the negative utility is associated with decreased planting density, the positive utility is associated with increases in stated water yield (models 2A and 3: p < 0.001); similarly, we observe a higher preference for receipt of funds through an annual tax credit versus a monthly electric bill credit (models2B and 3: p < 0.001). For these same models, landowners were, on average, willing to accept ∼$13 to $15 less per acre per year if it meant increasing the probability of success in meeting stated water yields by one percentage point (p < 0.001) (see Among all interaction terms, fairly strong results were found for landowners who identified as more willing to take risks in general: higher preference for decreased planting density (model 2A: p < 0.001).
Here, landowners required less compensation, albeit an almost negligible amount (under a penny per acre per year), for every unit decrease in planting density; landowners who received financial compensation in the past five years to undertake a conservation practice were willing to accept $0.014 more per acre per year for decreased planting density (model 3: p < 0.001).
Other significant interactions included terms, CFA × PWY and RSK × PWY. Landowners who identified as receiving governmental financial assistance wanted $10.406 more per acre per year, given a percentage point increase in the probability of success in meeting stated water yields (model 2B: p < 0.05). Landowners who identified with a higher risk tolerance were WTA $0.745 and $2.345 less per acre per year in respective models 2A (p < 0.05) and 3 (p < 0.001) given the same percentage point increase in the probability of success in meeting stated water yields.

Discussion
While it is understood that general biophysical estimates of water yield may, in reality, be highly variable due to climatic factors, overall findings from this study indicate private forest landowners could be open to the idea of adopting forest management strategies designed to enhance water yield, if appropriately compensated. In general, the directionality of marginal compensation amounts appeared to grow with greater restrictions on forest management practices in line with prior work (Mutandwa et al 2019). This is relevant given that existing stakeholders on the 'consumer' side may be willing to fund such practices; for example, aside from households located downstream, consumer groups may include hydroelectric generators, biomass power generators, and even parties with interest in wildfire reduction (Downing 2015).
The positive utility associated with increased rates of success in meeting stated water yield targets (all models), in addition to the significant results found for stated water yield amounts (models 2A and 4), are perhaps hardly surprising since one may expect a group of respondents such as members of GTFP, a group committed to managing their forestlands in an environmentally friendly manner, to assign higher utility to an increased probability of meeting a particular ecosystem service target, i.e. increased water yields. More interesting is the relatively high bid amount (i.e. the largest reduction in WTA out of all the attributes considered in the two models) seemingly attached to an increased probability of success in meeting stated water yields by one percentage point. This may infer that in the context of PES programs, landowners may be more willing to accept smaller compensations for switching management regimes, given a higher probability of achieving ultimate environmental targets, all else equal. Perhaps even more noteworthy still, our results diverge from Kang et al (2019), who found risk-averse Georgia forest landowners required less compensation for PES contracts than less risk-averse Georgia forest landowners, all else equal. Yet this same study also estimated higher WTA payments (∼$7 per acre per year more) for limiting pine plantation acreage (similar to the concept of decreased planting density) in Georgia to preserve riparian corridors. For added perspective, Matta et al (2009) found private family forest landowners across Florida were WTA $3.7 per acre per year to conduct more frequent prescribed burns (every two to three years), another option potentially available for reducing biomass and ultimately helping attain water yield targets.
More broadly observed is the importance and opportunity to integrate the impacts of changes in forest cover on water yields as part of cost-share programs, both federal and local. The Conservation Reserve Program has been well documented as contributing to significant environmental benefits, notably improved water quality through field buffers and reduced fertilizer use (Stubbs 2014). Similarly, EQIP payments have supported significant reductions in biochemical oxygen demand and nitrogen, also indicative of improvements to water quality (Liu et al 2022). Whether to account for changes in post-disturbance water yields will depend on the region's topography, most likely sensitive to residual vegetation, latitude, and aspect (Goeking and Tarboton 2020). Programs are beginning to recognize this at more local levels. Florida's St. Johns River Water Management District's 2023 Districtwide agricultural cost-share program, for example, engages farmers, growers, and ranchers alike to attain united water quantity and water quality goals. By embracing such shared impacts, program areas may better extend a more holistic view of forest cover dynamics emanating as a result of implemented conservation practices on private lands and associated watersheds.

Conclusion
Our analysis reveals there is potential for increasing the production of water yields to downstream user groups across Georgia. by altering existing forest practices in vegetation management. The presented WTA amounts add to the literature concerning applications of stated preference techniques for valuing ecosystem services, specifically for increases in water yield. This can help to establish a baseline range of bid amounts for the producer side; and, coupled with consumer analysis (i.e. identification of demand curves) can provide for a neat estimation of a market price that could indicate what's necessary to sustain a reallocation of water yields.
Similar studies to value forest ecosystem services in the future may find it worthwhile to incorporate a particular tax credit as the payment vehicle. For example, Georgia is one of nine states that tax timber harvested from private land based on its value (Howard 2019); in addition to annual tax credits, ad valorem/property tax credits and/or timber tax credits (at the year of sale or harvest) could be included.
At the same time, it is crucial to keep in context the range of WTA values presented in the current study. Values will tend to vary widely depending upon the multitude of ecosystem services considered. Shrinkages in forest cover to promote increases in water yield downstream would likely lead to the loss of carbon sequestration, biodiversity, and recreational services. We have not accounted for the trade-offs across these ecosystem services and expect that future research will fill the critical gap.

Data availability statement
The data cannot be made publicly available upon publication because they contain sensitive personal information. The data that support the findings of this study are available upon reasonable request from the authors.