2. Stated Preferences, Rotational Grazing on Public Land, and Survey Response Behavior

As is the case for all voluntary survey research methods, stated preference surveys are vulnerable to response bias (Dalecki, Whitehead, and Blomquist, Reference Dalecki, Whitehead and Blomquist1993)—with hypothetical bias, nonresponse, and avidity effects particularly relevant to ex ante analyses of agricultural production topics. This study, however, offers several advantages in terms of respondents’ prior experiences with main features of the ex ante rotational grazing land rental decision. Our target population already raises beef cattle and is likely knowledgeable about private land market transactions (Paine and Gildersleeve, Reference Paine and Gildersleeve2011). They may also be land constrained and therefore have a stake in the potential availability of public land for grazing purposes (Kloppenburg et al., Reference Kloppenburg, Cates, Gildersleeve, Johnson, Mahalko, Paine and Thomforde2012). In contrast, because only some producers currently utilize MIG methods, there may be differences in the level of familiarity with required inputs and in their interest in renting public land specifically for these purposes. In our case, both previous experience with land rental arrangements and MIG can (and do) turn out to be predictors of who chose to respond, as well as factors that influence stated rental decisions.

The value of transactional and land management experiences is that they help respondents make meaningful statements about their intentions to rent land for rotational grazing. This minimizes the potential for hypothetical bias that can arise in valuation contexts that pertain to unfamiliar environmental goods and services (Carson, Flores, and Meade, Reference Carson, Flores and Meade2001). Respondents to our survey should therefore be more likely to offer accurate answers to CV scenarios based on their knowledge, relevance, and ongoing commitment to the activities described in the questions (Kling, Phaneuf, and Zhao, Reference Kling, Phaneuf and Zhao2012; Whitehead et al., Reference Whitehead, Blomquist, Hoban and Clifford1995). In contrast, nonresponse becomes a concern if those who choose not to respond differ in key characteristics from those who do respond (Edwards and Anderson, Reference Edwards and Anderson1987; Groves, Reference Groves2006). Avidity effects similarly arise if individuals with greater interest in a particular issue are more likely to respond to a survey about an issue than those with less interest (Ethier et al., Reference Ethier, Poe, Schulze and Clark2000). Missing data on explanatory variables that are not missing at random or missing completely at random are of similar concern (Little, Reference Little1998; Tsikriktsis, Reference Tsikriktsis2005). In these cases, the response behavior could result in survey data similar to that drawn from a nonrandom sample selection process that targeted participants with more interest.

Nonrandom selection is a well-known specification issue in econometrics (e.g., Heckman, Reference Heckman1979), and several methods exist to control for sample selection bias in the analysis of stated preference data. The first is to use stratified random sampling methods and apply postsurvey sampling weights. To extend inference from respondents to the general population, constructed weights adjust for over- or underrepresentation within strata relative to a known population frame (Mitchell and Carson, Reference Mitchell and Carson1989; Peress, Reference Peress2010). This approach assumes that respondents are representative of population members within their respective strata and therefore only partially addresses the potential for bias (Loomis, Reference Loomis1987). A second method for surveys with multiple waves of respondent contacts, such as those following the Dillman method (Dillman, Smyth, and Christian, Reference Dillman, Smyth and Christian2014), is to use late responders as a proxy for nonresponders (Studer et al., Reference Studer, Baggio, Mohler-Kuo, Dermota, Gaume, Bertholet, Daeppen and Gmel2013). This approach assumes that nonrandom selection issues are more likely to occur when response rates are low (Edwards and Anderson, Reference Edwards and Anderson1987). Mitigating strategies to increase response rates include improving the salience of the survey, reducing the length of the survey instrument, conducting multiple survey mailings, or offering incentives. Mixed evidence is available on the effectiveness of this approach, with several researchers finding no support for it (Dalecki, Whitehead, and Blomquist, Reference Dalecki, Whitehead and Blomquist1993; Lahaut et al., Reference Lahaut, Jansen, van de Mheen, Garretsen, Verdurmen and Van Dijk2003).

A final method is to compare characteristics of survey respondents with nonrespondents. The primary challenge here is that data on nonrespondents are often unavailable or otherwise costly to collect (Hudson et al., Reference Hudson, Seah, Hite and Haab2004). Some studies in this vein collected data on nonrespondents via postsurvey phone calls (Dalecki, Whitehead, and Blomquist, Reference Dalecki, Whitehead and Blomquist1993; Whitehead, Groothuis, and Blomquist, Reference Whitehead, Groothuis and Blomquist1993). In other cases, and more commonly found in medical settings, researchers have access to a rich sampling frame or matched data sets that contain supplemental information on all members of the sample (Groves, Reference Groves2006). When data on both respondents and nonrespondents are available, probit models with nonrandom selection can be used to test and control for selection bias (Van de Ven and Van Pragg, Reference Van de Ven and Van Praag1981; Whitehead, Groothuis, and Blomquist, Reference Whitehead, Groothuis and Blomquist1993). Edwards and Anderson (Reference Edwards and Anderson1987) outline this approach for use in CV studies, and Messonnier et al. (Reference Messonnier, Bergstrom, Cornwell, Teasley and Cordell2000) and Whitehead and Cherry (Reference Whitehead and Cherry2007) apply the approach to environmental and energy choices.

Cooper and Keim (Reference Cooper and Keim1996) applied a selection model to producer demand for water quality improvements in an ex ante context, but recent efforts generally ignore the issue or rely primarily on postsurvey weighting methods. In this article, we exploit information on respondents and nonrespondents to control for response behavior. Our research strategy involves (1) collection of survey data on producer responses to questions about their willingness to rent public lands for rotational grazing and (2) estimation of a bivariate probit model that jointly estimates producers’ willingness to rent public grazing land and their survey response decisions. The econometric model ensures that the identification of factors shaping producer willingness to rent public lands accounts for potential bias from nonresponse or avidity effects. Accurately determining these factors is important because they can help land managers and policy makers to site public grazing programs, design effective outreach to potential participants, and estimate program costs.

3. The Ex Ante Land Rental Decision

Consider a utility-maximizing producer who chooses whether to rent land for rotational grazing. Consistent with utility maximization, the producer is willing to rent land whenever the expected utility gain from switching to the CV state is positive (Haab and McConnell, Reference Haab and McConnell2003). A typical approach to estimating binary CV choices is the probit model, where the utility difference between CV and non-CV states is explained by the CV offer price and other factors thought to influence the decision and then transformed into a probability using properties of the cumulative normal distribution function (Hanemann, Reference Hanemann1984). Because this model relies on survey data voluntarily provided by real decision makers, we also incorporate the potential effects of response behavior.

The decision to respond to a mail survey can similarly be cast in a random utility maximization framework. An assumption implicit in studies that disregard response behavior is that the expected utility of responding is a random variable not explained by factors that also influence the outcome of interest. In the absence of such effects, inferences based on the respondent sample can be extended to the population of interest. However, if the outcome and selection choices are correlated, then avidity or nonresponse behavior can result in nonrandom selection (positive or negative) that potentially leads to biased estimates for the outcome equation. In this case, extrapolating inferences from the sample to the population of interest could result in misleading conclusions about the significance and magnitude of certain factors.

We therefore analyze Wisconsin beef producers’ stated land rental decisions using a probit model with nonrandom selection to account for the potential effects of response behavior (Van de Ven and Van Pragg, Reference Van de Ven and Van Praag1981). The bivariate model yields consistent parameter estimates under nonrandom selection and consists of (1) a binary outcome equation that explains producer willingness to rent land for rotational grazing and (2) a binary selection equation that explains survey response behavior. The model we employ is the following:

(1) $$\begin{eqnarray} REN{T_i}{\rm{\ }} &=& {\rm{\ }}\left\{ {\begin{array}{@{}*{2}{c}@{}} {1{\rm{\ if\ }}Y_i^{\rm{*}} > 0}&{{\rm{where\ }}Y_i^{\rm{*}} = {{\bm{X}}_{\bm{i}}}{\bm{\beta }} + {u_{1i}}}\\ {0{\rm{\ if\ }}Y_i^{\rm{*}} \le 0}&\, \end{array}} \right. \nonumber\\ RESPON{D_i}{\rm{\ }} &=& {\rm{\ }}\left\{ {\begin{array}{@{}*{2}{c}@{}} {1{\rm{\ if\ }}W_i^{\rm{*}} > 0}&{{\rm{where\ }}W_i^{\rm{*}} = {{\bm{Z}}_{\bm{i}}}{\bm{\gamma }} + {u_{2i}}}\\ {0{\rm{\ if\ }}W_i^{\rm{*}} \le 0}&\, \end{array}} \right.\nonumber\\ CORR\left( {{u_1},{u_2}} \right) &=& \rho \end{eqnarray}$$

where RENT is the dependent variable in the outcome equation; RESPOND is the dependent variable in the selection equation; the latent variables Y*_i and W*_i represent the expected utility gain from the land rental and survey response decisions, respectively; β and γ are parameters to be estimated; and u _1i and u _2i are error terms assumed to be normally distributed. The model permits a test of ρ = 0 to evaluate if estimation of an ordinary probit without selection would yield biased coefficient estimates. This strategy allows us to control for observed factors that may shape response behavior, as captured in Z, as well as unobserved ones that could be correlated with the land rental decision. The unobserved factors are accounted for by the correlation of error terms across the two equations. With effective observed control variables, it is possible that the selection term ρ may or may not be significant in the joint bivariate estimation.

Covariates X and Z include factors hypothesized to influence the land rental and survey response decisions, respectively, with specific variables to be included drawn from related CV studies and the agricultural technology adoption literature. Such factors typically include measures of farm size or scale of operation, demographic characteristics such as age and education level, current management practices, attitudinal measures, and farm specialization (e.g., income source) measures. These factors are applicable to the adoption of rotational grazing practices and have been included in previous analyses of MIG strategies on beef and dairy farms (Brock and Barham, Reference Brock and Barham2009; Foltz and Lang, Reference Foltz and Lang2005; Gillespie et al., Reference Gillespie, Wyatt, Venuto, Blouin and Boucher2008; Jensen et al., Reference Jensen, Lambert, Clark, Holt, English, Larson, Yu and Hellwinckel2015; Kim, Gillespie, and Paudel, Reference Kim, Gillespie and Paudel2005). Descriptions of the specific variables used to control for these factors in our analysis are introduced in Section 5.

4. Mail Survey of Beef Cattle Producers

Information on producer willingness to rent public land for rotational grazing comes from a 2016 mail survey of Wisconsin beef cattle producers. The 2012 U.S. Census of Agriculture listed this population at 18,433 producers, and sample construction was based on a confidential list frame maintained by the USDA National Agricultural Statistics Service (NASS) regional field office in Des Moines, Iowa. The sampling procedure used a stratified design based on herd size and MIG practices. We defined seven herd size strata: less than 20 head, 20–49 head, 50–99 head, 100–199 head, 200–499 head, 500–999 head, and more than 1,000 head. Designation as an MIG or non-MIG producer was based on whether producers used MIG practices as indicated in the 2012 U.S. Census of Agriculture (USDA-NASS, 2013). The final sample consisted of 1,172 producers, of whom 22% were MIG practitioners.

This analysis uses 105 observations from active producers who returned a completed survey, for an effective response rate of 16% after removing returns from ineligible members of the population. We suspect that the relatively low response rate stemmed from a combination of disinterest in grassland rental among non-MIG farmers and the inability to implement a third round of survey mailing because of institutional constraints. Among respondents, 59% checked the MIG box in the census, which means that MIG producers were more than three times as likely to respond to our survey as non-MIG producers. The low overall response rate combined with the marked avidity effect for MIG producers affirms the need to consider nonrandom selection in our analysis.

Stated land rental intentions come from a CV module in the study questionnaire. It asked respondents whether they would rent public land for rotational grazing at a given land rental offer price. The module included an introduction, summary of grazing conditions, list of required inputs to be supplied by the producer, and contract length. Although rental decisions are complex, and require the producer to consider a variety of variables including distance from their farm and infrastructure availability, respondents receive sufficient details to allow them to form an expectation of profitability and other related trade-offs for their decision. We piloted the survey instrument with grazing experts and beef cattle producers.

Each questionnaire included two CV scenarios for rotational grazing: one for grass-dominant and another for shrub-dominant land types. The scenarios were posed to respondents independently such that they could choose to participate in one, both, or neither program. Respondents indicated their willingness to rent public land by agreeing to the given CV grazing scenario. Three questionnaire versions were used that varied only in terms of rental rate offer price. Each version had either low, medium, or high offer prices assigned at random across the sample. The offer prices ranged from a low of $10/acre in both scenarios to a high of $40/acre in the grass scenario and $30/acre in the shrub scenario and were determined through conversations with cattle producers and grazing professionals in Wisconsin. The decision to rent was voluntary and elicited via dichotomous choice questions.

5. Study Variables and Estimating Equations

We estimate the probit model with and without selection for the grass and shrub CV scenarios separately, as well as for the pooled CV scenarios using maximum likelihood. The empirical specification is

(2) $$\begin{eqnarray} {\it{Pr}}\left( {{\it{RENT}}} \right) & = & {{\bf \Phi }}\big( {{{\bf \beta }}_0} + {{{\bf \beta }}_1}{\it{PRICE}} + {{{\bf \beta }}_2}{\it{HERDSIZE}} + {{{\bf \beta }}_3}{\it{MIG}} \nonumber\\ && + {{{\bf \beta }}_4}{\it{PASTURE}} + {{{\bf \beta }}_5}{\it{INCFARM}} + {{{\bf \beta }}_6}{\it{RENTHIST}} \nonumber\\ && + {{{\bf \beta }}_7}{\it{AGE}} + {{{\bf \beta }}_8}{\it{DIVERSE}} + {{{\bf \beta }}_9}{\it{ATTITUDE}} + {{\it{u}}_1} \big)\nonumber\\ {\it{Pr}}\left( {{\it{RESPOND}}} \right) & = & {{\bf \Phi }}({{{\bf \gamma }}_0} + {{{\bf \gamma }}_1}{\it{HERDSIZE}} + {{{\bf \gamma }}_2}{\it{MIG}} + {{{\bf \gamma }}_3}{\it{PASTURE}}{\rm{\ }}\nonumber\\ && + {{{\bf \gamma }}_4}{\it{INCFARM}} + {{{\bf \gamma }}_5}{\it{RENTHIST}} + {{{\bf \gamma }}_6}{\it{AGE}} + {{\it{u}}_2}), \end{eqnarray}$$

where Φ is the cumulative distribution function of the standard normal distribution, and the expressions inside of parentheses determine the latent index variables Y^*_i and W _i^* defined in equation (1), respectively. In addition to controlling for the survey response decision, we also evaluated whether dropping observations because of missing values for explanatory variables might affect our estimates but did not find support for this possibility.Footnote ²

Median predicted values of WTP are recovered using the estimated coefficients from equation (2) as (Haab and McConnell, Reference Haab and McConnell2003) follows:

(3) $$\begin{eqnarray} WTP &=& [{{\rm{\beta }}_0} + {{\rm{\beta }}_2}\overline {HERDSIZE} + {{\rm{\beta }}_3}\overline {MIG} + {{\rm{\beta }}_4}\overline {PASTURE} \nonumber\\ && + {{\rm{\beta }}_5}\overline {INCFARM} + {{\rm{\beta }}_6}\overline {RENTHIST} + {{\rm{\beta }}_7}\overline {AGE} + {{\rm{\beta }}_8}\overline {DIVERSE} \nonumber\\ && + {{\rm{\beta }}_9}\overline {ATTITUDE} ]/{{\rm{\beta }}_1}, \end{eqnarray}$$

where the bar above variable names denotes sample average values. To provide a measure of spread, we report the interquartile range for WTP values subsequently, recovered using individual values of the explanatory variables.

Variables are constructed using data from two sources. First, all explanatory variables in the RESPOND equation come from the USDA-NASS sample frame used to administer the mail survey (Table 1). The frame drew on the 2012 U.S. Census of Agriculture and included data for both respondents and nonrespondents. Therefore, no mail survey data were introduced at this stage beyond the response itself. Two variables pertain specifically to the livestock enterprise—namely, herd size (HERDSIZE), which is included as a measure of operation size, and an indicator for whether the producer currently employs an MIG practice (MIG). Another three variables relate to the farming operation more generally and include pasture area (PASTURE), the share of household income the producer receives from farming activities (INCFARM), and previous experience with land rental transactions (RENTHIST). Finally, we controlled for age (AGE) as a demographic characteristic. To explore response behavior, we tested for differences in the descriptive statistics by response status, under the null that no differences exist. Test results reported in the last column of Table 1 confirm that significant differences do exist between respondent and nonrespondent characteristics. Notably, producers who currently practice MIG and have previous land rental experience and fewer pasture acres were more likely to respond. This suggests that nonrandom selection attributable to nonresponse or avidity behavior is present.

Table 1. Descriptive Statistics for Variables in the Selection Equation by Response Status^a

^a Data are drawn from the mail survey sample frame and were analyzed at the U.S. Department of Agriculture, National Agricultural Statistics Service regional field office in Des Moines, Iowa. The anonymity of producers selected into the sample frame was maintained throughout and the summary statistics reported here in order to summarize respondent characteristics in aggregate.

^b Difference tests for continuous variables evaluated the difference in means using t-statistics. Difference tests for binary variables evaluated the difference in proportions using z-statistics. Asterisks (***, **, *) indicate significant differences at the 0.01, 0.05, and 0.10 levels, respectively.

Second, variables in the RENT equation use data from the producer mail survey (Table 2). The dependent variable is constructed from responses to the CV land rental scenarios. We expect the CV land rental offer price (PRICE) to be negative in accordance with the law of demand. A measure of herd diversification (DIVERSE) is captured by an index variable that reflects the number of different cattle types managed within a producer's operation. We expect this index to have a negative effect on willingness to rent land for rotational grazing because of the added management complexity of diverse animal feeding demands. We also hypothesize that favorable attitudes toward public agencies involved in grassland management could positively influence the willingness to rent land for rotational grazing. To measure this, we created an attitude index (ATTITUDE) based on the responses to two Likert-type statements where higher scores reflect more favorable attitudes toward working with public land agencies.

Table 2. Descriptive Statistics for Variables in the Outcome Equation^a

^a Data are from a 2016 mail survey of Wisconsin beef cattle producers.

^b Binary variables coded as 1 = yes, 0 = otherwise.

^c Index constructed as the count of different cattle types currently managed within the operation among the following six choices: dry beef cows, cow-calf pairs, finish animals, young stock, dairy heifers, and other.

^d Index constructed as the sum of Likert-scale responses to two statements related to public agencies where the Likert values ranged from 1 (least favorable) to 5 (most favorable) and the statements were “I am interested in grazing public land” and “I am willing to work with a public agency, such as the Wisconsin Department of Natural Resources,” respectively.

The remaining variables in Table 2 are as previously defined. We expect MIG to have a positive effect on the willingness to rent public land because producers with previous MIG experience are already familiar with grazing plans and regimes and may perceive more value in public lands than would non-MIG operations. We expect PASTURE to negatively influence the willingness to rent public land for grazing because producers with more pasture area are less likely to be land constrained. Producers with a greater share of income from farming have a greater dependence on these activities for their livelihood, and we expect INCFARM to positively influence the rental decision. Younger producers are typically more willing to adopt new technologies and practices as compared with older producers, and we expect AGE to have a negative effect. Transaction costs associated with renting land for the first time (e.g., search costs, screening, contracting and legal advice, and negotiation) are high, and therefore, we expect RENTHIST to increase their willingness to participate in this market.