2. Previous Research on Best Management Practice Adoption

The BMP adoption literature analyzes the effects of incentive rates and a variety of other nonpecuniary factors on the voluntary adoption of structures or practices designed to mitigate the environmental impacts of agriculture. Cooper (Reference Cooper1997) concluded that participation rates in cost-share programs were relatively unresponsive (e.g., inelastic) to changes in incentive levels. Lichtenberg (Reference Lichtenberg2004) found that row crop producers were cost responsive to incentives and preferred to adopt BMP practices in bundles. Lichtenberg and Smith-Ramírez (Reference Lichtenberg and Smith-Ramírez2011) found that incentives may induce higher participation rates but may have little or no effect on “participation intensity” or the extent of BMP provision given voluntary program participation.

Cooper and Signorello (Reference Cooper and Signorello2008) analyzed premiums encouraging the voluntary adoption of conservation plans. They examined what proportion of the willingness to adopt amount could be attributed to risk premiums. Their finding was that risk premiums accounted for approximately 36% of the mean willingness to accept value. Kurkalova, Kling, and Zhao (Reference Kurkalova, Kling and Zhao2006) estimated the financial incentives required for adopting conservation tillage, distinguishing between the expected payoff and adoption premium based on the observed behavior of Iowa farmers. Some nonadopters did not use conservation tillage because the expected profit gain alone did not compensate for the increased risk and possibility of irreversible lost profits associated with conventional tillage practices. Kurkalova, Kling, and Zhao also found that if a uniform conservation tillage adoption subsidy was offered, then approximately 86% of the program payments would have been income transfers to existing, low-cost adopters.

Rolfe et al. (Reference Rolfe, Windle, Reeson and Whitten2006) examined the effects of payment levels on adoption of selected measures of improvements in grazing practices (buffer strip width and forage biomass). Results from their study suggested that respondents were more likely to select alternatives with higher payment levels and less likely to select alternatives with extended buffer widths or minimum biomass conditions.

Foltz and Lang (Reference Foltz and Lang2005) found that education and owned acres operated positively influenced the likelihood of adopting rotational grazing by Connecticut dairy farmers. Jayasinghe-Mudalige and Weersink (Reference Jayasinghe-Mudalige and Weersink2004) found that the number of environmental management systems adopted by Canadian farmers, including rotational grazing for livestock, was positively influenced by farm profitability, farm size, and land ownership, but inversely related with age. Farms with mixed crop and livestock systems had the highest adoption rates, whereas livestock-only operations had the lowest.

Kim, Gillespie, and Paudel (Reference Kim, Gillespie and Paudel2008) examined the effects of cost-share levels and farmer demographic variables on the willingness to adopt rotational grazing by Louisiana cattle producers. Cost-share levels positively influenced willingness to adopt. Their results also suggest that the probability of adoption could decline by as much as 0.85% for each percentage increased of the cost-share burden. Use of any rotational grazing type, higher debt to asset ratio, and plans for family members to take over the farm positively influenced adoption.

Prescribed grazing has potential drawbacks. For some producers, the initial investment costs and increased labor and management time may be too high (Gillespie et al., Reference Gillespie, Wyatt, Venuto, Blouin and Boucher2008). The profitability of prescribed grazing will vary across the large geographic area studied here due to differences in climate, land quality, and forages grown. Not all forage crops have the same response to rotational grazing. In some cases, prescribed grazing may not improve forage growth. Briske et al. (Reference Briske, Derner, Brown, Fuhlendorf, Teague, Havstad, Gillen, Ash and Willms2008) found that multipaddock grazing does not significantly increase vegetation or animal production over continuous stocking practices.

This study builds on the findings from previous research, encompassing a much wider geographic area (east of the 100th meridian) than is typically investigated. The area east of the 100th meridian encompasses the region of the United States where the majority of pastureland rather than rangeland is located. The study results include estimates of the effects of per acre incentive payments on program participation and also on acres enrolled into a hypothetical prescribed grazing program. Interest in adoption or expansion and willingness to participate in a cost-share program to add prescribed grazing acreage are conditioned on relevant demographic and attitudinal factors.

3. Survey Data

The survey conducted for this study used a random sample of beef cattle, cow/calf, and backgrounding/stocker operations from the eight USDA Economic Research Service (USDA/ERS, 2000) regions east of the 100th meridian (Figure 1). The survey is available at http://beag.ag.utk.edu/pub/GrazingSurvey.pdf. The ERS regions are based on commodity production, geographic specialization, and other geographic characteristics. The stratified sample was drawn by USDA's National Agricultural Statistics Service (NASS) and was limited to operations with at least 20 head of cattle as reported by the 2007 Census of Agriculture to decrease the likelihood of sampling hobby farms. Strata were based on ERS production regions (Heartland, Northern Crescent, Northern Great Plains, Prairie Gateway, Eastern Uplands, Southern Seaboard, Fruitful Rim, and Mississippi Portal) and farm sales classes (<$10,000; $10,000–$29,999; $30,000–$49,999; $50,000–$99,999; $100,000–$149,999; $150,000–$199,999; $200,000–$499,999; >$500,000). A total of 8,875 operations were randomly selected from the population of 267,413 producers. The survey sample represented 3% of the total beef cattle farm population in the surveyed region. Sampling intensity and design were based on a 3% margin of error and a 95% confidence interval. Poststratification weights, used to weight the data in this analysis, were developed based on the cross tabulation of farm sales classes and ERS regions (Lambert et al., Reference Lambert, English, Harper, Larkin, Larson, Mooney, Roberts, Velandia and Reeves2014). The procedure adjusts survey sample means toward expected population means based on two criteria: (1) the cell frequencies of respondents in given sales class and farm production regions, and (2) the cell frequencies based on USDA/NASS estimates along the same cell dimensions. The survey weights proportionally adjust the central tendencies of the survey sample to the expected frequency distribution of the farm population according to survey region and farm sales classes. The original procedure was first used by the U.S. Census of 1940 (Lohr, Reference Lohr1999). The mail survey was fielded by USDA/NASS in early 2013 with an initial mailing, a reminder postcard (1 week later), and second follow-up mailing (2 weeks after the reminder postcard). A total of 2,258 completed surveys were returned for a 26% response rate.

The survey instrument included three sections. The first section contained questions about the characteristics of the respondent's farming operation. The next section informed respondents about what prescribed grazing is and the on-site and off-site benefits of prescribed grazing systems (Figure 2). The second section also provided details about the management practices defining prescribed grazing (Figure 3). USDA/NRCS technical guidance was used as the basis for the prescribed grazing specifications (USDA/NRCS, 2007). The prescribed grazing information was followed by questions asking respondents if they used any practices identified with prescribed grazing in the previous year and, if so, which ones. If respondents used some of the management practices, they were asked if they had received government payments for these practices through federal programs such as EQIP.

Figure 2. Survey Description of Prescribed Grazing and Potential Benefits

Figure 3. Survey Description of Management Practices Used in Prescribed Grazing

Respondents were provided with installation cost estimates. Installation cost estimates were based on existing cost estimates from program payment structures (EQIP) and aggregated to the USDA farm commodity production regions (Figure 4; USDA/NRCS, 2013b).

Figure 4. Estimated Regional Costs of Prescribed Grazing

Respondents were also provided cost estimates for additional components needed for prescribed grazing (i.e., installing temporary or permanent fencing, providing watering facilities in each paddock, and providing heavy-use protection), as shown in Figure 4. Respondents were then asked to indicate which of the following best describes whether they would adopt or expand prescribed grazing:

1. 1. I would not adopt or expand prescribed grazing even if it was profitable to do so.

2. 2. I would adopt or expand prescribed grazing even if it was not profitable to do so.

3. 3. I would adopt prescribed grazing only if it was profitable to do so.

Respondents who chose (1) were considered nonadopters/nonexpanders, whereas those who choose (2) or (3) were categorized as adopters/expanders.

Adopters/expanders were then informed of a hypothetical program offering an incentive composed of a 75% structure installation cost share and annual payments for 10 years to either expand the number of acres managed with prescribed grazing (for respondents already using these management practices and receiving government payments) or manage a portion of their farm area using a prescribed grazing system (for respondents not currently using prescribed grazing systems; Figure 5).Footnote ^{3 ,} Footnote ⁴ Note that respondents were provided with a description and cost estimates (Figures 2, 3, and 4) prior to being asked about their responsiveness to the hypothetical incentive program. Respondents indicating willingness to accept the incentive and participate in the program were then asked how many acres they would enroll in the program and convert to prescribed grazing. Enrollment in the program could represent either adoption by farmers not currently using prescribed grazing or expansion onto additional acres by those already using prescribed grazing. Five versions of the survey were randomly distributed across the survey sample. Each version differed only in the amount of the hypothetical incentive offered to enroll pasture acres into the prescribed grazing program. The incentive levels were $10, $30, $50, $70, and $90 per acre per year over a 10-year horizon. These levels were based on the results of a pilot survey conducted before the primary survey. The final section of the survey included questions about respondent characteristics, including operator age, income, household size, farming experience, and education. After eliminating incomplete records, there were 1,153 observations available for analysis. Expanding this sample by the survey weights results in a projected 145,723 farms.

Figure 5. Program Description and Participation Question

4. Conceptual Model

The survey design compels three levels of analysis: (1) willingness to adopt or expand prescribed grazing (absent an incentive); (2) willingness to participate in the hypothetical incentive program, given interest in adopting or expanding prescribed grazing; and (3) participation intensity (acres enrolled, given acceptance of the incentive).

4.1. Adoption/Expansion of Prescribed Grazing

Cattle farmers maximize the stream of returns from livestock production less variable costs by choosing optimal feeding and animal replacement schedules. Producers make decisions about stocking density and pasture maintenance, with weather, plant growth, and plant-growth/animal interactions typically beyond the producer's control (Kennedy, Reference Kennedy1985). In addition to this management decision dynamic, producers may voluntarily participate in a prescribed grazing program that could reduce production risk or increase profits by enhancing pasture productivity.

In the absence of an incentive, adoption or expansion of a BMP is hypothesized to occur when the producer's utility (u) from adopting or expanding (A) the practice is at least as great as the producer's utility without adoption or expansion of the practice. In other words, a producer adopts or expands use of a BMP when u_A (1, I; x) ⩾ u_A (0, I; x), where 0 denotes lack of adoption or expansion of the BMP, and 1 adoption or expansion; I is income; and x is a vector of operator characteristics and farm attributes affecting the decision to adopt or expand the practice.

McFadden's (Reference McFadden and Zarembka1974) random utility model is commonly applied in the technology adoption literature to explain the systematic (observable) component of utility as a function of the measurable covariates, x. For example,

(1) \begin{equation} u_A^j = x\beta ^j + \varepsilon _A^j ,\end{equation}

where j = 0,1 is the state of adoption or expansion; xβ ^j is the observable, systematic component of utility; and ε ^j _A is an unobservable, independent, and identically distributed disturbance. Producers adopt or expand use of the BMP when the latent variable $\bar u_A = u_A^1 - u_A^0 $ is positive. The likelihood of adopting or expanding the BMP is extended to a probabilistic framework, namely

(2) \begin{equation} {\rm Pr}\left( {j = 1} \right) = {\rm Pr}\left( {x\beta _A^0 + \varepsilon _A^0 \le x\beta _A^1 + \varepsilon _A^1 } \right) = {\rm Pr}\left( {\varepsilon _A^0 - \varepsilon _A^1 \le x\beta } \right)\end{equation}

after the typical normalization β = β¹ − β⁰. The probability of adopting or expanding use of the technology is Pr(j = 1) = F _εA (xβ), where F _εA is a cumulative distribution function of ε _A .

4.2. Program Participation

Producers considering participation in a program subsidizing BMP adoption or expansion with an incentive may employ a slightly different reasoning. A producer is willing to participate in the program when the expected utility of adopting or expanding and participating exceeds the utility of not doing so, or when u(1, I + B; x, ε _A ) ⩾ u(0, I; x, ε _A ), where 0 denotes failure to participate and 1 is participation; B is an incentive; and I and x are previously defined. Unobserved factors determining the adoption or expansion decision may be correlated with the participation decision. Following Cooper (Reference Cooper1997), B can be thought of as a net program incentive, where any extra costs associated with program participation beyond the costs of adopting or expanding the practice, such as the costs of documenting compliance with program requirements, are deducted from the amount of the incentive paid to producers.

In practice, the producer's utility function is unknown because some components are unobserved. From the researcher's perspective, utility is observed as a systematic and random component, with

(3) \begin{equation} v\left( {j,I + jB;x,\varepsilon _A } \right)\end{equation}

the mean of utility in state j, and v() is an indirect utility function. Including an independent and identically distributed stochastic component, ε ^j denotes the incomplete observability of utility. Provided these assumptions, producer willingness to participate in the program, given the net incentive B, is

(4) \begin{equation} v\left( {1,I + B;x,\varepsilon _A } \right) + \varepsilon ^1 \ge v\left( {0,I;x,\varepsilon _A } \right) + \varepsilon ^0 .\end{equation}

The dichotomous choice contingent valuation literature commonly parameterizes the indirect utility function as an argument linear in terms,

(5) \begin{equation} v\left( {j,I + jB;x,\varepsilon _A } \right) = \gamma _0^j + \gamma _1 I,\end{equation}

with γ₁ strictly positive. Producers participate (i.e., accept B) to voluntarily change their practices when γ⁰ ₀ + γ₁ · I + ε⁰ ⩽ γ¹ ₀ + γ₁ · (I + B) + ε¹. The likelihood that a producer participates in the program is extended to a probabilistic framework, namely

(6) \begin{equation} {\rm Pr}( {{\it PARTICIPATE} \le B} ) = {\rm Pr}( {v^0 + \varepsilon ^0 \le v^1 + \varepsilon ^1 } ) = {\rm Pr}( {\varepsilon ^0 - \varepsilon ^1 \le \gamma _0 + \gamma _1 B} )\end{equation}

after the normalization γ₀ = γ¹ ₀ − γ⁰ ₀. Other covariates (x) may systematically influence program participation. In this case, the probability of participating, given incentive payment B, is

(7) \begin{equation} {\rm Pr}( {{\it PARTICIPATE} \le B} ) = F_\varepsilon (\gamma _0 + \gamma _1\cdot B + x\cdot \gamma ),\end{equation}

where F _ε is a cumulative distribution function of the error term ε.

5. Empirical Model and Estimation

Acres enrolled in the hypothetical prescribed grazing program are modeled as a sequence of decisions beginning with willingness to adopt or expand prescribed grazing (ADOPT); willingness to participate in the hypothetical prescribed grazing program, given the cost share and annual payment offered (PARTICIPATE); and the number of acres the respondent is willing to enroll in the program (ACRES), given the incentive offered. A triple hurdle regression models this decision sequence as a tiered series of latent variables.

(8) \begin{equation} \hbox{{\it ADOPT}}_i^* = \beta^\prime X_{1i} + \varepsilon _{Ai}\end{equation}

\begin{equation*} {\it ADOPT}_i = \left\{ {\begin{array}{*{20}c} {1,\quad {\it ADOPT}_i^* > 0} \\ {0,\quad {\it ADOPT}_i^* \le 0} \end{array}} \right.\end{equation*}

(9) \begin{equation} \hbox{{\it PARTICIPATE}}_i^* = \gamma^\prime X_{2i} + \varepsilon _i\end{equation}

\begin{equation*} {\it PARTICIPATE}_i = \left\{ {\begin{array}{*{20}c} {1,\quad {\it PARTICIPATE}_i^* > 0|{\it ADOPT}_i^* > 0} \\ {0,\quad {\it PARTICIPATE}_i^* \le 0|{\it ADOPT}_i^* > 0} \end{array}} \right.\end{equation*}

(10) \begin{equation} \ln {\it ACRES}_i^* = \eta' X_{3i} + e_i\end{equation}

\begin{equation*} \ln {\it ACRES}_i = \left\{ {\begin{array}{c@{\quad}c} {\ln {\it ACRES}_i^*} ,& {{\it PARTICIPATE}_i^* > 0} \\ - ,&{{\it PARTICIPATE}_i^* \le 0} \end{array}} \right.\end{equation*}

In the first hurdle (equation 8), producers were asked if they would adopt or expand prescribed grazing following a description of the practice and an estimate of prescribed grazing costs. This first hurdle separates the participation decision from the consumption or level of expenditure decision (Blaylock and Blisard, Reference Blaylock and Blisard1992; Qualls et al., Reference Qualls, Jensen, Clark, English, Larson and Yen2012; Yen, Reference Yen2005). Applied researchers often use this type of screening question in surveys with choice experiments to determine whether respondents really “belong to” a particular market or not, to reduce the burden on respondents, and to minimize yea-saying (Blamey, Bennett, and Morrison, Reference Blamey, Bennett and Morrison1999). For example, a certain portion of individuals will not smoke or drink no matter how cheap cigarettes or alcohol are; these individuals do not belong to these markets. Asking this type of screening question allows researchers investigating willingness to pay (WTP) for cigarettes or alcohol to distinguish these individuals (i.e., those for whom WTP is equal to zero) from those whose reservation price has not been met. One might argue that this logic does not hold in a willingness-to-adopt study, as a large enough subsidy would likely induce all or almost all producers to participate. However, inducing participation in the hypothetical program among individuals who would be unwilling to expend the resources necessary to learn about a real program has the potential to introduce its own form of bias. In this analysis, producers who answered “no” to ADOPT are considered in the overall probability estimates of the ADOPT model but do not contribute to the incentive response part of the acreage supply model. In these cases, accounting for the individuals self-selecting out of the willingness-to-adopt exercise is important to minimize willingness-to-adopt estimate bias arising from sample selection. This is accomplished by estimating the first tier of the model (equation 8) jointly with participation (equation 9) and participation intensity (equation 10).

In the second hurdle (equation 9), producers who were willing to adopt or expand prescribed grazing (ADOPT = 1) were offered an up-front cost share and a per acre annual payment for enrolling pasture acres into the hypothetical program. Producers either refused (PARTICIPATE = 0) or accepted the offer (PARTICIPATE = 1). The outcome equation (equation 10) models the acres supplied by producers given their willingness to adopt or expand prescribed grazing and participate in the incentive program (i.e., ADOPT = 1 and PARTICIPATE = 1). The natural logarithm of the acres enrolled is used to ensure that enrolled acreage predictions are positive because enrolled acres reported are strictly greater than zero.

The error terms of equations (8)–(10) are correlated and assumed to be multivariate normally distributed each with an expected value of zero:

(11) \begin{equation} \left[ {\begin{array}{*{20}c} {\varepsilon _{Ai} } \\ {\varepsilon _i } \\ {e_i } \end{array}} \right]\sim MVN\left( {\begin{array}{*{20}c} {\left[ {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \end{array}} \right],} & {\left[ {\begin{array}{*{20}c} 1 & {\rho _{12} } &\quad {\sigma \rho _{13} } \\ {\rho _{12} } & 1 &\quad {\sigma \rho _{23} } \\ {\sigma \rho _{13} } &\quad {\sigma \rho _{23} } &\quad {\sigma ^2 } \end{array}} \right]} \end{array}} \right).\end{equation}

Given these assumptions, the parameter vectors (β, γ, η)′ and the covariance matrix in equation (11) can be jointly estimated using full information maximum likelihood. The log likelihood function for the system is:

(12) \begin{equation} \begin{array}{l} \ln L = \sum _{{\it ADOPT}_i^* \le 0} \ln \left[ {{\rm \Phi }\left( { - \beta' X_{1i} } \right)} \right]\\ \qquad\quad + \mathop \sum _{\scriptsize\begin{array}{*{20}c} {{\it ADOPT}_i^* > 0} \\ {{\it PARTICIPATE}_i^* \le 0} \\ \end{array}} \ln \left[ {{\rm \Phi }_2 \left( {\beta' X_{1i} , - \gamma' X_{2i} , - \rho _{12} } \right)} \right] \\ \quad \qquad+ \mathop \sum _{\scriptsize\begin{array}{*{20}c} {{\it ADOPT}_i^* > 0} \\ {{\it PARTICIPATE}_i^* > 0} \\ \end{array}} \ln [ {h( {\ln \, ACRES_i {\rm |}\beta' X_{1i} ,\gamma' X_{2i} ,\eta' X_{3i} ,\rho _{12} ,\rho _{13} ,\rho _{23} ,\sigma } )} ]. \\ \end{array}\end{equation}

5.1. Marginal Effects

The marginal effects of each outcome are calculated from the conditional and unconditional expected values of acres enrolled into the program. Extending Yen and Rosinski (Reference Yen and Rosinski2008) and Cameron and Trivedi's (Reference Cameron and Trivedi2009) derivation to a bivariate normal selection sequence, the unconditional expected mean pasture acres enrolled are calculated as:

(13) \begin{equation} \hspace*{-9pt}E\left( {{\rm ln} \ {\it ACRES}_i } \right) = {\rm exp}\left( {\eta' X_{3i} + \frac{{\sigma ^2 }}{2}} \right)\cdot {\rm \Phi }_2 \left( {\beta' X_{1i} + \sigma \rho _{13} ,\gamma' X_{2i} + \sigma \rho _{23} ,\rho _{12} } \right).\end{equation}

The conditional mean of acres enrolled into the program is calculated as:

(14) \begin{eqnarray} &&E( {{\rm ln} \ {\it ACRES}_i {\rm |}{\it ACRES}_i > 0,{\it ADOPT}_i = 1} )\nonumber\\ &&\quad = {\rm exp}\left( {\eta' X_{3i} + \frac{{\sigma ^2 }}{2}} \right)\cdot \frac{{{\rm \Phi }_2 \left( {\beta' X_{1i} + \sigma \rho _{13} ,\gamma' X_{2i} + \sigma \rho _{23} ,\rho _{12} } \right)}}{{{\rm \Phi }_2 \left( {\beta' X_{1i} ,\gamma' X_{2i} ,\rho _{12} } \right)}}.\end{eqnarray}

The marginal effect equations (equations 13 and 14) are estimated using a finite difference approximation algorithm (Cameron and Trivedi, Reference Cameron and Trivedi2009). For the willingness to adopt and willingness to participate portions of the model, the marginal effects are derived from the numerator and denominator of the bivariate cumulative density ratio in the conditional mean expression. It is important to note that variables included in superior tiers indirectly influence the marginal effect calculations of dependent variables in lower tiers even if those variables do not directly enter the equation. For example, variables in X ₁ and X ₂ not included in X ₃ indirectly affect acres enrolled through the derivative chain rule.

6. Explanatory Variables

The explanatory variables included in the ADOPT, PARTICIPATE, and ACRES equations are different for theoretical reasons and purposes of estimation. Linear identification of the decision sequence typically requires excluding variables in lower-tiered outcomes. In the absence of exclusion restrictions, the proposed model is identified only through nonlinear correlation between the error terms, which may introduce collinearity or cause solver nonconvergence.

It is also important to distinguish the interest in adoption or expansion of a BMP from participation in a program offering incentives with a specific set of requirements, and further still the intensity of adoption given participation in the hypothetical program. We assume that many of the variables included in the ADOPT equation are irrelevant in the participation equation. Likewise, nonpecuniary variables included in the ADOPT and PARTICIPATE equations may not relate directly to the acreage enrollment decision (ACRES). For example, operator age will likely be negatively correlated with the adoption decisions. Less clear would be the influence of age on acreage enrollment, given that the producer already committed to voluntary participation.