Additionality and the Adoption of Farm Conservation Practices

Propensity Score Matching Estimator

Our empirical goal is to estimate the ATT from enrollment, while also decomposing ATT into the relative contributions from new adopters and voluntary adopters. We define an indicator variable D equal to one if a farmer enrolled in a cost-share program to fund the adoption of a conservation practice, and D equals zero if a farmer did not enroll. Further, we define the potential outcome variables Y₁ and Y₀ for each farmer and practice type. Let Y₁ be the proportion of farm acreage in the conservation practice if a farmer enrolled in a program (D = 1), and let Y₀ be the proportion of farm acreage in the conservation practice if the farmer did not enroll (D = 0), where 0 ≤ Y₀ ≤ 1 and 0 ≤ Y₁ ≤ 1. We can observe only one of these two outcome variables for any given farmer.

The treatment effect of enrollment in a cost-share program is defined as the increase in the proportion of conservation acreage adopted with program enrollment relative to the proportion without being enrolled, τ = Y₁ − Y₀. We define the additionality as the average treatment effect on the treated (enrolled) group of farmers:

[1]

The application of matching estimators to estimate the ATT requires that two identification assumptions be made. The first assumption, often called the unconfoundedness assumption, states that the potential outcome Y₀ must be independent of program enrollment, conditional on the set of observable covariates X, in other words, (Heckman, Ichimura, and Todd 1997). This assumption implies that differences in outcomes between enrolled and nonenrolled farmers with the same values for covariates are attributable to enrollment. The vector of covariates X should affect both the farmer decision on enrollment and the potential outcomes. Rosenbaum and Rubin (1983) demonstrated that if the unconfoundedness condition is satisfied, then it is also true that Y₀ is independent of program enrollment conditional on the propensity score, in other words, , where the propensity score is defined as the probability of enrollment conditional on X, P = P (D = 1⎪X). The propensity scores are often estimated using discrete choice models, typically a probit or logit model.

The second identification assumption states that for all farmer characteristics X, there is a positive probability for both enrolled or nonenrolled farmers, that is, 0<P(D = 1⎪X) < 1. This overlap assumption, also known as the common support condition, implies that for each enrolled farmer there exists a positive probability of a match within the group of nonenrolled farmers with a similar set of covariates X.

Let H₁ denote the set of I enrollees and H₀ the set of J nonenrollees that are on common support. Each enrollee and nonenrollee has a vector of characteristics, X_iand X_j, and propensity scores, P_i and P_j, respectively, where i = 1, ..., I and j = 1, ..., J. Propensity scores on the probability of enrollment are estimated from a probit model, such that P_i= P(D_i = 1⎪X_i) for i ∈ H₁ and P_j = P(D_j = 1 ⎪X_j) for j ∈ H₀.

The primary goal of the matching process is to obtain for all i ∈ H ₁, a counterfactual estimate, of what the enrolled farmer would have done without cost-share funding. The counterfactual estimate, is a weighted average,

[2]

where is the observed outcome for the nonenrollee j ∈ H₀.¹ A variety of matching algorithms are available to construct the weights W(i, j) in [2] (Guo and Fraser 2010). For example, the propensity score kernel matching uses the nonenrollees in H 0 as matches, and the weights W (i, j) are determined based on a kernel function, a bandwidth parameter, and the differences between P_i and P_j. The weights are normalized so that for each enrolled farmer i. The matching estimators for E[Y₁⎪D = 1] and E [Y₀⎪D = 1] in equation [1] are, respectively,

[3]

Hence, the matching estimator for the ATT in equation [1] is

[4]

Decomposing the ATT for New Adopters and Voluntary Adopters

As discussed above, we define voluntary and new adopters based on their potential outcome Y₀. The potential outcome Y₀ for enrolled farmers is not observed and must be estimated. Hence, we define the probabilities P_n = P(Y₀ = 0⎪D = 1) and P_v= P(Y₀ > 0⎪ D = 1), which are, respectively, the expected probabilities that the enrolled farmers are either new adopters or voluntary adopters. Given that Y₀ ≥ 0, it holds that

[5]

Using conditional expectations and these probabilities based on Y₀, the ATT in equation [1] can be decomposed into two parts reflecting the relative amounts of the ATT that are attributable to new adopters and voluntary adopters, respectively:

[6]

The first part represents the portion of the ATT that corresponds to new adopters. The term E [Y₁⎪Y₀ = 0,D = 1] is the expected proportion of acreage that new adopters dedicate to the conservation practice when receiving funding. Meanwhile, E [Y₀⎪Y₀ = 0, D = 1] is the expected proportion new adopters dedicate to the practice when not receiving funding, which equals zero by definition. The difference of these two terms equals the expected additional proportion of acreage that new adopters dedicate to the conservation practice when receiving funding. The second part in [6] represents the portion of the ATT that corresponds to voluntary adopters. The difference in the two terms E[Y₁⎪Y₀ > 0, D = 1] and E[Y₀⎪Y₀ > 0, D = 1] is equal to the expected additional proportion of acreage that voluntary adopters dedicate to the conservation practice as a result of receiving funding. The overall ATT in equation [6] equals the weighted average of these two expected increases in the proportion of conservation acreage adopted attributable to receiving funding.

To simplify notation, we define the respective ATT for enrolled new adopters and voluntary adopters as

[7]

The decomposed ATT in [6] can be rewritten as

[8]

Below we derive the estimators for each of the decomposed terms in equation [8].

Estimators for the Probabilities of New Adopters and Voluntary Adopters

In this section, we derive the estimators for P_n and P_v in equation [8]. We first define a binary variable B₀ to explain how matching estimators are used to derive the estimators for these probabilities. Specifically, B₀ equals one if a farmer would adopt a practice without funding, and zero otherwise, that is, B₀ = 1 if Y₀ > 0, and B₀ = 0 if Y₀ = 0. The probability that Y₀ is greater than zero, P_v, can be expressed in terms of the expectation of B₀:

[9]

An estimator for E [B₀⎪D = 1] can be obtained using a matching estimator, analogous to the approach used on the estimator for E [Y₀⎪D = 1] in equation [3]. This yields the estimate for P_v, and the estimate for the other probability, P_n, can be obtained using [5].

Similar to equation [2], the matching estimator for is the weighted average

[10]

where is the B₀ for nonenrollee j. Note that is the estimate of the probability that an enrolled farmer with propensity score P_i is a voluntary adopter, such that . The matching estimator for E [B₀⎪D = 1] is then the average of the for the set of I enrollees in H₁, such that

Consequently, given equations [9] and [10], the estimator for P_v is

[11]

and the estimator for P_n is obtained by substituting [11] into [5]:

[12]

Estimators for the ATT of New Adopters and Voluntary Adopters

In this section, we provide estimators of ATT_n for new adopters and ATT_v for voluntary adopters that are defined in equation [7], respectively. We first provide estimators for the conditional expectations of Y₁, then for the conditional expectations of Y 0, and finally take the difference in the conditional expectations to arrive at respective estimators for ATTn and ATTv.

The estimator for the conditional expectation of Y₁ for new adopters is

[13]

This estimator is the average value of Y₁ across all I enrollees weighted by the estimated probability that the enrollee is a new adopter, . Likewise, the estimator for the conditional expectation of Y₁ for voluntary adopters is

[14]

which is the estimator for the average value of Y₁ across all I enrollees weighted by the estimated probability that the enrollee is a voluntary adopter, .

The estimator for the conditional expectation of Y₀for new adopters, E[ Y ⎪Y₀= 0,D =1], equals zero by definition, as noted previously. The estimator for the conditional expectation of Y ₀ for voluntary adopters is

[15]

where we have substituted E^ˆ [Y0⎪D = 1] in equation [3] and P^ˆ(Y₀>0⎪D = 1) in equation [11] into equation [15] above.²

After substituting [13] into the expression for ATT_n found in equation [7] and noting that E [ Y₀⎪Y₀ = 0, D = 1] = 0, we obtain the estimator for the ATT of new adopters:

[16]

Similarly, after substituting [14] and [15] into the expression for ATT_v in equation [7], we obtain the estimator for the ATT of voluntary adopters:

[17]

The estimator for the overall ATT in equation [8] is

[18]

where the proposed estimators for the decomposed parts in equations [11], [12], [16], and [17] are substituted into equation [18] above. In the Appendix, we validate that this yields the same expression as the estimator for the overall ATT in equation [4].

Additionality and Decomposed Effects

In this section, we provide the estimation results on additionality and the decomposed components of the ATT for the six conservation practices. Table 5 provides the estimates for the overall ATT, %ATT, and each component of the decomposed ATT for all practices types. The estimation in Table 5 is performed using propensity score kernel matching with the Gaussian kernel type, where the common support requirement is enforced and the kernel bandwidth is 0.06.⁹ The standard errors and 95% confidence intervals were generated using a bootstrap procedure based on 1,000 simulations.¹⁰

The %ATT in Table 5 is defined as

[19]

Note that the ATT is equal to E[Y₁⎪D = 1] − E[Y₀ ⎪ D = 1], which therefore has an upper bound of E [ Y₁⎪D = 1]. The %ATT can be interpreted as the percentage of the observed conservation practices for enrolled farmers that can be attributed to the treatment effect. The %ATT is thus equal to the percent additionality.

The overall ATT is positive and statistically significant for all six practices (Table 5). That is, the bootstrapped 95% confidence intervals on ATT for each of the six practice types do not contain zero. This suggests that enrollment in cost-share programs achieves a significantly positive level of additionality for each practice type. The ATT values in Table 5 are higher for field practices than those for environmentally sensitive areas. This is not surprising because filter strips and grass waterways are solely focused along stream banks and in natural drainage areas and, thus, represent a smaller proportion of the total farm acreage. Recall that the proportion of conservation acreage adopted by enrolled farmers is less than 0.02 for both filter strips and grass waterways (Table 1).

To compare the level of additionality between practice types, we use the %ATT in equation [19]. The largest %ATT is found for hayfield establishment, cover crops, and filter strips with 93.3%, 90.6%, and 88.9%, respectively (Table 5). Moderate percent additionality was found for grid sampling and grass waterways with %ATT at 65.8% and 61.1%, respectively. Conservation tillage had the lowest percent additionality at only 19.3%. In sum, this suggests that while cost-share funding from enrollment in conservation programs achieves a positive ATT for all practice types, certain practice types achieve higher percent additionality than others.

To test whether the %ATT values are statistically different across practice types, we construct bootstrapped confidence intervals of the difference in %ATT for all pairwise combinations of practice types (Table 6). For example, the difference in %ATT between cover crops relative to conservation tillage has a 95% bootstrapped confidence interval spanning lower and upper bounds of 61.6% to 81.1%, respectively. This indicates that cover crops have a much higher %ATT than conservation tillage. Meanwhile, the difference in %ATT between cover crops and hayfield establishment is not statistically significant from zero because the bootstrapped confidence interval spans from - 10.3% to 13.2%. When comparing the two practice types for environmentally sensitive areas, filter strips have a statistically larger %ATT than grass waterways.

The components of the decomposed ATT show the relative contributions of new adopters and voluntary adopters to the overall ATT, which, in turn, explains the differences in %ATT between practice types. Table 5 highlights that ATT_v is less than ATT_n for all practice types, as expected. Interestingly, ATT_v is positive but not statistically different from zero for all practices except for grid sampling. This result indicates that those farmers who would have adopted the practice without funding typically do not significantly expand their conservation acreage when receiving cost-share funding, with the exception of grid sampling. This could potentially reflect lumpy technology with fixed costs for expanding the adoption of conservation practices.

Practices for which a large fraction of enrolled farmers are voluntary adopters (i.e., P_v is large) typically have a lower %ATT. Consider conservation tillage where ATT_n is 0.73, whileATT_v is only 0.06. The estimated fraction of enrolled farmers for conservation tillage that are voluntary adopters, P_v = 0.86, is much larger than that of new adopters, P_n = 0.14. Consequently, the overall ATT is small relative to the total proportion of conservation acreage adopted, and thus, the %ATT is relatively low for conservation tillage.

In general, practices where P_n is considerably larger than P_v have higher %ATT values. When comparing the two environmentally sensitive practice types, the fraction of enrolled farmers who are new adopters for filter strips is P_n = 0.83, while for grass waterways P_n = 0.53 (Table 5). This is the principal reason why the %ATT is larger for filters strips (88.9%) than for grass waterways (61.1%). Similarly, when comparing the four field practices, cover crops and hayfield establishment have larger P_n values than either grid sampling or conservation tillage. As such, the %ATT values for cover crops (90.6%) and hayfield establishment (93.3%) exceed that of either grid sampling (65.8%) or conservation tillage (19.3%).

The heterogeneity in P_v and P_n, and consequently in %ATT, may in part be related to differences in the onsite net benefits to the farmer provided by the different practice types. Higher onsite net benefits should increase the likelihood that a farmer would adopt a practice even without funding, increasing the proportion of voluntary adopters for this practice type. Consider a comparison of the two environmentally sensitive practice types. Filter strips are typically located along stream banks and, therefore, mainly provide offsite benefits in terms of improved water quality by reducing nutrients and sediments from entering downstream water bodies. Grass waterways, in contrast, are typically installed in natural drainage areas within cultivated lands, which provides both onsite and offsite benefits. The results in Table 5, showing that P_n and %ATT are higher for filter strips than grass waterways, coincide with the expectation that farmers would be less likely to adopt filter strips without cost-share funding.

When evaluating whether to adopt a conservation field practice, farmers typically consider the impact such a practice would have on factors such as crop yields and operating costs. Hayfield establishment, for instance, would result in a complete loss in grain crop yields for the length of the enrollment contract. Meanwhile, conservation tillage often results in only modest changes in yields and may even lower operating costs, stemming from reduced fuel consumption. The results in Table 5, showing that %ATT is higher for hayfield establishment than conservation tillage, are consistent with the expectation that there are higher opportunity costs from losses in yield for hayfield establishment than for conservation tillage.

It is interesting to note that many farmers choose to self-fund the adoption of practices. In fact, Table 1 shows that adoption without enrollment (i.e., self-funded practices) is more common than adoption with enrollment for most practices. Some reasons for self-funding include government contract restrictions, such as engineering specification on practices or continuous adoption for entire contract period, which farmers may not want to comply with. Other reasons include government eligibility restrictions, such as “redlining,” where the farmer does not have the cropping history needed to qualify for the cost-share program. Transaction costs (e.g., paperwork) and attitudes to the government also make some farmers reluctant to participate in these programs. Additional quantitative and qualitative research is needed to understand the underlying reasons for self-funding, since increasing additionality is essentially an attempt to understand why farmers would adopt without funding.

Robustness Checks

As a robustness check to the estimation results presented in Table 5, we estimate the ATT, %ATT, and the decomposed effects using a variety of matching estimators that differ in the model specifications on the weights. Specifically, we conduct sensitivity analysis on the estimation results for all combinations of the following specifications: two matching methods (kernel and local linear), two kernel functions (Gaussian and Epanechnikov), and four bandwidths (bandwidths = 0.02, 0.06, 0.1, and 0.15).¹¹ This yields a total of 16 different model specifications. The various model specifications provide a trade-off between bias and variance. For instance, smaller (larger) bandwidth typically results in lower (higher) bias because it provides weight to controls that are higher-quality matches, but higher (lower) variance because less information is used to construct the counterfactual for each enrolled farmer.

The main results in Table 5 are generally robust across all the model specifications.¹² First, the overall ATT is positive and significant for each practice type across all 16 model specifications. Second, the %ATT for each practice is similar in magnitude to the results in Table 5 across all model specifications, varying generally by less than 5%. The %ATT results also maintain the same ordering for three groups of practices. Third, the ATT_v is not statistically significant for hayfield establishment, filter strips, cover crops, and grass waterways for all 16 model specifications and was significant only for 2 and 4 of the 16 model specifications, for conservation tillage and grid sampling, respectively.

It should be acknowledged that there is the potential for farmer adoption and enrollment decisions to be correlated across practices, which could lead to biased estimates. Hence, we examine the sensitivity to the potential influence of cross-practice correlation for the field practices (conservation tillage, cover crops, hayfields, and grid sampling) and the environmentally sensitive practices (filter strips and grass waterways). To do so, we first limited the set of farmers in the control group for matching to only those farmers that did not receive cost-share funding for any field practice. We then reestimated the ATT, %ATT, and the decomposed components for each field practice using the limited set of controls. The same procedure was used for the two environmentally sensitive practices, where sets of farmers in the control group were only those farmers that did not receive cost-share funding for any environmentally sensitive practice. In general, when comparing the estimation results for each practice based on the limited set of controls with those in Table 5, we find that qualitatively the main findings remain largely unchanged. The only minor exception is that ATT_v is statistically significant for grid sampling in Table 5, but it is no longer significant in the estimation with the limited set of controls.¹³ Hence, this suggests that at least for this study, the issue of correlation is unlikely to be a major concern.

Another issue that merits further analysis is whether additionality for a given practice varies significantly between programs. Of particular concern is the CSP, which specifically allows funding for both new and existing practices, thereby potentially resulting in lower levels of additionality relative to other programs. As a robustness check, we performed bootstrapped simulations to test whether the estimation results on %ATT differ significantly based on pairwise comparisons across the three largest programs (EQIP, CRP, and CSP). We restrict our analysis to only those pairwise comparisons that have greater than 10 enrolled farmers in each program for the given practice (Table 2). Table 7 provides the estimated %ATT for each of the programs for conservation tillage, grid sampling, grass waterways, and filter strips. The other two practices were not included in Table 7 because the number of enrolled farmers was insufficient to perform program-level comparisons. Estimation results in Table 7 indicate that the %ATT does not differ significantly between programs for all practices since the 95% bootstrapped confidence intervals contain zero for all pairwise program-level comparisons. For this reason, we maintained our focus on the additionality estimation results for enrollment in all programs (i.e., receiving any cost-share funding versus no funding). Nonetheless, the results in Table 7 depend on a relatively small sample of enrolled farmers in each program, and therefore program-level differences in additionality are an important issue for future study. Similarly, it would be informative to assess subgroup heterogeneity of the treatment effect based on farm-level variation in covariates. This would require splitting the sample into subgroups based on some chosen set of covariates to perform this disaggregated analysis of the ATT for each subgroup. This is another issue for future research that would benefit from a larger sample size, similar to the analysis on program-level heterogeneity in Table 7.

Slippage is another issue to consider since conservation programs have been previously found to induce slippage, which can offset the additionality benefits provided by such programs (Lichtenberg and Smith-Ramirez 2011). We also examine whether enrollment in conservation programs induces slippage, using our survey data on the proportion of the property in “other uses,” which includes woodland, wildlife habitat, and buildings. When estimating the ATT on this outcome variable, a decrease in the proportion in other uses would be indicative of slippage since there is a decrease in the land dedicated to nonfarm uses. The estimated ATT on other uses was negative (–0.0124), indicating that enrolled farmers had on average about 1.2% less land in other uses; however, this result was not significantly different from zero at the 95% level. Hence, unlike Lichtenberg and Smith-Ramirez (2011), we did not find significant evidence of slippage in our study region.

It should be acknowledged that estimation of the ATT using propensity score matching is based on the unconfoundedness assumption. If there exist unobserved covariates that influence both enrollment and outcome variables, then the estimated ATT may be biased. For example, unobserved characteristics may explain why some farmers choose to voluntarily adopt conservation practice even when funding is available. Although the unconfoundedness assumption cannot be verified in practice, Rosenbaum (2002) developed a method to test the extent to which a matching estimator is sensitive to hidden bias. Specifically, Rosenbaum's approach assumes that the propensity score, P(D =1⎪ X ), is influenced not only by observed covariates X, but also by an unobserved covariate. As a result of this unobserved covariate, farmers that are matched based on similar propensity score values, may actually differ in their odds of enrolling by a factor of Γ, where Γ = 1 represents the baseline case of no hidden bias. The higher the level of Γ to which the ATT remains statistically different from zero, the more robust are the estimation results to the potential influence of hidden bias.

We conduct a Rosenbaum bounds sensitivity analysis to estimate the extent to which selection on unobservables may bias the estimates of the ATT (Rosenbaum 2002; DiPrete and Gangl 2004). Using this approach, which relies on a signed rank test, we determine the upper bounds on the significance level (i.e., critical p-values) of the ATT for different levels of hidden bias in terms of Γ. Estimation results from the Rosenbaum bounds sensitivity analysis are provided in Table 8. The first column provides the Γ values, and the second column (sig + ) provides the corresponding upper bound on the p-value for the ATT. The filter strips practice is the most robust to the potential presence of hidden bias, where the estimated ATT remains statistically different from zero at the 5% level for a critical threshold Γ value at 10.2. Conservation tillage, on the other hand, is the least robust to hidden bias, where the critical Γ value is 1.24. The other practice types have moderate to high critical Γ values ranging from 2.2 for cover crops to 5 for grid sampling.