Measuring tillage adoption impact on farming efficiency
Technical efficiency (TE) improvement can be defined as the ability of an economic unit to produce a given bundle (fixed) of output for a maximum reduction of inputs (Färe et al. 1994). Estimating TE of technology adoption involves the application of either one of the two general approaches: parametric stochastic frontier analysis (SFA) and/or non-parametric data envelopment analysis (DEA). Rahman et al. (2009) and Wollni and Brümmer (2012) recently employed SFA with a selection model proposed by Greene (2010) to analyze the TE of rice and coffee farms in Thailand and Costa Rica, respectively. To account for observed and unobserved variable biases in technology adoption, several recent studies utilize propensity score matching (PSM) with SFA frameworks to correct selection bias (Villano et al. 2015; González-Flores et al. 2014; Bravo-Ureta et al. 2012). Although PSM eliminates a larger proportion of the baseline differences between adopters and non-adopters, its ability to account for unobservable factors such as farmers’ inherent skills and individual capabilities is limited. This can add bias and model dependence. King and Nielsen (2016) recently showed that even when the selection model is balanced and inclusive, PSM can increase imbalance and bias due to approximation of a completely randomized experiment, rather than a more efficient fully blocked randomized experiment.
Out of the two available approaches for TE estimation, we apply an input-oriented DEA model (Banker et al. 1984) to estimate TE gains of wheat farmers using different CT practices. The DEA approach has advantages as there is no requirement to specify a functional form, which is highly restrictive to subsistence level farming context, or to include the prices of the factors of production (Färe et al. 1985; Seiford and Thrall 1990). Using this approach, the frontier is calculated through a piecewise linear envelopment of observed input-output combinations by employing scaling and disposability assumptions (Olesen and Petersen 1995). A farmer qualifies as technically efficient (i.e. it lies on the ‘best practice frontier’ as suggested by Cook et al. 2014), if he or she maintains the current output level (in our case wheat production) using the possible minimum quantity of labor, capital, and technology (nutrients, agrochemicals, seeds, and tillage) inputs. In this study, while farmers manage enterprises consisting of multiple crops—often in rotation with a monsoon kharif season rice crop—we focus exclusively on wheat production as wheat tends to be the only crop in the rotation to which CT is widely employed (Erenstein 2009; Aravindakshan et al. 2015; Keil et al. 2015).
Since CT in wheat includes different tillage and crop establishment technology bundles, the estimate of a single frontier for all farmers under different subsets of CT practices is inherently inferior. As such, a meta-frontier (DEA) framework, based on the concept of the meta-production function as an envelope of neoclassical production functions (Hayami and Ruttan 1985), can be used to calculate TE for the global technology and group-specific frontiers for farmers using CT or TT. Technology gaps for farmers following different tillage technologies are then estimated by calculating meta-technology ratio following Battese et al. (2004) and O’Donnell et al. (2008). We therefore employ a bias-corrected DEA meta-frontier estimation, graphically represented and detailed in Figure S1 (see supplementary material). Both group-specific and meta-frontier efficiencies are modeled using wheat yield as the output per farm produced with eight inputs used in wheat production alone. Land, labor, seed, irrigation water, fertilizers, pesticides and fuel are incorporated in physical quantities, tillage machinery use was captured in monetary terms (Table 2).
Table 2 Summary statistics of samples showing output and inputs (both per ha and per farm), farm household, management and tillage adoption related variables Group specific frontier efficiency
We assume that farmers (DMU
j
, j = 1,…, n) use a vector of m discretionary inputs X = (x1, …, x
m
) to produce wheat (Y) by adopting any of the k tillage technologies. k differs with the group we consider while comparing technical efficiencies, that is k = {TT, CT} when we compare the efficiency between traditional and conservation tillage of wheat, and k = {TT,PTOS,BP,ST}while we compare specific tillage technologies with each of the other separatelyFootnote 1. Wheat production can be characterized by an input requirement set (Lovell 1993): L(Y) = {X:(Y,X) is feasible}. Production technology can be defined as:
$$T = \left\{ {(X,Y):X \in L\left( Y \right)} \right\}$$
(1)
The Farrell (1957) input-oriented measure of technical efficiency of DMU
j
is given by:
$$TE_j = \min \left\{ {\delta :\delta X_j \in L\left( {Y_j} \right)} \right\}$$
(2)
This input-oriented technical efficiency model in Eq. 2 depends on the definition of boundary of the observed production of Y as:
$${\mathrm{Isoq}}\,{\mathrm{L}}\left( {\mathrm{Y}} \right) = \left\{ {{\mathrm{X}}:{\mathrm{X}} \in {\mathrm{L}}\left( {\mathrm{Y}} \right){\mathrm{,}}\,\phi \,{\mathrm{X}}\, \notin \,{\mathrm{L}}\left( {\mathrm{Y}} \right),\phi \in \left[ {0,\left. 1 \right)} \right.} \right\}$$
(3)
TE is calculated for the farmer j in the tillage technology group k using piecewise linear programming approach under the following specifications:
$$TE_{kj} = \mathop {{\min }}\limits_{\delta ,\lambda } \delta ,\,{\mathrm{subject}}\,{\mathrm{to}}\,\mathop {\sum }\limits_{j = 1}^n \lambda _{kj}y_{kj} \ge y_{k0},\,\mathop {\sum }\limits_{j = 1}^n \lambda _{kj}x_{mkj} \le \delta x_{mk0}\,\forall m$$
(4)
with the assumption of either constant return to scale (CRS)—λ
kj
≥ 0 or variable return to scale (VRS)—\({\sum }_{j = 1}^n\, \lambda _{kj} = 1,\,\lambda _{kj} \ge 0\). The VRS assumption is better accepted for farmers in the smallholder dominated wheat production system of Bangladesh (this assumption is tested later in this paper). For any individual farmer j in the group k, 0 ≤ δ
kj
≤ 1 and for any technology group j, the average TE scores, δ
k
lie between 0 ≤ δ
k
≤ 1.
The DEA procedure ignores noise that can arise from sampling or other types of errors, for example one-off events that can impact farmers’ input use decisions and lead to biased δ
kj
estimates (Simar 1992). We employed a bootstrapping technique suggested by Simar and Wilson (2007, 2011) to correct biased TE scores (δ
kj
), thereby accounting for the non-zero probability mass at one in any given sample. The bias is computed by estimating the pseudo-efficiency estimates \(\left( {\hat \delta _{kj}^{\ast (1)}, \ldots , \ldots , \ldots ,\,\hat \delta _{kj}^{\ast (T)}} \right)\)by using simulated data set drawn from the original data set, repeated for T times (t = 1, 2, …., T).
$${\mathrm{The}}\,{\mathrm{estimated}}\,{\mathrm{bias}},\,\hat b_k = \frac{1}{T}\mathop {\sum }\limits_{t = 1}^T \hat \delta _{kj}^{{\mathrm{\ast }}(T)} - \delta _{kj}\,{\mathrm{and}}$$
(5)
the bias-corrected technical efficiency (BC.TE) score is as follows:
$$\overline{\overline \delta } _{kj} = \delta _{kj} - \hat b_k.$$
(6)
Meta-frontier efficiency and the meta-technology ratio
The tillage-specific efficiency model (TE
k
) described above does not allow the direct comparison of TE between individual CT options and TT because these scores are relative to each group’s own frontier (González-Flores et al. 2014). A meta-frontier model is therefore advantageous where several technologies are compared. Similar to the measurement of group frontier efficiency, we specified an input oriented DEA for meta-frontier efficiency estimation (TE
G
). However, instead of defining group frontiers as the boundaries of a restricted technology set in each group (e.g., a given tillage option), these meta-frontier efficiency scores are calculated relative to a global or meta-frontier (MF) defined to be the boundary of an unrestricted technology set (i.e. produced by pooling all the farms pertaining to the studied tillage options).
Let TE
k
(x
mk
, y
k
; δ
k
) be the input-oriented TE function for the group-frontier representing the group benchmark technology: Tk (Tk = {TTT, TBP, TPTOS, TST}) and TE
G
(x
m
, y; δ
G
)be the distance function of the meta-frontier representing global technology, TG. The gap between TE
G
and TE
k
is represented by the meta-technology ratio (MTR), which is defined as the ratio of output of the group-specific production frontier relative to the potential output described by the meta-frontier (Battese et al. 2004). That is, the MTR measures the proximity of the tillage specific group frontier (TTT,TBP,TPTOS,TST) to the meta-frontier (TG) with an unrestricted technology set. The MTR between CT and TT is given by:
$$MTR^k\left( . \right) = \frac{{1 - TE_G(.)}}{{1 - TE_k(.)}} = \frac{{1 - \left( {\overline \delta _G - \hat b_G} \right)}}{{1 - \left( {\overline \delta _k - \hat b_k} \right)}} = \frac{{1 - \overline{\overline \delta } _G}}{{1 - \overline{\overline \delta } _k}}$$
(7)
Equation 7 captures productivity differences between different tillage technologies. It is indicative of the efficiency improvement potential of wheat farmers in a specific tillage group, that would be possible if they switched to a better tillage technology practiced by other groups of farmers. For example, a relatively high average MTR for a specific tillage group suggests a lower technological gap between farmers in that tillage group in relation to the all available set of tillage technology represented in the meta-frontier. Significant improvements in TE can be realized by switching to technologies that have a higher MTR, wherever feasible. The feasibility of farmers switching to CT is greatly contingent upon the capacities and capital, technological, information and other constraints of individual farm households and on cultural, biophysical, socio-economic and institutional contexts (Ruttan and Hayami 1984). Nevertheless, we hypothesize that TT farmers adopting CT will generally impart a greater gain in efficiency and shrink the technological gap than farmers switching from one CT technology to another CT.
Factors affecting group-frontier efficiency of farmers
Simar and Wilson (2007) noted that DEA efficiency estimates are biased and serially correlated, which invalidates conventional inference in two-stage approaches employing Tobit or ordinary least squares models (Ramalho et al. 2010). However, as more recently evidenced by Solís et al. (2007) and Bravo-Ureta et al. (2012), parameter estimates of TE may be subjected to endogeneity bias due to self-selection. This requires correction for sample selection in parameter estimation models. In case of estimating group-specific efficiency effects, the samples within a particular tillage technology are not systematically different from one another accounting for any selection bias. Bootstrapped truncated regression therefore appears to be pertinent in our case, which we specified as:
$$\overline{\overline \delta } _{kj} = \alpha + Z_j\phi + \varepsilon _j,\,j = 1, \ldots ,n$$
(8)
where \(\overline{\overline \delta } _{kj}\) is the bias-corrected estimate of group-specific efficiency scores (analyzed separately for BP, PTOS, ST and TT), \(\varepsilon _j\sim N\left( {0,\sigma _\varepsilon ^2} \right)\) with right-truncation at 1−Z
j
φ ; α is a constant term and Zj is a vector of farmer/farm specific variables. For more details, see Simar and Wilson (2007, 2011).
Factors affecting tillage adoption and meta-frontier efficiency
Kneip et al. (1998) pointed out that DEA scores converge slowly and are consistent estimators of true efficiency, but biased downwards. In our approach we addressed this bias using bootstrap procedures as explained in Section 3.1.1 and following Simar and Wilson (2007), while employing bootstrapped truncated regression to estimate the factors influencing group level efficiency. Although bootstrapped truncated regression yields unbiased parameter estimates for the determinants of group level efficiency scores, and is therefore preferred to Tobit models, when it comes to estimating the counterfactual effect of technology adoption on meta-frontier efficiency scores, an endogenous switching regression model performs better. Additionally, unlike the traditional OLS and truncated models such as Tobit, these models do not require the conditional distribution of DEA scores (e.g. switching regression and fractional regression) and can yield better estimates (Ramalho et al. 2010). The former approaches may also lead to biased estimates because the decision to adopt CT is voluntary, yet influenced by farmers’ characteristics. For example, farmers who adopt CT may be systematically different from those who do not. Moreover, unobservable characteristics of a given farmer and their farm affects both the CT adoption decision and the resulting efficiency impacts, generating inconsistent estimates of the effect of adoption on household welfare (e.g., if only the most skilled or motivated farmers choose to adopt, the failure to control for skills may result in an upward bias). In addition, some of the factors determining agricultural technology adoption may also influence efficiency, leading to endogeneity problems.
We estimated a standard endogenous switching regression (ESR) model (Maddala and Nelson 1975; Maddala 1983) to deal with problems presented by both sample selection bias and endogeneity (Heckman 1979; Hausman 1978), allowing for interactions between technology adoption and other covariates (Alene and Manyong 2007). This model has two parts: in the first part, endogeneity due to self-selection is addressed using a probit selection model in which farmers are sorted into those who have adopted conservation tillage and those who have not. The second part of the model focusses on the outcome equations on factors influencing efficiency.
Drawing from Maddala (1983) and Lokshin and Sajaia (2004), a probit selection equation for CT adoption is specified as:
$$CT_j^ \ast = \gamma S_j + u_j,\,\,\,\,\,\,with\,{\mathrm{A}}_j = \left\{ {\begin{array}{*{20}{c}} 1 & {if\,CT_j^ \ast > 1} \\ 0 & {otherwise} \end{array}} \right.$$
(9)
where \(CT_j^ \ast\) is the unobservable (or latent) variable for CT adoption; CT
j
is the observable counterpart (equal to one if the farmer j has adopted either BP, PTOS, or ST for wheat during the cropping season studied, and zero otherwise). S
j
are non-stochastic vectors of observed farm and non-farm characteristics determining adoption, and u
j
are the random disturbances associated with CT adoption. Among S
j
, a particular concern is with the dummy variable for CT machine drill scarcity due to its potential for endogeneity bias in selection equation (Eq. 9). Identifying a valid instrument having high correlation with the CT machine scarcity variable, but with low correlation to the dependent variable \(CT_j^ \ast\), is important in two stage estimations. Given this precondition, the distance from the farm to the nearest place at which farmers can receive CT extension advice was selected as the instrument after testing for exclusion restriction and endogeneity.
We subsequently specified the endogenous switching regression model of CT technical efficiency involving two regimes as:
$$Regime\,1:\overline{\overline \delta } _{Gj1} = \beta _1S_{1j} + \tau _{1j},if\,CT_j = 0\,\,\,{\mathrm{and}}$$
(10a)
$$Regime\,2:\overline{\overline \delta } _{Gj2} = \beta _2S_{2j} + \tau _{2j},if\,CT_j = 1,$$
(10b)
where \(\overline{\overline \delta } _{Gj1}\) and \(\overline{\overline \delta } _{Gj2}\) are the meta-frontier technical efficiency scores in the outcome equations, and S1j and S2j are vectors of exogenous variables assumed to influence technical efficiency. The vectors β1, β2, and γ are coefficient parameters to be estimated, with error terms u
j
, τ1j and τ2j. The standard switching regression model assumed no covariance between τ1 and τ2 with the following covariance matrix:
$$cov\,\left( {\tau _{1j},\tau _{2j},u_j} \right) = \left[ {\begin{array}{*{20}{c}} {\sigma _{\tau _1}^2} & . & {\sigma _{\tau _1u}} \\ . & {\sigma _{\tau _2}^2} & {\sigma _{\tau _2u}} \\ . & . & {\sigma _u^2} \end{array}} \right]$$
(11)
The covariance between τ1 and τ2 is not defined since \(\overline{\overline \delta } _{Gj1}\) and \(\overline{\overline \delta } _{Gj2}\) are never observed simultaneously. In the literature, a two-step ESR procedure involving estimation of probit selection model and outcome equations are employed by Perloff et al. (1998). This approach suffers from heteroskedastic errors when inverse mills ratios from probit equations are inserted manually into outcome equations. The full-information maximum likelihood (FIML) yield consistent estimators in which both the probit selection (Eq. 9) and two regime equations (Eqs. 10a and 10b) are estimated simultaneously (Lokshin and Sajaia 2004; Gkypali and Tsekouras 2015). As noted previously, a benefit of switching regression is the ability to consider a counterfactual scenario by using the parameters of one regime (e.g. 10a) to predict values for the other regime (e.g., 10b), and vice versa. Such hypothetical predictions assume that the coefficients obtained in the switching regression for CT adopters are unbiased estimates of the effect of CT adoption and hence would also apply to non-adopters were they to adopt the CT technology. Conversely, the coefficients obtained for CT non-adopters would apply to CT adopters to simulate disadoption.