1 Introduction

Wheat is the second most important source of calories and protein to the Ethiopian diet after maize, contributing 13.41% of the total calorie intake and 13.82% of the total protein intake (FAO, 2022). According to CSA (2022), in 2021/22 production year, wheat covered 1.867 million hectares of land at the national level, which accounts for approximately 18.67% of the total area covered by cereal crops. The total volume of wheat production in the same year amounted to 58.078 million quintals, representing 19.97% of the total cereal crop output. The Oromia region produced the largest volume, accounting for 55% of the wheat area coverage and 59% of the production, followed by the Amhara region, which covered 36% of the area and contributed 33% of the production (CSA, 2022).

Despite the importance of wheat as a food and industrial crop, its productivity remains low. CSA (2022) and FAO (2022) indicate that the average productivity of wheat in Ethiopia is 31.11qt/ha, which is lower than average global productivity (35.47 qt/ha) and the average productivity of other African countries, such as Egypt (64.5 qt/ha) and South Africa (43.12 qt/ha) in 2021. The production and productivity of wheat in Ethiopia face significant challenges, including soil degradation, disease, insect pests, a decrease in farm size, the use of local varieties, rainfall variability, and recurrent drought/water stress due to climate change (Sewenet et al., 2021; Wato, 2021). Research by Solomon et al. (2021) indicates that wheat production is highly vulnerable to climate change, with a projected decrease of 25.5% in 2050. The low level of productivity, exacerbated by climate change, alongside the increasing demand for wheat in Ethiopia, is expected to worsen food shortages in the country (Workineh et al., 2020). Therefore, it is crucial to widely adopt yield-enhancing technologies and practices that not only improve wheat productivity but also ensure environmental sustainability, while mitigating greenhouse gas emissions (Mekonnen, 2017).

Since 2010, the Ethiopian government, in collaboration with the Food and Agricultural Organization (FAO), has introduced climate-smart agriculture practices (CSAPs). The aim is to enhance agricultural productivity in a sustainable manner, adapt and build resilience to climate change, and reduce greenhouse gas emissions (FAO, 2016). Climate-smart agriculture practices have the potential to improve soil fertility, reduce erosion, break pest life cycles, lower GHG emissions, suspend weeds, and ultimately enhance crop productivity (Bongole et al., 2020; Hallama et al., 2019). For example, crop rotation and row planting are vital practices that mitigate the risk of pest and weed infestations, enhance nitrogen fixation and organic matter formation, improve water and nutrient distribution in the soil profile, and notably reduce greenhouse gas emissions while enhancing productivity (FAO, 2016; Martey et al., 2020). The use of improved crop varieties reduces the risk of crop failure resulting from rainfall variability and enhances productivity (Martey et al., 2020; Tekelewold et al., 2019).

Several studies have been conducted in Ethiopia that have evaluated the impact of CSAPs on crop productivity and household welfare. However, previous studies have mostly considered single CSA practices (Merga et al., 2023; Mossie, 2022; Workineh et al., 2020) and their impact on crop yield and income (Adego et al., 2019; Fentie & Beyene, 2019; Mossie, 2022; Sedebo et al., 2022). Additionally, most of the previous studies measured the aggregate effects of CSAPs on yield and welfare (Adego et al., 2019; Belay et al., 2023; Sedebo et al., 2022), yet each CSAPs may not contribute equally. Thus, an independent study is required to provide detailed CSAP measures for designing specific interventions. In addition, many studies were focused on other crop than wheat (Adego et al., 2019; Beyene, 2019; Merga et al., 2023; Shako et al., 2021). To the best of our knowledge, there is a dearth of studies on the impact of CSAPs on technical efficiency in Ethiopia, including the study area.

Furthermore, a significant portion of the studies relied on econometric models that may not adequately control for both observable and unobservable differences between users and nonusers of CSAPs, which can impact outcome variables. For instance, Abate et al. (2023), Belay et al. (2023), Fentie and Beyene (2019), Mossie (2022) and Wordofa et al. (2021) relied on the propensity score matching (PSM) model, which does not account for the unobservable characteristics of farmers. If there are unobservable characteristics that can influence adoption decisions and the outcome variable, the result from PSM is likely to be biased (Ma & Abdulai, 2016). Besides, most of the previous studies did not consider selection bias in favor of a single production frontier model to estimate technical efficiency by assuming that adopters and non-adopters have similar production characteristics. For instance, Ho and Shimada (2019) study the effects of climate-smart agriculture and climate change adaptation on the technical efficiency of rice farming, not accounting for selection bias from unobserved characteristics. Pangapanga-Phiri and Mungatana (2021) also did not consider selection bias when analyze the effect of CSAPs on the technical efficiency of maize production under extreme weather events. The reported impacts from these studies, which do not account for selection bias, are likely to be biased estimations (González-Flores et al., 2014; Greene, 2010). According to Greene (2010), a stochastic frontier model with correction for sample selection takes into account the selection bias from observed and unobserved factors by assuming that the unobserved characteristics in the selection equation are correlated with the noise in the stochastic frontier.

Hence, unlike previous studies, this study tries to control for both observed and unobserved heterogeneities to estimate production efficiency and evaluate the impact of CSAPs on technical efficiency. Accordingly, we applied the multinomial endogenous switching regression model and the recently introduced frontier model, which corrects for sample selection bias, to measure the impact of the adoption of CSAPs on the technical efficiency of wheat farmers (Greene, 2010). Hence, this study aimed to examine the individual and combined effects of wheat row planting, crop rotation, and improved wheat varieties on the technical efficiency of wheat farmers in northwestern Ethiopia. This empirical study will, therefore, be vital for designing appropriate policies and strategies that can stimulate the adoption of CSAPs to enhance the technical efficiency of wheat farmers and ultimately improve food security and overall livelihoods without harming the environment. This study will also contribute to the literature by identifying factors affecting the adoption of CSAPs and its impact on technical efficiency.

2 Methodology

2.1 Study area description

The study area, East Gojjam zone is one of the administrative zones of the Amhara National Regional State (ANRS), which is located in the northwestern part of Ethiopia (Fig. 1). East Gojjam is bordered on the south by the Oromia Region, on the west by West Gojjam, on the north by South Gondar, and on the east by South Wollo. The East Gojjam zone has sixteen districts and four urban administrations. The total land area of the zone is 14,010 km2. The average annual rainfall varies from 900–1800 mm, while there is a short rainy season (Belg) during February and March in highland agro-ecology. The average temperature ranges from 7.5° C—27° C. The zone is generally characterized by mixed crop-livestock production. East Gojjam is among the high potential crop production areas in the Amhara National Regional State with a marketable surplus for urban markets. Food grain production is the dominant subsector in the zone (CSA, 2022).

Fig. 1
figure 1

Study area map

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East Gojjam stands out as the leading zone in terms of area coverage, production and productivity of wheat in the Amhara region. In 2021/22, the east Gojjam zone produced 5.3 million quintals of wheat from 166,578 hectares of land. Moreover, wheat is the first crop, followed by maize and teff, in terms of their contribution to total food grain production in the zone, which accounts for nearly 29%, 24% and 23%, respectively, of the total food grain production in the zone. The average productivity of wheat in the east Gojjam zone is 31.84 qt/ha, which is higher than the average productivity of Ethiopia (31.11 qt/ha) (CSA, 2022), but lower than the world average productivity (35.47 qt/ha) (FAO, 2022).

This may be because crop production systems are predominantly dependent on rain-fed farming systems, which makes the sector most vulnerable to climate change and variability. In addition, the prevalence of diseases, insect pests, soil degradation, unreliable rainfall, temperature rise and variability, and recurrent drought are major climate change related problems that undermine the productivity and sustainability of the agriculture sector in the area (Ferede et al., 2020). In response, different CSAPs have been adopted to a limited extent, such as improved crop production technology, agronomic management practices, soil and water conservation, crop rotation, and past management practices.

2.2 Sampling procedure and sample size determination

The target population for this study was smallholder wheat producer farmers in the east Gojjam zone. A combination of purposive and random sampling procedures was used to select the sample wheat producer smallholder farmers. The east Gojjam zone was chosen because it is the leading zone of wheat production in the Amhara region. Debre Elias, Gozamin, and Basoliben districts of the East Gojjam zone were chosen purposively for high level wheat production in the area and for the importance of the crop in rural livelihoods. Then, a total of seven kebelesFootnote 1 within the three districts were randomly selected based on the proportion of Kebeles found in each district. From the selected rural Kebeles, wheat producer households were identified, and a total of 385 wheat producer farmers were selected randomly using a probability proportional sampling method based on the numbers of wheat producer farmers in each Kebele (Table 1). Moreover, the data were collected at the smallholder farmers’ plot level leading to 702 wheat plots cultivated in the 2021/2022 production period. The total sample size was determined using a formula that provides the maximum size to ensure the desired precision (acceptable error) using the formula given by (Kothari, 2004). Kothari is considered essentially appropriate in a situation with a large or unknown population and where the population is divided into distinct subgroups or strata. According to Cochran (1977), assume there is a large population but the variability of the proportion “p” is not known, p = 0.5 variability can be taken at 95% confidence level and ± 5% precision. This value will give a sample size sufficiently large to guarantee an accurate prediction.

$$n=\frac{{Z}^{2} pq }{{e}^{2}} =385$$

where, n is the desired sample size; Z is the standard cumulative distribution that corresponds to the level of confidence with the value of 1.96; e is the level of precision its value equals to 0.05; p is the estimated proportion of an attribute present in the population, with a value of 0.5 as recommended by (Cochran, 1977) to get the desired minimum sample size of households at a 95% confidence level and ± 5% precision; q = 1 − p.

Table 1 Selected districts, kebeles, and their sample sizes
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2.3 Data collection method

The study relied on data collected from primary and secondary sources. Face-to-face personal interviews using a semi-structured questionnaire were employed to collect primary data. Prior to the survey, the questionnaire underwent pretesting with 15 sample households to assess appropriateness, and necessary modifications were made to the questionnaire. The questionnaire was intended to generate information related to demographic, socioeconomic, institutional, and farm plot characteristics of the sample households, while it was also used to provide information related to different kinds of CSAPs adopted in the study area. Primary data were supplemented with secondary data collected from the zone and district offices of agriculture and rural development.

2.4 Method of data analysis

2.4.1 Estimation of technical efficiency

Technical Efficiency (TE) refers to the ability of a decision-making unit to produce the maximum feasible output from a given bundle of inputs (Chen et al., 2005; Farrell, 1957). Technical efficiency measures how well the inputs are combined to produce maximum output in the production process (FAO, 2017). Any deviation from this maximal output is considered inefficient (Coelli et al., 2005). Production efficiency is measured using either Parametric or nonparametric methods. Nonparametric production efficiency techniques, such as data envelopment analysis, assume that the decision-making unit has complete control over the production process and that any deviations from the frontier are considered inefficient (Coelli, 1995; Kumbhakar & Lovell, 2000). However, in agriculture, the prevalence of factors outside of farmers’ control, thus it is difficult to accept that any departure from the frontier is inefficient (Bauman et al., 2019). Hence, the parametric production efficiency technique was employed. The technical efficiency of wheat production was measured by the Stochastic Production Frontier (SPF) correcting for sample selection bias, which was developed by (Greene, 2010). This model was used by (Ahmed et al., 2017; Dagnew et al., 2024) to analyze the impact of improved seed and contract farming on productivity.

The stochastic production frontier approach requires a prior specification test of the functional form of the production function, and a log-likelihood ratio (LR) test was used to choose from Cobb–Douglas and translog production functions, which are the most commonly used to measure technical efficiency. The Cobb–Douglas production functional equation can be expressed as follows:

$${lny}_{i}={\beta }_{0}+\sum {\beta }_{i}{lnX}_{i}+{v}_{i}-{u}_{i}$$
(1)

where, ln denotes the natural logarithm; yi is the observed wheat production of the ith farmer, xi is the inputs used by the ith farmer (land, labor, DAP, urea, oxen, and wheat seed), β0 and βi are unknown parameters, ˅i is a random variable beyond the farmers control, µi is a nonnegative random variable assumed to account for production inefficiency.

Given the level of input, the technical efficiency of the ith wheat farmers is the ratio of the observed output to the maximum potential output (frontier output):

$$TE_{i} = \frac{actual output}{{potential output}} = \frac{{f\left( {x_{i} ;\beta } \right){\text{exp}}\left( {v_{i} - \mu_{i} } \right)}}{{f\left( {x_{i} ;\beta } \right){\text{exp}}\left( {v_{i} } \right)}} = {\text{exp}}\left( { - \mu_{i} } \right)$$
(2)

A stochastic production frontier model correcting for sample selection bias assumes that the unobserved characteristics in the selection equation are correlated with the noise in the stochastic frontier model. Then, the selected approach for the SPF analysis equations can be formulated as:

Selection equation:

$$A_{im} = 1\left[ {\alpha Z_{im} + \omega_{im} > 0} \right],\,\, \omega_{im} \sim N\left( {o,1} \right)$$
(3)

SPF:

$$y_{im} = \beta X_{im} + \varepsilon_{im} ,\,\,\varepsilon_{im} \sim N\left( {o,\sigma_{2} } \right); \,\,\left( {y_{im} , X_{im} } \right)are\; observed\;only\;when\;A_{im}=1 $$
(4)

The error structure is specified as follows: \({\varepsilon }_{im}={v}_{im}-{u}_{im},\)

$${u}_{im}={|\sigma }_{\mu }{u}_{im}|={\sigma }_{\mu }|{u}_{im}| where, {u}_{im}\sim N(o,1)$$
(5)
$$v_{im} = \sigma_{\mu } v_{im} \,\,where, \,\,v_{im} \sim N\left( {o,1} \right)$$
$$\left( {v_{im} ,\omega_{im} } \right)\sim N\left( {o,1} \right), \,\,\left( {1, \rho \sigma_{v} , \sigma_{v}^{2} } \right)$$

where, Aim is a binary variable equal to 1 for adopters of different combinations of CSAPs and 0 for non-adopters; \({y}_{im}\) is the amount of wheat produced by the ith farmer; zim is an explanatory variables included in the sample selection equation; xim is a vector of inputs used in the production frontier; α and β are parameters to be estimated; vim is the stochastic effect beyond the farmer’s control, measurement errors and other statistical noise; and uim is a nonnegative random variable assumed to account for technical inefficiency in production. It is useful to underscore that the parameter ρ captures the presence or absence of selectivity bias.

2.4.2 Impact of climate smart agriculture practices on technical efficiency

To determine the accurate impact of CSAPs on technical efficiency, it is important to take into account both observable and unobservable characteristics of wheat farmers. The farmers’ decision to adopt CSAPs does not fully depend on the observed factors. It also depends on unobserved factors such as managerial ability, skills, and motivation, which in turn affect the outcome variables that cause endogeneity problems. Failure to capture this endogeneity may result in inconsistent and biased estimates (Greene, 2008). To control for unobserved and observed heterogeneity and self-selection bias, this study used the MNESR model. This framework has the advantage of evaluating both individual and alternative combinations of CSAPs while capturing self-selection bias (Teklewold et al., 2013).

The two-stage MNESR model was developed by (Deb & Trivedi, 2006). The first stage is farmers’ decision on the adoption of CSAP combinations, which was estimated using an MNL selection model. In the second stage, the impact of each combination of CSAP on technical efficiency was evaluated. Economic theory suggests that farmers adopt a single or a combination of CSAPs that can maximize their utility. This means that adoption occurs when the expected utility of the chosen CSAP is greater than that of the other alternative CSAPs. However, because the utility obtained from adopting CSAPs is not observed but only its choice of CSAPs observed, one can assume an expected utility model that states conditional probability choice given a farmer’s choice. To formalize this, consider the following latent variable:

$${{A}^{*}}_{im}={{\beta }_{m}X}_{i}+{\mu }_{im}$$
(6)

where, \({{A}^{*}}_{im}\) is a latent variable that captures the ith farmer’s expected utility in adopting alternative combinations of CSAPs m with respect to another alternative K. \({X}_{i}\) is a vector of observed independent variables (household characteristics, socioeconomic factors, institutional factors, and farm plot characteristics), and \({\mu }_{im}\) are unobserved characteristics that are relevant to the farm household’s decision maker but are unknown to the researcher, such as expectations, skills, perceptions, and motivations.

Thus, the farmer chose a combination of CSAP “m” over any other CSAP combination k, if it provides greater expected utility than any other alternative k, k ≠ m.

$${A}_{im}=\left\{\begin{array}{c}1 if {{A}^{*}}_{i1}>{{{\text{max}}_{k\ne 1}A}^{*}}_{ik}or {\eta }_{i1}<0\\ 2 if {{A}^{*}}_{i2}>{{{\text{max}}_{k\ne 2}A}^{*}}_{ik}or {\eta }_{i2}<0\\ \begin{array}{c}\dots \\ m if {{A}^{*}}_{im}>{{{\text{max}}_{k\ne m}A}^{*}}_{ik}or {\eta }_{im}<0\\ { \eta }_{im}={}_{k\ne m}{}^{max}({{A}^{*}}_{ik}-{{A}^{*}}_{im})<0\end{array}\end{array}\right.$$
(7)

where,\({A}_{im}\) indicates the farmer’s observed choice of a combination of CSAPs; and \({\eta }_{im}\) is the expected utility difference between alternative combination m and any other alternative k. Assuming that \({\mu }_{im}\) are independent and identically distributed, that is under the independence of irrelevant alternatives (IIA) hypothesis. The probability of choosing an alternative package of m can be computed as:

$$p_{im} = pr\left( {\eta_{im} \left\langle 0 \right|X_{i} } \right) = \frac{{{\text{exp}}\left( {\beta_{m} X_{i} } \right)}}{{\sum\limits_{k = 1}^{m} {{\text{exp}}\left( {\beta_{k} X_{i} } \right)} }}$$
(8)

Selecting a valid instrumental variable is a difficult task; following several other studies, this study used sources of information (development agents and cooperatives) as instrumental variables for the household decision to adopt CSAPs (Sileshi et al., 2019). A valid instrumental variable should influence the adoption decision of CSAPs but should not influence the outcome variable (technical efficiency of wheat farmers). Thus, the validity of the instrument variables was tested using a falsification test. In the second stage, we apply the selection bias correction model to examine the impact of each alternative CSAP choice on the outcome variables. The outcome equation for each possible regime (m) can then be expressed as:

$$\left\{ {\begin{array}{*{20}c} {Regime 1; \,Y_{i1} = \beta_{1} X_{i} + \upsilon_{i1} \,\,if\,\,A_{i1} = 1; } \\ {Regime 2;\,Y_{i1} = \beta_{2} X_{i} + \upsilon_{i2} \,\,if\,\,A_{i2} = 1 } \\ \ldots \\ {Regime m;\,Y_{im} = \beta_{m} X_{i} + \upsilon_{im} \,\,if\,\,A_{im} = m } \\ \end{array} } \right.$$
(9)

where,\({Y}_{im}\) indicates the TE of wheat farmers, Xi are exogenous variables that affect the outcome variable; and \({v}_{im}\) denotes error terms that capture the uncertainty faced by farmers and are unobserved and satisfy zero mean and constant variance. To obtain consistent estimates, one can take into account the correlation between the error terms \({\mu }_{im}\) from the multinomial logit model estimated in the first stage and the error term \({\upsilon }_{im}\) from the outcome equation.

$$\left\{\begin{array}{c}Regime 1; {Y}_{i1}={{\beta }_{1}X}_{i}+{{\sigma }_{1}\lambda }_{i1}+{\omega }_{i1} if{ A}_{i1}=1; \\ Regime 2;{Y}_{i1}={{\beta }_{2}X}_{i}+{{\sigma }_{2}\lambda }_{i2}+{\omega }_{i2} if {A}_{i2}=2\\ \dots \\ Regime m;{Y}_{im}={{\beta }_{m}X}_{i}+{{\sigma }_{m}\lambda }_{im}+{\omega }_{im} if{ A}_{im}=m\end{array}\right.$$
(10)

where, \({\sigma }_{m}\) is the covariance between \({\mu }_{im}\) and \({\upsilon }_{im}\), ωim is the error term with an expected value of zero, and \({\lambda }_{im}\) is the inverse Mills ratio computed as;

$$\lambda_{im} = \mathop \sum \limits_{k \ne m}^{m} \rho_{m} \left[ {\frac{{p_{ik} {\text{ln}}(p_{ik} )}}{{1 - p_{ik} }} + {\text{ln}}(p_{im} )} \right]$$
(11)

where, \({\rho }_{m}\) in the above equation represents the correlation coefficient between \({\mu }_{im}\) and \({\upsilon }_{im}\)

At this point, a counterfactual analysis will be performed to examine average treatment effects (ATT) by comparing the expected outcomes of adopters with and without adoption of a particular CSA strategy following (Di Falco & Veronesi, 2014). The ATT in the actual and counterfactual scenarios will be determined as follows:

Adopters with adoption (actual adoption observed in the sample):

$$\in \left( {Y_{im} {|}A_{im} = m} \right) = \beta_{m} X_{im} + \sigma_{m} \lambda_{im}$$
(12)

Non-adopters with non-adoption (observed in sample):

$$\in \left( {Y_{i1} {|}A_{i1} = 1} \right) = \beta_{1} X_{i1} + \sigma_{1} \lambda_{i1}$$
(13)

The counterfactual case in which adopters did not adopt is also stated as follow:

$$\in \left( {Y_{i1} {|}A_{im} = m} \right) = \beta_{1} X_{im} + \sigma_{1} \lambda_{im}$$
(14)

Non-adopters with adoption (counterfactual):

$$\in \left( {Y_{im} {|}A_{i1} = 1} \right) = \beta_{m} X_{i1} + \sigma_{m} \lambda_{i1}$$
(15)

Equations (12) and (13) model the actual expected outcomes for CSA adopters and non-adopters, respectively, which are observed in the data. In contrast, Eqs. (14) and (15) represent the counterfactual outcomes; that is, the outcomes that adopters would achieve without adoption and non-adopters would achieve with adoption. Thus, the difference between Eq. (12) and (14), that is, adopters with adoption and counterfactual adopters who did not adopt was the ATT, which is calculated as follows:

$$ATT = \in \left( {Y_{im} {|}A_{im} = m} \right) - \user2{ } \in \left( {Y_{i1} {|}A_{im} = m} \right)$$
$$ATT = \beta_{m} X_{im} + \sigma_{m} \lambda_{im} - \left( {\beta_{1} X_{im} + \sigma_{1} \lambda_{im} } \right)$$
$$ATT = X_{im} \left( {\beta_{m} - \beta_{1} } \right) + \lambda_{im} \left( {\sigma_{m} - \sigma_{1} } \right)$$
(16)

The first term on the right-hand side of Eq. (16) represents the expected change in the mean outcomes (TE) of the CSA adopters, assuming that the adopters had the same characteristics as non-adopters. The second term (λim) is the selection term that captures all potential differences between adopters and non-adopters that arise due to unobserved variables.

Similarly, the average treatment effect on the untreated (ATU) is the difference between Eqs. (13) and (15). This indicates the counterfactual impact of CSAPs on non-adopting farmers if they had adopted the practices and can be specified as:

$$ATU = \left( {Y_{im} {|}A_{i1} = 1} \right) - \in \left( {Y_{i1} {|}A_{i1} = 1} \right)$$
$$ATU = \beta_{m} X_{i1} + \sigma_{m} \lambda_{i1} - \left( {\beta_{1} X_{i1} + \sigma_{1} \lambda_{i1} } \right)$$
$$ATU = X_{i1} \left( {\beta_{m} - \beta_{1} } \right) + \lambda_{i1} \left( {\sigma_{m} - \sigma_{m1} } \right)$$
(17)

The first term of Eq. (17) shows the expected change in non-adopter TE if they had decided to adopt alternative CSAPs given that adopters had the same characteristics as non-adopters.

3 Result and discussion

3.1 Characteristics of sample household

Table 2 summarizes the characteristics of the sampled farm households. The majority of the sampled household heads (88.89%) were male. The average household size, measured in adult equivalents, was 5. The average age of the sampled households was 45 years. The average education level of the sampled household heads was grade 3. Most of the sampled households practiced integrated farming systems (a mix of crop production and livestock rearing). The mean number of livestock owned by the sampled farmers, measured in the TLU, was 8.426. Agriculture was the only activity and income source for most of the sampled households. Only 27.07% of the sampled farmers engaged in off-farm activities such as petty trade, handcraft, and daily labor, the remaining 72.93% participated in agricultural activities such as crop production and livestock rearing.

Table 2 Characteristics of the household
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Among the sample respondents, only 37.32% had access to credit. This indicates that more than half of the respondents lacked access to credit. The average distance from the household residence to the input supplier institution was 30 min. The descriptive statistics in Table 2 show that approximately 45.87% of the sample respondents had access to training on climate change and CSAPs to adapt to climate change effects. Concerning information access, 55.13% and 47.29% of the sample households have information from development agents and cooperatives about the effect of climate change on production and its adaptation strategy, respectively.

In this study various plot specific characteristics including the average walking distance to the plot (plot distance), slope of the plot, soil fertility status of the plot, and plot size were considered. The average time that the farmers spent to reaching their wheat plots was 25 min. The average wheat plot size for the sampled households was 0.54 hectares. Table 2 shows that 68.09% of the wheat plots had flat slopes, with 7.55%, 64.96% and 27.49% of the sampled wheat plots had fertile, moderately fertile and less fertile soil fertility, respectively.

3.2 Adoption of climate smart agriculture practices

Different CSAPs were implemented by wheat producer smallholder farmers in the study area. The most commonly implemented CSAPs were wheat row planting, crop rotation and improved wheat variety. Smallholder farmers used these CSAPs either solely or simultaneously in their wheat plots. Table 3 illustrates the various combinations of CSAPs implemented in 702 smallholder farmers’ wheat plots. Out of 8 possible combinations of CSAPs, 7 were implemented in the study area. The combined use of crop rotation with improved wheat varieties (R0C1IV1) was not implemented during the study period. Smallholder wheat farmers mostly implemented the three CSAPs together in their plots, followed by wheat row planting, which was performed independently. In contrast, a small proportion of wheat farmers (6.13%) adopted crop rotation (R0C1IV0), while approximately 7.26% of the framers did not use CSAPs.

Table 3 CSAP adoption status of the plots of sampled households
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3.3 Estimation of stochastic production frontier and measurement of technical efficiency

3.3.1 Model test

Before the estimation of the SPF, various tests were conducted, and the results were reported in Table 4. First hypothesis tests were conducted to determine the correct functional form, i.e., the choice between Cobb–Douglas vs. translog functional forms. To determine the best functional form, the generalized likelihood ratio (LR) test computed as \(LR=-2[\text{ln}\left({H}_{O}\right)-\text{ln}\left({H}_{1}\right)]\) was used. where, \(\text{ln}\left({H}_{O}\right)\) and \(\text{ln}\left({H}_{1}\right)\) are the log-likelihood values of the Cobb–Douglas (null hypothesis) and translog functional (alternative hypothesis) functions, respectively. The results of the LR test showed that we cannot reject the null hypothesis that Cobb–Douglas is more appropriate than the less restrictive translog functional form in this study. The critical value was greater than the computed LR value and statistically significant at a 5% significant level.

Table 4 The generalized likelihood ratio hypothesis test
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The second hypothesis test was the existence of the inefficiency component of the composed error term of the SPF model. This finding indicates that wheat producing farmers were efficient and had no room for efficiency improvement (null hypothesis of \(\gamma =0\)). The alternative hypothesis states that there is inefficiency in the production of wheat in the study area (\(\gamma \ne 0\)). This was used to decide whether the traditional average production function (OLS) best fit the data set compared to the SPF model. The hypothesis test was conducted based on the generalized likelihood ratio (LR) test as expressed in the above paragraph. The test results showed that the calculated LR value is 9.365, which is greater than the critical value of 3.84 at 1 degree of freedom and a 5% significant level. Thus, the alternative hypothesis was accepted, proving the presence of inefficiency in wheat production in the study area.

To determine whether the inefficiency effect model has an effect on the inefficiency of wheat producer farmers in the study area, the likelihood ratio (LR) for the inefficiency effect was computed. The computed LR value (86.25) was greater than the 5% critical value (19.67) at 11 degrees of freedom, indicating that the null hypothesis (Ho) that all the explanatory variables are equal to zero was rejected.

3.3.2 Estimation of the stochastic production frontier model with corrected selectivity bias

In Table 5, the results of the maximum likelihood estimate of the SPF model corrected for selectivity bias estimated by NLOGIT 5 software were presented. The coefficient of Rho, which indicates the presence of selection bias, was significant for both non-adopters and adopters of the three CSAPs simultaneously. This suggests the presence of selection bias, which supports the use of a sample selection framework to estimate separate SPFs for adopters of each CSAP combination. The results revealed that the output of wheat increased with the wheat plot area in all the SPF model specification at a 1% significant level.

Table 5 Cobb–Douglas SPF with correction for selectivity bias model estimation results
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In the pooled SPF model, the amount of wheat seeds and the amount of urea used had a positive and significant impact on wheat production efficiency. The amount of wheat seed had a positive significant effect on the production of wheat crops for non-adopter farmers (R0C0IV0), who adopted the R1C0IV0, and R0C1IV0 SPF selection correction models. Endalew et al. (2023) also reported that wheat farm size, amount of urea, and amount of seeds used had significant positive effects on wheat production efficiency.

Oxen labor was also positively and significantly related to wheat productivity in the adoption of R1C0IV0 SPF selection correction model at a 5% significance level. However, oxen labor was negatively and significantly relation to wheat output in the adoption of R0C1IV0 and R0C0IV0 SPF selection bias correction model at the 5% and 10% significance levels, respectively. The amount of urea used also increased wheat output in the SPF selection bias correction model specifications of adoption of R0C1IV0, R1C1IV1, and R0C0IV0. The amount of human labor used and the amount of urea used had a negative and significant impact on wheat output in the SPF correction for selectivity bias model specification of R0C0IV0 at a 1% significance level. The production of wheat was significantly and negatively related to the amount of DAP fertilizer used for the pooled and R0C1IV0 SPF selection correction models at the 1% and 5% significance levels. This negative sign suggests the excessive use of DAP fertilizer in the production of wheat in the study area.

The coefficient related to the input variables measures the elasticity of output with respect to inputs. The sum of all partial production elasticities of inputs, i.e., return to scale (RTS), for all frontier models except for the non-adopters of CSAPs and the adopters of crop rotation only are consistently greater than one. This result shows that there is potential for wheat producers to expand their production; hence, farmers are in the stage I production area. Thus, a unit increase in all inputs proportionally would increase wheat output by more than a unit amount. Getachew et al. (2020) also found that wheat production in the north Shewa Zone of Ethiopia had an increasing return to scale. In contrast, Endalew et al. (2023) revealed that wheat production in northwestern Ethiopia follows decreasing returns to scale.

3.3.3 Technical efficiency of wheat farmers

After estimating the SPF corrected for both observed and unobserved heterogeneities, the technical efficiency score of each sample of wheat farmers was predicted and presented in Table 6. Accordingly, the overall average technical efficiency of the wheat farmers was 84.5%, with a range between 32.8% and 99.8%. This implies that wheat farmers could increase production by 15.5% by improving their technical efficiency. Specifically, the mean technical efficiency of non-adopter (R0C0IV0) wheat farmers was 78.9%, whereas for the adopter of R1C0IV0, the mean technical efficiency was 85.6%. The mean technical efficiency of the adopter of R0C1IV0 was estimated to be 81.9%, implying that 18.1% of the production was lost due to technical inefficiency alone. The mean technical efficiency of the adopter of R0C0IV1 was estimated to be 80.4%. This shows that wheat farmers could increase production by 19.6% by improving their technical efficiency. When looking at the combined adoption of CSAPs including, R1C1IV0, R1C0IV1, and R1C1IV1, the mean technical value was estimated to be 87.1%, 83.8% and 86.1%, respectively.

Table 6 The mean technical efficiency score estimated after bias correction for each CSAP
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3.4 Determinants of adoption of climate smart agriculture practices

The first stage of the MNESR model for each adoption choice estimation result is presented in Table 7. The base category or reference was non-adopters of any of the alternative CSAPs (R0C0IV0). The model fits the data reasonably well. The Wald test in which all regression coefficients are jointly equal to zero was rejected (Χ2 = 207.365; p = 0.000). The results show that the estimation coefficients differ substantially across the alternative packages.

Table 7 First stage of MNESR model estimation results
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The demographic characteristics of the household such as the sex of the household head and family size were significantly associated with the adoption of R0C0IV1 and R1C1IV0. Male-headed households are more likely to adopt R0C0IV1 than female headed households. A study conducted by Beyene et al. (2017) reported that male-headed households were more likely to adopt CSAP packages than to female-headed households. This might be because women are resource and time constrained. Family size positively and significantly affected the adoption of R0C0IV1 and R1C1IV0. This may be due to the availability of labor at the household level to utilize different CSAPs at the same time. Similarly, Erekalo and Yadda (2023) and Alemu et al. (2023) reported that availability of labor could be deployed to accomplish additional tasks that are associated with implementing adaptation and mitigation strategies that minimize the cost that farmers pay for other daily labor workers.

Household head education level had a positive and significant effect on the adoption of R0C1IV0 and R1C1IV1. This might be because better education is associated with greater access to information and awareness about climate change-related problems, CSAPs, and their benefits, which motivate them to adopt. In addition, education makes farmers more open, rational, and able to analyze the benefits of new technology. This finding is in line with the finding of Beyan et al. (2023), who reported that education enhances farmers’ ability to acquire and analyze new ideas, thereby facilitating the adoption of CSAPs.

The adoption of alternative combinations of CSAPs was also affected by wheat plot specific characteristics, including plot slope, soil fertility status of the plot and plot distance. If the plot is flat, then the probability of adoption of R1C0IV0, R1C1IV0, and R1C0IV1 decreases. This suggests that households with steep or hilly lands are more inclined to adopt CSAPs, likely due to their increased vulnerability to climate change impacts such as floods and erosion. Similar results were reported in a previous study (Beyene et al., 2017). Plot distance is the other variable that negatively affects the probability of adoption of R1C1IV1. This implies that for farmers whose wheat plots are far from their home residence, the likelihood of the adoption of this practices decrease. In line with this result, Alemu et al. (2023) found that a longer walking distance between plots and household homesteads had a negative and significant correlation with the continuous adoption of CSAPs. The soil fertility status of a plot is another factor that determines the adoption decision of CSAPs. By taking the fertile plot as a reference, soil fertility had a positive and significant effect on the adoption of R1C1IV0 and R1C1IV1. The study results revealed that farmers are more likely to adopt R1C1IV0 on medium and less fertile plots than on fertile plots. Similarly, farmers are more likely to adopt R1C1IV1 on less fertile plots than on fertile plots. This result is consistent with the findings of (Beyene et al., 2017; Tilahun et al., 2023).

Institutional factors such as credit access, access to training, source of information and distance to the input supplier institution center determined the adoption of different combinations of CSAPs. The result in Table 7 show that access to credit had a positive and significant relation with the adoption of R1C0IV1 and R1C1IV1. This shows that the probability of adoption of R1C0IV1 and R1C1IV1 increases as smallholder farmers gain access to credit. Beyan et al. (2023) also found that access to credit positively affects the adoption of medium level CSAPs.

The other institutional variable that affects the probability of adoption of CSAPs is access to training. Access to training had a positive and significant impact on the adoption of all alternative CSAPs except the adoption of R0C0IV1. This finding is consistent with the findings of (Beyan et al., 2023). Additionally, obtaining information from development agents and cooperatives about climate change and its effect on crop production, different climate change adaptation strategies, and the importance of adaptation strategies for production and productivity will enable farmers to adopt different CSAPs. Zegeye et al. (2022) found that extension agents provide information about the application and benefit of agricultural technologies, thus, in turn, increasing the likelihood of adoption of agricultural technology packages. In addition, distance to the input supplier institution significantly and negatively affects the adoption of R0C0IV1, R1C1IV0, and R1C1IV1. This could be mainly due to the increase in agricultural input transportation costs as farmers are far away from input supply institutions. In addition, distance to the input supply institution could also be taken as a proxy for distance to obtain information about the use and availability of agricultural inputs, technology and practices. This finding is congruent with the finding of (Tilahun et al., 2023).

3.5 The impact of climate smart agriculture practice on technical efficiency

The average effects of the adoption of a combination of CSAPs on the technical efficiency of wheat farmers are presented in Table 8. To estimate the average treatment effects on the treated (ATT), the technical efficiency of wheat farmers who adopted CSAPs (actual) was compared with the technical efficiency of wheat farmers if they had not adopted (counterfactual). The ATT result indicates that the technical efficiency of adopters of any alternative CSAPs would significantly decrease if households chose not to adopt these practices.

Table 8 The impact of climate smart agriculture practices on technical efficiency
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When looking at the impact of various CSAPs independently, wheat row planting (R1C0IV0) had the greatest impact on technical efficiency, followed by crop rotation (R0C1IV0). As shown in Table 8, households who adopt R1C0IV0 might shift to not adopt this practice, the mean technical efficiency would be significantly reduced by 7.2%. Similarly, if R0C1IV0 adopters decide not to adopt this practice, the average technical efficiency would significantly decrease by 7%. The mean technical efficiency of wheat farmers could be reduced by 4.9%, if farmers adopting improved wheat varieties (R0C0IV1) decide not to adopt them, which has the lowest impact of all alternative practices. However, when these practices are implemented in combination the returns are even greater. In particular, the adoption of R1C1IV0 and R1C1IV1 has the greatest impact, decreasing the technical efficiency by 10.1% and 10.3%, respectively, if wheat farmers decide not to adopt these practices. The adoption of R1C0IV1 have the lowest impact, which decrease in technical efficiency by 7.2%, even compared to R1C1IV0 and R1C1IV1. However, R1C0IV1 had the greatest impact compared to the separate use of CSAPs.

To estimate the average treatment effects on untreated (TTU), the technical efficiency of non-adopters is compared with the technical efficiency of wheat farmers if they have adopted alternative CSAPs (counterfactual). Accordingly, wheat farmers who did not adopt CSAPs would have gained more if they had adopted CSAPs in isolation or in combination except for the use of improved wheat varieties. If non-adopter wheat farmers choose to implement wheat row planting (R1C0IV0), the mean technical efficiency would significantly increase by 5%. Similarly, if non-adopter wheat farmers choose to implement crop rotation (R0C1IV0), the mean technical efficiency would significantly increase by 4.5%. Households that have not adopted CSAPs would experience greater improvements in technical efficiency if they choose to implement these practices collectively rather than individually. If a combination of CSAPs (R1C1IV0, R1C0IV1, and R1C1IV1) is implemented by non-adopter wheat farmers, the mean technical efficiency could be increased by 7.6%, 5.6% and 7%, respectively.

Moreover, the result shows that the adoption of any of CSAPs in isolation or in combination provide higher average technical efficiency as compared to the non-adopters. In addition, the adoption of a combination of CSAPs provides more technical efficiency than does the adoption of each CSAP implemented in isolation. The result reveals that, from the combination of CSAPs, the highest technical efficiency is obtained when farmers adopt the three CSAPs (R1C1IV1) simultaneously in the same plot. Thus, adopting multiple CSAPs simultaneously guarantees the maximum return.

In line with this finding, Ahmed et al. (2017) reported that improved maize varieties resulted in a 4.42% increase in technical efficiency compared to their non-adopter counterparts. Similarly, Ho and Shimada (2019) studied the effects of climate-smart agriculture and climate change adaptation on the technical efficiency of rice farming in Vietnam. Their finding shows that climate-smart agriculture and climate change adaptation play crucial roles in improving the technical efficiency of rice production by increasing 13–14% compared to no adaptation response. Besides, the adoption of soil and water conservation, maize improved variety, and adopting organic manure and inorganic fertilizers in combination significantly improves maize technical efficiency by 9%, 15%, and 18%, respectively (Pangapanga-Phiri & Mungatana, 2021).

4 Conclusion

This study was conducted in northwestern Ethiopia with the aim to examined the impact of CSAPs on the technical efficiency of wheat farmers. In this study, various climate smart agriculture practices were considered, including crop rotation, wheat row planting, the use of improved wheat varieties, and alternative combinations of these practices. The study used primary data collected from 385 smallholder farmers (702 wheat plots) selected by using purposive and two-stage sampling methods. The stochastic production frontier with a selection correction model was used to estimate the technical efficiency, and the MNESR mode was applied to analyze the impact of CSAPs on the technical efficiency of the wheat farmers.

The result of the first stage of the MNESR model show that, sex of the household head, education level, family size, slope of the plot, plot distance, soil fertility status of the plot, credit access, training access, access to information from development agents and cooperatives and distance to the input supplier institution are the major factors that determine the adoption of alternative combinations of CSAPs in the study area. The second stage of the MNESR result revealed that, the adoption of wheat row planting, crop rotation, and improved wheat variety in isolation as well as in combination had significant contribution to improve technical efficiency of wheat farmers. Thus, the government and stakeholders should prioritize scaling up the adoption of multiple CSAPs to enhance technical efficiency. This can be achieved by improving farmers’ skills through providing technical and practical training about CSAPs; strengthening the contact of development agents with farmers, and facilitating and reinforcing the existing input supply market centers and credit supply institutions.

Although this study is informative, it relies on cross-sectional data, which limits the investigation of the dynamics of CSAPs intervention over time. Additionally, this study focused on only three CSAPs. This narrow scope may not fully capture the diverse range of CSAPs available and their varying impacts on agricultural productivity and sustainability. Therefore, future studies should use panel data collected from both participants and non-participants before and after the intervention to evaluate the long-term effects and dynamic nature of CSAPs.