The decision to adopt fertilizer and the extent of its application can be conceptualized within a utility- and profit-maximization framework, given farmers’ behavioural assumptions and production constraints (David 2012; John et al. 2015). In this framework, farmers are assumed to be rational decision-makers who allocate their limited resources to maximize expected utility or profit, typically reflected in outcomes such as yield and income (David 2012; Penson 2015). The adoption decision constitutes the first stage, determining whether or not a farmer uses fertilizer, while the second stage concerns the intensity of fertilizer application, conditional on adoption. Both the decision to adopt and the level of use are influenced by a range of interrelated factors (Fig. 1), including demographic characteristics, socioeconomic conditions, institutional arrangements, and plot-specific attributes (Deresse and Tekilu 2019). Collectively, these factors shape smallholder farmers’ decisions regarding fertilizer use and the extent of its application.

The study was conducted in three districts (Sekota, Tehuledere, and West Belesa) found within three zones in the Amhara region, which were selected purposively based on their lower/non-fertilizer-use experience. These districts represent diverse agroecological conditions, including variations in rainfall, soil fertility status, and topography (Fig. 2).

Sekota District is located in the Wag-himra zone of the Amhara Region. It is one of the eight districts in the zone, comprising 25 kebeles. It lies approximately 720 km northeast of Addis Ababa and 420 km from Bahir Dar. Geographically, the district is situated between 12°23' and 13°16’N latitude and 38°44' and 39°21'E longitude. The altitude ranges from 1,500 to 2,200 meters above sea level. The district is characterized by low and erratic rainfall from 350 to 650 mm annually (Tewodros et al. 2017; Getamesay et al. 2021).

The Tehuledere district is found in the South Wollo zone of the Amhara Region, located about 430 km from Addis Ababa. It is one of the 22 districts in the zone and covers a total area of 44,030 hectares. The altitude ranges from 1,488 to 2,900 meters above sea level. The area receives a mean annual rainfall of approximately 1,030 mm and has an average annual temperature of 21 °C. Geographically, it is positioned at 11°17'N latitude and 39°42'E longitude (Seid 2013; Adera and Noah 2019).

The West Belesa district is one of the Central Gondar zone districts located approximately 706 km north of Addis Ababa and is included within the Tekeze lowland sorghum and goat livelihood zone. Geographically, it is found at 12°15'N latitude and 37°45'E longitude. The district exhibits considerable topographic variation, with altitudes ranging from 150 to 1,500 meters above sea level. It is characterized by relatively high temperatures, with an average annual temperature of 33.5 °C, and receives an annual rainfall range of 800 to 1,200 mm (Tsigie 2020; Yasin 2022).

The sampling frame for this study comprised both fertilizer users and non-users residing in the same kebeles and engaged in cereal crop production. A multistage sampling technique was employed to obtain a representative sample. In the first stage, the Wag-himra, North Wollo, and Central Gondar Zones, with their respective districts, were purposively selected considering their relatively low or negligible fertilizer application. In the second stage, five kebeles were selected from the three districts using simple random sampling. Subsequently, households within the selected kebeles were stratified as fertilizer users and non-users to ensure representation of both groups. Finally, 313 households were selected proportionally from each stratum using systematic random sampling from a total population of 1,673 major cereal-producing households. A non-response rate of 2.875% was recorded from the total sample of 313 households, resulting in 304 valid observations used for the final analysis. The sample size was determined using Kothari’s (2004) sample size determination formula as follows.

n=Z2⋅P⋅q⋅Ne2(N−1)+Z2⋅P⋅q (1)

Where: n is the sample size, Z is the Z-value corresponding to the desired confidence level (1.96 for a 95% confidence level), p is the estimated population proportion (0.5), q is 1-p, and N is the population size.

Before the start of the main survey, the data collection instruments were revised and finalized based on feedback obtained from the pretest. Both quantitative and qualitative data were collected from primary and secondary sources. Primary data were gathered through a household survey using a semi-structured questionnaire. To complement the survey data, key informant interviews (KIIs) were conducted to provide in-depth insights and contextual understanding. In each district, four key informants were purposively selected, including a development agent, a district agricultural officer, a cooperative officer, and a kebele administrator. Secondary data were obtained from both published and unpublished sources, including books, official reports, academic journals, conference proceedings, and working papers.

The collected data were analyzed using various statistical techniques, including descriptive and inferential statistics, as well as an econometric model using STATA software version 17.

Data were analyzed using both descriptive and inferential statistical methods. Descriptive statistics—specifically means, standard deviations, frequencies, and percentages—were employed to summarize the demographic and socioeconomic characteristics of the sampled households. Inferential statistical techniques were applied to examine differences between fertilizer users and non-users. An independent samples t-test was used to compare continuous variables, while a chi-square test was employed to assess differences in categorical variables (Ruth 2011). Furthermore, the level of fertilizer application (Urea and NPS) for major crops was estimated using a fertilizer intensity index, as specified below.

Yi=FiAi (2)

Where:

The Tobit, Heckman, and Double Hurdle models (DHM) are commonly used to analyze the determinants of technology adoption and usage intensity. However, both the Tobit and Heckman models have inherent limitations. The Tobit model assumes normally distributed errors, which may not always hold, and constrains participation and intensity decisions to a single underlying process (Tobin 1958; Maddala 1983; Green 2002). The Heckman two-stage model is not specifically designed to handle corner solutions, in which a substantial number of observations take on genuine zero values (Heckman 1979; Green 2002).

In contrast, the Double Hurdle model overcomes these limitations by modeling the adoption decision and the intensity of use as two separate processes. It accommodates voluntary zero outcomes and provides greater flexibility, effectively addressing issues of dual endogeneity and heteroscedasticity between the decision to adopt and the level of use (Cragg 1971; Jones 1989; Burke 2009; Bhekani 2020). Importantly, the DHM assumes no selectivity bias, further enhancing the reliability of its estimates (Bhekani 2020). Based on these advantages and the results of model specification tests, the DHM was selected for this study (Adem 2023). Equation (3) represents the first stage of the household’s decision to use fertilizer (Cragg 1971).

d1i∗=αiXi+ui,ui≈N(0,1) (3)

D i = 1 if α i X i + u i > 0 , 0 if α i X i + u i ≤ 0

Where i = 1, 2, 3 …n, d^*_i represents the latent variable for the decision to adopt fertilizer, X_i denotes the vector of explanatory variables hypothesized to influence adoption, a_i is a vector of parameters to be estimated, and u_i denotes the error term. The observed binary outcome Di reflects the actual decision of the i^th smallholder farmer, such that Di = 1 if the farmer adopted fertilizer and Di = 0 otherwise. According to Green (2002), the following equation is a truncated regression part of the model for use intensity.

y∗i2⋅=⋅βXi⋅+εi,⋅εi⋅≈⋅N⋅(0,δ2) (4)

y i = y i ∗ if y i ∗ > 0 and D i = 1 , 0 = otherwise

Where: Y^*_i2 represents the intensity of inorganic fertilizer use, which depends on the latent variable Y^*_i1 being greater than zero and conditional on the decision to use D_i fertilizer. X_i is the vector of explanatory variables hypothesized to determine the intensity of inorganic fertilizer use, β denotes the unknown parameters to be estimated in the model, ε_i and u_i are the respective error terms assumed to be independent and distributed.

As noted by Green (2002), the following equation represents the truncated regression component of the model for technology use intensity.

log⁡LDH=∑0[ln⁡{1−Φ(αiXi)Φ(βXiσ)}+ (5)

Σ + [ ln ⁡ { Φ ( ( α i X i ) ) 1 σ ∅ ( y i − β X i σ ) }

Where: Φ = standard normal cumulative distribution function, and Ø = density function.

To justify the use of the Double Hurdle model (DHM), a likelihood ratio (LR) test was conducted by comparing the log-likelihood values obtained from separate estimations of the probit, truncated regression, and Tobit models, following the procedure outlined in Green (2002).

λ=−2[lnLT−(lnLP+lnTR)] (6)

Where: L_T = likelihood for the Tobit model with the same coefficients, L_P = likelihood for the Probit model, fit separately, L_TR = likelihood for the truncated regression model, fit separately. Variables used in the double hurdle model are listed in Table 1 as follows.

Descriptive and inferential analyses were performed for both dummy and continuous variables. Table 2 shows that 63% of the total samples were fertilizer users and 37% were non-users. The comparison between fertilizer users and non-users reveals statistically significant differences in several key variables. Specifically, a household’s cooperative membership, extension contact, and knowledge of fertilizer application are significantly different between the two groups.

The comparison of smallholder farmers’ characteristics between fertilizer users and non-users indicates that there were no statistically significant differences in the mean values of any continuous variables (Table 3).

Before the main analysis, post-estimation diagnostic checks and model specification tests were conducted for both the Double Hurdle Model (DHM) and the Tobit model to ensure robustness and identify the most appropriate specification. Multicollinearity among the explanatory variables was assessed using the Variance Inflation Factor (VIF), and the results indicated no evidence of multicollinearity, confirming that the models were well specified.

To compare model performance, the DHM was tested against the Tobit model using a likelihood ratio (LR) test and the Akaike Information Criterion (AIC), following Cragg (1971). The LR test statistic (2344.287) substantially exceeded the critical chi-square value (χ² (21) ≈ 20.337) at the 5% significance level, leading to rejection of the Tobit model in favour of the DHM. Additionally, the DHM reported a lower AIC value, further supporting its superiority. These results indicate that fertilizer adoption and intensity decisions are governed by two distinct behavioural processes rather than a single underlying mechanism (Cragg 1971; Akaike 1974).

Furthermore, the inverse Mills ratio was statistically insignificant, suggesting the absence of sample selection bias and indicating that the Heckman selection model was not required (Heckman 1979).

The intensity of fertilizer application for major crops was quantified using the intensity index method (Green 2002). Empirical results indicate that farmers applied an average of 19.01 kg/ha of urea and 24.32 kg/ha of NPS—rates that fall considerably below the recommended levels of 50 kg/ha and 100 kg/ha, respectively. This disparity represents a substantial application gap of 61.98% for urea and 75.68% for NPS. These results underscore a significant ‘application gap’ that, if bridged, could substantially enhance regional crop yields.

Yi Urea = 6041.5 317.795 = 19.01 Kg

and

Yi NPS = 7729 317.795 = 24.32 Kg

Extension contact had a positive and statistically significant effect on fertilizer adoption. Farmers who received more frequent extension visits were 2.1% more likely to adopt inorganic fertilizer, consistent with the findings of Muhammed et al. (2020), Mideksa (2021), who reported that extension services have a substantial impact on farmers’ agricultural input utilization. Similarly, knowledge of fertilizer application positively influenced adoption decisions; farmers with adequate knowledge were 13% more likely to use fertilizer. This result is supported by Bhekani (2020), who reported that knowledgeable farmers are 17.28% more likely to adopt fertilizer.

Distance to input centers exhibited a negative and significant effect. Specifically, each additional minute of travel time reduced the probability of fertilizer use by 0.02%, underscoring the importance of proximity in minimizing transaction and transport costs and ensuring timely access to inputs. This finding aligns with Hassen et al. (2012), who identified proximity to input centers as a critical constraint to effective input utilization.

Farmers’ perceptions also played an important role. Those with favourable perceptions toward fertilizer use were 3.7% more likely to adopt it, consistent with Atinkugn (2022). In contrast, fertilizer price had a negative and statistically significant effect; higher prices reduced the likelihood of fertilizer use by 2.0%. This finding corroborates Akpan et al. (2012), who found that rising input prices discourage fertilizer adoption, particularly among resource-constrained households.

The second hurdle model, which examines the intensity of fertilizer use among adopting farmers, shows that several factors significantly influence the quantity of fertilizer applied. Education level, knowledge of fertilizer use, household income, experience with fertilizer application, and cooperative membership all had positive and significant effects, whereas farm size and distance to market negatively affected fertilizer application intensity (Table 4).

Cooperative membership significantly increased fertilizer application by 11.69 kg per hectare compared to non-members (p < 0.10). This finding underscores the vital role cooperatives play in bridging the gap between farmers and essential inputs, fostering a culture of more intensive fertilizer use through collective bargaining and shared knowledge—an observation consistent with Mertey et al. (2014). In contrast, farm size exerted a strong negative influence (p < 0.01); each additional hectare of land was associated with a 9.27 kg reduction in fertilizer application. This suggests a strategic trade-off in management: farmers with larger holdings often prioritize total volume, spreading limited resources across a broader landscape. Conversely, smallholders, operating with limited space, treat every plot as a critical asset, applying inputs more precisely and intensively to squeeze the highest possible yield from every square meter. These results align with the findings of André and Mulat (1996), Akpan et al. (2012), and Tewodros et al. (2020), who all observed that smaller-scale farmers tend to invest more heavily in per-unit land productivity to compensate for their lack of acreage.

Annual household income exerted a positive and significant influence on fertilizer application (p < 0.05). While the coefficient of 0.0001 kg per additional Ethiopian Birr (ETB) appears small, it reflects the broader capacity of wealthier households to overcome liquidity constraints and allocate more capital toward agricultural inputs. This relationship confirms that financial liquidity is a prerequisite for technology adoption in resource-poor settings, a finding supported by Martey et al. (2014) and Mengistu and Degefu (2017). Conversely, market distance was found to be a significant barrier (p < 0.01). Each additional minute of travel time to the nearest market reduced fertilizer use by 0.189 kg, reinforcing the findings of Akpan et al. (2012) and Aman et al. (2022). This highlights how high transaction costs and the physical burden of transporting inputs to remote areas directly suppress application intensity. Technical knowledge regarding fertilizer application had the most substantial positive impact (p < 0.01). Households with a firm grasp of application techniques applied 30.18 kg more fertilizer per hectare than their less-informed counterparts. The results show that simply providing the input is insufficient; capacity building is critical for intensification, as previously argued by Alexandra and Barrett (2015). Finally, fertilizer price negatively and significantly impacted use intensity (p < 0.10), indicating that if the price increases, fertilizer application would be reduced by 0.019 kg, which is consistent with Akpan et al. (2012).