Impact of Improved Maize Varieties on Production Efficiency in Nigeria: Separating Technology from Managerial Gaps

Abstract

Researchers and policymakers are concerned about the substantial and increasing yield gap between sub-Saharan Africa and the rest of the world. High-yielding improved varieties are widely perceived as a means to close this gap. This study combines impact evaluation and production analysis techniques, which mitigate estimation biases stemming from observed and unobserved heterogeneity, to estimate the effects of improved varieties on maize productivity using a unique, recent, and nationally representative household survey. A linear endogenous treatment–effect model based on a matched sample obtained from propensity score matching indicated that the improved maize varieties increased yield by 38.7%. Simultaneously, selectivity-corrected and stochastic metafrontier approaches show that the yield advantage of improved varieties is mainly due to technological change; however, the technical efficiency of improved varieties is similar to those of traditional varieties.

1. Introduction

In sub-Saharan Africa (SSA), about 60% of the population depends on agriculture for food and livelihood [1]. However, most sub-Saharan African nations have not achieved food security at the household or national levels [2], mainly because of the low productivity of the primary staple foods on which most of the population relies. Maize is the most important staple cereal crop with vast potential to address the challenge of food insecurity in SSA [3,4]. More than 300 million Africans depend on maize as the main staple food crop; it provides over half of the calories and protein consumed in Eastern and Southern Africa and one-fifth of the calories and protein consumed in West Africa [4,5,6]. Yet maize yield is persistently low, with widened gaps in Africa compared to the rest of the world over the years. Food system analysts, development economists, and policymakers are actively debating historical and continued lags in SSA maize yields [7,8,9,10,11] and the design of interventions to overcome these yield gaps.

For decades, improved varieties have been introduced in SSA countries to increase maize production [7,12,13]. The literature on the impact of this intervention is extensive in most parts of SSA; however, the estimation results are inconsistent. For example, the percentage of productivity increase caused by improved maize variety adoption varies from 13% in Wossen et al. [14] to 30% in Abdoulaye et al. [3] and up to 70% in Oyinbo et al. [15]. Although earlier studies adjusted for observed characteristics, most did not address the impact of unobserved factors on productivity; thus, the studies’ estimates may be biased. Although empirical studies have shown the positive impact of improved varieties on maize production, none have responded whether this was due to an increase in technical efficiency or technological change. However, an estimation of the impact of improved varieties on technical efficiency and technological change will shed light on the dynamics and sustainability of the benefits of improved varieties.

This study focuses on maize production in Nigeria for various reasons. First, Nigeria, the most populous country in SSA, is expected to double its population to about 400 million people in 2050 [16]. Thus, boosting food security via increased maize production becomes necessary. The use of traditional varieties may not be able to sustain production that can meet up with the ever-increasing population of Nigeria. Second, Nigeria has one of the lowest maize yields in SSA despite having favorable ecology for maize production. The average grain yield in Nigeria was approximately 1.89 tons/ha in 2021, which is 16% of the SSA [17,18]. Third, maize is the main cultivated arable crop and staple food among farming households in Nigeria [19]. Besides being the leading staple food, it is also a major commercial crop for livestock feed. Fourth, Nigeria is the largest maize producer in West Africa [3], with a domestic production level of 2.0 million metric tons and domestic demand of about 3.5 million metric tons [20]. This imbalance results in a significant import surplus for maize. The agricultural transformation agenda includes maize as one of the seven main crops [20,21,22]. The Nigerian government recently partnered with the International Institute of Tropical Agriculture (IITA) to increase aggregate maize production by developing and disseminating improved varieties.

This study aims to overcome the limitations of previous studies. First, it quantitatively measures the impact of improved varieties on maize yield by controlling both the observed and unobserved characteristics. In the analysis, we control the observed factors with a matched sample chosen using propensity score matching (PSM), while a linear endogenous treatment–effect model controls the impact of unobserved factors. Second, this study further disentangles the positive impact of improved varieties on maize productivity using a matched sample and selectivity-corrected metafrontier model.

2. Material and Methods

2.1. Data and Descriptive Statistics

This study’s data are drawn from the fourth wave of the Nigerian General Household Survey Panel, a recent nationally representative dataset. The data were collected in 2018/2019 by the Nigeria National Bureau of Statistics in collaboration with the World Bank Living Standard Measurement Study—Integrated Surveys on Agriculture (LSMS-ISA) program. The sample size was approximately 5000 households across 36 states and the Federal Capital Territory. Studies by Dedehouanou and McPeak [23] and Dilion et al. [24] also describe this dataset.

The survey collected agricultural data at the disaggregated levels (crop, plot, and household). Detailed information on inputs, harvested outputs, and soil characteristics were collected at the plot level. In contrast to the three previous surveys, this recent LSMS-ISA wave included whether farmers used improved seeds on a specific plot. This essential feature was helpful for the identification strategy. Hence, the farm plots were disaggregated into improved and traditional crop plots. Other plot characteristics, such as soil quality, organic fertilizers, plot slope, and whether machines were used in the plots, were also included in the questionnaire.

At the crop level, data are available on the number of seeds planted, fertilizer and chemical use, total labor used, and the approximate percentage of the plot planted with the crops, which helps account for the crop plot size when two or more crops are interplanted. The key socio-economic data collected at the household level include characteristics of the household head (such as sex, gender, and age), characteristics of household assets (such as household size, wealth index, and farm size), and other household characteristics, such as participation in non-farm enterprises, access to extension agents, and credit access. The data and documentation are freely available online (For information on the LSMS-ISA project and links to the data, see https://microdata.worldbank.org/index.php/catalog/lsms/ (accessed on 20 January 2022)).

The descriptive statistics of the variables are summarized in

Table 1. Description and summary statistics of variables used in the models.

Variables	Definition	Mean	Std. Dev.
Variables used in PSM and Probit Model
Variety type	1 if farmers grow improved varieties on the farm plot, 0 otherwise	0.118	0.322
Gender	1 if farmer is male, 0 otherwise	0.826	0.379
Age	Age of the household head in years (Years)	50.302	14.932
Education	Number of years of formal education of household head (Years)	5.396	5.185
Household size	Number of family members	6.743	3.908
Wealth index	Wealth index (NGN 1000)	183.148	150.812
Farm size	Total crop area planted in hectares (Hectares)	0.544	0.587
Soil quality	1 if farm plot soil is good, 0 otherwise	0.833	0.373
Mixed cropping	1 if crops is under mixed cropping, 0 otherwise	0.708	0.455
Plot slope	1 if farm plot is flat, 0 otherwise	0.756	0.429
Access to extension agent	1 if farmer attended training session on improved varieties, 0 otherwise	0.065	0.247
Credit access	1 if the farmer has access to credit	0.151	0.358
Participation in non-farm enterprise	1 if the farmer participated in non-farm enterprise, 0 otherwise	0.505	0.500
Use machine on plots	1 if the farmer uses machine or implement on the farm plot, 0 otherwise	0.101	0.301
Use inorganic fertilizer on plot	1 if the farmer uses inorganic fertilizers on the plot, 0 otherwise	0.452	0.498
Variables used in the SPF models
Output	Total production of corps in kilograms	518.472	691.117
Seed	Seed used in kilograms	6.606	8.285
Fertilizer	Total NPK and Urea (kilograms of active ingredient)	61.199	99.929
Chemical	Total active ingredients of chemical used in kilograms	2.099	2.964
Labor	Total labor used in crop production (worker/hour)	385.495	380.692
Share adopting	Proportion of household in enumeration area	0.117	0.191
Improved varieties	1 if the plot is planted improved varieties, 0 otherwise	0.118	0.322
Number of observations		2519

Note: NGN (Naira) is the Nigerian currency (USD 1 = NGN 416 in 2022).

. This table shows that 11.8% of the sample farm plots had improved maize varieties (Table 1, row 1). Several studies have also reported low adoption of improved maize in Nigeria [25,26,27]. In contrast, the Consultative Group for International Agricultural Research (CGIAR) reported that 95% of Nigerian maize land was under improved maize varieties in 2012 [28]. There may be two reasons for the significant difference in the adoption rate between this study and the CGIAR estimates. First, CGIAR estimates are based on studies in a specific region and expert opinions [28,29], which may be misleading. Second, it may be possible for farmers who have adopted improved varieties to again choose traditional varieties in 2019 [30,31].

Before estimating the regression discussed in the next section, it would be instructive to examine the differences between the improved and traditional varieties in the data. We present the mean differences in the characteristics between adopters and non-adopters of improved maize varieties. The first three columns of

Table 2. Mean differences in characteristics between matched and unmatched improved and traditional varieties.

	Unmatched Sample			Matched Sample
Variables	Improved	Traditional	Diff.	Improved	Traditional	Diff.
Gender	0.882	0.818	0.063 ***	0.905	0.885	0.020
Age	47.439	50.683	−3.244 ***	47.401	47.550	−0.149
Education	5.747	4.991	0.756 ***	5.989	6.035	−0.045
Household size	7.236	6.677	6.743 **	7.243	7.657	−0.414
Wealth index	193.674	181.747	11.927 ***	192.838	161.172	31.666 **
Credit access	0.162	0.149	0.013	0.148	0.142	0.006
Access to extension agent	0.175	0.050	0.126 ***	0.176	0.094	0.082
Soil quality	0.760	0.843	−0.082 ***	0.768	0.779	−0.011
Plot slope	0.706	0.763	−0.057 **	0.701	0.692	0.009
Mixed cropping	0.605	0.722	−0.117 ***	0.609	0.578	0.031
Participation in non-farm enterprise	0.578	0.496	0.082 ***	0.581	0.542	0.039
Use machine on plots	0.142	0.095	0.047 **	0.148	0.114	0.034
Use inorganic fertilizer on plot	0.530	0.441	0.089 ***	0.535	0.528	0.007
North	0.693	0.562	0.131***	0.701	0.702	0.002
Production	695.055	494.960	200.095***	701.812	623.346	78.466
Farm size	0.644	0.537	0.107 ***	0.643	0.634	0.009
Labor	349.708	390.260	−40.552 *	350.212	367.699	−17.487
Seed	8.284	6.284	1.901 ***	8.410	7.965	0.446
Fertilizer	86.127	57.880	28.247 ***	88.516	75.571	12.282
Chemical	3.095	1.967	1.128 ***	3.137	2.439	0.698
Number of observations	296	2223		281	2041

Notes: Asterisks indicate significance at the 1% (***), 5% (**) and 10% (*) levels. Diff. refers to the mean differences in the characteristics between adopters and non-adopters.

show that adopters of improved varieties are systemically different from traditional variety growers. For example, adopters tend to be wealthier, younger, and have access to extension services compared to traditional variety growers.

In addition, Table 2 shows that improved variety growers’ average yield (production) was 40% higher than the traditional variety. The yield difference in this study is very similar to those reported by Wossen et al. [14] and Abdoulaye et al. [3]. On the other hand, Table 2 also shows that adopters use more resources (such as farm size, seed, fertilizer, and chemical use). Hence, the descriptive analysis does not answer whether the improved varieties perform better than the traditional varieties. The next section discusses the econometric models to isolate the improved varieties’ effects on crop yields.

2.2. Empirical Model

This study uses a multistage approach to account for both observable and unobservable sources of heterogeneity between improved and traditional variety growers. First, PSM accounted for the selection bias resulting from the observable characteristics of an improved farm plot with comparable time-invariant features. Second, after obtaining the matched sample, a linear endogenous treatment–effect method was used to control the unobservable characteristics. A stochastic production frontier (SPF) was then estimated to test whether the correction for sample selection is necessary [32]. Finally, the stochastic metafrontier proposed by Huang et al. [33] was employed to separate the impact on technical efficiency from technological progress. Details are as follows.

2.2.1. Propensity Score Matching

Although PSM does not account for estimation bias due to unobserved characteristics, compared to other studies (for example, Refs. [3,15,34]), we first employed PSM to create an appropriate counterfactual dataset to mitigate biases arising from observable factors. Empirically, the adoption model can be expressed as follows:

$$D_i={\alpha }_0+{\alpha }_1{X}_i+{\epsilon }_i$$

(1)

In Equation (1), D is a binary variable for adopting improved varieties, and 0 otherwise. α is a vector of parameters to be estimated; i is the ith plot, and ε is a random error term. Finally, X is a vector that represents household and plot-level characteristics. Specifically, household characteristics included the household head’s age, sex, and education. The plot-level characteristics included farm size, plot slope, soil quality, and machine use.

After identifying suitably matched samples, adopting improved varieties was measured as the average treatment effect on treated (ATT) [35], which denotes the average impact of planting improved varieties on farm plots. Following Villano et al. [34], the empirical model is expressed as follows:

$$ATT=E\left(Y_1|D=1\right)-E\left(Y_0|D=0\right)$$

(2)

where $Y_1$ and $Y_0$ are the average output values in kilograms per hectare for the improved and traditional varieties, respectively.

2.2.2. Linear Endogenous Treatment–Effect Model

This study employs a linear endogenous treatment–effect model using an instrumental variable (IV) to consider the impact of unobserved characteristics. In addition, since our IV estimation is based on matched data (PSM), the estimation bias due to observed and unobserved characteristics is avoided. However, when the endogenous regressor is binary, the linear model in the first stage of the IV method may not be appropriate [35]. Empirically, our IV model can be specified as follows:

$$D_i={\beta }_0+{\beta }_1{Z}_i+{\beta }_2{X}_i+u_i$$

(3)

$$Y_i={\gamma }_0+{\gamma }_1{X}_i+{\gamma }_2\left(\widehat{{\beta }_0}+\widehat{{\beta }_1}{Z}_i+\widehat{{\beta }_2}{X}_i+u_i\right)+{\tau }_i$$

(4)

In Equation (3), Z, meets the following criteria: (1) Correlated with $D:cov\left(Z,D\right)\ne 0$, and (2) uncorrelated with $\tau :cov\left(Z,\epsilon \right)=0$ [35]. Following previous literature on agricultural technology adoption [3,36,37,38], maize varietal information sources were used, which included information from extension agents and farmer networks as an instrument for adoption. According to the technology adoption theory, farmers will only adopt an improved variety if they access information about a particular variety. Therefore, information about improved varieties is expected to spread by extension services or neighboring farmers. A district-based instrumental variable is the share of improved variety growers in the enumeration area. This variable represents a proxy for the local adoption norms. This variable may influence farmers’ adoption of improved varieties but does not directly influence maize yield (Y) in Equation (4).

2.2.3. Stochastic Metafrontier Approach

Finally, this study employs stochastic metafrontier analysis, which has been widely used in many studies to measure the technological gaps between the observed and potential outputs that each farm could produce at the most productive frontier [34,39,40,41,42]. The main feature of this method is that firms are split into different groups based on a priori sample separation information, such as variety type, ownership, and location. Once such a classification has been made, separate analyses for each specific group are performed. Inefficiency is then estimated relative to the group-specific frontier, and the difference in technology frontiers across groups is viewed as the technology gap [42,43]. This study employs the two-step stochastic metafrontier approach proposed by Huang et al. [33], which allows the statistical properties necessary to draw a statistical inference in the second step.

We assume that production functions have a translog functional form owing to their well-known flexibility in technology presentation [43]. The first step of the stochastic metafrontier model can be written as follows:

$$ln{Y}_{ji}={\delta }_{j0}+{{\displaystyle \sum }}_{j=1}^J{\delta }_{j1}ln{X}_{ji}+1/2{{\displaystyle \sum }}_{j=1}^J{{\displaystyle \sum }}_{k=1}^K{\delta }_{j2k}ln{X}_{ij}ln{X}_{ik}-u_{ji}+v_{ji}$$

(5)

where $ln{Y}_i$ represents the natural logarithm of the total maize production in kilograms of the i^th farm; $u_{ji}$ and $v_{ji}$ are the two components of the composed error term, $\epsilon$. Subscript j denotes the jth group. This study had two groups (i.e., j = 1 and 2): improved and traditional varieties.

Following Huang et al. [33], the stochastic metafrontier model estimated in the second step is expressed as:

$$\widehat{ln{Y}_i^M}={\theta }_0+{{\displaystyle \sum }}_{k=1}^K{\theta }_{1}ln{X}_{ki}+1/2{{\displaystyle \sum }}_{n=1}^N{{\displaystyle \sum }}_{k=1}^K{\theta }_{2}ln{X}_{ni}ln{X}_{ki}-u_i^M+v_i^M$$

(6)

The dependent variable, $\widehat{ln{Y}_i^M}$ is the ML estimate from Equation (5) for each group. The superscript M denotes the metafrontier.

However, the estimation result of Equation (6) might be biased because of the endogeneity of improved varieties caused by unobserved characteristics. As discussed above, the observed characteristics can be controlled using a matched sample selected by PSM. Unobserved characteristics should also be controlled in Equation (5) to obtain an unbiased estimation result. Specifically, unobserved characteristics (such as farming ability) correlate with noise in the selection equation (i.e., improved variety adoption) and noise in the stochastic frontier model. To deal with biases from unobserved variables within an SPF formulation, we used the model recently introduced by Greene [32]. This method has been widely used in previous studies, such as Bravo-Ureta et al. [44] and Villano et al. [34].

After estimating the metafrontier, we calculated the technical efficiency and technology gap ratio (TGR) for the improved and traditional varieties. Specifically, the farm-level technical efficiency estimates can be obtained as follows:

$$T{E}_i^j=\exp \left(-u_i^j\right)$$

(7)

Technical efficiency $T{E}_i^j$ denotes each farm’s distance from the frontier of its individual variety. Aside from $T{E}_i^j,$ the farm distance to the metafrontier is expressed as:

$$TG{R}_i^j=\exp \left(-u_i^{jM}\right)$$

(8)

The TGR was estimated for each variety (j = 1 for traditional varieties; j = 2 for improved varieties). As in O’Donnell et al. [42] and Huang et al. [33], a high TGR score indicates close proximity of the group frontier to the metafrontier, and this group has a yield advantage over others with lower TGR values.

Finally, the MTE calculates the product of the two previous metrics to determine the overall distance of each farm from the metafrontier as follows:

$$MT{E}_i^j=TG{R}_i^j\times T{E}_i^j$$

(9)

Note that technical efficiency estimates ($T{E}_i^j$) cannot determine the variety with the most productive technology.$TG{R}_i^k$ compares which variety frontier operates closest to the metafrontier, and the $MT{E}_i^k$ compare the variety type to the metafrontier.

3. Results and Discussion

3.1. Determinants of Improved Maize Variety Adoption

Table 3. Probit estimates of factors that influence improved maize adoption.

	Matched Sample		Unmatched Sample
Variables	Coefficient	Std. Error	Coefficient	Std. Error
Gender	0.031	0.118	0.048	0.117
Age	−0.005 *	0.003	−0.006 **	0.003
Education	0.007	0.007	0.008	0.007
Household size	0.023 **	0.011	0.025 **	0.011
Wealth index	0.226 ***	0.071	0.243 ***	0.071
Farm size	0.022	0.067	0.024	0.066
Credit access	−0.006	0.099	−0.010	0.099
Access to extension agent	0.657 ***	0.115	0.681 ***	0.114
Soil quality	−0.223 **	0.088	−0.230 ***	0.088
Plot slope	−0.135 *	0.079	−0.140 *	0.079
Mixed cropping	−0.128	0.083	−0.137 *	0.082
Participation in non-farm enterprise	0.119	0.072	0.118	0.072
Use machine on plots	0.104	0.109	0.122	0.108
Use inorganic fertilizer on plot	0.040	0.076	0.045	0.076
North	0.183 *	0.103	0.180 *	0.103
Constant	−3.760 ***	0.904	−3.960 ***	0.894
Log-likelihood function	−811.987		−815.022
Chi-squared test statistic	89.41		104.77
Number of observations	2322		2519

Notes: Asterisks indicate significance at the 1% (***), 5% (**), and 10% (*) levels.

presents the factors influencing improved variety adoption for the matching and unmatched samples (i.e., the estimation results of Equation (1)). The dependent variable was binary improved maize adoption (1 for farmers who planted improved varieties and 0 otherwise). The goodness-of-fit tests indicate that the selected covariates provide a good estimate of the conditional density of adoption. For instance, the chi-squared test statistics are 89.41 for the matched sample and 104.77 for the unmatched sample. They are both statistically significant at the 1% significance level, implying the joint significance of the parameters for the improved variety adoption variables.

The estimation results in Table 3 are similar to those of previous studies [3,14,34]. Results of the current study indicated that household size, wealth index, age of the household head, soil quality and slope, and access to extension information significantly influenced the decision to adopt improved maize varieties. This finding is consistent with those of Zegeye et al. [45] and Villano et al. [34], who have shown that most of these factors are determinants of improved technology adoption.

3.2. Impact of Improved Maize Varieties on Productivity

The matching procedure yielded 2322 observations, including 281 adopters of improved varieties and 2041 non-adopters (traditional varieties). Following Leuven and Sianesi [46], t-tests were conducted before and after matching to evaluate the null hypotheses that the means of the observed characteristics of improved varieties and traditional varieties plots are similar. Results for this study show (Table 2) that the differences in all variables except for credit access between improved varieties plots and traditional varieties plots are statistically significant for the unmatched sample. However, all of these variables are similar for the matched sample (the last three columns of Table 2).

Table 4. Effects of improved maize varieties adoption on productivity.

Yield (kg/ha)	ATT	Std. Error
Propensity score matching ×
Kernel	0.215 **	0.091
Radius	0.213 ***	0.086
Stratification	0.138 *	0.084
Linear endogenous treatment effect †
Yield (kg/ha)	0.387 ***	0.106

Notes: Asterisks indicate significance at the 1% (***), 5% (**), and 10% (*) levels. × and † stand for propensity score matching and linear endogenous treatment–effect model, respectively. The results estimated from propensity score matching account for only observable characteristics, while the estimated results from linear endogenous treatment effect account for both observed and unobserved characteristics. Matching and instrumented variables: Male household head, household size, education and age of household head, mixed cropping, slope, soil quality, farm size, access to extension, credit, machine, non-farm income, inorganic fertilizer, and proportion of farmers in enumeration area growing improved maize varieties.

reports the average adoption effects estimated using the kernel-based matching, radius matching, and stratification matching methods. The results show a statistically significant difference between our samples’ improved and traditional maize variety yields per hectare. For instance, the kernel-based result shows that the average treatment of the treated (ATT) in kilograms per hectare for maize output for improved maize variety adoption is 21.5%. The findings on the low yield from traditional varieties justify the need to adopt improved maize varieties for increased productivity and to meet the food requirement of the populace. Apart from increased productivity, the adopters tend to be better off compared to non-adopters, as increased productivity may positively correlate with increased income. Expectedly, this facilitating acquisition of more land and non-productive outputs would provide a trend for expanding maize farming. The information in Figure 1 confirms that adopters and non-adopters have common support after matching.

However, the impact of improved varieties on maize yield based on PSM suffers from an estimation bias resulting from unobserved characteristics. The estimation result for Equation (3) is listed in

Table A1. First stage of linear endogenous treatment—effect result.

Variable	Coefficient	Std. Error
The proportion of improved growers	4.735 ***	0.238
Land	−0.194	0.172
Labor	−0.030	0.049
Seed	0.014	0.060
Fertilizer	−0.010	0.020
Chemical	0.212 ***	0.061
Mixed cropping	−0.070	0.098
Education	0.075 *	0.040
Household size	0.101	0.076
Age	0.009	0.160
Soil quality	−0.206 *	0.106
Slope	−0.089	0.098
Constant	−2.044 ***	0.670
Test for joint significance of IV
Athrho	−0.279 ***
Chi-square	12.85 ***
Log Pseudo-likelihood	−3775.219
Observations	2313

Notes: Asterisks indicate significance at the 1% (***), 5% and 10% (*) levels.

Appendix A. The estimated correlation between the treatment-assignment errors and the outcome errors, ρ, is −0.279. The negative association shows that unobservable increases in observed yields are more likely to occur with unobservable characteristics that lower the impact of improved maize varieties adoption. In addition, the estimated coefficient of the proportion of households in the enumeration area that grow improved varieties is consistently positive and statistically significant (row 14), suggesting an excellent instrumental variable.

As shown in the last column of Table 4, there was a statistically significant difference between the yield per hectare of improved maize varieties adopters and non-adopters. The average treatment effect on the treated (ATT) is positive, indicating that improved variety adopters benefit more than traditional growers. The linear endogenous treatment effect suggested that the adoption of improved maize varieties had a significant impact (38.7%) on the output kilogram per hectare (row 1, Table A1). This finding aligns with previous research on improved varieties adoption [3,47,48].

In summary, both PSM and the linear endogenous treatment–effect models show a statistically significant impact of improved variety on yield. Whether the increase in yield was due to managerial or technological factors remains unclear. To answer this question, a stochastic metafrontier model was used to estimate the impact of improved varieties on crop yield and technical efficiency.

3.3. Production Technology and Technical Efficiency Estimates

Two tests were carried out prior to discussing the metafrontier’s result (Estimation results of Equation (6) are shown in

Table A2. Maximum likelihood estimate models for the metafrontier.

	Conventional SPF Models		Selectivity-Corrected SPF Models
Variables	Pooled		Pooled
	Coefficient	Std. Error	Coefficient	Std. Error
Area	1.240 ***	0.063	1.206 ***	0.061
Labor	0.298 ***	0.026	0.286 ***	0.025
Seed	1.037 ***	0.021	1.042 ***	0.021
Fertilizer	−0.152 ***	0.008	−0.156 ***	0.008
Chemical	0.959 ***	0.023	0.958 ***	0.022
Area2	−1.251 ***	0.062	−1.164 ***	0.061
Labor2	−0.038 ***	0.005	−0.034 ***	0.005
Seed2	−0.451 ***	0.008	−0.438 ***	0.008
Fertilizer2	0.216 ***	0.002	0.216 ***	0.002
Chemical2	0.218 ***	0.011	0.225 ***	0.011
Area × Labor	0.049 ***	0.011	0.045 ***	0.010
Area × Seed	0.185 ***	0.013	0.193 ***	0.012
Area × Fertilizer	−0.101 ***	0.004	−0.101 ***	0.004
Area × Chemical	−0.143 ***	0.013	−0.152 ***	0.013
Labor × Seed	0.039 ***	0.004	0.031 ***	0.003
Labor × Fertilizer	−0.030 ***	0.001	−0.029 ***	0.001
Labor × Chemical	−0.079 ***	0.004	−0.079 ***	0.004
Seed × Fertilizer	0.008 ***	0.002	0.007 ***	0.002
Seed × Chemical	−0.058 ***	0.005	−0.060 ***	0.004
Fertilizer × Chemical	−0.062 ***	0.002	−0.061 ***	0.001
Constant	2.690 ***	0.071	2.961 ***	0.066
$\mathrm{Sigma}-\mathrm{u} {\sigma }_{\left(u\right)}$	0.001	0.031	0.095 ***	0.007
$\mathrm{Sigma}-\mathrm{v} {\sigma }_{\left(v\right)}$	0.120 ***	0.002	0.102 ***	0.003
Lambda	0.004	0.031	0.929 ***	0.009
$\mathrm{Rho} {\rho }_{w,v}$			−0.086 ***	0.004
Log-likelihood	1619.427		1683.292
Observations	2322		2322

Significance at the 1% (***) levels.

.). We first tested the null hypothesis that the improved varieties’ technology is the same as the traditional varieties, using the generalized likelihood ratio test by Battese et al. [39]. Testing this hypothesis is necessary because a two-step procedure to estimate the metafrontier is unnecessary if valid [39]. The likelihood ratio statistic $\lambda =-2\left\{\ln \left[L\left(H_0\right)-\ln \right[L\left(H_1\right)]\right\}$, where $\ln \left[L\left(H_0\right)\right]$ represents the logarithmic likelihood value of the second-step stochastic frontier, and $\ln \left[L\left(H_1\right)\right]$ denotes the sum of the likelihood values over each group frontier. $\lambda$ was equal to 2930.464 and 1400.671 for the conventional and selectivity-corrected models, respectively. Given the Kodde and Palm critical value, the null hypothesis that improved and traditional varieties share the same technology is rejected at the 1% level [43,49], showing that the use of a metafrontier to estimate efficiency is appropriate.

The null hypothesis of the second test is that the noise of the technology adoption equation does not correlate with that of the stochastic frontier equation. That is, unobserved characteristics have no significant impact on estimation bias. The estimation of the selectivity-corrected SPF model shows that the selectivity coefficient, Rho ${\rho }_{w,v}$, for traditional (

Table 5. Maximum likelihood estimate of the conventional and selectivity-corrected SPF models using matching sample.

	Conventional SPF Models				Selectivity-Corrected SPF Models
Variables	Improved		Traditional		Improved		Traditional
	Coefficient	Std. Error	Coefficient	Std. Error	Coefficient	Std. Error	Coefficient	Std. Error
Area	−0.967	1.431	1.638 ***	0.508	−0.958	1.431	1.648 ***	0.508
Labor	0.124	0.667	0.251	0.204	0.144	0.666	0.252	0.204
Seed	1.880 ***	0.527	0.987 ***	0.173	1.881 ***	0.527	0.970 ***	0.173
Fertilizer	−0.448 ***	0.174	−0.135 **	0.066	−0.433 **	0.174	−0.140 **	0.066
Chemical	1.079 **	0.531	0.910 ***	0.185	0.984 *	0.532	0.925 ***	0.185
Area2	−0.500	1.381	−1.472 **	0.505	−0.439	1.378	−1.468 ***	0.500
Labor2	−0.007	0.134	−0.027	0.038	0.001	0.134	−0.026	0.038
Seed2	−0.373 **	0.158	−0.458 ***	0.063	−0.365 **	0.158	−0.451 ***	0.063
Fertilizer2	0.223 ***	0.051	0.213 ***	0.019	0.216 ***	0.051	0.213 ***	0.019
Chemical2	0.240	0.223	0.211 **	0.091	0.214	0.223	0.213 **	0.091
Area × Labor	0.393 *	0.235	−0.021	0.085	0.384	0.234	−0.024	0.086
Area × Seed	−0.540 **	0.274	0.308 ***	0.106	−0.563 **	0.274	0.313 ***	0.105
Area × Fertilizer	−0.064	0.095	−0.119 ***	0.035	−0.068	0.093	−0.121 ***	0.035
Area × Chemical	0.517 **	0.286	0.185 *	0.103	0.578 **	0.289	−0.187 *	0.103
Labor × Seed	−0.095	0.095	0.040	0.029	−0.094	0.095	0.040	0.029
Labor × Fertilizer	0.030	0.031	−0.033 ***	0.010	0.029	0.031	−0.032 ***	0.010
Labor × Chemical	−0.218 **	0.091	−0.056 *	0.032	−0.205 **	0.091	−0.059 *	0.032
Seed × Fertilizer	−0.012	0.032	0.014	0.013	−0.012	0.032	0.013	0.013
Seed × Chemical	0.079	0.093	−0.087 **	0.037	0.084	0.094	−0.086 **	0.037
Fertilizer × Chemical	−0.090 ***	0.031	−0.056 ***	0.012	−0.088 ***	0.031	−0.056 ***	0.012
Constant	3.363 **	1.668	2.749 ***	0.535	3.457 **	1.668	2.912 ***	0.542
$\mathrm{Sigma}-\mathrm{u} {\sigma }_{\left(u\right)}$	0.948 ***	0.184	0.968 ***	0.071	0.937 ***	0.187	0.959	0.073
$\mathrm{Sigma}-\mathrm{v} {\sigma }_{\left(v\right)}$	0.656 ***	0.088	0.718 ***	0.033	0.657 ***	0.088	0.721 ***	0.033
Lambda	1.445 ***	0.264	1.349 ***	0.101	1.427 ***	0.266	1.330 ***	0.102
$\mathrm{Rho} {\rho }_{w,v}$					−0.117	0.085	−0.077 *	0.041
Log-likelihood	−357.586		−2727.073		−356.634		−2725.329
Observations	281		2041		281		2041

Significance at the 1% (***), 5% (**), and 10% (*) levels. The results estimated from the conventional SPF models account for only observed selection bias, while the results estimated from the selectivity-corrected SPF models account for both observed and unobserved selection bias.

) is −0.077, which is statistically significant. This finding suggests that selection bias is relevant in this analysis because of unobserved characteristics [50,51]. Thus, the use of the selectivity-corrected SPF model was justified. Hence, the following discussion is based on the estimation results of the selectivity-corrected SPF model using a matched sample.

Notably, the estimation results of the metafrontier indicated that improved varieties technology is higher than that of the traditional variety. After estimating the metafrontier, we calculated the TGR and technical efficiency derived from Equations (7) and (8). The higher the TGR value, the closer the variety-specific production technology was to the metafrontier [40]. As shown in

Table 6. Descriptive statistic of technical efficiency estimates for matched samples.

	Selectivity-Corrected SPF Models			Conventional SPF Models
Item	Improved	Traditional	Metafrontier	Improved	Traditional	Metafrontier
TGR efficiency
Mean	0.905	0.733	0.830	0.999	0.896	0.896
Standard Deviation	0.072	0.009	0.028	0.182	0.182	0.180
Minimum	0.562	0.674	0.562	0.996	0.810	0.810
Maximum	0.991	0.958	0.991	0.999	0.999	0.999
Technical efficiency
Mean	0.543	0.536	0.536	0.540	0.533	0.534
Standard Deviation	0.150	0.146	0.147	0.152	0.148	0.148
Minimum	0.064	0.028	0.028	0.062	0.027	0.026
Maximum	0.862	0.859	0.862	0.863	0.861	0.863
MTE efficiency
Mean	0.491	0.393	0.445	0.540	0.478	0.477
Standard Deviation	0.141	0.136	0.137	0.152	0.148	0.148
Minimum	0.059	0.027	0.027	0.062	0.026	0.027
Maximum	0.844	0.800	0.844	0.863	0.863	0.863

, the TGR value of the improved varieties was 0.905, which was 23.5% higher than that of traditional varieties (0.733). The difference is statistically significant at the 1% level with the Kruskal–Wallis equality test of chi-square 478.573. This result indicates that the production techniques employed by the improved maize farm are superior to those of the traditional maize varieties, which is consistent with the results of the PSM and linear endogenous treatment–effect models (Table 3). The results for conventional SPF models indicate that similar results are obtained if the unobserved characteristics are ignored (fourth–sixth columns, Table 6), even though the TGR difference between the improved and traditional varieties is smaller (0.999 − 0.896 = 0.103).

As expected, the technical efficiency of the improved varieties was similar to that of the traditional variety. The technical efficiency of the improved maize varieties was 0.543, which was similar to that of the traditional maize varieties (0.536, Table 6). We obtained similar results (0.540 vs. 0.533), ignoring the impact of unobserved characteristics. This result was expected as most farming practices are the same for plots with improved and traditional varieties [50,52].

Finally, the results show a substantial output gap. The average MTE for improved maize variety adopters was 0.491, while for the farms with traditional varieties was 0.393 (Table 6), and both values were less than 0.5. Hence, the estimation results are similar to those of other crops, such as those of Zheng et al. [53] for bananas and Villano et al. [34] for rice. The study’s ability to account for selection bias due to observable and unobservable factors in the research verifies the improved variety adopters’ performance, implying the benefit of adopting improved maize varieties.

4. Conclusions and Policy Implications

Researchers and policymakers are concerned about SSA’s substantial yield gap. We assessed the impact of improved maize varieties on productivity and the mechanism of its effect using Nigerian maize farm plots as a case study. This study combines impact evaluation and production analysis techniques to mitigate the estimation biases stemming from both observed and unobserved heterogeneity. A linear endogenous treatment–effect model based on a matched sample obtained from PSM shows that improved varieties increase maize yields by 38.7%. At the same time, the selectivity-corrected and stochastic metafrontier approaches show that the yield advantage of improved varieties results from their high technology.

The estimation results have important policy implications. First, policies and subsidies should be implemented to increase the improved maize varieties’ adoption rate and production level. Consistent with previous studies (e.g., as [3]), this study shows scope for improved output production at the current levels of input use by maize farms. Development policies for agricultural transformation in Nigeria are needed to solve this situation and aggressively increase access to modern maize varieties. Further studies and developmental efforts are recommended to improve the variety available to farmers.

Second, in policy formulation, the provision of improved seed varieties is often uniquely treated as a necessary and sufficient condition for crop yield—no wonder most African policies have focused on the subsidy aspect of these improved seeds. The consequence of designing a policy this way is that policymakers and technology designers believe improved varieties are sufficient for farmers to achieve a high yield. However, the results of this study show that even for improved variety adopters, high-yield gaps persist, resulting from a low level of technical efficiency, which might be associated with poor agronomy and a lack of complementary modern inputs [54,55]. Hence, to increase crop yield, it is necessary to provide more technical extension support for farmers’ managerial capabilities to obtain the full potential of improved varieties.