Technology adoption and the multiple dimensions of food security: the case of maize in Tanzania

Abstract

The paper analyses the impact of agricultural technologies on the four pillars of food security for maize farmers in Tanzania. Relying on both matching techniques and endogenous switching regression models, we used a nationally representative dataset collected over the period 2010/2011 to estimate the causal effects of using improved seeds and inorganic fertilizers on food availability, access, utilization, and stability. Our results show that the adoption of both technologies have positive and significant impacts on food availability while for access, utilization and stability we observe heterogeneity between improved seeds and inorganic fertilizers as well as across the food security pillars. The study supports the idea that the relationship between agricultural technologies and food security is a complex phenomenon, which cannot be limited to the use of welfare indexes as proxy for food security.

Appendix

A1 - The Endogenous Switching Regression model

The endogenous switching regression model is defined by a selection Eq. (A.1) which establishes the regime of the household and two equations describing the food security outcome for adopters (A.2a) and non adopters (A.2b):

$$ {\mathrm{T}}_{\mathrm{i}}^{*}={\beta X}_{\mathrm{i}}+{\mathrm{u}}_{\mathrm{i}} $$

(A.1)

$$ {Y}_{1i}={\alpha}_1{C}_{1i}+{e}_{1i}\kern0.75em \mathrm{if}\kern0.75em {T}_i=1 $$

(A.2a)

$$ {Y}_{0i}={\alpha}_0{C}_{0i}+{e}_{0i}\kern0.75em \mathrm{if}\kern0.75em {T}_i=0 $$

(A.2b)

where ${T}_i^{*}$ is the unobservable latent variable defining the technology adoption regime, T _i its observable counterpart and X _i the vector of covariates determining adoption. Y _i refers to the food security outcome in regime 1 (adopters) and 0 (non adopters), while the set of covariates C are their determinants. The error terms u _i , e _1i and e _0i are assumed to have a trivariate normal distribution with zero mean and a covariance matrix:

$$ \left[\begin{array}{ccc}\hfill {\upsigma}_{\mathrm{e}1}^2\hfill & \hfill \cdot \hfill & \hfill {\upsigma}_{\mathrm{e}1\mathrm{u}}\hfill \\ {}\hfill \cdot \hfill & \hfill {\upsigma}_{\mathrm{e}0}^2\hfill & \hfill {\upsigma}_{\mathrm{e}0\mathrm{u}}\hfill \\ {}\hfill \cdot \hfill & \hfill \cdot \hfill & \hfill {\upsigma}_{\mathrm{u}}^2\hfill \end{array}\right] $$

(A.3)

Since σ _e1u . and σ _e0u are different from zero, the expected values of the error terms of the food security outcomes are non-zero and equal to:

$$ E\left[\left.{e}_{1i}\right|{T}_i=1\right]={\sigma}_{e1u}\frac{\phi \left(\beta {X}_i\right)}{\varPhi \left(\beta {X}_i\right)}={\sigma}_{e1u}{\lambda}_{1i} $$

(A.4a)

$$ E\left[\left.{e}_{0i}\right|{T}_i=0\right]={\sigma}_{e0u}\frac{\phi \left(\beta {X}_i\right)}{1-\varPhi \left(\beta {X}_i\right)}={\sigma}_{e0u}{\lambda}_{0i} $$

(A.4b)

Where ϕ(⋅) and Φ(⋅) indicate, respectively, the standard normal density and standard normal cumulative functions. If the estimated covariances (${\hat{\sigma}}_{e1u}$ and ${\hat{\sigma}}_{e0u}$) turn out to be statistically significant, then the decision to adopt improved seed and inorganic fertilizers is correlated with the food security outcome, that is there is evidence of endogenous switching and the presence of sample selection bias (Maddala and Nelson, 1975; Di Falco et al. 2011).

The model is usually estimated using full information maximum likelihood (FIML) because it allows estimation simultaneously of the probit regression for technology adoption and the regression equations of the food security outcomes. Following Heckman et al. (2001), the results of the FILM estimation can be used to calculate the average treatment effect on the treated (ATT) by comparing the expected food security outcomes for adopters with their counterfactual scenario. In this case:

$$ \mathrm{E}\left[\left.{\mathrm{Y}}_{1\mathrm{i}}\right|{\mathrm{T}}_{\mathrm{i}}=1\right]={\upalpha}_1{\mathrm{C}}_{1\mathrm{i}}+{\upsigma}_{\mathrm{e}1\mathrm{u}}{\uplambda}_{1\mathrm{i}} $$

(A.5a)

$$ \mathrm{E}\left[\left.{\mathrm{Y}}_{0\mathrm{i}}\right|{\mathrm{T}}_{\mathrm{i}}=1\right]={\upalpha}_0{\mathrm{C}}_{1\mathrm{i}}+{\upsigma}_{\mathrm{e}0\mathrm{u}}{\uplambda}_{1\mathrm{i}} $$

(A.5b)

$$ ATT=E\left[\left.{Y}_{1i}\right|{T}_i=1\right]-E\left[\left.{Y}_{0i}\right|{T}_i=1\right]={C}_{1i}\left({\alpha}_1-{\alpha}_0\right)+{\lambda}_{1i}\left({\sigma}_{e1}^2-{\sigma}_{e0}^2\right) $$

(A.6)

A2 - The VEP estimation procedure

The calculation of the VEP index is based on the 3-steps Feasible Generalized Least Squares (FGLS) econometric procedure suggested by Amemiya (1977) to correct for heteroskedasticity. The starting point is the estimation through Ordinary Least Square (OLS) of a standard reduced-form of the consumption function based on the following simple linear econometric specification:

$$ {c}_{it}={X}_{it}\beta +{\varepsilon}_{it} $$

(A.7)

where c_itis the log of the real total consumption expenditure per adult-equivalent of household i at time t; X_it is the vector of exogenous variables which controls for the household’s characteristics and ε_it is an error term. In order to have robust estimates, the second step of the VEP method is calculating the residuals from the Eq. A.7 and running the following:

$$ {\varepsilon}_{OLS, it}^2={X}_{it}\theta +{\eta}_{it} $$

(A.8)

The predictions of Eq. (A.8) are thus used to weight the previous equation, obtaining the following transformed version:

$$ \frac{\varepsilon_{OLS, it}^2}{X_{it}{\hat{\theta}}_{OLS}}=\left(\frac{X_{it}}{X_{it}{\hat{\theta}}_{OLS}}\right)\theta +\left(\frac{\eta_{it}}{X_{it}{\hat{\theta}}_{OLS}}\right) $$

(A.9)

As reported by Chaudhuri et al. (2002), the OLS estimation of (A.9) gives us back an asymptotically efficient FGLS estimate, ${\hat{\uptheta}}_{\mathrm{FGLS}}$, and thus ${\mathrm{X}}_{\mathrm{it}}{\hat{\uptheta}}_{\mathrm{FGLS}}$ is a consistent estimate of ${\upsigma}_{\mathrm{it}}^2$, the variance of the idiosyncratic component of household consumption. Then, we use the square root of the estimated variance, i.e. ${\hat{\upsigma}}_{\mathrm{FGLS},\mathrm{it}}$, for transforming Eq. A.7 and obtaining asymptotically efficient estimates of β:

$$ \frac{c_{it}}{{\hat{\sigma}}_{FGLS,\mathrm{it}}}=\left(\frac{X_{it}}{{\hat{\sigma}}_{FGLS, it}}\right)\beta +\left(\frac{\varepsilon_{it}}{{\hat{\sigma}}_{FGLS, it}}\right) $$

(A.10)

Once we have these estimates, it is possible to compute both the expected log consumption and its variance for each household of our sample as follows:

$$ \widehat{E}\left[\left.{c}_{it}\right|\ {X}_{it}\right]={X}_{it}{\widehat{\beta}}_{FGLS} $$

(A.11)

$$ \widehat{var}\left[\left.{c}_{it}\right|\ {X}_{it}\right]={X}_{it}{\widehat{\theta}}_{FGLS} $$

(A.12)

Under the assumption that consumption is log-normally distributed and then log-consumption is normally distributed, we can calculate the probability that household i will be poor in the future, given its characteristics X at time t as follow:

$$ {\widehat{V}}_{it}= \Pr \left[\left(\operatorname{}{C}_{i,t+1}<Z\right)\left|{X}_{it}\right)\right]=\Phi \left(\frac{lnz-\widehat{E}\left(\operatorname{}{c}_{it}\Big|{X}_{it}\right)}{\sqrt{\widehat{var}\left(\operatorname{}{c}_{it}\Big|{X}_{it}\right)}}\right) $$

(A.13)

where Φ(⋅) indicates the cumulative density function of the standard normal.

Table 6

Table 6 Scoring factors and summary statistics for the asset index

Table 7

Table 7 Balancing property of covariates