Farmers’ Livelihoods and Welfare in the Wa West District, Upper West Region of Ghana

Abstract

This paper examines the socioeconomic determinants of farmer livelihood diversification and its effects on welfare. We selected 184 farmers in the Wa West District of the Upper West Region of Ghana through a comprehensive, multistage process based on agro-ecological, engineering, and socioeconomic resilience/vulnerability profiles. A simultaneous equation model was estimated using the two-stage least squares method. The results suggest that the number of livelihood activities is highest for female farmers, relatively young farmers, farmers with little or no formal education, farmers with large families, and richer/wealthier farmers. On the other hand, welfare is highest for older farmers, female farmers, farmers with little or no formal education, farmers with small family size, and farmers with higher number of livelihood activities. Thus, despite the fact that younger and large-sized families engage in more livelihood activities, they have relatively low welfare. Therefore, these categories of farmers should be targeted for policy interventions. However, in general, we recommend the promotion of more livelihood activities to increase the welfare of farmers. These livelihood activities should not be vulnerable to the adverse effects of climatic factors.

Appendix

1.1 Demonstration of the Mechanics of the Two-Stage Least Squares (2SLS) Method

Given the following structural equation:

$$ {y}_i={b}_{i1}{y}_1+{b}_{i2}{y}_2+\cdots +{b}_{iG}{y}_G+{\gamma}_{i1}{x}_1+\cdots +{\gamma}_{iK}{x}_K+{u}_i $$

(7.5)

where the ys are endogenous variables, the xs are exogenous variables, and the bs and γs are parameters to be estimated. The first stage in applying 2SLS involves expressing each of the endogenous variables as a function of all the exogenous variables and predetermined variables. This is the same as regressing each endogenous variable on all the predetermined (exogenous) variables. This generates the reduced-form equation as follows:

$$ \begin{array}{l}{y}_1={\pi}_{11}{x}_1+{\pi}_{12}{x}_2+\cdots +{\pi}_{1k}{x}_k+{v}_1\hfill \\ {}{y}_2={\pi}_{21}{x}_1+{\pi}_{22}{x}_2+\cdots +{\pi}_{2k}{x}_k+{v}_2\hfill \\ {}{y}_G={\pi}_{G1}{x}_1+{\pi}_{G2}{x}_2+\cdots +{\pi}_{Gk}{x}_k+{v}_G\hfill \end{array}\Big\} $$

(7.6)

Using the values of the πs, we can predict the values of the ys as ${\widehat{y}}_1,{\widehat{y}}_2\dots {\widehat{y}}_G$.

Having estimated these values, we can move on to the second stage by simply replacing the ys with ${\widehat{y}}^{\prime}\mathrm{s}$ in the structural equation above. This gives

$$ {y}_i={b}_{i1}{y}_1+{b}_{i2}{y}_2+\cdots +{b}_{iG}{y}_G+{\gamma}_{i1}{x}_1+\cdots +{\gamma}_{iK}{x}_K+{u}_i\ast $$

(7.7)

The random component is no longer ${u}_1$ but rather u _i ∗ = u _i + b _i1 v ₁ + b _i2 v ₂+ ⋯ + b _iG v _G . Estimating Eq. 7.7 with the ordinary least squares method provides consistent and unbiased parameters. To make the estimates of the parameters easily understandable, we limit the explanation to only two explanatory variables. Thus,

$$ {y}_i={b}_2{y}_2+{\gamma}_1{x}_1+u. $$

(7.8)

Going through the process explained earlier,

$$ {y}_1={b}_2{\widehat{y}}_2+{\gamma}_1{x}_1+\left(u+{b}_2{v}_2\right) $$

(7.9)

The normalized equations can be given as

$$ {\displaystyle \sum }{y}_1{\widehat{y}}_2={b}_2^{\ast }{\displaystyle \sum }{{\widehat{y}}_2}^2+{\gamma}_1^{\ast }{\displaystyle \sum }{x}_1{\widehat{y}}_2 $$

(7.10a)

$$ {\displaystyle \sum }{y}_1{x}_1={b}_2^{\ast }{\displaystyle \sum }{x}_1{\widehat{y}}_2+{\gamma}_1^{\ast }{\displaystyle \sum }{x}_1^2 $$

(7.10b)

The parameter estimates can be obtained by

$$ {b}_2^{\ast }=\kern0.5em \frac{\left|\begin{array}{l}{\displaystyle \sum }{y}_1{\widehat{y}}_2{\displaystyle \sum }{x}_1{y}_{\widehat{2}}\hfill \\ {}{\displaystyle \sum }{y}_1{x}_1{\displaystyle \sum }{x}_1^2\hfill \end{array}\right|}{\left|\begin{array}{l}{\displaystyle \sum }{{\widehat{y}}_2}^2{\displaystyle \sum }{x}_1{\widehat{y}}_2\hfill \\ {}{\displaystyle \sum }{x}_1{\widehat{y}}_2{\displaystyle \sum }{x}_1^2\hfill \end{array}\right|}\kern0.5em =\kern0.5em \frac{\left({\displaystyle \sum }{y}_1{\widehat{y}}_2\right)\ \left({\displaystyle \sum }{x}_1^2\right)}{\left({\displaystyle \sum }{{\widehat{y}}_2}^2\right)\kern0.5em \left({\displaystyle \sum }{x}_1^2\right)\ {\left({\displaystyle \sum }{x}_1{\widehat{y}}_2\right)}^2} $$

(7.11)

$$ {b}_2^{\ast }=\frac{\left|\begin{array}{l}{\displaystyle \sum }{{\widehat{y}}_2}^2{\displaystyle \sum }{y}_1{\widehat{y}}_{\widehat{2}}\hfill \\ {}{\displaystyle \sum }{x}_1{\widehat{y}}_2{\displaystyle \sum }{y}_1{x}_1\hfill \end{array}\right|}{\left|\begin{array}{l}{\displaystyle \sum }{{\widehat{y}}_2}^2{\displaystyle \sum }{x}_1{\widehat{y}}_2\hfill \\ {}{\displaystyle \sum }{x}_1{\widehat{y}}_2{\displaystyle \sum }{x}_1^2\hfill \end{array}\right|}=\frac{\left({\displaystyle \sum }{{\widehat{y}}_2}^2\right)\left({\displaystyle \sum }{y}_1{x}_1\right)}{\left({\displaystyle \sum }{{\widehat{y}}_2}^2\right)\left({\displaystyle \sum }{x}_1^2\right){\left({\displaystyle \sum }{x}_1{\widehat{y}}_2\right)}^2} $$

(7.12)