5. Data and methods
5.1 Data
5.2.3 Models determining income diversification
As described in Chapter 3.2, the following equation, which according to Escobal (2001) is a reduced-form equation of the demand and supply functions derived from the agricultural household equilibrium equation, has been used in several studies as a basis for analysing the determinants of rural income diversification. It was also chosen as a basis for the present study:
Sij = f(p; Zag, Znag, Zk, Zh, Zpu, Zg),
where Sij represents the net income shares of farm and non-farm income for the ith house- hold, p is the vector of exogenous input and output prices, and the Z-vectors are the different fixed assets available to the household: Zag for farm assets, Znag for non-farm assets, Zk for key financial assets, Zh for human capital assets, Zpu for public assets, and Zg for other key assets of the area. The sustainable rural livelihoods framework introduced in Chapter 4.2 provides a tool for determining and categorising the variables for the above equation. The aim in the present study was, among other things, to analyse the determinants of the proportions and levels of income coming from different sources. The equation specified for the analyses is the following:
f (household demographic characteristics, agro-ecology, financial assets, physical endow- ments, social capital, vulnerability)
A common set of explanatory variables was used for the proportions of income from each particular source and the levels of both total income and that coming from each source in order to enable comparison of the effects of the variables between the models:
Incshare25 or Inclevel26 = β0 + β1a1 + β2a2 + β3a3 + β4a4 + β5a5 + β6a6+ β7a7 + β8a8 + β9a9 + β10a10 + e.
In determining the probability of a household belonging to a certain income-mix group27 it was assumed that rural households were rational decision makers and as such would adopt an activity portfolio maximising their utility from the expected income from those activities. The household could obtain utility from a certain choice category, which was closely associ- ated with the characteristics of the category and of the household, as well as the local de- mand for the products resulting from the activity (Dercon and Krishnan 1996). Berhanu et al. (2005) describe the discrete-choice formulation of the utility-maximisation assumption for a household (h) choosing from j alternatives as:
Uhj = Ûhj + ehj = X’hj β + ehj ,
where Ûhj = X’hj β stands for the deterministic component of the utility function and ehj is a vector of the error term representing measurement errors and unobserved attributes. X is the vector for the independent variables.
In the line with the approach of Berhanu et al. (ibid.), the equation used estimating the prob- ability of a household belonging to a certain income-mix group was the following:
Incgroup= β0 + β1c1 + β2c 2 + β3c3+ β4c4 + β5c5+ β6c6 + β7c7 + β8c8 + β9c9 + e . The codes of the variables stand for:
A. Dependent Variables
Incshare: the proportion of income coming from crops, livestock, forest, business activities, wages and transfers.
Inclevel: the household’s total income and income from crops, livestock, forest, business ac- tivities, wages, and transfers in Kwacha.
Incgroup: probability of a household belonging to a certain income-mix group (five alterna- tives)
25 A similar equation was formed for the proportions of the other sources of income: livestock, forest, business activities, wages and transfers.
26 A similar equation was formed for the levels of income from each individual source: crops, livestock, forest, business activities, wages and transfers.
27 The concept of an income-mix group is explained in Chapter 6.1.7. There were five possible income-mix groups: crop growers, a crop-livestock group, a crop-forest-wages-transfer group, a crop-business group, and a mixed group.
a1, c1 = sexhead: the sex of the household head (0=male, 1=female). a2, c2 = agehead: the age of the household head in years.
a3 = tochipa: the distance from the household to the provincial capital in kilometres/100. a4, c3 =educat: the educational level of the household head, varying from 0 to 19 and based on the Zambian educational system.
a5 = cultadul: the size of the cultivated land in hectares divided by the number of adult household members.
a6, c8 = mambwe: a dummy for the Mambwe district (Mambwe = 1, other districts = 0). a7 =vulnerab: the household vulnerability index, varying from zero to five (0=very low vul- nerability, 5= very high vulnerability).
a8, c9 = particip: the household’s participation rate which is used as a proxy for social capital, varying from zero to five (0= no participation, 5=very active participation).
a9 = totasse: the total value of the household assets in Kwacha/100,000. a10 = depratio: the dependence ratio = the number of children/ adults. c4 = noadult: the number of adult household members.
c5 = children: the number of children in the household. c6 = cultsize: the size of cultivated land in hectares
c7 = toboma: the distance from the household to the nearest township in kilometres. e = error term.
In accordance with the sustainable rural livelihoods framework, the independent variables were divided into household-asset categories as illustrated in Table 5.
Table 5. The independent variables divided by asset category. Category Variable
Human Capital Dependency ratio, number of adults and children Age, sex, and education of the household head
Natural Capital Cultivated land size/number of adults, Cultivated land size, Dummy for the Mambwe district
Physical Capital Distance to markets km/100 (either provincial capital or nearest township)
Financial Capital Value of the household’s physical assets in Kwacha/100,000 Social Capital Participation (constructed variable)
Additional Vulnerability (constructed variable)
5.2.4 Choosing the estimation methods
As discussed previously, depending on the research question and the quality of the data the equations and estimation methods take different forms. It may, for example, be a question of the household’s choice or probability of engaging in a certain activity. Households that do not engage in the activity are considered to obtain zero income from it. This gives grounds for applying a model for censored variables, i.e., the variables that are observed in only some of the ranges (Maddala 1987). Censoring means that in a sample of size n (y1*,y2*,…, yn*) only the values of y* greater than the constant c are recorded, and for those smaller or equal to c, the value c is recorded. Hence the observations are: yi = yi*, if yi* > c; otherwise yi = c. In such a case the censored regression model (the Tobit estimation procedure) can be ap- plied.
According to Maddala (ibid.), the Tobit model is defined as follows: yi = β’xi + ui, if RHS > 0
yi = 0, otherwise.
In the model β is a k x 1 vector of unknown parameters; xi is a k x 1 vector of known con- stants; ui are residuals that are independently and normally distributed, with a mean of zero and a common variance of σ2. The Tobit equation is often solved using the maximum- likelihood method.
The research questions addressed in the present study focus on among other things, the pro- portions and levels of income from different sources, and the respective determinants. The observations for both could be considered censored since both are given the value zero but not negative values. The determinants are therefore analysed using the Tobit model accord- ing to the procedure followed by Escobal (2001), Woldenhanna and Oskam (2001), Brons (2005) and Croppenstedt (2006), for example, except in cases in which the data are not cen- soredi.e., in analyses of total income in which the OLS method can be used.
Deaton (1997) criticised the Tobit model on account of the inconsistencies (estimates biased upwards) caused by heteroscedasticity in censored regression models. Therefore, corrective measures to minimise the heteroscedasticity bias were taken during the specification of the equation as well as during estimation of the coefficients. An alternative would have been to use two-stage models, however, considering the quality of the data in the present study, the Tobit model was chosen to be the most appropriate one.
It was also of interest in this study to analyse the probability of a household belonging exclu- sively to a certain income-mix group. A multinomial logit model is suitable for such pur- poses. Schmidt and Strauss (1975), for example, contributed to the development of such a model in their analysis of occupational choices using race, sex, education and labour-market
one of the categories with a certain probability. The equations in a three-choice case, for ex- ample, are:
log 𝑃2𝑃1 = α21 + β21X log 𝑃3𝑃1 = α31 + β31X log 𝑃3𝑃2= α32 + β32X ,
where Pj, j=1,2,3 indicates the probability that the jth choice will be made. Each equation assumes that the logarithm of the odds of one choice relative to a second choice is a linear function of the variable X. The sum of the individual probabilities equals one. (Pindyck and Rubinfeld 1997)
Once the parameters have been estimated it is possible to predict probabilities in question - in the case of Schmidt and Strauss the probability of an individual choosing a particular oc- cupation. A similar approach has been used in analysing the characteristics of households belonging to different income-mix groups: examples include Dercon and Krishnan (1996) in Ethiopia and Tanzania, and Woldenhanna and Oskam (2001) and Berhanu et al. (2005) in Ethiopia.
6. Results
The results of the data analyses are presented in this chapter. First, the focus will be on the results and findings based on the whole dataset (n=197) collected in February-May 200328 with the aim to establish an overall picture of rural income generation and diversification patterns among the interviewed households in Eastern Province. This includes also econo- metric analyses aiming at defining the household characteristics and other determinants of income diversification patterns. Then, the focus will be shifted to analysing the changes in income generation and diversification among the 67 households present in both the 1985/86 and 2003 surveys.