population in 2012/13 using 2002 data and vice versa. The ability to do this is needed later to perform the decompositions. These models are discussed in turn.

# **4.1.1. Educational Choice**

First, the allocation of individuals across educational levels is estimated with a standard multinomial logit model as a function of age, gender, area, and region. This is done for all working-age individuals following a Roy (1951) model of choice where individuals choose their level of education in order to maximize their utility. The allocation of individuals across levels of education is estimated with a multinomial logit model (McFadden 1974a, 1974b), specified as follows: � � � I�� �1 if Z��Ψ<sup>�</sup> �v� �����0, Z��Ψ<sup>�</sup> �v��, j �1, ... , J, ∀j �s (9) I��� �0 for all s �1, ... , J if Z��Ψ<sup>�</sup> �v�� �0 for all s �1, ... , J (3) where Z�� is a vector of characteristics specific to individual i and household h, Ψ<sup>�</sup> are vectors of � coefficients for educational levels j, and v� are random variables identically and independently distributed across individuals and activities according to the law of extreme values. Within a discrete utilitymaximizing framework, Z��Ψ<sup>�</sup> �v�� is interpreted as the utility associated with educational level s, with v�� being the unobserved utility determinants of educational level s and the utility of no education being arbitrarily set to 0.

We estimate the conditional distributions of levels of education for each survey year based on age group, gender, region, area, and ethnicity. This is estimated separately for household heads and other members within the working age population. Table A3.1 reports the results of these estimates for heads of household and other household members for 2002 and 2012/13. Despite relatively low R squares, simulations using these regressions do a fairly good job in replicating the educational structure of the workforce in 2012/13 using 2002 data and 2012/13 coefficients (Table A3.4).

# **4.1.2. Choice of Sector and Activity**

The second element in the model is the allocation of individuals across activities. In particular, following Roy (1951), individuals choose the sector and type of activity they are engaged in to maximize their utility. As above, this is estimated with a multinomial logit, where the choice of activity j={salaried nonfarm, salaried farm, nonfarm self-employed, farm self-employed, not employed} is modeled as a function of age, gender, ethnicity, area, region, educational attainment, marital status, the number of young children. Tables A3.2 report the results of these estimates for heads of household and other household members for 2002 and 2012/13. Again, despite relatively low R squares, the simulations using these regressions do a fairly good job in replicating the activity structure of the workforce in 2012/13 using 2002 data and 2012/13 coefficients (Table A3.4). Note that since the choice of sector and activity depend on the level of education of individuals, any simulated change in education will imply a change in the activity composition of the workforce.

# **4.1.3. Household Income**

The third step is to estimate household income using individual wage equations for salaried workers, and household net revenue functions for households with self-employed workers. Total household income can be written as: 6