Structural Equations Model

Methodology
In order to analyze the distributional effects of access to basic services on household welfare, we use Benefit Incidence Analysis (BIA) method (see Demery, 2000 and Davoodi et al., 2003 for the description of the BIA method). In order to take account of the multidimensional character of the well-being and the simultaneous nature of its dimensions, we use the Structural Equations Model (SEM) with latent variables. This section describes the SEM and the data sources used.
3.1. The Structural Equations Model (SEM)
Our goal here is to provide a measurement of well-being using the capability approach. To achieve this goal, we consider three dimensions of well-being (the capabilities) namely wealth, basic services and housing There

They are the key endogenous variables of our model. Achievements are measurable and are linked to the underlying capabilities through a set of measurement equations. We assume that wealth capabilities influence on basic services capabilities and that these two dimensions have an impact on access to housing. Thus the level of wealth of a household may have an influence on its possibilities for accessing basic services, and the reverse is also true. Similarly, these two dimensions probably have an impact on the access to housing. Figure 4 presents the interrelationships between the variables of the model, namely the three latent variables, the observed endogenous variables representing the functioning, and the exogenous variables from structural equations. The observed variables are enclosed in boxes and the unobserved or latent variables are circled. Straight single-headed arrows represent causal relations between the variables connected by arrows in the direction shown by the arrow. Two straight single-headed arrows connecting two variables signify feedback relation or simultaneous

Like krishnakumar and Ballon (2008) we apply a two-stage procedure to test for identification. In the first step, we treat the model as a confirmatory factor analysis, that is, we only focus on the measurement equations and we test for identification applying, for example, the t -rule. In a second step, we examine the latent variable part and we treat it as if it were a structural equation model in observed variables. Then, we test for identification using typical identification rules for observed structural equations models, that is, rank and order conditions. If both steps show that the respective parameters are identified then the whole model is