The role of villages in households’ poverty exit: evidence from a multilevel model for rural Vietnam

For details on the Living Standards Measurement Study of the World Bank see http://​www.​worldbank.​org/​lsms/​guide/​select.​html.

In Vietnam there is a large population of ethnic minorities that tends to be significantly poorer than Kinh majority. An analysis of the disparities in living standards among the different ethnic groups in Vietnam can be found in Baulch et al. (2007).

The random-effect model is estimated using quadrature which is an approximation whose accuracy depends (also) on the number of integration points used. We assessed the sensitivity of parameter estimates according to the number of integration points. We started with the default 12 quadrature points and compared the results to two different choices: 8 and 16 quadrature points. The relative and absolute differences were small among the three cases and so we concluded that the quadrature technique is stable.

This kind of analysis is common in the education research literature where it is used in the study of school performance (see e.g., Goldstein and Thomas 1996).

Standard errors for VPC are calculated using the delta method (Oehlert 1992). This is expected to be quite a valid approximation in our case since we have a sufficient number of clusters at village level. Moreover, the random intercept variance was tested through a Likelihood Ratio Test (LRT). We have to note in this case that, since variances are always positive, the null hypothesis falls on the boundary of the parameter space. As a consequence, the limiting distribution of the LRT statistic is not the usual \(\chi ^{2}\) with 1 degree of freedom, but is instead a 50:50 mixture of such a distribution and a point mass at 0 (Self and Liang 1987). To keep this complication into account, Snijders and Bosker (1999) suggest halving the p-value resulting from a standard LRT. Results, not shown here, confirm the statistical significance of the between-cluster variability.

These are the square root of the variances of the prediction errors (Skrondal and Rabe-Hesketh 2004). They are referred to as the comparative standard errors because they can be used for inferences regarding differences between predictions of the random effects. They have to be distinguished from the sampling standard deviation that is the square root of sampling variance of the EB predictions distribution. These are referred as diagnostic standard errors since they can be used to find aberrant predictions.