# **Annex 2: The synthetic panel methodology and its application to Nepal**

A proper study of economic mobility that is being proposed has fairly demanding data requirements. At the minimum, it is necessary to be able to observe the same household in at least two time periods and the richer the amount of information available on the household, the richer the analysis that can be done. These “panel data sets” as they are called are fairly hard to come by in many developing countries. In the case of Nepal, the three rounds of NLSS that have been completed have an integrated panel component, i.e., a subset of the sampled households have been tracked over time, but due to sample attrition, it has been found that the surviving households are no longer representative of the nation as a whole.

As the name suggests, the proposed methodology overcomes these shortcomings and builds on an imputation based methodology to construct a “synthetic panel” that makes it seem like the same households were observed in two time periods. The approach relies fundamentally on time-invariant individual and household characteristics. Specifically, it entails predicting consumption of households surveyed in time _t_ for period _t-k_ using the estimated “returns” to these time-invariant characteristics in period _t-k_ . The comparison of “predicted” consumption in _t-k_ with the actual consumption in period _t_ forms the basis of the analysis of mobility, particularly movement in and out of poverty.

To write more formally, consider two rounds of cross sectional surveys (denoted as rounds 1 and 2) and let �� and ��be the corresponding consumption for the two rounds (these are consumption for household _i_ , but we suppress those subscripts). For a given poverty line, say, _z_ , we are interested in estimating (a) the fraction of poor households in the first round who escaped poverty (Pr(�� ��| �� ���) or remained in poverty in the second round, (Pr(�� ��| �� ���); (b) the fraction of non-poor households in the first round who became poor (Pr(�� �� | �� ���) or the fraction of non-poor households that remained non-poor (Pr(�� � � | �� ���). However, this cannot be done in a straightforward manner because of the fact that we do not observe the same household in the two periods.

Instead we apply the synthetic panel methodology in the following steps:

**STEP 1:** Estimate the relationship between consumption and time invariant characteristics in each round and obtain estimates for �<sup>�</sup> � and **�** � for _i = 1, 2._

**STEP 2:** Use the estimates of ��� and the error term to predict period 1 consumption for households surveyed in period 2. Since we do not a priori know the empirical distribution of the correlation between �� and �� we consider two extreme cases and use the two scenarios to define the upper and lower bounds of mobility. In one case, we assume there is zero correlation between the error terms. In this case, the income prediction for the first round is done by randomly drawing with replacement from the empirical distribution of the first-round estimated residuals for each household _i_ in the second round. Thus, the period 1 predicted household consumption for each household surveyed in period 2 can be written as:

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