transformation has to be used to assign first period characteristics to the second-period observations (Inchauste et al., 2012; Azevedo et al., 2013a; Azevedo et al., 2013b).

Rank preservation implies anonymity, where the identity of the individual experiencing a particular outcome (such as income) is irrelevant—a permutation of outcomes between any two individuals in any of the two distributions being compared has no effect on the comparison. With this assumption, one can compare across the same quantiles of two distributions (including distributions at two periods of time) _as if_ they are the same observations. But such a comparison may not account for the true nature of mobility trajectories (Bourguignon, 2010).<sup>5</sup> By using panel data, where the assumption of rank preservation is not needed since households can be observed over both periods, we account for the true trajectories of mobility, which results in more precise estimates of the contribution of each component to poverty reduction. As we will see later, the ability to account for mobility is particularly important in this case, given the vast differences in the distribution of income growth across households that are observed, depending on whether one uses an anonymous or nonanonymous measure of growth incidence.

# **3. Data and Descriptive Statistics**

We use the India Human Development Survey (IHDS) for 2005 and 2012, a nationally representative survey that was conducted in all states and union territories of India (with the exception of Andaman and Nicobar and Lakshadweep). Both rounds of the IHDS provide household level aggregates for job status, job sector, earnings from labor activities and other sources of income (i.e., remittances, government transfers, etc.), and consumption.

The data presents some limitations, which require making the reasonable assumption that only individuals 15 years of age or older can be considered as workers, which also implies that households with positive labor income must be deemed to have at least one working adult.<sup>6</sup> More specifically, we assume that there is at least one adult-worker per household in any activity that reports positive earnings for the household.<sup>7</sup> Likewise, in order to assess accurately the relative contributions of different income sources to welfare improvements, we consider only those activities that generate earnings as “work.” Finally, we consider individuals as workers if they were engaged for at least 240 hours in a given activity during the last year; activities can include taking care of animals, working on the household farm or business, or for a wage or salary.

We restrict ourselves to households in the IHDS balanced panel—that is, about 83% of the households from IHDS-I were re-interviewed in IHDS-II—which comprises of 34,643 out of a total of 41,554 households surveyed for both periods. In order to get a one-to-one matching of households, we

> 5 This is most easily seen by a thought experiment of two households with vastly different incomes, where the incomes switch perfectly from one period to another (household A’s income in period 1 becomes household B’s income in period 2, and vice-versa), while every other household’s income remains constant. With anonymity, no change can be detected; whereas in a panel data, there will be change.

> 6 In some cases there is information on labor income even when no household member appears to be working, or only children (14 years of age or less) are reported as working. These problems can occur due to measurement error and/or child labor. The former is quite likely, as in some cases we find individuals as young as 3 years of age working.

> 7 In our sample only 0.05 percent of households report having kids working and no adults working. We also find that less than 2 percent of the households report labor income but no adult-workers.

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