The inability of any of our models to replicate poverty rates in years 2004/05, 2009/10 and 2014/15 raises concerns whether this method correctly forecasts poverty in 2017/18.<sup>16</sup> This contrast with Newhouse and Vyas (2019) who validate their model by replicating poverty rates in rural areas in 2004/05.<sup>17</sup> Given these limitations, we explore another method to project poverty rates for India in the absence of survey data.

# **4. Pass-through method**

While we should expect that the growth of consumption in national accounts is positively correlated with growth of mean consumption measured from surveys, a substantial literature has found that growth in national accounts does not pass-through one-to-one to household surveys. The difference between these two growth rates is referred to as a pass-through rate. More precisely, and following Ravallion (2003), the pass-through rate is the coefficient estimate β in the regression of the growth in the survey mean, gsurvey, on the growth in national accounts, gNAS: where _i_ is a growth spell between two survey years, and the residual, ui, has mean zero. gsurvey is the growth rate of the survey welfare aggregate, here measured as household income or consumption expenditure per capita. gNAS is the real growth rate in national accounts, for which we consider either Gross Domestic Product (GDP) per capita or Household Final Consumption Expenditure (HFCE) per capita. The pass-through rate, β, captures the rate of growth in consumption that is passed through from national accounts to surveys. If β= 1, then mean consumption in the survey grows at the same rate as consumption in national accounts. Typically, the literature finds β< 1 (see more details below), which implies that mean consumption in the survey grows slower than the growth in national accounts.

The literature has discussed several channels for why there are systematic differences in growth of consumption as measured in national accounts and in the survey microdata; for example, see Ravallion (2003), Deaton (2005) and Pinkovskiy and Sala-i-Martin (2016).<sup>18</sup> First, there are

> 16 The S2S method has been used to generate plausible poverty estimates in other contexts and has often been successfully validated. Any imputation model is forced to make strong assumptions, such as the stability of the consumption model over six years (from 2011/12 to 2017/18) in our case. The availability of additional variables could also improve the predictive performance of our model. In some specifications, we successfully validate the 2014/15 estimates, as well as the 2004/05 estimates in urban areas, but do not accurately backcast the large decline in rural poverty between 2011/12 and 2004/05. This is likely because the estimated parameters, including the intercept term, is fixed at the estimated 2011/12 levels. Including a linear time trend in the model would greatly overestimate the decline in poverty between 2004/05 and 2011/12 in both urban and rural areas. This suggests that incorporating data on expenditures of particular services, which was possible when projecting into 2014/15 (Newhouse and Vyas 2019) but not into 2017/18, helps the linear time trend model perform much better at backcasting.

> 17 They fail to replicate poverty rates for urban areas in 2004/05, and make no reference to attempts to replicate 2009/10.

> 18 For a general discussion around the differences between household survey data and the data from national accounts, as well as potential adjustments for such differences, among others see Altimir (1987), Bourguignon (2015), and Prydz et al. (Forthcoming).

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